Increased concentration of metabolic enzymes

Proteins can be targeted into microcompartments via an 18-amino acid leader sequence that forms a well-defined helical structure (Lawrence AD, 2014). We added this leader sequence to dcmA in both E. coli and P. putida. The resulting accumulation of dcmA in the microcompartments leads to an increased local concentration of the metabolic enzyme. This allows more rapid degradation of DCM, which can diffuse freely through the plasma membrane and into microcompartments.



Oxford iGEM 2014

Stochastic Reaction-Diffusion models

Because of the relatively small number of molecules we are expecting to have in our cells (≈10^5 enzymes per cell and 10^3 enzymes per microcompartment), we developed stochastic reaction-diffusion models to predict the distribution of formaldehyde within the system. These stochastic models build in an element of randomness that reflects the nature of diffusion for systems with few elements in a way that deterministic relationships such as Fick’s law do not.

We approached this problem in a number of different ways. Initially, we built a system in which molecules would move a scaled random distance selected from a normal distribution at every time interval dt. This was adapted from the Smoluchowski equations which state:

X(t+ ∆t)=X(t)+ √2D∆t ε
Y(t+ ∆t)=Y(t)+ √2D∆t ε
Z(t+ ∆t)=Z(t)+ √2D∆t ε

X(t),Y(t),Z(t) = particle co-ordinates at time t

D = diffusion constant

ε = normally distributed random variable

∆t = small time interval

Plotted above are the trajectories of three molecules in 3-D diffusion according to the Smoluchowski equations.

Modelling the effect of introducing a microcompartment on reaction rate

Our main approach to reducing the accumulation of toxic intermediates in the DCM degradation pathway is the expression of Pdu microcompartments in our bacteria that will contain high concentrations of both the DcmA enzyme and FdhA enzyme. In doing so, we increase the likelihood of a formaldehyde molecule produced by the action of DcmA encountering an FdhA enzyme before it leaves the microcompartment thus reducing the accumulation of formaldehyde.

To model the increased likelihood of reaction, we started with the Smoluchowski diffusion model above but discretized the system such that molecules could only occupy a fixed set of co-ordinates. This was done in order to define a reaction as occurring whenever two molecules occupied the same co-ordinate at the same time. While this does not necessarily ensure a reaction in the real system, we are assuming that collision rate is proportional to reaction rate and can therefore be used as an analogy.

Plotted here are two systems- one with complete freedom of molecular movement and one in which spatial constraints have been placed such that molecules which encounter the defined boundaries are reflected back into the system to represent the presence of the microcompartment:

In the models above, collisions are indicated through red marks. As suspected, the likelihood of a collision in a spatially constrained environment are far higher than in one where the molecules have complete freedom of movement. This is particularly true not only because of the region of movement allowed by the microcompartment, but also the initial distance between the enzyme and substrate at the point of substrate formation. Note also that the rate of diffusion of the enzyme, in green, has been made substantially lower than that of the formaldehyde- the far lighter and therefore more diffusive compound.

Formaldehyde is genotoxic because it forms protein-DNA and DNA-DNA cross-links. This interferes with DNA replication, repair, and transcription, as well as other processes. It has previously been reported that expression of dcmA in E. coli in the presence of DCM leads to cell death. We hypothesise to be caused by the formaldehyde that is released in the dcmA reaction. The localisation of dcmA into microcompartments means that the formaldehyde is also only locally produced within the microcompartment, thus preventing it from causing damage to DNA.



Oxford iGEM 2014

Predicted effect of microcompartments on formaldehyde concentration

Having deduced that microcompartments will increase the rate at which intermediate compounds are degraded, the next step was to create a simulation that would predict how microcompartments would therefore affect the concentration of formaldehyde molecules in the system. To do so, we created a 1-D simulation in which we started with a fixed number of molecules while constraining degradation and production of a species to within pre-defined spatial limits- representing the fact that both these phenomena can only occur in the microcompartment in our actual system.

In our system, the relative likelihood of degradation is far greater than that of production- this is done in order to ensure that accumulation of toxic compounds does not occur. The increased rate of degradation is the result of several factors:

1. Greater relative expression of FdhA than of DcmA- their expression ratios have been defined as approximately 2.5:1

2. Kcat in FdhA is substantially higher than in DcmA

3. The effect of the microcompartment will increase the relative likelihood of degradation of formaldehyde while leaving the rate of DCM degradation unchanged.

What our models suggest is that the microcompartments will not constrain the concentration of intermediates to be high only within the system. This is because the rate of diffusion of formaldehyde through the microcompartment barrier is unaffected, since its molecular size is much smaller than the pore size of the microcompartment. The significance of introducing the microcompartment is in fact to further increase the relative probability of degradation. This results in, as we expected, a net decrease in the total number of formaldehyde molecules, even when a high initial concentration is introduced, coupled with a decrease in concentration gradient throughout the system.

Displayed below is one realization of a stochastic simulation (grey) alongside the deterministic response (red) of intermediate concentration at two points in time- one at 30 a.u. and the other at 200 a.u..

Oxford iGEM 2014