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The word "counter" may remind you of the machine with which you can count the number of objects, such as persons and vehicles. Some people familiar with electronic circuits may remind of the logic circuit. In each case, the system is regarded as memory device that remember the number of inputs, which is important for our lives.

In the natural world, cellular counters also memorize the number of events. For example, there are telomere length regulation[1][2], cell aggregation[3][4], etc. Telomere length of Saccharomyces cerevisiae is regulated by the number of the Rap1 protein, indicating the existence of counting system. The cell aggregation size of Dictyostelium is regulated by counting factor (CF). CF counts the number of aggregating cells and negatively regulates the cell adhension. In these ways, cellular counters are widely utilized for the regulation of biological systems.

With synthetic biological approach, Ari et al constructed a cellular counter termed the riboregulated transcriptional cascade (RTC) counter[5]. The state transition occurs after an arabinose induction (Fig. 1). The system is regulated by riboregulators. The Biobrick part of this cellular counter has already existed, which was constructed by Tokyo-Nokogen 2009 and was named BBa_K225002, BBa_K25003 [6].

In order to expand the function of this counter, we added "reset system". The reset system enables the transition from any state to the initial state after a particular input. The property is expected to apply for a deterministic finite automaton, which is the system developed from information science. Within the finite number of states, the system makes the transition to another state in responce to a particular input.

As the key of its resetting mechanism, our counter utilizes the regulation system based on sigma factor and anti-sigma factor. Sigma factor is a subunit of RNA polymerase and help it bind to the specfic sequence of the promoter. Anti-sigma factor blocks sigma factors from interacting with RNA polymerase. The utilization of this regulation system brings about benefit for attempt to make automaton.Firstly, the number of states can be increased easily because what we have to concern is the combination of sigma and anti-sigma factor. Secondly, the crosstalk between sigma and anti-sigma factors can be circumvented even if you raise the number of states. That is because we can choose such combinations between sigma and anti-sigma factors that have little crosstalk.

Fig. 1 The concept of RTC counter. After first, second and third induction of arabinose, the state of cells moves from 0 to 1, 1 to 2 and 2 to 3, respectively.

sigma factor

Sigma factor is a subunit of RNA polymerase related to promoter recognitions. There are two types of sigma factors, one that is housekeeping (expressed constantly) and another that is expressed under some conditions. It is possible to deliver genes of sigma factors that are not derived from some species to another species, so we can use many kinds of sigma factor. Which promoter RNA polymerase tends to bind to is decided by which sigma factor RNA polymerase is bound. Especially some sigma factors promote only transcription of a specific promoters. Therefore if we choose a set of sigma factors and promoters skillfully, we can controll transcription without crosstalk. Here, “without crosstalk” means every sigma factor in the set promotes only transcription of the cognate promoter.

Anti-sigma is also a protein which is related to transcriptional control by sigma factors. Anti-sigma prevents sigma factors from binding to RNA polymerase. Consequently, sigma factor cannot activates transcription of cognate promoters. Similarly as sigma factor, there are many kinds of anti-sigma and some anti sigmas prevent only specific sigma factors from transcriptional control. Therefore if we choose a set of sigma factors, anti sigmas, and promoters skillfully, we can activate control, not only activate but also repress, transcription without crosstalk.

Transferred sigma factors or anti sigmas may have negative effects on the growth of the host cell. For example, anti sigma may prevent housekeeping sigma factors from transcriptional control. However it is no problem since not all sigma factors and anti sigmas have negative effect and there are many kind of sigma factors and anti sigmas.［1］

sigma-memory construction

This is the construction of our sigma-memory.This gene circuits is composed of three parts. The gene of a sigma factor is placed at the downstream of the promoter that is induced by a substance A and at the downstream of Psigma, which is induced by the sigma factor. The gene of the cognate anti sigma is placed at the downstream of promoter which is induced by a substance B.

At first, there is no sigma factors. If input A exists, sigma factor is expressed. Then the positive feedback circuits of sigma factor starts producing sigma factor, and consequently sigma factor will remain. Though if input B exists, anti-sigma is expressed and the positive feedback circuits is inhibited. Both sigma factor and anti-sigma are subjects to degradation［2］, so all of them are decomposed after some time and sigma-memory returns to its original state.

We can regard existence/absence of sigma factor as 1/0 of memory, and this values of memory can switch by input A or input B. Using the promoter which is cognate to the sigma factor, the information whether the value of memory is 1 or 0 can be derived. For example, consider the circuits on the right. The repotor is expressed if and only if sigma-memory's value is 1 (i.e. sigma factor exists).

In addition, no crosstalk sets of sigma factors, promoters, and anti-sigmas enable us to make multi-sigma-memory gene circuits. To make the explanation easier, consider the case in which E. coli has two sigma memories, sigmaA-memory and sigmaB-memory. SigmaA The value of sigmaA-memory change from 0 to 1 if input A1 exists and change from 1 to 0 if inputs B1 exists. Also the value of sigmaB-memory change from 0 to 1 if input A2 exists and change from 1 to 0 if input B2 exists. If the four input A1, B1, A2, and B2 have no crosstalk, sigmaA-memory and sigmaB-memory also have no crosstalk. For example, when input A1 exists, only the value of sigmaA-memory change from 0 to 1 since sigmaA promotes only transcription from PsigmaA (promoter that is cognate to sigmaA). Since the transcription from PsigmaB is not activated, sigmaB is not expressed and the value of sigmaB dose not change. The same is true of input A2. When input B1 exist, anti sigmaA is expresses and the value of sigmaA-memory changes from 1 to 0. However, anti sigmaA has no effect on the transcription of PsigmaB and the value of sigmaB dose not change. The same is also true for the input B2. So it can be confidently said that E. coli has two sigma memories.

Since this construction has a positive feedback, leakage of promoter may be a serious problem. If the promoter has leakage and sigma factor is expressed when input A dose not exist, this error may be enlarged by positive feedback. (Whether the error is really enlarged depends on whether the leakage of sigma factor is large compared to the degradation of sigma factor.) However if the leakage of anti-sigma is considerably large, sigma factor dose not produced from positive feedback when leak of sigma factor occurs. Therefore leakage is not an obstacle of our project if we choose the promoter skillfully.

sigma-memory and automaton

Speaking easily, an automaton is referred to what has states and transition rules. Every state has a transition rule, say it is decided what is the next state if an input exists. For example, the automaton on the right has five states, 0, 1, 2, 3, 4, and transition rules are represented by arrows. If the current state is 0 and the input is b, the next state is 2. Transition rules having loops or feedbacks are allowed.

sigma-memory can be considered an automaton. Every tuple of the value if sigma-memory (say, (1, 1, 0, 1, 0)) corresponds to a state, and the promoter which is used in the construction of sigma-memory decides transition rules. It is possible to use the value of one sigma-memory as an inputs of another sigma-memory. This fact enables us to make complicated transition rules.

For example, consider the case where E. coli has two sigma-memory. The value of sigmaA-memory( a sigma-memory which uses sigmaA in the construction as a sigma factor) change from 0 to 1 if a substance A1 exists, also the value of sigmaB-memory change from 0 to 1 if the value of sigmaA and a substance A2 exists. (This condition can be written in terms of mathematical logic, namely AND(sigmaA, IPTG)) Gene circuits which work as logic circuits (says AND, OR, NAND, etc...) have been designed.［3］ Therefore such gene circuit can be made. The value of sigmaA-memory changes from 1 to 0 when a substance B1 exists and that of sigmaB-memory changes from 1 to 0 when a substance B2 exist. In this case, it is characteristic that sigmaB-memory is affected by sigmaA memory. These gene circuits can be considered as the automaton on the below.

resettable counter by sigma-memory

Resettable counter is a device that can count the number of induction events of arabinose, and expresses a reporter correspond to each states. In addition, the count can be reset by IPTG induction. Resettable counter can be considered as an automaton. The automaton has two inputs, input A and input B. Each states corresponds to the count, namely the states of the automaton is 0,1,2,...etc. The transition rule is very simple. When the current states is n and the input is A, the next states is n+1, and when the current state is n and the input is B, the next states is 0. Since a counter is one kind of automata, sigma-memory can be applied for making resettable counters.

2-counter is a counter that can count up to 2, and is an automaton that has three states, 0, 1, and 2. This automaton can be constructed by sigma-memory as following. Two kinds of sigma factor are necessary for constructing the 2-counter, so for the convenience we will call these two kinds of sigma factors sigmaA and sigmaB. In state 0, both sigmaA and sigmaB do not exist (i.e. sigmaA-memory and sigmaB-memory is 0). In state 1, only sigmaA exists and in states 2, both sigma factors exist. The input is the induction of arabinose or IPTG, and the transition rules with it are showed in the Figure.

A gene circuit that realizes this automaton can be represented as following. The value of sigmaA changes from 0 to 1 after arabinose induction (i.e. sigmaA is expressed when arabinose exists). This change corresponds to the transition from state from 0 to 1.The value of sigmaB-memory changes from 0 to 1 when both arabinose and sigmaA exist. The conditional branch can be made by using AND function. This change corresponds to the transition from state 1 to state 2. Both the value of sigmaA-memory and sigmaB-memory change from 1 to 0 after IPTG induction (i.e. anti-sigmaA and sigmaB is expressed when IPTG exist).

riboregulator

According to the discussion in 2-1, it is necessary to use AND function for the construction of a resettable counter. Therefore a riboregulator is used for the realization of the AND function.

A riboregulator is a post-transcriptional regulation system composed of two kinds of RNAs, Cis-repressed mRNA (crRNA) and trans-activating RNA (taRNA). CrRNA forms a stem-loop and its ribosomal binding site (RBS) is covered. Consequently the gene coded in cis-repressed mRNA isn't translated. However if trans-activating RNA exist, crRNA and taRNA are hybridized and RBS gets exposed and translation starts.［4］

Namely, the gene coded in crRNA is expressed only when both crRNA and taRNA is transcripted. Therefore this system can be considered as the AND function. For example, consider the gene circuit, Plac-taRNA-d.term-Pbad-cr-RBS-GFP-d.term.(cr is the sequence in crRNA which binds to RBS) If and only if both IPTG and arabinose exists, GFP is expressed. Therefore, the riboregulator can combine two promoters and produce AND functions

resettable counter construction

The construction of our resettable counter is explained here.

Ecf20_992 (Sigma20) and Ecf11_3726 (Sigma11) are used as sigmaA and sigmaB as mentioned above respectively. These two sigma factors strongly activate the cognate promoters, and their inhibition of growth is negligible. ［1］The promoters correspond to sigma20 and sigma11 are Pecf20_992(Psigma20) and Pecf11_3726(Psigma11), respectively. The sequences of these two promoters has no restriction site of Ecor1, Xba1, Spe1, and Pst1. The cognate anti-sigmas are anti-20 and anti-11 respectively. These two anti-sigmas considerably prevent the cognate sigma factors from activating transcription, and their inhibition of growth is also negligible. These sigma factors, cognate promoters, and cognate anti-sigmas has no cross talk.

Cis-repress sequence is crR12 and trans-activating RNA is taR12. This pair is selected because the leakage is small. ［4］The reporter in this construction is GFP.

mechanism and extension

At first, both the value of sigma20-memory and sigma11-memory are 0. Only the crRNA coding sigma20, which is at downstream of constitutive promoter is translated. After the first induction of arabinose, taRNA at the downstream of PBAD is transcribed and the crRNA coding sigma20 is translated, and the value of sigma20-memory changes from 0 to 1. Since sigma20 exists, crRNA coding sigma11 at the downstream of Psigma20 is transcribed. After the second induction of arabinose, taRNA is transcribed and sigma11 is expressed, and the value of sigma11-memory changes from 0 to 1. At this time, GFP at the downstream of Psigma11 is expressed and we can check the count as 2.

After an induction of IPTG, anti-sigma20 and sigma11 are expressed, and the value of sigma20-memory and sigma11-memory will be 0. Therefore the count is reset.

Since there are many kinds of pair of sigma factors and cognate promoters which have no crosstalk, n-counter can be made by the same way. Besides, the construction of 2-counter can be simplified.

This simplified counter is made by only one sigma factor. It works as the same way as original 2-counter unill 1 count. After 1 count, crRNA coding GFP is transcribed at the downstream of Psigma. Therefore when the next arabinose induction occurs, GFP is translated. This expression can be considered a report of 2 count. This simplified counter can be also extended to n count. Simplified counter can count up to larger numbers compared to the original counter even when the same number of sigma factors are used, but cannot be reset from their final count. We did experiments on this simplified counter.

comparison with previous counter

Our sigma-Recounter is improved version of the previous counter constructed by Ari.［5］In the previous counter, T7 RNA polymerase and T3 RNA polymerase is used, while in our counter sigma factors is used. Using sigma factor has two merits. One is the ease of extension for n-counter. The number of RNA polymerase derived from virus is limited, but sigma factor has great divergence. Consequently it is more easy to construct n-counter by using sigma factor. Another is the existence of inhibitor. Anti-sigma is inhibitor of sigma factor which has no cross talk. Inhibitor is necessary to realize reset function.

Other difference is the positive feedback circuits. Previous counter has no feedback circuits. Since sigma factor is more subject to degradation than RNA polymerase, positive feedback circuits is necessary to keep "memory" (i.e. for sigma factor to remain) in our counter.

The genetic circuit we constructed can be considered as an automaton. In a previous study[1], many orthogonal sigma and anti-sigma have been reported. (what “orthogonal” means here is to make almost no crosstalk to other promoters or sigma factors) Thus, an automaton that have many states can be constructed.

Examples of an automaton are such as biocomputer, SUDOKU or lifegame etc. Bringing this concept from algorithmic world into synthetic biology was our challenge. Though in our project input is a single short intermittent signal ,a more general circuit that responds to more general input is possible to be considered by integrating additional circuits into our circuit.

For example, the change of balnce between 2 elements itself can be considered as a input. Considering elements A and B, this additional circuit is possible:

pA-repressorB-reporterA-activatorX-pX-repressorA

pB-repressorA-reporterB-activatorY-pY-repressorB

This additional circuit essentially contains toggle switch structure.Therefore, change of dominance relation between A and B can be converted into a pulse with transition from a stable point to another which can be used as input in our circuit. Consequently, this additional circuit is thought to be an AD converter and if elementB is constant this can trace elementA by regarding reporterA as a spokesman.If A is industrial waste, this circuit can be a monitor of a milieu.

As described above, our genetic circuit can be applied to much wider range of problems.

lab note

colony PCR

D-7(Ampicillin), D-7(Chloramphenicol)

1kbp Ladder, D-7(Amp) #1~4, D-7(CP) #1~4
(ここに20140814_4を貼付)

ligation → TF

D-6 (A-7 SP + 4-11L XP), A-7 (linear XP + pSB1A2 XP)
A-9, A-10, B-1 (linear XP + pSB1A2 XP)

8,15,2014

Lab member

Yoshikawa,Nakashima,Tara,Takemura,Nakamura

8,16,2014

Lab member

A-4 SP, A-7 SP #1, A-7 SP #2, A-9 SP
(ここに20140902_1を貼付)
(ここに20140902_2を貼付)
A-8XP
(ここに20140902_3を貼付)
(ここに20140902_4を貼付)

B-1 #1, B-1 #2, B-3 XP, B-10 XP, D-7 XP, D-8 XP, E-20 XP, F-2 SP
(ここに20140902_5を貼付)
(ここに20140902_6を貼付)
D-8:???

sequence

A-7 #1~4, B-1 #1~4
D-8 #1~4
A-9, A-4, E-5, E-6, E-20

PCR

B-2, D-9

check & colony PCR

M-1~3 #1~4
(ここに20140902_7を貼付)
OK!
M-4 #1~4, B-2, D-9, PC(VF2→B-10←VR )
NC, G-5
(ここに20140902_8を貼付)
M-4 #1~4,PC(VF2→B-10←VR ):OK!
(M-4 #2~4 is a little longer?)

ligation → TF

C-4(A-7 SP + B-3 XP), C-5(A-7 SP + B-10 XP), E-17(A-9 SP + D-7 XP)
D-1(B-1 SP + D-8 XP), E-21(A-4 SP + D-8 XP), J-4 (F-2 SP + E-20 XP)

preculture

B-2 linear XP (did not extracted)
N-1,2,4~6 ES
(ここに20140908_1を貼付)
(ここに20140908_2を貼付)
A-4 SP, pSB1C3 (A-4) XP, A-6 SP, B-7 #2 XP, B-7 #3 XP, D-9 #1 XP, K-2,3,5 EX
(ここに20140908_3を貼付)
B-7 #2, D-9 #1:disposed(incomplete cut)
B-7 #3:disposed(a little longer)(This band proved to be correct.9/9 wrote)
(ここに20140908_4を貼付)

colony PCR

E-11,12,14,15 #1~4
(ここに20140908_5を貼付)
OK!
O-3 #1,2
(ここに20140908_6を貼付)
#2:OK!

PCR

B-2
(ここに20140908_7を貼付)
B-7,D-9
(ここに20140908_8を貼付)
The band of the longest DNA is OK!

ligation → TF

O-1 (N-1 ES + K-2 EX), O-2 (N-2 ES + K-3 EX), O-4 (N-4 ES + K-5 EX), O-5 (N-5 ES + K-3 EX)
O-6 (N-6 ES + K-5 EX), B-2 (B-2 linear XP (9/8

PCR

) + pSB1C3 XP)
B-2' (B-2 linear XP + pSB1C3 XP), D-9, B-7

preculture

D-5, D-6, N-3, E-21, A-3, K-4
E-11 #1, E-12 #1, E-14 #1, E-15 #1, O-3 #2, B-7 #6, D-9 #5,6

9,9,2014

Lab member

Yoshikawa,Nakashima,Nakamura,Takemura,Yamanaka

9,10,2014

Lab member

Nakashima,Hiura,Takemura,Yamanaka,Yoshikawa(Fresh)

9,11,2014

Lab member

Yoshikawa,Nakashima,Nakamura,Hiura,Itoh,Tsukada

9,12,2014

Lab member

miniprep

H-5CP,G-5CP,J-5(made glycerol stock)

sequence order

E-2,E-8,E-9,E-19,F-1,F-3,F-4,G-5,H-1,H-4
H-5(VF-VR,Psigma2F-anti2R),J-2,J-4,J-5,J-6

10,2,2014

Lab member

Nakashima,Nakamura,Tara

10,3,2014

Lab member

Nakashima,Tara,Nakamura

10,4,2014

Lab member

Yoshikawa

assay1

F-2 in 20mL culture
When OD600=0.516,we put 10% arabinose 20uL.
F-1 in 20mL culture
When OD600=0.514,we put 10% arabinose 20uL.
Z-1 in 20mL culture
When OD600=0.544,we put 10% arabinose 20uL.
O/N culture

Culture in 3mL:disposed(OD600 value did not agrees with each other.)

colony PCR

digestion,gel extraction

E-19 XP,E-20 XP,H-1deg SP,H-4deg SP

making gel

making plate

Chloramphenicol*10

ligation

J-5deg(E-19XP+H-1degSP)
J-6deg(E-20XP+H-4degSP)
We did not have competent cell of E.coli MG1655, so put it in freezer.

preculture

F-1,E-17,E-15,Z-1,I-2:both in LB medium and M9 medium.
MG1655:LB medium

10,10,2014

assay1,3

I-2,E-15,Z-1,F-1,E-17(made glycerol stock,subculture in 20 fold dilution)
MG1655 did not grow, because we accidentally put antibiotics.
OD600(O/N culture)
E-15:1.795
E-17:1.781
F-1:1.937
I-2:1.886
Z-1:1.780

making M9 medium

Modeling is an attempt to describe, in a precise way, an understanding of the elements of a system of interest, their states, and their interactions with other elements.

The purpose of our modeling team is to peel back the layer of appearance of the device to reveal it's underlying nature. We tried to improve the device, cooperating with the experiment team. To achieve our goal, we have developed three fundamental themes. These three themes divide the modeling part into three parts. At the beginning, we con�rmed whether our circuit realizes a reaction:this for part 1. Next, we adjusted the parts and the conditions, for the device to reproduce a satisfactory value suitable for naming the device as a counter:this for part 2. Finally, we discussed what would be appropriate modeling, frequent issue to attack, in order to �nd the best strategy of modeling and wrote how we constructed our model:this for part 3.

In Part1(Deterministic Model,Stochastic Model), we approached the problem in two ways.

・Deteministic model:In this model,chemical reactions are discribed as differential equations and concentration of reaction product can be calu- culated by those of reactants. This model is intutive, simple and hence popular to estimate the result of experiment.

・Stochastic model:The most common formulation of stochastic models for biochemical networks is the chemical master equation (CME). We used Gillepie Algorithm to solve CME.

In Part2(Result), changing measured values of gene copy numbers, strength of pConst, sequence of taRNA and etc. in silico, we estimated in which combination of values the counter outputs a sufficient amount of data.

In Part3(Guide for Modeling), what is modeling, aims of modeling and differernt stochastic approaches and their interrelationShips

First of all, we constructed the deterministic model to estimate the behavior of the counter. In this model, chemical reactions are discribed as differential equations and concentration of reaction product can be calu- culated by those of reactants. This model is intutive, simple and hence popular to estimate the result of experiment. We could therefore get some parameters for modeling of the counter.[→ parameter]

We had simpli�ed the counstruction of mathematical model before described time evolution in which concentrations of mRNAs and proteins change as differential equations. First, we regarded that the reaction between taRNA(transactivating RNA) and crRNA(cis-repressor RNA) in riboregulator is much faster than that of transcription or translation and equilibrium reaction. This diminution of parameters enable us to use the equilibrium constant as a parameter and prevent us from over �tting when we adapt this model to raw data.

$\text{[math]}$

We decided to describe mRNAs and the coupling of taRNA and crRNA as stated above. Subscript mean coding sequence of its mRNA. We regarded that affinities of two riboregulators which the counter had is equal. The dissociation constant of equilibrium reaction was therefore shown as following.

$\text{[math]}$

Using dissociation constant, concentrations of reaction products such as [mcr_cr-σ] could be discribed as function of those of taRNA and mRNA of σ and GFP. We put X, A and B as the total quantity of taRNA, σ and GFP.

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Using these equations((3)-(7)) and equilibrium constant, concentrations of binding taRNA or not mRNA coding σ and GFP were discribed as following. These are all of simpli�cations.

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Finally, we built up differential equations about concentrations of reaction products including mRNA of σ which has no riboregulator. (It makes positive feedback loop.) We hypothesized that the amount of transcriptional product increasing per unit time is in proportion to the number of promotor if the promotor expressed constitutively and determined by Hill equation when the inducer controled its promotor. We also hypothesized propotional connection between decomposition amount of mRNA and protein and concentration of that. Some of used parameters were cited from references.[1]～[6]

We aimed to determine parameters about $\sigma$ through experiment and used provisonal parameter deter- mined in reference to other promotor.

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

The amount of sigma mRNA transcribed in positive feedback loop and that of anti sigma mRNA transcribed by IPTG induction to reset the counterwere described as following.

$\text{[math]}$ $\text{[math]}$

In our project, IPTG induction was aimed at enough production of anti-sigma to reset the counter and the sensitivity of lac promoter was not our main interest. Therefore, we used simple equation,(15) to describe how lac promoter behave. $ P_{lac} $ depend on the concentration of IPTG but we regarded it as a fixed number in this modeling.

Taking into account that translation coincide with transcription in prokaryotes, we hypothesized linear relationship between transcriptional product and the amount of translational product increasing per unit time and that this relationship does not depend on the kind of translational product. We also hypothesized that anti σ combine with σ and form inert matter and reaction velocity of that is proportional to product of these.

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Using above-mentioned differential equations, we simulated behavior of the counter by Euler's method.

We explained the parameters of the deterministic model. PoPS (promoter per second) is 0.03\cite{promoter}, so its promoter activity is $0.03/6.0*10^{23}\cdot 1.0\cdot 10^{-15}$[M], 0.051[nM/sec]. The switch point and hill coefficients of pBAD is writen in \cite{pBAD1}. RPU (relative promoter unit) is $\frac{5}{60}\cdot1.7$[nM]. We set the RPU of pLac as 2 when induced. We don't consider the leak expression from pLac.

The average half life of mRNA is 2-5 min\cite{Uri}, so we ser the degradation rate of mRNA as 0.020[/sec]. The half life of GFP is $\infty$\cite{GFP}, so we set the degradation of GFP as 0.0[sec]. The degradation rate of sigma factor[2] is fast. So we set as 0.0001[/sec]. The equilibrium constant of the equations (1)(2) is 80.0[nM]\cite{taRNA}. The number of plasmids copied is 100$\sim$300\cite{plasmid1}\cite{plasmid2} , so we set as 200. The number of ribosomes on a mRNA is about 20 and the time for a ribosome to translate is about 2 minute, so we set the translational rate as 1.43[/sec].

The summary of the parameters of this model is given in Table 1.

The unit of vertical axis is [nM], and that of the horizontal axis is [sec]. We can see that only after the second induction GFP was expressed.

By conducting sensitivity analysis, we can know what parameters have the most influential to the system.

horizontal axis : the pulse length of the arabinose induction

vertical axis:$\displaystyle \frac{\mathrm{fluorescense~after~the~first~induction}}{\mathrm{fluorescense~after~the~second~induction}}$

If there are a lot of molecules, modeling usually uses ordinary differntial equations, but some in vivo reactions involve only a few molecules. For example, transcription involves the cell's genomic DNA which is one copy or plasmids which are about 200 copies \cite{plasmid1}\cite{plasmid2} in a cell of {\em Escherichia coli}. The average size of a cell of {\em E. coli} is about $1.0 \cdot 10^{-15}$[L]\cite{volume}, so the concentration of DNA is about $1.7$[nM] and the concentration of plasmids is about 200 times of it. This is obviously weak. Reactions like this are well affected by fluctuations due to the reactants's limited copy numbers. So, we need to take this fluctuations into our modeling which is derived from stochastic methods. We also introduce delay effect.

First we explain about the Gillespie algorithm which is often used in stochastic simulations. In the Gillespie algorithm, we treated not the concentration of molecules but the number of them. Reactions are also viewed as descrete, essentially instantaneous physical events. What we have to determine when using the Gillespie algorithm is (1) when the next reaction is going to occur and (2) which type of the reaction it will be. Looking more closely at the Gillespie algorithm by the next set of reaction formulas;

$\text{[math]}$

Let $n_{1}, n_{2}$, and $n_{3}$ denote the respective copy number of the components $X_{1}, X_{2}$, and $X_{3}$. Notice that they are all integer. First we have to determine how easily each reactions could happen. It depends on the number of components copied. In stochatic simulations, we often determine the paremeter called stochastic rate constant, which is often written as ``$c$''. We assume that each possible combinations of reactant molecules have the same probability $c$ per unit time to react. In other words, $c \cdot\mathrm{dt}$ gives the probability that a particular combination of reactant molecules will react in a short time interval [t,t+dt). We call the stochastic rate constant of a reaction j $c_{j}$. Considering the all combinations of reactant molecules, the probability that the reaction 0 occur in [t,t+dt) is $c_{0}\cdot n_{1} \cdot n_{2}$. We now define the propensity function as the function of which product with dt gives the probability that a particular reaction will occur in the next infinitesimal time dt, which is often written as ``$a$''. Later on, the propensity function of a reaction j is $a_{j}$. Following the equation;

$\text{[math]}$

Notice that $c_{j}$ is invariant parameter, but $a_{j}$ changes as the state changes. In the same way, $a_{1} = c_{1} \cdot n_{3}$.

First we answer the question (1) when is the next reaction going to occur? Now, to simplify the situation we assume the situation that only the reaction 0 occurs. Set the time as 0, and define P(t) as the probability that the reaction 0 doesn't occur in [0,t). Then from the definition of $a$,we obtain the equation; P(t+dt) = P(t)$\cdot$(1$-$a$\cdot$dt). (Because the probability that the reaction 0 doesn't occur in [0,t+dt) is the product of the probability that the reaction 0 doesn't occur in [0,t) with the probability that the reaction 0 doesn't occur in [t,t+dt).) Using P(t+dt) = $\displaystyle \mathrm{P(t)} + \frac{d\mathrm{P(t)}}{\mathrm{dt}} \cdot \mathrm{dt}$, we get ;

$\text{[math]}$

Because the probability that the reaction0 doesn't occur in a 0 second interval is zero; $P(0)=1$. Solving the above ordinary differential eqaution we get ;

$\text{[math]}$

If $r_{1}$ is a uniform number from [0,1], the time of the next reaction should be determined by solving P(t) = $r_{1}$. Using (2), we get t = $\displaystyle -\frac{a_{0}}{\mathrm{log}r_{1}}$.

Now we suppose there is N types of reactions. Let $a_{1},a_{2},\dots,a_{N}$ denote the respective propensity function of reaction 1,2$,\dots,$N. From previous method;

$\text{[math]}$

Let dt be so small that we can ignore the term of higher than two orders of dt. The equation(3) becomes;

$\text{[math]}$

Solving (4) ($\displaystyle a = \sum_{j=1}^{N}a_{j}$);

$\text{[math]}$

Setting $\tau$ as the time of the next reaction, we get;

$\text{[math]}$

Second we answer the question (2) what types of the reaction will it be? We determined the time of the next reaction, so what we have left to do is to determine what kind of reaction occured. Some people may feel queer, but in the Gillespie algorithm, first the time of next reaction will be determined, and second the kind of reaction will be determined. It is natural to determine that the probability that the reaction j occurs is $\displaystyle \frac{a_{j}}{a}$. If $r_{2}$ is a uniform number from [0,1], j is the only number that meets below inequations;

$\text{[math]}$

In the case $a_{0} \geq a \cdot r_{2}$, the reaction that occured is reaction 0.

Now we can run the Gillespie algorithm by following the next steps.($t_{MAX}$ is the finish time of the simulation.)
1.Initialize the system at $t = 0$ with initial numbers of molecules for each spieces,$n_{0},\cdots ,n_{s}$
2.For each j = 0,1,$\cdots $,r, calculate $a_{j}(n)$ based on the current state n using (21)
3.Calculate the exit rate $\displaystyle a(n) = \sum_{j=0}^{r} a_{j}(n) $.
4.Compute a sample $\tau $ of the time until the next time using (27)
5.Update the time $t = t + \tau$
6.Compute a sample j of the reaction index using (28)
7.Update the state n according to the reaction j.
8.If $t < t_{MAX}$, return to Step 2

Stochastic rate constant can be determined by the parameters we used in the deterministic model (if we modeled the reaction in the determinsitic model) . If there are a lot of reactant molecules, stochastic simulations have to show similar results as those of determinisitic simulations. For this reason, stochastic rate constant, $c$, can be calculated from the chemical reaction rate constant, $k$. See \cite{gillespie1} if you want to know the deriving process. Here we just write the result.

For a unimolecular reaction, $c$ numerically equals to $k$, whereas for a bimolecular reaction, $c$ equals to $\displaystyle \frac{k}{N_{A}V}$ if the species of the reactant molecules are different, or $\displaystyle \frac{2k}{N_{A}V}$ if they are the same. $V$ is the volume of the system and $N_{A}$ is the Avogadro's constant.

However, these results should not be taken to imply that the mathematical forms of the propensity functions are just heuristic extrapolations. The propensity functions are grounded in molecular physics, and the formulas of deterministic chemical kinetics are approximate consequences of the formulas of stochastic chemical kinetics, not the other way around.

The Gillespie algorithm is so clear and useful that it is often used. However, this algorithm is not suitable for describing transcriptions and translations beacuse they are very slow and complex reactions involving many kinds of reactant molecules. If we treat transcription from plasmids as one reaction, assuming the copy number of plasmids as 200, then the propensity function $a$ equals to the stochastic rate constant multiplied by 200 ($200\cdot c$). So it will take about one of a two hundred times of an average transcription time to finish one transcription. Of course, in the time scale of average transcription time it is not a big problem, but this may not be good for simulating, like in our project, the system that uses the time for transcriptions and translations cannot be shortened. We introduce time-delay into the Gillespie algorithm based on \cite{delay1}$\sim$\cite{delay3}. The mathematical rightness of this algorithm is proved in \cite{delay3}. Time-delay means treating reactions as following;

$\text{[math]}$

Furthermore, transcriptions and translations are too complex to list up all of the reactions step by step. Therfore it is better to treat them as time-delay than reaction formulas.

Now we begin to model our project, $\sigma$ re-counter. In our model, there are only three reactions: transcription, translation, and an association and disassociation of crRNA and taRNA. We introduce time-delay into only transcription and translation. Then, we explain how we treat these three reactions in general.

First we explain transcription's model\cite{stochastic}. When the RNA polymerase binds to the promoter region, first they take the RNAP/promoter close complex. At this state, the complex can disociate. But with a certain probability, the close complex turn to the open complex which doesn't disociate. After the RNA polymerase and the promoter region take the open complex, a transcription starts. Then the reaction formula of transcription can be described as following's reactions;

$\text{[math]}$

combining reaction$3'$ and reaction$3''$, we get;

$\text{[math]}$

Second, we refer to the translational model [8]. Similary to the transcrptional model we model as following;

$\text{[math]}$

combining reaction2' and reaction2'', we get;

$\text{[math]}$

Last, the model of association and disassociation of crRNA and taRNA is a reversible reaction. So we model as following;

$\text{[math]}$

We can conclude that reaction formulas of our model are as follows:

In this section we have discussed the improved models of the σ-recounter.

First, we modeled the triple σ-recounter, the expansion of the double counter. Below is the construct of the triple re-counter.

The explanation on this construct is available here. The reaction formulas were established just like as the above-mentioned deterministic model. The result of the modeling of the triple recounter:

The unit of vertical axis is [nM], and that of the horizontal axis is [sec].

Fig 3count result is the result of the modeling of the triple recounter. Although there seems to be a few leak expression, the count is precisely conducted. Here we did not model resetting, because it is obvious from its orthogonality that resetting will be precisely conducted if the pulse length is long enough.

Second, we thought of genetic circuits that would not be affected by the pulse length of the arabinose induction. The current σ re-counter depends much on pulse length; when the pulse length is too long, it would count 2 or more (if there is). （Non-improved version）

induction time: 20000-40000, 60000-80000

If the induction is too long, there will be no difference in the first induction and the second induction; that is, it has no function of counting.

However, by improving this construct a little, our counter would not count more than 1 by a single pulse, as long as the pulse length is long enough (longer than $\tau_{0}$) for it to count. The figure shown below is the improved constructs.

X and Y are substances that bind together to activate pX\&Y promoter.

Before arabinose is induced, pTet and pConst express Y and crRBS-σ. When the arabinose is induced (for longer than time τ0), pBAD becomes activated and TetR and X are expressed. X binds to Y and the transcription of taRNA from pX\&Y occur, which leads to counting. At that time, expression of Y is repressed by TetR and the amount of Y decreases exponentially. Thus, pX\&Y is again repressed, the amount of taRNA decreases, and the counter never counts more than 1. You might be afraid that pX\&Y also begins transcription of taRNA when the induction ends; however, supposed degradation of X is faster than that of TetR, it will not occur. When the induction ends, X first degrades while still a lot of TetR remain and Y is not abundant. Since pTet has a simoidal transcriptional response, the production rate of Y will change little even if the concentration of TetR decrease a little. When TetR degrades so much that it finishes repression of Y, most of X have already decomposed, and pX\&Y will not be activated to begin transcription of taRNA.

We modeled this construct to test if it can be realized. We did not modeled resetting this time, either.

The inductions were modeled to be conducted just the same as non-improved version. Although pulse length is long, counts are precisely done. Thus, theoretically, the counter independent of the pulse length is suggested to be available. Only thing we have to do is to research for the substances that satisfy these conditions!

What is modeling

The model should be sufficiently detailed and precise so that it can in principle be used to simulate the bevavior of the system on a computer.

In the context of molecular cell biology, a model may describe the mechanisms involved intranscription, translation, gene regulation, cellular signaling, DNA damage and repair processes, homeostatic processes, the cell cycle, or apotosis. Indeed any biochemical mechanism of interest can, in principle, be modelled. At a higher level, modeling may be used to describe the functioning of a tissue, organ, or even an entire organism. At still higher levels, models can be used to describe the behavior and time evolution of populations of individual organisms.

The first issue to confront when embarking on a modeling project is to describe on exactly which features to include in the model, and in particular, the level of detail model is intended to capture. Interacting with other cells and/or its environment, the cell realizes four key functions: growth, proliferation, apotosis, and defferentiation. The processes that realize these functions of a cell can be further organized into three processes levels: gene regulation, signaltransduction and metabolism. So, a model of an entire organism is unlikely to describe the detailed functioning of every individual cell, but a model of a cell is likely to include a variety of very detailed description of key cellular processes. Even then, however, a model of a cell is unlikely to contain details of every single gene and protein.

Indeed, really accurate modeling of the process would require a model far more detalied and complex than most biologists would be comfortable with, using molecular dynamic simulations that explicitly manage the position and momentum of every molecule in the system.

The "art" of building a good model is to capture the essential features of the biology without burdening the model with non-essential details. Every model is to some extent a simplification of the biology, but models are valuable because they take ideas that might have been expressed verbally or diagrammatically and make them more explicit, so that they can begin to be undestood in a quantitative rather than purely qualitative way.

Aims of modeling

The features of a model depend very much on the aims of the modeling excercise. We therefore need to consider why people model and what they hope to achieve by so doing. Often the most basic aim is to make clear the current state of knowledge regarding a particular system, by attempting to be precise about the elements involved and the interactons between them. Doing this can be a particularly effective way of highlighting gaps in understanding. In addtion, having a detailed model of a system allows people to test that their understanding of a system is correct, by seeing if the implications of their models are consistent with observed experimental data. In practice, this model validation stage is central to the systems biology approach. However this work will often represent only the initial stage of the modeling process. Once people have a model they are happy with, they often want to use their models predictively, by conducting "virtual experiments" that might be difficult, time-consuming, or impossible to do in the lab. Such experiments may uncover important indirect relationships between the model components that would be hard to predict otherwise. An additional goal of modern biological modeling is to pool a number of samll models of well-understood mechanisms into a large model in order to investigate the effect of interactions between the model components. Models can also be extremely useful for informing the design and analysis of complex biological experiments.

In summary, modeling and computer simulation are becoming increasingly important in post-genomic biology for integrating knowledge and experimental data and making testable predictions about the behavior of complex biological systems.

Stochastic Approaches

The most common formulation of stochastic models for biochemical networks is the chemical master equation (CME). The analytical nature of the early stochastic approaches was highly complicated and, in some cases, intractable so that they received little attention in the biochemical community. Later, the situation changed with the increasing computational power of modern computers. And finally Gillespie presented an ground-breaking algorithm for numerically generating sample trajectories of the abundances of chemical species in chemical reaction networks. The so-called "stochastic simulation algorithm," or "Gillespie algorithm," can easily be implemented in any programming or scripting language that has a pseudorandom number generator. Several software packages implementing the algorithm have been developed. Differernt stochastic approaches and their interrelationchips are depicted in Figure.

For large biochemical systems, with many species and reactions, stochasitc simulations (based on the original Gillespie algorithm) become computationally demanding. Recent years have seen a large interest in improving the efficiency/speed of stochastic simulations by modification/approximation of the original Gillespie algorithm. These improvements include the "next reaction" method of Gibson and Bruck, the "τ-leap" method and its various improvements and generalizations and the "maximal time step method", which combines the next rection and the τ-leap methods.

While stochastic simulations sre a practical way to realize the CME, analytical approxinmations offer more insihgts into the influence of noise on cell function. Formally, the CME is a continuous-time discrete-state Markov process. For gaining intuitive insight and a quick characteriztion of fluctuations in biochemical networks, the CME is usually approximated analytically in different ways, including the frequently used chemical Langevin equation (CLE), the linear noise approximation (LNA), and the two-moment approximation (2MA).

The traditional Langevin approach is based on the assumption that the time-rate of abundance (copy number or concentration) or the flux of a component can be decomposed into a deterministic flux and a Lngevin moise term, which is a Gaussian (white noise) process with zero mean and amplitude determined by the system dynamics. This separation of noise from system dyanmics may be a reasonable assumption for external noise that arises from the interaction of the system with the other systems (such as the environment), but cannot be assumed for the internal noise that arises from within the system. Internal noise is not something that can be isolated from the system, because it results from the descrete nature of the underlying molecular events. Any noise term in the model must be derived from the system dynamics and cannot be presupposed in an ad hoc manner. However, the CLE does not suffer from above criticism because because Gillespie derived it from the CME description. The CLE allows much faster simulations compared to the exact stochastic simulation algorithm (SSA) and its variants. The CLE is a stochastic diiferent equation (dealing directly with random variables rather than moments) and has no direct way of representing the mean and (co)ariantce and the coupling between the two. That does not imply tha CLE, like the LNA, which has the same mean as the solution of deterministic model, ignores the coupling.

Markov processes form the basis of the vast majority of stochastic models of dynamical systems. At the center of a stochastic analysis is the Chapman-Kolmogorov equation (CKE), which describes the evolution of a Markov process over time. From the CKE stem three equations of practical importance: the master equation for jump Markov processes, the Fokker-Planck equation for continuous Markov processes, and the differential Chapman-Kolmogorov equation (dCKE) for processes made up both the continuous and jump parts.

Stochastic Formulation and Markov Process

Since the occurrence of reactions involves discrete and random events at the microscopic level, it is impossible to deterministically predict the progress of recations interms of the macroscopic variables (obsevables) N(t) and Z(t). To acount for this uncertainty, one of the observables N()Z()

Our goal is to determine how the process N(t) of copy numbers evolves in time. Starting at time t=0 from some initial state N(0), every sample path of the process remains in state N(0) for a random amount of time W\_1 until the occurrence of a reaction takes process to a new state N(W\_1); it remains in state N(W\_1) for another random amount of time W\_2 until the occurrence of another reaction takes the process to a new state N(W\_1+W\_2), and so on. In other words, the time-dependent copy number N(t) is a jump process.

The stochasitc process N(t) is characterized by a collection of state probabilities and transition probabilities. The state probability P(n,t)=Pr[N(t)=n] is the probability that the process N(t) is the state n at a time t. The transition probability Pr[N(t\_0+t)=n|N(t\_0)=m] is the conditional probability that process N(t) has moved from state m to state n during the time interval [t\_0,t\_0+t]. The analysis of a stochastic process becomes greatly simplified when the above transition probability depends on (i) the starting state m but not on the states before time t\_0 and (ii) the interval length t but not on the. Property (i) is the well-known Markov process. The process holding property (ii) is said to be homogeneous process.

[1]D.J.Wilkinson.Stochastic Modelling for Systems Biology.Mathematical \& Computational Biology. Chapman \& Hall/CRC, London, Apr. 2006. ISBN 1584885408

[2]Mukhtar Ullah \& Olaf Wolkenhauer Stochastic Approaches for Systems Biology.

References

[1] Uri Alon『An introductio to Systems Biology: Design Principles od Biological Circuits』

[2] Sheri A.Emory, et al A 5' terminal stem-loop structure can stabilize mRNA in Escherichia coli.

[3] Farren J Isaacs, et al engineered riboregulators enable post-trasncriptional control of gene expression.

[4] Jason R Kelly, Adam J Rubin,et al Measuring the activity of BioBrick promoters using an in vivo reference standard

[5] Daniel T.Gillespi A General Method For Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reaction.

[6] Andrzej M.Kierzek,et al The Effect of Transcription and Translation Initiation Frequencies on the Stochastic Fluctuations in Prokaryotic Gene Expression

[7] Marc R Roussel and Rui Zhu Validation of an algorithm for delay stochastic simulation of transcription and translation in prokaryotic gene expression.

[8] Andre S. Ribeiro Stochastic and delayed stochastic models of gene expression and regulation.

[9] Robert Schlicht and Gerhard Winkler A delay stochastic process with applicartions in molecular biology.

[10] JENS BO ANDERSEN, et al New Unstable Variants of Green Fluorescent Protein fot Studies of Transitent Gene Expression in Bacteria.

[11] Moises Santillan, et al Influence of Catabolite Repression and Inducer Exclusion on the Bistable Behavior of the lac Operon.

[12] Judith A.Megerle, Georg Fritz, et al Timing and Dynamics of Single Cell Gene Expression in the Arabinose Utilization System

[13] D.J.Wilkinson.Stochastic Modelling for Systems Biology.Mathematical & Computational Biology.Chapman & Hall/CRC, London, Apr. 2006. ISBN 1584885408

[14] Mukhtar Ullah & Olaf Wolkenhauer Stochastic Approaches for Systems Biology.

[15] Part:BBa I13453 ( We �nally accessed on 2014/8/20)

[16] iGEM Kyoto 2010

[17] pSB1A2 ( We �nally accessed on 2014/8/20)

[18] pSB1C3 ( We �nally accessed on 2014/8/20)

We will paste some part of the safety form of our team.

We also discussed safety in human practice page.

Your Training

a) Have your team members received any safety training yet?

We have not had any safety training officially, but have been taught by learned people.

b) Please briefly describe the topics that you learned about (or will learn about) in your safety training.

We learned about techniques for preventing diffusion of Escherichia coli or other organisms including ogenetically modified organisms into environment and risks concerning DNA assembly experiments.

c) Please give a link to the laboratory safety training requirements of your institution (college, university, community lab, etc). Or, if you cannot give a link, briefly describe the requirements.

Division for Environment, Health and Safety in our university is responsible for training laboratory safety.
（http://www.adm.u-tokyo.ac.jp/office/anzeneisei/index.html）
Taking lab safety training course is not mandatory, but strongly recommended for those who are involved in experiments. However, this course is for the graduate school students and senior stuffs, and not open to undergraduate students. We thus had a training directly from the PI.

Your Local Rules and Regulations

a) Who is responsible for biological safety at your institution? (You might have an Institutional Biosafety Committee, an Office of Environmental Health and Safety, a single Biosafety Officer, or some other arrangement.) Have you discussed your project with them? Describe any concerns they raised, and any changes you made in your project based on your discussion.

Office for Life Science Research Ethics and Safety is responsible for biological safety at our university. We haven't discussed our project with the office, but we carry out all of our biological experiments under the supervision of the PI and his lab staffs within the category of the experiments of the lab officially permitted by the Office.

b) What are the biosafety guidelines of your institution? Please give a link to these guidelines, or briefly describe them if you cannot give a link

http://www.u-tokyo.ac.jp/ja/administration/lifescience/kumikisoku.html

c) In your country, what are the regulations that govern biosafety in research laboratories? Please give a link to these regulations, or briefly describe them if you cannot give a link.

http://www.lifescience.mext.go.jp/bioethics/kankeihourei.html

The Organisms and Parts that You Use

Species name (including strain)	Risk Group	Risk Group Source	Disease risk to humans?	Part number/name	Natural function of part	How did you acquire it?	How will you use it?	Notes
Escherichia coli JM109	1	DSMZ	no			from our Lab	DNA asssembly
Escherichia coli MG1655	1	DSMZ	no			from our Lab	Assay
Pseudomonas fluorescens?	2	http://www.absa.org/riskgroups/bacteriasearch.php?genus=Pseudomonas	yes	sigma factor	polymerize RNA with RNA polymerase	order the part DNA from a synthesis company	transcriptional control	The bacteria causes opportunistic infection and it affects with usually patients with compromised immune systems.
Pseudomonas protegens	1	http://www.dsmz.de/catalogues/details/culture/DSM-19095.html	no	anti sigma factor	prevent combination between RNA polymerase and specific sigma factor	order the part DNA from a synthesis company	transcriptional control
Pseudomonas syringae?	1	DSMZ	no	sigma factor	polymerize RNA with RNA polymerase	order the part DNA from a synthesis company	transcriptional control
Pseudomonas syringae?	1	DSMZ	no	anti sigma factor	prevent combination between RNA polymerase and specific sigma factor	order the part DNA from a synthesis company	transcriptional control
Chlorocebus aethiops COS-1	1	DSMZ	no			receive the cells from another lab	Assay
Chlorocebus aethiops COS-7	1	DSMZ	no			receive the cells from another lab	Assay
Homo sapiens HL-60	1	DSMZ	no			receive the cells from another lab	Assay
Homo sapiens oral epithelial cell	1	http://www.lifescience.mext.go.jp/bioethics/data/anzen/syourei_02.pdf	no	EGP2 promoter	the promoter of EpCAM	from the member of our team	transcriptional control

Risks of Your Project Now

Please describe risks of working with the biological materials (cells, organisms, DNA, etc.) that you are using in your project. If you are taking any safety precautions (even basic ones, like rubber gloves), that is because your work has some risks, however small. Therefore, please discuss possible risks and what you have done (or might do) to minimize them, instead of simply saying that there are no risks at all.

a) Risks to the safety and health of team members, or other people working in the lab

When we are exposed to E. coli cells, we have a chance to have irritation in our eyes, skin, and respiratory system. Furthermore, ethidium bromide which we use to detect DNA band is carcinogen. We also use mammalian cells in assay. These cells can be infected by viruses which can also infect us. We also use harmful reagent, such as membrane binding solution.

b) Risks to the safety and health of the general public (if any biological materials escaped from your lab):

As maintained above, our lab has harmful organisms and substances. If they diffused outside, there might be health hazard.

c) Risks to the environment (from waste disposal, or from materials escaping from your lab)

We might dispose chips or tubes which contain a bit amount of genetically modified organisms without sterilizing. It offenses the law of our country; they may effect on biodiversity in our country. The bacteria we used also have drug resistance against ampicillin or CP, and if escaped, they could not be killed by those drugs. Mammalian cells are so weak that they can hardly live in the natural world.

d) Risks to security through malicious mis-use by individuals, groups, or countries

There seems to be no risks with this subject. In today's cognition, parts that we use do not seem to lead the expression of harmful materials.

e) What measures are you taking to reduce these risks? (For example: safe lab practices, choices of which organisms to use.)

In order to avoid the risks about bacterial cells shown above, we autoclave all wastes, sterilize all equipments that contain the organisms with detergent or hypochlorous acid. When bacteria exposed outside the tubes or examiners, we immediately seterilize them with ehtanol. Furthermore, in order to keep ethidium bromide away from our skin, we use kimwipes to wrap the chips used to taking it up before throwing away, and we take care that our bare hands do not touch the gel polluted by the substance.

Risks of Your Project in the Future

What would happen if all your dreams came true, and your project grew from a small lab study into a commercial/industrial/medical product that was used by many people? We invite you to speculate broadly and discuss possibilities, rather than providing definite answers. Even if the product is "safe", please discuss possible risks and how they could be addressed, rather than simply saying that there are no risks at all.

a) What new risks might arise from your project's growth? (Consider the categories of risk listed in parts a-d of the previous question: lab workers, the general public, the environment, and malicious mis-uses.) Also, what risks might arise if the knowledge you generate or the methods you develop became widely available?

In sigma-Recounter project, the circuit we constructed has potential for the application for defeating pests or bacteria by means of the expression of toxic proteins. In this case, there is a risk that you mistakenly output the toxin.
In CTCD project, the role of the circuits is to detect CTCs by GFP, thus it is thought to be difficult to have a risk of doing humans or environment harm.

b) Does your project currently include any design features to reduce risks? Or, if you did all the future work to make your project grow into a popular product, would you plan to design any new features to minimize risks? (For example: auxotrophic chassis, physical containment, etc.) Such features are not required for an iGEM project, but many teams choose to explore them.

In the future study of sigma-Recounter project, in addition to the reset system, we intend to increase the number of nodes and to enable one state to move to any other states. Therefore, if our project is used to express a toxin to defeat pest or bacteria, you can prepare an anti-toxin node or a reset system for mistakenly expressing the toxin.

Our activities involved in iGEM were all conducted by undergaduates alone!!
Based on fund-raisings and public relations, all team members had a lot of brainstoming, investigations and discussions in order to select project carefully. And we conducted experiments and FINALLY saw results.
We also designed and composed all publish tools, and of course, polished all scripts and presentation by ourselves.

Project

All we had a lot of brainstorming, investigations and discussion when we decide our projects.
σ-ReCounter:
Shunsuke Sumi(idea)
So Nakashima(idea and comformation)
Takefumi Yoshikawa(comformation)

CTCD:
Masayuki Osawa(conformation)
Shigetaka Kobari(investigation and conformation)
Shunsuke Sumi(conformation)
Senkei Hyo(investigation)
Yoshihiko Tomofuji(conformation)
Yshiki Okesaku(investigation)

Experiment

Lab. Leader:
Takefumi Yoshikawa(construction, assay;σ-ReCounter)

Lab. Members:
Atsuki Ito(construction)
Hajime Takemura(construction)
Keisuke Tsukada(construction)
Kentaro Tara(construction)
Kento Nakamura(construction, assay;σ-ReCounter)
Naruki Yoshikawa(construction)
Nobuhiro Hiura(construction)
Shigetaka Kobari(assay;CTCD)
So Nakashima(construction, Assay;σ-ReCounter)
Yoshihiko Tomofuji(assay;CTCD)
Yuto Yamanaka(construction)

Modeling

Keisuke Tsukada, Kentaro Tara, Manabu Nishiura, Masaki Ono

Web

Almost all members wrote drafts of our team wiki.
Cristian David(check our English)
Hiroki Tsuboi(team website, implementation of our team wiki)

App

Naruki Yoshikawa

Design

Cristian David(parker design)
Yoshiki Okesaku(all design, all figure)

Presentation

Kento Nakamura, Manabu Nishiura, Masato Ishikawa, Yumeno Koga, Yuto Yamanaka

Poster

Public Relation

Ding Yuewen, Keisuke Tsukada

Adviser

Kota Tosimitsu

Promega KK.for chamical reagents

Teiyukai, Faculty of Engineering, The University of Tokyofor fund

Integrated DNA Technologies MBL

COSMO BIO Co., Ltd.for fund

Leave a Nest Co., Ltd.(Hiroyuki Takahashi)for advice for public relations & introduction of Promega KK.

iGEM UT-Tokyo

YOICHI IRIE

Name: Yoichi Irie
Belong to: The University of Tokyo, Arts and Sciences
Job: Team leader

My dream is to make me robuster against stress caused by iGEM in synthetic biology!

iGEM UT-Tokyo

MASAKI ONO

Name: Masaki Ono
Belong to: The University of Tokyo, Literature, Sophmore
Job: Modeling

I want to be a doctor.

iGEM UT-Tokyo

MASAKI ONO

Name: Masaki Ono
Belong to: The University of Tokyo, Arts and Sciences, Sophmore
Job: Modeling

I want to be a doctor.

iGEM UT-Tokyo

MASAKI ONO

Name: Masaki Ono
Belong to: The University of Tokyo, Literature, Sophmore
Job: Modeling

I want to be a doctor.

iGEM UT-Tokyo

MASAKI ONO

Name: Masaki Ono
Belong to: The University of Tokyo, Literature, Sophmore
Job: Modeling

I want to be a doctor.

iGEM UT-Tokyo

KENTO NAKAMURA

Name: Kento Nakamura
Belong to: College of Arts and Sciences, The University of Tokyo
Job: Experimenter, Presenter

"I think, therefore I am" by R. Descartes
"I multiply, therefore I am" by E.coli
"I hope so..." by Experimenter

iGEM UT-Tokyo

SOH NAKASHIMA

Name: Soh Nakashima
Belong to: College of Arts and Sciences, The University of Tokyo
Job: Experimenter

I want to be a doctor.

iGEM UT-Tokyo

MANABU NISHIURA

Name: Manabu Nishiura
Belong to: The University of Tokyo, Arts and Sciences
Job: Modeling,Presenter

I am a Feynman Diagram.

iGEM UT-Tokyo

YOSHIKI OKESAKU

Name: Yoshiki Okesaku
Belong to: Department of Physics, Graduate School of Science, The University of Tokyo
Job: Design(DOKATA)

I am majoring in the MDS theory. The MDS theory can describe how our universe had begun and will end.

iGEM UT-Tokyo

HAJIME TAKEMURA

Name: Hajime Takemura
Belong to: The University of Tokyo, Junior,Faculty of Pharmaceutical Science
Job: Experiment

I want to make a new medicine.

iGEM UT-Tokyo

KENTARO TARA

Name: Kentaro Tara
Belong to: Arts and Sciences, The University of Tokyo
Job: Experiment, Modeling

Maps relax me.

iGEM UT-Tokyo

MASAKI ONO

Name: Masaki Ono
Belong to: The University of Tokyo, Literature, Sophmore
Job: Modeling

I want to be a doctor.

iGEM UT-Tokyo

MASAKI ONO

Name: Masaki Ono
Belong to: The University of Tokyo, Literature, Sophmore
Job: Modeling

I want to be a doctor.

iGEM UT-Tokyo

MASAKI ONO

Name: Masaki Ono
Belong to: The University of Tokyo, Literature, Sophmore
Job: Modeling

I want to be a doctor.

iGEM UT-Tokyo

KEISUKE TSUKADA

Name: Keisuke Tsukada
Belong to: Department of Biophysics and Biochemistry , Faculty of Science, The University of Tokyo
Job: Experiment, Modeling

itininnmaenokenkyuusyaninaretaraiina

iGEM UT-Tokyo

MASAKI ONO

Name: Masaki Ono
Belong to: The University of Tokyo, Literature, Sophmore
Job: Modeling

I want to be a doctor.

iGEM UT-Tokyo

SHUNSUKE SUMI

Name: Shunsuke Sumi
Belong to: The University of Tokyo, Literature, Sophmore
Job: Modeling

I want to be a doctor.

iGEM UT-Tokyo

NARUKI YOSHIKAWA

Name: Naruki Yoshikawa
Belong to: The University of Tokyo, Literature, Sophmore
Job: Modeling

I want to be a doctor.

iGEM UT-Tokyo

NOBUHIRO HIURA

Name: Nobuhiro Hiura
Belong to: The University of Tokyo, Literature, Sophmore
Job: Modeling

I want to be a doctor.

iGEM UT-Tokyo

HIROKI TSUBOI

Name: Hiroki Tsuboi
Belong to: Waseda University, School of Fundamental Science and Engineering, Computer Science and Engineering
Job: Web

iGEM UT-Tokyo

SHIGETAKA KOBARI

Name: Shigetaka Kobari
Belong to
Job

iGEM UT-Tokyo

MASATO ISHIKAWA

Name: Masato Ishikawa
Belong to
Job

iGEM UT-Tokyo

MASAYUKI OSAWA

Name: Masayuki Osawa
Belong to
Job

iGEM UT-Tokyo

TAKEHUMI YOSHIKAWA

Name: Takehumi Yoshikawa
Belong to
Job

@@ Line 42: / Line 42: @@
 </ul>
 </li>
-<li id="Safety"><a href="Javascript:open('Safety')"><img src="https://static.igem.org/mediawiki/2014/4/4c/Link_safetyclose.png" class="contList" alt="https://static.igem.org/mediawiki/2014/0/0d/Link_safetyopen.png" /></a>
+<li id="Safety"><a href="Javascript:loadContent('Safety-block','top')"><img src="https://static.igem.org/mediawiki/2014/4/4c/Link_safetyclose.png" class="contList" alt="https://static.igem.org/mediawiki/2014/0/0d/Link_safetyopen.png" /></a></li>
-<ul class="subContList">
-<li><a href="#">Contents1</a></li>
-<li><a href="#">Contents2</a></li>
-</ul>
-</li>
 <li id="Attribution"><a href="Javascript:open('Attribution')"><img src="https://static.igem.org/mediawiki/2014/1/1f/Link_attributionclose.png" class="contList" alt="https://static.igem.org/mediawiki/2014/f/f5/Link_attributionopen.png" /></a>
 <ul class="subContList">
@@ Line 2,192: / Line 2,187: @@
 					<p>b) Does your project currently include any design features to reduce risks? Or, if you did all the future work to make your project grow into a popular product, would you plan to design any new features to minimize risks? (For example: auxotrophic chassis, physical containment, etc.) Such features are not required for an iGEM project, but many teams choose to explore them.</p>
 					<p>In the future study of sigma-Recounter project, in addition to the reset system, we intend to increase the number of nodes and to enable one state to move to any other states. Therefore, if our project is used to express a toxin to defeat pest or bacteria, you can prepare an anti-toxin node or a reset system for mistakenly expressing the toxin.</p>
-				</div>
-			</div>
-			<!-- Attribution -->
-			<div id = "Attribution-block" style = "display:none;">
-				<div id = "Attribution-1">
-					<img src="https://static.igem.org/mediawiki/2014/4/44/Sub_attribution.png" class = "contTitle" />
-					<p>Our activities involved in iGEM were all conducted by undergaduates alone!!<br>Based on fund-raisings and public relations, all team members had a lot of brainstoming, investigations and discussions in order to select project carefully. And we conducted experiments and FINALLY saw results.<br>We also designed and composed all publish tools, and of course, polished all scripts and presentation by ourselves.</p>
-					<h3>Project</h3>
-					<p>All we had a lot of brainstorming, investigations and discussion when we decide our projects.<br>σ-ReCounter:<br><b>Shunsuke Sumi</b>(idea)<br><b>So Nakashima</b>(idea and comformation)<br><b>Takefumi Yoshikawa</b>(comformation)<br><br>CTCD:<br><b>Masayuki Osawa</b>(conformation)<br><b>Shigetaka Kobari</b>(investigation and conformation)<br><b>Shunsuke Sumi</b>(conformation)<br><b>Senkei Hyo</b>(investigation)<br><b>Yoshihiko Tomofuji</b>(conformation)<br><b>Yshiki Okesaku</b>(investigation)</p>
-					<h3>Experiment</h3>
-					<p>Lab. Leader:<br><b>Takefumi Yoshikawa</b>(construction, assay;σ-ReCounter)<br><br>Lab. Members:<br><b>Atsuki Ito</b>(construction)<br><b>Hajime Takemura</b>(construction)<br><b>Keisuke Tsukada</b>(construction)<br><b>Kentaro Tara</b>(construction)<br><b>Kento Nakamura</b>(construction, assay;σ-ReCounter)<br><b>Naruki Yoshikawa</b>(construction)<br><b>Nobuhiro Hiura</b>(construction)<br><b>Shigetaka Kobari</b>(assay;CTCD)<br><b>So Nakashima</b>(construction, Assay;σ-ReCounter)<br><b>Yoshihiko Tomofuji</b>(assay;CTCD)<br><b>Yuto Yamanaka</b>(construction)</p>
-					<h3>Modeling</h3>
-					<p><b>Keisuke Tsukada, Kentaro Tara, Manabu Nishiura, Masaki Ono</b></p>
-					<h3>Web</h3>
-					<p>Almost all members wrote drafts of our team wiki.<br><b>Cristian David</b>(check our English)<br><b>Hiroki Tsuboi</b>(team website, implementation of our team wiki)</p>
-					<h3>App</h3>
-					<p><b>Naruki Yoshikawa</b></p>
-					<h3>Design</h3>
-					<p><b>Cristian David</b>(parker design)<br><b>Yoshiki Okesaku</b>(all design, all figure)</p>
-					<h3>Presentation</h3>
-					<p><b>Kento Nakamura, Manabu Nishiura, Masato Ishikawa, Yumeno Koga, Yuto Yamanaka</b></p>
-					<h3>Poster</h3>
-					<br>
-					<h3>Public Relation</h3>
-					<p><b>Ding Yuewen, Keisuke Tsukada</b></p>
-					<h3>Adviser</h3>
-					<p><b>Kota Tosimitsu</b></p>
-				</div>
-				<div id = "Attribution-2">
-					<img src="https://static.igem.org/mediawiki/2014/4/44/Sub_Ackno.png" class="contTitle" />
-				</div>
-				<div id = "Attribution-3">
-					<img src="https://static.igem.org/mediawiki/2014/3/38/Sub_sponsors.png" class="contTitle" />
-					<img src="https://static.igem.org/mediawiki/2014/7/72/Promega.png" class="sponsor">
-					<p><b>Promega KK.</b>for chamical reagents</p>
-					<p><b>Teiyukai, Faculty of Engineering, The University of Tokyo</b>for fund</p>
-					<p><b>Integrated DNA Technologies MBL</b></p>
-					<img src="https://static.igem.org/mediawiki/2014/3/30/Cosmobio.png" class="sponsor">
-					<p><b>COSMO BIO Co., Ltd.</b>for fund<br></p>
-					<img src="https://static.igem.org/mediawiki/2014/1/17/Liveanest.png" class="sponsor">
-					<p><b>Leave a Nest Co., Ltd.(Hiroyuki Takahashi)</b>for advice for public relations & introduction of Promega KK.</p>
-				</div>
-			</div>
-			<!-- Human Practice -->
-			<div id = "Humanpractice-block" style = "display:none;">
-				<div id = "Humanpractice-1">
-				</div>
-			</div>
-			<!-- Teamここから -->
-			<div id = "Team-top" style = "display:none">
-			<img src = "https://static.igem.org/mediawiki/2014/d/d3/Member_title.png" class = "contTitle"/>
-			<div id="isotope">
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/2/28/Irie.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">YOICHI IRIE</p>
-							<img src = "https://static.igem.org/mediawiki/2014/6/6a/Irie_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Yoichi Irie</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Arts and Sciences</dd>
-								<dt>Job</dt>
-								<dd>Team leader</dd>
-							</dl>
-							<p class ="comment">My dream is to make me robuster against stress caused by iGEM in synthetic biology!</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/3/31/Chris.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">MASAKI ONO</p>
-							<img src = "https://static.igem.org/mediawiki/2014/f/f1/Chris_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Masaki Ono</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Literature, Sophmore</dd>
-								<dt>Job</dt>
-								<dd>Modeling</dd>
-							</dl>
-							<p class ="comment">I want to be a doctor.</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/8/8d/Cocoa.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">MASAKI ONO</p>
-							<img src = "https://static.igem.org/mediawiki/2014/7/78/Cocoa_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Masaki Ono</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Arts and Sciences, Sophmore</dd>
-								<dt>Job</dt>
-								<dd>Modeling</dd>
-							</dl>
-							<p class ="comment">I want to be a doctor.</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/a/a1/Ishikawa.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">MASAKI ONO</p>
-							<img src = "https://static.igem.org/mediawiki/2014/7/78/Cocoa_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Masaki Ono</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Literature, Sophmore</dd>
-								<dt>Job</dt>
-								<dd>Modeling</dd>
-							</dl>
-							<p class ="comment">I want to be a doctor.</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/3/35/Koga.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">MASAKI ONO</p>
-							<img src = "https://static.igem.org/mediawiki/2014/6/63/Koga_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Masaki Ono</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Literature, Sophmore</dd>
-								<dt>Job</dt>
-								<dd>Modeling</dd>
-							</dl>
-							<p class ="comment">I want to be a doctor.</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/8/85/Nakamura.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">KENTO NAKAMURA</p>
-							<img src = "https://static.igem.org/mediawiki/2014/8/87/Nakamura_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Kento Nakamura</dd>
-								<dt>Belong to</dt>
-								<dd>College of Arts and Sciences, The University of Tokyo</dd>
-								<dt>Job</dt>
-								<dd>Experimenter, Presenter</dd>
-							</dl>
-							<p class ="comment">"I think, therefore I am" by R. Descartes<br />"I multiply, therefore I am" by E.coli <br />"I hope so..." by Experimenter</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/1/1d/Nakashima.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">SOH NAKASHIMA</p>
-							<img src = "https://static.igem.org/mediawiki/2014/7/74/Dolicas_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Soh Nakashima</dd>
-								<dt>Belong to</dt>
-								<dd>College of Arts and Sciences, The University of Tokyo</dd>
-								<dt>Job</dt>
-								<dd>Experimenter</dd>
-							</dl>
-							<p class ="comment">I want to be a doctor.</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/0/05/Nishiura.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">MANABU NISHIURA</p>
-							<img src = "https://static.igem.org/mediawiki/2014/2/22/Nishiura_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Manabu Nishiura</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Arts and Sciences</dd>
-								<dt>Job</dt>
-								<dd>Modeling,Presenter</dd>
-							</dl>
-							<p class ="comment"> I am a Feynman Diagram.</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/b/b3/Oke.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">YOSHIKI OKESAKU</p>
-							<img src = "https://static.igem.org/mediawiki/2014/d/d0/Oke_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Yoshiki Okesaku</dd>
-								<dt>Belong to</dt>
-								<dd> Department of Physics, Graduate School of Science, The University of Tokyo</dd>
-								<dt>Job</dt>
-								<dd>Design(DOKATA)</dd>
-							</dl>
-							<p class ="comment">I am majoring in the MDS theory. The MDS theory can describe how our universe had begun and will end.</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/3/3f/Takemura.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">HAJIME TAKEMURA</p>
-							<img src = "https://static.igem.org/mediawiki/2014/3/35/Takemura_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Hajime Takemura</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Junior,Faculty of Pharmaceutical  Science</dd>
-								<dt>Job</dt>
-								<dd>Experiment</dd>
-							</dl>
-							<p class ="comment">I want to make a new medicine.</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/2/2b/Tara.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">KENTARO TARA</p>
-							<img src = "https://static.igem.org/mediawiki/2014/e/ef/Tara_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Kentaro Tara</dd>
-								<dt>Belong to</dt>
-								<dd>Arts and Sciences, The University of Tokyo</dd>
-								<dt>Job</dt>
-								<dd>Experiment, Modeling</dd>
-							</dl>
-							<p class ="comment">Maps relax me.</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/3/33/Te.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">MASAKI ONO</p>
-							<img src = "https://static.igem.org/mediawiki/2014/0/0e/Tei_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Masaki Ono</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Literature, Sophmore</dd>
-								<dt>Job</dt>
-								<dd>Modeling</dd>
-							</dl>
-							<p class ="comment">I want to be a doctor.</p>
-						</div>
-					</div>
-				</div>
-				<div class = "element-item">
-					<div class = "thumbnail">
-						<img src = "https://static.igem.org/mediawiki/2014/a/a4/Tomohuji.png" class ="member-thumbnail" />
-					</div>
-					<div class = "detail">
-						<div class = "meta">
-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
-						</div>
-						<div class = "member">
-							<p class = "name">MASAKI ONO</p>
-							<img src = "https://static.igem.org/mediawiki/2014/2/21/Tomohuji_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Masaki Ono</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Literature, Sophmore</dd>
-								<dt>Job</dt>
-								<dd>Modeling</dd>
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-							<p class ="comment">I want to be a doctor.</p>
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-							<p>iGEM UT-Tokyo</p>
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-							<p class = "name">MASAKI ONO</p>
-							<img src = "https://static.igem.org/mediawiki/2014/7/7c/Toshimitsu_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Masaki Ono</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Literature, Sophmore</dd>
-								<dt>Job</dt>
-								<dd>Modeling</dd>
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-							<p class ="comment">I want to be a doctor.</p>
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-							<p>iGEM UT-Tokyo</p>
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-							<p class = "name">KEISUKE TSUKADA</p>
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-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Keisuke Tsukada</dd>
-								<dt>Belong to</dt>
-								<dd>Department of Biophysics and Biochemistry , Faculty of Science, The University of Tokyo</dd>
-								<dt>Job</dt>
-								<dd>Experiment, Modeling</dd>
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-							<p class ="comment">itininnmaenokenkyuusyaninaretaraiina</p>
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-							<p>iGEM UT-Tokyo</p>
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-							<p class = "name">MASAKI ONO</p>
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-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Masaki Ono</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Literature, Sophmore</dd>
-								<dt>Job</dt>
-								<dd>Modeling</dd>
-							</dl>
-							<p class ="comment">I want to be a doctor.</p>
-						</div>
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-							<p>iGEM UT-Tokyo</p>
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-							<p class = "name">SHUNSUKE SUMI</p>
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-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Shunsuke Sumi</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Literature, Sophmore</dd>
-								<dt>Job</dt>
-								<dd>Modeling</dd>
-							</dl>
-							<p class ="comment">I want to be a doctor.</p>
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-							<p>iGEM UT-Tokyo</p>
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-							<p class = "name">NARUKI YOSHIKAWA</p>
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-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Naruki Yoshikawa</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Literature, Sophmore</dd>
-								<dt>Job</dt>
-								<dd>Modeling</dd>
-							</dl>
-							<p class ="comment">I want to be a doctor.</p>
-						</div>
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-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
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-							<p class = "name">NOBUHIRO HIURA</p>
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-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Nobuhiro Hiura</dd>
-								<dt>Belong to</dt>
-								<dd>The University of Tokyo, Literature, Sophmore</dd>
-								<dt>Job</dt>
-								<dd>Modeling</dd>
-							</dl>
-							<p class ="comment">I want to be a doctor.</p>
-						</div>
-					</div>
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-						<img src = "https://static.igem.org/mediawiki/2014/8/8c/Tsuboi.png" class ="member-thumbnail" />
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-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
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-							<p class = "name">HIROKI TSUBOI</p>
-							<img src = "https://static.igem.org/mediawiki/2014/b/b6/Tsuboi_comb.png" class ="member-detail" />
-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Hiroki Tsuboi</dd>
-								<dt>Belong to</dt>
-								<dd>Waseda University, School of Fundamental Science and Engineering, Computer Science and Engineering</dd>
-								<dt>Job</dt>
-								<dd>Web</dd>
-							</dl>
-							<p class ="comment"></p>
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-							<p>iGEM UT-Tokyo</p>
-							<img src = "https://static.igem.org/mediawiki/2014/9/98/Ui_close_40.png" class = "closebutton" />
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-							<p class = "name">SHIGETAKA KOBARI</p>
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-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Shigetaka Kobari</dd>
-								<dt>Belong to</dt>
-								<dd></dd>
-								<dt>Job</dt>
-								<dd></dd>
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-							<p>iGEM UT-Tokyo</p>
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-							<dl class = "profile">
-								<dt>Name</dt>
-								<dd>Masato Ishikawa</dd>
-								<dt>Belong to</dt>
-								<dd></dd>
-								<dt>Job</dt>
-								<dd></dd>
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-							<p>iGEM UT-Tokyo</p>
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-								<dt>Name</dt>
-								<dd>Masayuki Osawa</dd>
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-							<p>iGEM UT-Tokyo</p>
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-s an attempt to describe, in a precise way, an understanding of the elements of a system of interest, their states, and their interactions with other elements.</p>
-					<p>The purpose of our modeling team is to peel back the layer of appearance of the device to reveal it's underlying nature. We tried to improve the device, cooperating with the experiment team. To achieve our goal, we have developed three fundamental themes. These three themes divide the modeling part into three parts. At the beginning, we con�rmed whether our circuit realizes a reaction:this for part 1. Next, we adjusted the parts and the conditions, for the device to reproduce a satisfactory value suitable for naming the device as a counter:this for part 2. Finally, we discussed what would be appropriate modeling, frequent issue to attack, in order to �nd the best strategy of modeling and wrote how we constructed our model:this for part 3.</p>
-					<p>In Part1(Deterministic Model,Stochastic Model), we approached the problem in two ways.</p>
-					<p>・Deteministic model:In this model,chemical reactions are discribed as differential equations and concentration of reaction product can be calu- culated by those of reactants. This model is intutive, simple and hence popular to estimate the result of experiment.</p>
-					<p>・Stochastic model:The most common formulation of stochastic models for biochemical networks is the chemical master equation (CME). We used Gillepie Algorithm to solve CME.</p>
-					<p>In Part2(Result), changing measured values of gene copy numbers, strength of pConst, sequence of taRNA and etc. in silico, we estimated in which combination of values the counter outputs a sufficient amount of data.</p>
-					<p>In Part3(Guide for Modeling), what is modeling, aims of modeling and differernt stochastic approaches and their interrelationShips</p>
-				</div>
-				<div id = "Modeling-2">
-					<img src = "https://static.igem.org/mediawiki/2014/9/9e/Sub_deterministic.png" class = "contTitle" />
-					<p>First of all, we constructed the deterministic model to estimate the behavior of the counter. In this model, chemical reactions are discribed as differential equations and concentration of reaction product can be calu- culated by those of reactants. This model is intutive, simple and hence popular to estimate the result of experiment. We could therefore get some parameters for modeling of the counter.[→ parameter]</p>
-					<p>We had simpli�ed the counstruction of mathematical model before described time evolution in which concentrations of mRNAs and proteins change as differential equations. First, we regarded that the reaction between taRNA(transactivating RNA) and crRNA(cis-repressor RNA) in riboregulator is much faster than that of transcription or translation and equilibrium reaction. This diminution of parameters enable us to use the equilibrium constant as a parameter and prevent us from over �tting when we adapt this model to raw data.</p>
-					<img src = "https://static.igem.org/mediawiki/2014/9/9b/Ono_%281%29.png" class = "math" />
-					<p>We decided to describe mRNAs and the coupling of taRNA and crRNA as stated above. Subscript mean coding sequence of its mRNA. We regarded that affinities of two riboregulators which the counter had is equal. The dissociation constant of equilibrium reaction was therefore shown as following.</p>
-					<img src = "https://static.igem.org/mediawiki/2014/7/74/Ono_%282%29.png" class = "math" />
-					<p>Using dissociation constant, concentrations of reaction products such as [mcr<sub>cr-σ</sub>] could be discribed as function of those of taRNA and mRNA of σ and GFP. We put X, A and B as the total quantity of taRNA, σ and GFP.</p>
-					<img src = "https://static.igem.org/mediawiki/2014/0/0b/Ono_%283%29.png" class = "math" />
-					<img src = "https://static.igem.org/mediawiki/2014/0/04/Ono_%284%29.png" class = "math" />
-					<img src = "https://static.igem.org/mediawiki/2014/0/05/Ono_%285%29.png" class = "math" />
-					<p>Using these equations((3)-(7)) and equilibrium constant, concentrations of binding taRNA or not mRNA coding σ and GFP were discribed as following. These are all of simpli�cations.</p>
-					<img src = "https://static.igem.org/mediawiki/2014/7/71/Ono_%286%29.png" class = "math" />
-					<img src = "https://static.igem.org/mediawiki/2014/6/67/Ono_%287%29.png" class = "math" />
-					<img src = "https://static.igem.org/mediawiki/2014/5/5e/Ono_%288%29.png" class = "math" />
-					<img src = "https://static.igem.org/mediawiki/2014/1/18/Ono_%289%29.png" class = "math" />
-					<img src = "https://static.igem.org/mediawiki/2014/a/aa/Ono_%2810%29.png" class = "math" />
-					<p>Finally, we built up differential equations about concentrations of reaction products including mRNA of σ which has no riboregulator. (It makes positive feedback loop.) We hypothesized that the amount of transcriptional product increasing per unit time is in proportion to the number of promotor if the promotor expressed constitutively and determined by Hill equation when the inducer controled its promotor. We also hypothesized propotional connection between decomposition amount of mRNA and protein and concentration of that. Some of used parameters were cited from references.[1]～[6]</p>
-					<p>We aimed to determine parameters about $\sigma$ through experiment and used provisonal parameter deter- mined in reference to other promotor.</p>
-					<img src = "https://static.igem.org/mediawiki/2014/e/e5/Ono_%2811%29.png" class = "math" />
-					<img src = "https://static.igem.org/mediawiki/2014/3/31/Ono_%2812%29.png" class = "math" />
-					<img src = "https://static.igem.org/mediawiki/2014/7/7b/Ono_%2813%29.png" class = "math" />
-					<p>The amount of sigma mRNA transcribed in positive feedback loop and that of anti sigma mRNA transcribed by IPTG induction to reset the counterwere described as following.</p>
-					<img src = "https://static.igem.org/mediawiki/2014/0/0d/Ono_%2814%29.png" class = "math" />
-					<img src = "https://static.igem.org/mediawiki/2014/1/1b/Ono_%2815%29.png" class = "math" />
-					<p>In our project, IPTG induction was aimed at enough production of anti-sigma to reset the counter and the sensitivity of lac promoter was not our main interest. Therefore, we used simple equation,(15) to describe how lac promoter behave. $ P_{lac} $ depend on the concentration of IPTG but we regarded it as a fixed number in this modeling.</p>
-					<p>Taking into account that translation coincide with transcription in prokaryotes, we hypothesized linear relationship between transcriptional product and the amount of translational product increasing per unit time and that this relationship does not depend on the kind of translational product. We also hypothesized that anti σ combine with σ and form inert matter and reaction velocity of that is proportional to product of these.</p>
-					<img src = "https://static.igem.org/mediawiki/2014/0/0d/Ono_%2816%29.png" class = "math" />
-					<img src = "https://static.igem.org/mediawiki/2014/8/86/Ono_%2817%29.png" class = "math" />
-					<img src = "https://static.igem.org/mediawiki/2014/d/d2/Ono_%2818%29.png" class = "math" />
-					<p>Using above-mentioned differential equations, we simulated behavior of the counter by Euler's method.</p>
-					<p>We explained the parameters of the deterministic model. PoPS (promoter per second) is 0.03\cite{promoter}, so its promoter activity is $0.03/6.0*10^{23}\cdot 1.0\cdot 10^{-15}$[M], 0.051[nM/sec]. The switch point and hill coefficients of pBAD is writen in \cite{pBAD1}. RPU (relative promoter unit) is $\frac{5}{60}\cdot1.7$[nM]. We set the RPU of pLac as 2 when induced. We don't consider the leak expression from pLac.</p>
-					<p>The average half life of mRNA is 2-5 min\cite{Uri}, so we ser the degradation rate of mRNA as 0.020[/sec]. The half life of GFP is $\infty$\cite{GFP}, so we set the degradation of GFP as 0.0[sec]. The degradation rate of sigma factor[2] is fast. So we set as 0.0001[/sec]. The equilibrium constant of the equations (1)(2) is 80.0[nM]\cite{taRNA}. The number of plasmids copied is 100$\sim$300\cite{plasmid1}\cite{plasmid2} , so we set as 200. The number of ribosomes on a mRNA is about 20 and the time for a ribosome to translate is about 2 minute, so we set the translational rate as 1.43[/sec].</p>
-					<p>The summary of the parameters of this model is given in Table 1.</p>
-					<br />
-					<img src = "https://static.igem.org/mediawiki/2014/5/51/Ono_2count_result.png" class = "figure" />
-					<p>The unit of vertical axis is [nM], and that of the horizontal axis is [sec]. We can see that only after the second induction GFP was expressed.</p>
-					<p>By conducting sensitivity analysis, we can know what parameters have the most influential to the system.</p>
-					<img src = "https://static.igem.org/mediawiki/2014/9/98/Ono_arabinose_induce_time.png" class = "figure" />
-					<p>horizontal axis : the pulse length of the arabinose induction</p>
-					<p>vertical axis:$\displaystyle \frac{\mathrm{fluorescense~after~the~first~induction}}{\mathrm{fluorescense~after~the~second~induction}}$</p>
-				</div>
-				<div id = "Modeling-3">
-					<img src = "https://static.igem.org/mediawiki/2014/9/9c/Sub_stochastic.png" class = "contTitle" />
-					<p>If there are a lot of molecules, modeling usually uses ordinary differntial equations, but some in vivo reactions involve only a few molecules. For example, transcription involves the cell's genomic DNA which is one copy or plasmids which are about 200 copies \cite{plasmid1}\cite{plasmid2} in a cell of {\em Escherichia coli}. The average size of a cell of {\em E. coli} is about $1.0 \cdot 10^{-15}$[L]\cite{volume}, so the concentration of DNA is about $1.7$[nM] and the concentration of plasmids is about 200 times of it. This is obviously weak. Reactions like this are well affected by fluctuations due to the reactants's limited copy numbers. So, we need to take this fluctuations into our modeling which is derived from stochastic methods. We also introduce delay effect.</p>
-					<p>First we explain about the Gillespie algorithm which is often used in stochastic simulations. In the Gillespie algorithm, we treated not the concentration of molecules but the number of them. Reactions are also viewed as descrete, essentially instantaneous physical events. What we have to determine when using the Gillespie algorithm is (1) when the next reaction is going to occur and (2) which type of the reaction it will be. Looking more closely at the Gillespie algorithm by the next set of reaction formulas;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/8/8e/Ono_%2819%29.png" class = "math" />
-					<p>Let $n_{1}, n_{2}$, and $n_{3}$ denote the respective copy number of the components $X_{1}, X_{2}$, and $X_{3}$. Notice that they are all integer. First we have to determine how easily each reactions could happen. It depends on the number of components copied. In stochatic simulations, we often determine the paremeter called stochastic rate constant, which is often written as ``$c$''. We assume that each possible combinations of reactant molecules have the same probability $c$ per unit time to react. In other words, $c \cdot\mathrm{dt}$ gives the probability that a particular combination of reactant molecules will react in a short time interval [t,t+dt). We call the stochastic rate constant of a reaction j $c_{j}$. Considering the all combinations of reactant molecules, the probability that the reaction 0 occur in [t,t+dt) is $c_{0}\cdot n_{1} \cdot n_{2}$. We now define the propensity function as the function of which product with dt gives the probability that a particular reaction will occur in the next infinitesimal time dt, which is often written as ``$a$''. Later on, the propensity function of a reaction j is $a_{j}$. Following the equation;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/9/97/Ono_%2820%29.png" class = "math" />
-					<p>Notice that $c_{j}$ is invariant parameter, but $a_{j}$ changes as the state changes. In the same way, $a_{1} = c_{1} \cdot n_{3}$.</p>
-					<p>First we answer the question (1) when is the next reaction going to occur? Now, to simplify the situation we assume the situation that only the reaction 0 occurs. Set the time as 0, and define P(t) as the probability that the reaction 0 doesn't occur in [0,t). Then from the definition of $a$,we obtain the equation; P(t+dt) = P(t)$\cdot$(1$-$a$\cdot$dt). (Because the probability that the reaction 0 doesn't occur in [0,t+dt) is the product of the probability that the reaction 0 doesn't occur in [0,t) with the probability that the reaction 0 doesn't occur in [t,t+dt).) Using P(t+dt) = $\displaystyle \mathrm{P(t)} + \frac{d\mathrm{P(t)}}{\mathrm{dt}} \cdot \mathrm{dt}$, we get ;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/d/d5/Ono_%2821%29.png" class = "math" />
-					<p>Because the probability that the reaction0 doesn't occur in a 0 second interval is zero; $P(0)=1$. Solving the above ordinary differential eqaution we get ;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/3/3f/Ono_%2822%29.png" class = "math" />
-					<p> If $r_{1}$ is a uniform number from [0,1], the time of the next reaction should be determined by solving P(t) = $r_{1}$. Using (2), we get t = $\displaystyle -\frac{a_{0}}{\mathrm{log}r_{1}}$.</p>
-					<p>Now we suppose there is N types of reactions. Let $a_{1},a_{2},\dots,a_{N}$ denote the respective propensity function of reaction 1,2$,\dots,$N. From previous method;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/c/c9/Ono_%2823%29.png" class = "math" />
-					<p>Let dt be so small that we can ignore the term of higher than two orders of dt. The equation(3) becomes;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/f/f6/Ono_%2824%29.png" class = "math" />
-					<p>Solving (4) ($\displaystyle a = \sum_{j=1}^{N}a_{j}$);</p>
-					<img src = "https://static.igem.org/mediawiki/2014/8/81/Ono_%2825%29.png" class = "math" />
-					<p>Setting $\tau$ as the time of the next reaction, we get;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/3/3d/Ono_%2826%29.png" class = "math" />
-					<p>Second we answer the question (2) what types of the reaction will it be? We determined the time of the next reaction, so what we have left to do is to determine what kind of reaction occured. Some people may feel queer, but in the Gillespie algorithm, first the time of next reaction will be determined, and second the kind of reaction will be determined. It is natural to determine that the probability that the reaction j occurs is $\displaystyle \frac{a_{j}}{a}$. If $r_{2}$ is a uniform number from [0,1], j is the only number that meets below inequations;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/1/1a/Ono_%2827%29.png" class = "math" />
-					<p>In the case $a_{0} \geq a \cdot r_{2}$, the reaction that occured is reaction 0.</p>
-					<p>Now we can run the Gillespie algorithm by following the next steps.($t_{MAX}$ is the finish time of the simulation.)<br />1.Initialize the system at $t = 0$ with initial numbers of molecules for each spieces,$n_{0},\cdots ,n_{s}$<br />2.For each j = 0,1,$\cdots $,r, calculate $a_{j}(n)$ based on the current state n using (21)<br />3.Calculate the exit rate $\displaystyle a(n) = \sum_{j=0}^{r} a_{j}(n) $.<br />4.Compute a sample $\tau $ of the time until the next time using (27)<br />5.Update the time $t = t + \tau$<br />6.Compute a sample j of the reaction index using (28)<br />7.Update the state n according to the reaction j.<br />8.If $t < t_{MAX}$, return to Step 2</p>
-					<p>Stochastic rate constant can be determined by the parameters we used in the deterministic model (if we modeled the reaction in the determinsitic model) . If there are a lot of reactant molecules, stochastic simulations have to show similar results as those of determinisitic simulations. For this reason, stochastic rate constant, $c$, can be calculated from the chemical reaction rate constant, $k$. See \cite{gillespie1} if you want to know the deriving process. Here we just write the result.</p>
-					<p>For a unimolecular reaction, $c$ numerically equals to $k$, whereas for a bimolecular reaction, $c$ equals to $\displaystyle \frac{k}{N_{A}V}$ if the species of the reactant molecules are different, or $\displaystyle \frac{2k}{N_{A}V}$ if they are the same. $V$ is the volume of the system and $N_{A}$ is the Avogadro's constant.</p>
-					<p>However, these results should not be taken to imply that the mathematical forms of the propensity functions are just heuristic extrapolations. The propensity functions are grounded in molecular physics, and the formulas of deterministic chemical kinetics are approximate consequences of the formulas of stochastic chemical kinetics, not the other way around.</p>
-					<p>The Gillespie algorithm is so clear and useful that it is often used. However, this algorithm is not suitable for describing transcriptions and translations beacuse they are very slow and complex reactions involving many kinds of reactant molecules. If we treat transcription from plasmids as one reaction, assuming the copy number of plasmids as 200, then the propensity function $a$ equals to the stochastic rate constant multiplied by 200 ($200\cdot c$). So it will take about one of a two hundred times of an average transcription time to finish one transcription. Of course, in the time scale of average transcription time it is not a big problem, but this may not be good for simulating, like in our project, the system that uses the time for transcriptions and translations cannot be shortened. We introduce time-delay into the Gillespie algorithm based on \cite{delay1}$\sim$\cite{delay3}. The mathematical rightness of this algorithm is proved in \cite{delay3}. Time-delay means treating reactions as following;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/4/43/Ono_%2828%29.png" class = "math" />
-					<p>Furthermore, transcriptions and translations are too complex to list up all of the reactions step by step. Therfore it is better to treat them as time-delay than reaction formulas.</p>
-					<p>Now we begin to model our project, $\sigma$ re-counter. In our model, there are only three reactions: transcription, translation, and an association and disassociation of crRNA and taRNA. We introduce time-delay into only transcription and translation. Then, we explain how we treat these three reactions in general.</p>
-					<p>First we explain transcription's model\cite{stochastic}. When the RNA polymerase binds to the promoter region, first they take the RNAP/promoter close complex. At this state, the complex can disociate. But with a certain probability, the close complex turn to the open complex which doesn't disociate. After the RNA polymerase and the promoter region take the open complex, a transcription starts. Then the reaction formula of transcription can be described as following's reactions;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/c/cd/Ono_%2829%29.png" class = "math" />
-					<p>combining reaction$3'$ and reaction$3''$, we get;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/d/dd/Ono_%2830%29.png" class = "math" />
-					<p>Second, we refer to the translational model [8]. Similary to the transcrptional model we model as following;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/c/c1/Ono_%2831%29.png" class = "math" />
-					<p>combining reaction2' and reaction2'', we get;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/2/26/Ono_%2832%29.png" class = "math" />
-					<p>Last, the model of association and disassociation of crRNA and taRNA is a reversible reaction. So we model as following;</p>
-					<img src = "https://static.igem.org/mediawiki/2014/3/30/Ono_%2833%29.png" class = "math" />
-					<p>We can conclude that reaction formulas of our model are as follows:</p>
-				</div>
-				<div id = "Modeling-4">
-					<img src = "https://static.igem.org/mediawiki/2014/6/6f/Sub_implementation.png" class = "contTitle" />
-					<p>In this section we have discussed the improved models of the σ-recounter.</p>
-					<p>First, we modeled the triple σ-recounter, the expansion of the double counter. Below is the construct of the triple re-counter.</p>
-					<img src = "https://static.igem.org/mediawiki/2014/5/59/Ono_3count_construct.png" class = "figure" />
-					<p>The explanation on this construct is available <a href="Javascript:loadContent('Project-block','Project-3')">here</a>. The reaction formulas were established just like as the above-mentioned deterministic model. The result of the modeling of the triple recounter:</p>
-					<img src = "https://static.igem.org/mediawiki/2014/3/3b/Ono_3count_result.png" class = "figure" />
-					<p>The unit of vertical axis is [nM], and that of the horizontal axis is [sec].</p>
-					<p>Fig 3count result is the result of the modeling of the triple recounter. Although there seems to be a few leak expression, the count is precisely conducted. Here we did not model resetting, because it is obvious from its orthogonality that resetting will be precisely conducted if the pulse length is long enough.</p>
-					<p>Second, we thought of genetic circuits that would not be affected by the pulse length of the arabinose induction. The current σ re-counter depends much on pulse length; when the pulse length is too long, it would count 2 or more (if there is). （Non-improved version）</p>
-					<img src = "https://static.igem.org/mediawiki/2014/4/4e/Ono_implementation_failure.png" class = "figure" />
-					<p>induction time: 20000-40000, 60000-80000</p>
-					<p>If the induction is too long, there will be no difference in the first induction and the second induction; that is, it has no function of counting.</p>
-					<p>However, by improving this construct a little, our counter would not count more than 1 by a single pulse, as long as the pulse length is long enough (longer than $\tau_{0}$) for it to count. The figure shown below is the improved constructs.</p>
-					<img src = "https://static.igem.org/mediawiki/2014/c/cc/Ono_implementation_construct.png" class = "figure" />
-					<p>X and Y are substances that bind together to activate pX\&Y promoter.</p>
-					<p>Before arabinose is induced, pTet and pConst express  Y and crRBS-σ. When the arabinose is induced (for longer than time τ0), pBAD becomes activated and TetR and X are expressed. X binds to Y and the transcription of taRNA from pX\&Y occur, which leads to counting. At that time, expression of Y is repressed by TetR and the amount of Y decreases exponentially. Thus, pX\&Y is again repressed, the amount of taRNA decreases, and the counter never counts more than 1. You might be afraid that pX\&Y also begins transcription of taRNA when the induction ends; however, supposed degradation of X is faster than that of TetR, it will not occur. When the induction ends, X first degrades while still a lot of TetR remain and Y is not abundant. Since pTet has a simoidal transcriptional response, the production rate of Y will change little even if the concentration of TetR decrease a little. When TetR degrades so much that it finishes repression of Y, most of X have already decomposed, and pX\&Y will not be activated to begin transcription of taRNA.</p>
-					<p>We modeled this construct to test if it can be realized. We did not modeled resetting this time, either.</p>
-					<img src = "https://static.igem.org/mediawiki/2014/d/d0/Ono_implementation_result.png" class = "figure" />
-					<p>The inductions were modeled to be conducted just the same as non-improved version. Although pulse length is long, counts are precisely done. Thus, theoretically, the counter independent of the pulse length is suggested to be available. Only thing we have to do is to research for the substances that satisfy these conditions!</p>
-				</div>
-				<div id = "Modeling-5">
-					<img src = "https://static.igem.org/mediawiki/2014/7/76/Sub_guideformodeling.png" class = "contTitle" />
-					<h3>What is modeling</h3>
-					<p>The model should be sufficiently detailed and precise so that it can in principle be used to simulate the bevavior of the system on a computer. </p>
-					<p>In the context of molecular cell biology, a model may describe the mechanisms involved intranscription, translation, gene regulation, cellular signaling, DNA damage and repair processes, homeostatic processes, the cell cycle, or apotosis. Indeed any biochemical mechanism of interest can, in principle, be modelled. At a higher level, modeling may be used to describe the functioning of a tissue, organ, or even an entire organism. At still higher levels, models can be used to describe the behavior and time evolution of populations of individual organisms.</p>
-					<p>The first issue to confront when embarking on a modeling project is to describe on exactly which features to include in the model, and in particular, the level of detail model is intended to capture. Interacting with other cells and/or its environment, the cell realizes four key functions: growth, proliferation, apotosis, and defferentiation. The processes that realize these functions of a cell can be further organized into three processes levels: gene regulation, signaltransduction and metabolism. So, a model of an entire organism is unlikely to describe the detailed functioning of every individual cell, but a model of a cell is likely to include a variety of very detailed description of key cellular processes. Even then, however, a model of a cell is unlikely to contain details of every single gene and protein.</p>
-					<p>Indeed, really accurate modeling of the process would require a model far more detalied and complex than most biologists would be comfortable with, using molecular dynamic simulations that explicitly manage the position and momentum of every molecule in the system.</p>
-					<p>The "art" of building a good model is to capture the essential features of the biology without burdening the model with non-essential details. Every model is to some extent a  simplification of the biology, but models are valuable because they take ideas that might have been expressed verbally or diagrammatically and make them more explicit, so that they can begin to be undestood in a quantitative rather than purely qualitative way.</p>
-					<h3>Aims of modeling</h3>
-					<p>The features of a model depend very much on the aims of the modeling excercise. We therefore need to consider why people model and what they hope to achieve by so doing. Often the most basic aim is to make clear the current state of knowledge regarding a particular system, by attempting to be precise about the elements involved and the interactons between them. Doing this can be a particularly effective way of highlighting gaps in understanding. In addtion, having a detailed model of a system allows people to test that their understanding of a system is correct, by seeing if the implications of their models are consistent with observed experimental data. In practice, this model validation stage is central to the systems biology approach. However this work will often represent only the initial stage of the modeling process. Once people have a model they are happy with, they often want to use their models predictively, by conducting "virtual experiments" that might be difficult, time-consuming, or impossible to do in the lab. Such experiments may uncover important indirect relationships between the model components that would be hard to predict otherwise. An additional goal of modern biological modeling is to pool a number of samll models of well-understood mechanisms into a large model in order to investigate the effect of interactions between the model components. Models can also be extremely useful for informing the design and analysis of complex biological experiments.</p>
-					<p>In summary, modeling and computer simulation are becoming increasingly important in post-genomic biology for integrating knowledge and experimental data and making testable predictions about the behavior of complex biological systems.</p>
-					<h3>Stochastic Approaches</h3>
-					<p>The most common formulation of stochastic models for biochemical networks is the chemical master equation (CME). The analytical nature of the early stochastic approaches was highly complicated and, in some cases, intractable so that they received little attention in the biochemical community. Later, the situation changed with the increasing computational power of modern computers. And finally Gillespie presented an ground-breaking algorithm for numerically generating sample trajectories of the abundances of chemical species in chemical reaction networks. The so-called "stochastic simulation algorithm," or "Gillespie algorithm," can easily be implemented in any programming or scripting language that has a pseudorandom number generator. Several software packages implementing the algorithm have been developed. Differernt stochastic approaches and their interrelationchips are depicted in Figure.</p>
-					<img src="https://static.igem.org/mediawiki/2014/e/e8/Chart.png" class="figure" />
-					<p>For large biochemical systems, with many species and reactions, stochasitc simulations (based on the original Gillespie algorithm) become computationally demanding. Recent years have seen a large interest in improving the efficiency/speed of stochastic simulations by modification/approximation of the original Gillespie algorithm. These improvements include the "next reaction" method of Gibson and Bruck, the "τ-leap" method and its various improvements and generalizations and the "maximal time step method", which combines the next rection and the τ-leap methods.</p>
-					<p>While stochastic simulations sre a practical way to realize the CME, analytical approxinmations offer more insihgts into the influence of noise on cell function. Formally, the CME is a continuous-time discrete-state Markov process. For gaining intuitive insight and a quick characteriztion of fluctuations in biochemical networks, the CME is usually approximated analytically in different ways, including the frequently used chemical Langevin equation (CLE), the linear noise approximation (LNA), and the two-moment approximation (2MA).</p>
-					<p>The traditional Langevin approach is based on the assumption that the time-rate of abundance (copy number or concentration) or the flux of a component can be decomposed into a deterministic flux and  a Lngevin moise term, which is a Gaussian (white noise) process with zero mean and amplitude determined by the system dynamics. This separation of noise from system dyanmics may be a reasonable assumption for external noise that arises from the interaction of the system with the other systems (such as the environment), but cannot be assumed for the internal noise that arises from within the system. Internal noise is not something that can be isolated from the system, because it results from the descrete nature of the underlying molecular events. Any noise term in the model must be derived from the system dynamics and cannot be presupposed in an ad hoc manner. However, the CLE does not suffer from above criticism because because Gillespie derived it from the CME description. The CLE allows much faster simulations compared to the exact stochastic simulation algorithm (SSA) and its variants. The CLE is a stochastic diiferent equation (dealing directly with random variables rather than moments) and has no direct way of representing the mean and (co)ariantce and the coupling between the two. That does not imply tha CLE, like the LNA, which has the same mean as the solution of deterministic model, ignores the coupling.</p>
-					<p>Markov processes form the basis of the vast majority of stochastic models of dynamical systems. At the center of a stochastic analysis is the Chapman-Kolmogorov equation (CKE), which describes the evolution of a Markov process over time. From the CKE stem three equations of practical importance: the master equation for jump Markov processes, the Fokker-Planck equation for continuous Markov processes, and the differential Chapman-Kolmogorov equation (dCKE) for processes made up both the continuous and jump parts.</p>
-					<h3>Stochastic Formulation and Markov Process</h3>
-					<p>Since the occurrence of reactions involves discrete and random events at the microscopic level, it is impossible to deterministically predict the progress of recations interms of the macroscopic variables (obsevables) N(t) and Z(t). To acount for this uncertainty, one of the observables N()Z()</p>
-					<p>Our goal is to determine how the process N(t) of copy numbers evolves in time. Starting at time t=0 from some initial state N(0), every sample path of the process remains in state N(0) for a random amount of time W\_1 until the occurrence of a reaction takes process to a new state N(W\_1); it remains in state N(W\_1) for another random amount of time W\_2 until the occurrence of another reaction takes the process to a new state N(W\_1+W\_2), and so on. In other words, the time-dependent copy number N(t) is a jump process.</p>
-					<p>The stochasitc process N(t) is characterized by a collection of state probabilities and transition probabilities. The state probability P(n,t)=Pr[N(t)=n] is the probability that the process N(t) is the state n at a time t. The transition probability Pr[N(t\_0+t)=n|N(t\_0)=m] is the conditional probability that process N(t) has moved from state m to state n during the time interval [t\_0,t\_0+t]. The analysis of a stochastic process becomes greatly simplified when the above transition probability depends on (i) the starting state m but not on the states before time t\_0 and (ii) the interval length t but not on the. Property (i) is the well-known Markov process. The process holding property (ii) is said to be homogeneous process.</p>
-					<p>[1]D.J.Wilkinson.Stochastic Modelling for Systems Biology.Mathematical \& Computational Biology. Chapman \& Hall/CRC, London, Apr. 2006. ISBN 1584885408</p>
-					<p>[2]Mukhtar Ullah \& Olaf Wolkenhauer Stochastic Approaches for Systems Biology.</p>
-					<h3>References</h3>
-					<p>[1] Uri Alon『An introductio to Systems Biology: Design Principles od Biological Circuits』</p>
-					<p>[2] Sheri A.Emory, et al A 5' terminal stem-loop structure can stabilize mRNA in Escherichia coli.</p>
-					<p>[3] Farren J Isaacs, et al engineered riboregulators enable post-trasncriptional control of gene expression.</p>
-					<p>[4] Jason R Kelly, Adam J Rubin,et al Measuring the activity of BioBrick promoters using an in vivo reference standard</p>
-					<p>[5] Daniel T.Gillespi A General Method For Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reaction.</p>
-					<p>[6] Andrzej M.Kierzek,et al The Effect of Transcription and Translation Initiation Frequencies on the Stochastic Fluctuations in Prokaryotic Gene Expression</p>
-					<p>[7] Marc R Roussel and Rui Zhu Validation of an algorithm for delay stochastic simulation of transcription and translation in prokaryotic gene expression.</p>
-					<p>[8] Andre S. Ribeiro Stochastic and delayed stochastic models of gene expression and regulation.</p>
-					<p>[9] Robert Schlicht and Gerhard Winkler A delay stochastic process with applicartions in molecular biology.</p>
-					<p>[10] JENS BO ANDERSEN, et al New Unstable Variants of Green Fluorescent Protein fot Studies of Transitent Gene Expression in Bacteria.</p>
-					<p>[11] Moises Santillan, et al Influence of Catabolite Repression and Inducer Exclusion on the Bistable Behavior of the lac Operon.</p>
-					<p>[12] Judith A.Megerle, Georg Fritz, et al Timing and Dynamics of Single Cell Gene Expression in the Arabinose Utilization System</p>
-					<p>[13] D.J.Wilkinson.Stochastic Modelling for Systems Biology.Mathematical & Computational Biology.Chapman & Hall/CRC, London, Apr. 2006. ISBN 1584885408</p>
-					<p>[14] Mukhtar Ullah & Olaf Wolkenhauer Stochastic Approaches for Systems Biology.</p>
-					<p>[15] Part:BBa I13453 <http://parts.igem.org/Part:BBa_I13453> ( We �nally accessed on 2014/8/20)</p>
-					<p>[16] iGEM Kyoto 2010 <https://2010.igem.org/Team:Kyoto/Project/Goal_A></p>
-					<p>[17] pSB1A2 <http://parts.igem.org/Part:pSB1A2> ( We �nally accessed on 2014/8/20)</p>
-					<p>[18] pSB1C3 <http://parts.igem.org/Part:pSB1C3> ( We �nally accessed on 2014/8/20)</p>
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Team:UT-Tokyo/Counter/Project

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sigma factor

sigma-memory construction

sigma-memory and automaton

resettable counter by sigma-memory

riboregulator

resettable counter construction

mechanism and extension

comparison with previous counter

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Making Plate Culture

7,15,2014

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Making DW 100mL

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7,16,2014

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7,17,2014

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miniprep

making reagent

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7,18,2014

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miniprep

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7,22,2014

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Cut check

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7,23,2014

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miniprep

7,28,2014

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digestion,gel extraction

colony PCR

Measuring cfu

7,29,2014

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7,30,2014

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colony check

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7,31,2014

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miniprep

digestion,gel extraction

ligation

8,1,2014

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8,4,2014

Making　reagent