Team:ETH Zurich/modeling/qs

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{{:Team:ETH Zurich/tpl/head|Quorum Sensing}}
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== Model ==
== Model ==
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The Quorum sensing module is mainly involved in receiving signals from the sender cells. The sender cells secrete some signaling molecules (inducers) which diffuse out of their membrane, then diffuse in receiver cells membrane, and bind to the regulator molecules in the receiver cells, thus activating the transcription of certain genes. In order to characterize the quorum sensing module with a transfer function, we consider different initial inputs of external AHL, and see how much output is produced, as it was done in the [https://2014.igem.org/Team:ETH_Zurich/expresults#Quorum_Sensing quorum sensing experiments].
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The Quorum sensing module is mainly involved in receiving signals from the sender cells. The sender cells produce some signaling molecules (inducers) which diffuse out of their membrane, then diffuse in receiver cells membrane, and bind to the regulator molecules in the receiver cells, thus activating the transcription of certain genes. In order to characterize the quorum sensing module with a transfer function, we consider different initial inputs of external AHL, and see how much output is produced, as it was done in the [https://2014.igem.org/Team:ETH_Zurich/expresults#Quorum_Sensing quorum sensing experiments].
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As diffusion through the membrane is very fast<sup>[[Team:ETH_Zurich/project/references|[27]]]</sup>, according to Fick's law of diffusion, internal and external concentration of AHL can always be considered as equal. This can also be observed in the [https://2014.igem.org/Team:ETH_Zurich/modeling/diffmodel#Results diffusion model results]. When an initial external AHL concentration is given, AHL diffuses in the cells very quickly (less than 20 seconds)<sup>[[Team:ETH_Zurich/project/references|[27]]]</sup> until internal AHL concentration equals external concentration. Then as soon as some internal AHL is consumed in the cell, it is taken up again without affecting external concentration, because external volume is very high compared to internal volume. Therefore we can consider in this module that external AHL (which is equal to internal AHL) only degrades, with the rate of extracellular decay.
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As diffusion through the membrane is very fast<sup>[[Team:ETH_Zurich/project/references|[27]]]</sup>, according to Fick's law of diffusion, internal and external concentration of AHL can always be considered as equal. This can also be observed in the [https://2014.igem.org/Team:ETH_Zurich/modeling/diffmodel#Results diffusion model results]. When an initial external AHL concentration is given, AHL diffuses into the cells very quickly (less than 20 seconds)<sup>[[Team:ETH_Zurich/project/references|[27]]]</sup> until internal AHL concentration equals external concentration. Then as soon as some internal AHL is consumed in the cell, it is taken up again without affecting external concentration, because external volume is very high compared to internal volume. Therefore we can consider in this module that external AHL (which is equal to internal AHL) only degrades, with the rate of extracellular decay.
   
   
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The same holds true for the Las system.
The same holds true for the Las system.
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<strong>From the original set of reactions, we reduce the rate of production of mRNA<sub>Bxb1</sub> as a Hill function of RLux instead of Mass action kinetics in terms of P<sub>LuxON</sub>  and P<sub>LuxOFF</sub>. For more information please check the characterization section.</strong>
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'''From the original set of reactions, we reduce the rate of production of mRNA<sub>Bxb1</sub> to a Hill function of RLux instead of Mass action kinetics in terms of P<sub>LuxON</sub>  and P<sub>LuxOFF</sub>. For more information please check the [https://2014.igem.org/Team:ETH_Zurich/expresults characterization section].'''
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[[File:ETHZ_LuxParameterFitting.png|center|500 px|thumb|Lux QS Module fitted to experimental data from riboregulated Lux system.]]
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[[File:ETHZ_LuxParameterFitting.png|center|500 px|thumb|'''Figure 1''' Lux QS Module fitted to experimental data from riboregulated Lux system.]]
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respectively.
respectively.
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[[File:ETHZ_LasParameterFitting.png|center|500 px|thumb|Las QS Module fitted to experimental data from riboregulated Las system.]]
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[[File:ETHZ_LasParameterFitting.png|center|500 px|thumb|'''Figure 2''' Las QS Module fitted to experimental data from riboregulated Las system.]]
=== Range of validity of the assumptions ===
=== Range of validity of the assumptions ===
These assumptions hold true for all input LuxAHL and LasAHL concentrations.
These assumptions hold true for all input LuxAHL and LasAHL concentrations.
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== Retrieving degradation rates==
== Retrieving degradation rates==
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Curve
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[[File:ETH_Zurich_dGFP_Dynamic.png|500px|center|thumb| '''Figure 3''' Dynamic response of the promoter Plux to a dose entry at time t=0.]]
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== Leakiness ==
== Leakiness ==
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The leakiness of promoters is a major issue in our system. As the signal propagates row-wise, error diffusion could lead to a totally different pattern. The goal is then to master the leakiness. This issue was particularly observed in the case of the Lux promoter during our experiments set. This leakiness is dependent on the LuxR concentration in the cell. Therefore, an assumption would be that Lux(see the [http://parts.igem.org/Part:BBa_R0062:Experience Registry] for more exhaustive information)
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The leakiness of promoters is a major issue in our system. As the signal propagates row-wise, error diffusion could lead to a totally different pattern. The goal is then to control the leakiness. This issue was particularly observed and adressed in the case of the Lux promoter during our [https://2014.igem.org/Team:ETH_Zurich/expresults experiments set]. This leakiness is dependent on LuxR concentration in the cell(see our biobrick characterization in the [http://parts.igem.org/Part:BBa_R0062:Experience Registry] for more information).
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Leakiness was modeled as an offset in the classical Hill function.
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$$rFluo = a + b \frac{[AHL]^n}{K_m^n + [AHL]^n}$$
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$$\text{where rFluo is the relative fluorescence (absolute measured fluorescence value over OD),}$$
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$$\text{a the basal expression rate (Leakiness),}$$
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$$\text{b the maximum fold expression rate,}$$
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$$\text{n the Hill coefficient,}$$
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$$K_m\text{ the activation concentration of AHL.}$$
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Given this offset and the maximal expression, the signal over noise ratio can be derived. This ratio, which can then be compared amongst all curves, characterizes the impact of leakiness on the behavior of a system. The leakier a construct in its native form is, the more impact the riboregulator will have, and the more likely it is for the riboregulator to increase the signal over noise ratio. Our final constructs (Promoters with a [https://2014.igem.org/Team:ETH_Zurich/expresults riboregulating system]) have the following parameters:
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{| class="wikitable"
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|-
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! '''Promoter used'''
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! '''Signal over noise ratio'''
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|-
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|P<sub>Lux</sub> without riboregulating system
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|23
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|-
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|P<sub>Lux</sub> with riboregulating system
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|79
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|-
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|P<sub>Las</sub> without riboregulating system
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|84
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|-
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|P<sub>Las</sub> with riboregulating system
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|55
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|}
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We took the leakiness coefficients into account in our [https://2014.igem.org/Team:ETH_Zurich/modeling/whole whole cell model].
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== Cross-talk ==
== Cross-talk ==
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We investigated the existence of cross-talk between three quorum sensing systems (Lux, Las and Rhl). Cross-talk implies non-orthogonality of the communication systems. It corresponds to the fact that LasAHL can activate the Lux promoter, even if it is not its native communicating pathway.
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We investigated the existence of cross-talk between three quorum sensing systems (Lux, Las and Rhl). Each quorum sensing system is based on three components: a signaling molecule, a regulatory protein and a promoter. Cross-talk implies non-orthogonality of the communication systems. It corresponds to the fact that LasAHL can activate the Lux promoter, even if it is not its native communicating pathway. There are 27 combinations possible and only 3 native combinations between signaling molecule, regulatory protein and promoter.
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[[File:ETH Zurich Crosstalk.png|1500px|center|thumb|Each quorum sensing system is based on three components: a signaling molecule, a regulatory protein and a promoter. These elements are here ordered into three layers. Cross-talk evaluation can be done by comparing all combinations of those three elements. After collecting the [https://2014.igem.org/Team:ETH_Zurich/expresults experimental data] of all possible pathways, we modeled their influence.]]
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[[File:ETH Zurich Crosstalk.png|1500px|center|thumb|'''Figure 4''' Each quorum sensing system is based on three components: a signaling molecule, a regulatory protein and a promoter. These elements are here ordered into three layers. Cross-talk evaluation can be done by comparing all combinations of those three elements. After collecting the [https://2014.igem.org/Team:ETH_Zurich/expresults experimental data] of all possible pathways, we modeled their influence.]]
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From the [https://2014.igem.org/Team:ETH_Zurich/expresults exhaustive experimental data], the central role of regulatory proteins was identified, allowing the characterization of two-levels of cross-talk. The following parts in the Registry are presenting our results:
From the [https://2014.igem.org/Team:ETH_Zurich/expresults exhaustive experimental data], the central role of regulatory proteins was identified, allowing the characterization of two-levels of cross-talk. The following parts in the Registry are presenting our results:
*[http://parts.igem.org/Part:BBa_R0062:Experience BBa_R0062]
*[http://parts.igem.org/Part:BBa_R0062:Experience BBa_R0062]
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*[http://parts.igem.org/Part:BBa_C0171:Experience BBa_C0171]
*[http://parts.igem.org/Part:BBa_C0171:Experience BBa_C0171]
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Each experimental data set was fitted to an Hill function using the Least Absolute Residual method.  
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Each experimental data set was fitted to an Hill function using the [https://2014.igem.org/Team:ETH_Zurich/modeling/parameters Least Absolute Residual method].  
$$rFluo = a + b \frac{[AHL]^n}{K_m^n + [AHL]^n}$$
$$rFluo = a + b \frac{[AHL]^n}{K_m^n + [AHL]^n}$$
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$$\text{b the maximum fold expression rate,}$$
$$\text{b the maximum fold expression rate,}$$
$$\text{n the Hill coefficient,}$$
$$\text{n the Hill coefficient,}$$
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$$\text{K_m the activation concentration of AHL.}$$
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$$K_m\text{ the activation concentration of AHL.}$$
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We took cross-talk into account in our [https://2014.igem.org/Team:ETH_Zurich/modeling/whole whole cell model].
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=== Simulations ===
=== Simulations ===
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We implemented this solution in our [https://2014.igem.org/Team:ETH_Zurich/modeling#Alternate_Design whole-cell model]. As no parameter is known, we assumed their values to be in the range of standard rates. It gave a possible valid result that could work in our system.
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We implemented this solution in our [[Team:ETH_Zurich/modeling/whole#Alternate_Design|whole-cell model]]. As no parameters were known, we assumed their values to be in the range of standard rates. The results indicate that the system could work, the next step would be to test this prediction experimentally.
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Latest revision as of 11:26, 20 July 2015

iGEM ETH Zurich 2014