Due to increased concentration of metabolic enzymes

Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information

Prevents interference with other cell metabolic activity

Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information

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 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.

Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information

What we suspect is harmful to cell in degradation pathway ie. Formaldehyde and why it is bad

Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information

Colocosation of FdhA --> faster reaction rate

Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information

Driving the equilibrium forward by removing product

Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information Information

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 phenomenon 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. K_catin 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 because 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