General

The USNA iGEM project was separated into two main objectives. The first was to create mathematical models that can address the challenges of creating an efficient conotoxin counter measure in the respiratory microbiome, for example the rate of passage of conotoxins through the respiratory mucosa, toxicity, binding affinities of sensors, and respond modules. The mathematical model created over the summer represented a much simpler model of the rate of Potassium and Sodium ion movement through the E. Coli cellular membrane . This model will continue to be adjusted to meet the desired results that are needed to test.

The second objective was to insert a two-part Arc system into a chloramphenicol vector, which is a classic sense and respond mechanism, in a manner that would allow for quick detection of presence of conotoxin.

Lab Work

Mathematical Model

The mathematical model made by the team began with the Hodgkin-Huxley model. This model uses ordinary differential equations to find the membrane potential of a neuron undergoing action potential as a function of time. Some of the parameters for the model are membrane capacitance, ionic current through membrane, and external current, but the most important feature of the model is that it is a function of time.

The Nernst equation gives the membrane potential as a function of the concentrations of ions on both sides of the membrane. One of our major assumptions for this model was that the concentration of ions outside of the cell was essentially fixed. This allowed us to isolate the term for intracellular concentration of ions. Based on literature available, the primary ions we determined of interest were sodium and potassium, both with a charge of +1.

We based the model of an E. coli cell with three transporters. The first two were sodium import and potassium export channels, and then in order to reverse the polarity we included a sodium-potassium pump which moved sodium and potassium out of and into the cell respectively. All transporters were assumed to be voltage gated. These major assumptions are based on the fact that the sodium and potassium are the two major ions present in E. coli which means they likely contribute to the membrane potential.

Based on the process of action potential, we modeled that when the cation concentration was increasing slowly, it was due to sodium-potassium pumps, but if it was increasing quickly, then it was due to an open sodium channel. When the cation concentration was decreasing, it was due to an open potassium channel

The modeled system was heuristically found to become stable for an arbitrarily long time when the voltage threshold for the switch from pump to sodium channel was at -38.0389 mV. Thus, we conjecture that a voltage gated sodium channels in E. coli would open when the membrane potential is greater than -38.0489 mV.