Modeling

Overview

The purpose of our modeled system is to tune this system as a specific pH-sensing lysis device for releasing our phytase into the stomach. We aim to characterize the interaction between the H+/Cl- antiporter and the chloride-induced lysis cassette in our E. coli chassis. This model examines the effects of varied promoter strengths for the ClC-ec1 antiporter, as well as the plausibility of utilizing the system for nutritional purposes.

We start with a model cell that has entered the stomach. In this high pH environment, protons begin to leak into the cell. For our purposes, this flux of H+ ions into the cell is modeled by simple diffusion.

The leakage of protons due to the acidic environment begins to disrupt pH homeostasis. However, E. coli has acid resistance mechanisms in order to grow in low pH. One of these mechanisms is the ClC-ec1 antiporter protein, which pumps H+ out of the cell (against its gradient) by utilizing the chloride gradient. The flux of extracellular protons (He) into the cell as well as the production of the antiporter protein are illustrated below:

Each antiporter turnover moves one H+ out while importing two Cl-. We now begin by modeling with first order ordinary differential equations.

The equations that model these species in our system are as follows:

The extracellular proton and chloride rates of change are set to zero since the extracellular volume (the human stomach) is as much as 15 orders of magnitude larger than the individual cell volume. Thus molecular fluxes will have negligible effects on the ionic concentrations.

Our Phytastic E. coli use a chloride-inducible promoter, Pgad, to sense the change in chloride concentration as a way to detect the change in pH. The Pgad operon part, which we obtained from the Chinese University of Hong Kong iGem team, includes a constitutive promoter for a positive regulator gene, gadR. gadR binds upstream of the Pgad promoter, where it can be allosterically activated by chloride ions, which significantly increases transcription. Our Phytastic E. coli have a coding region for lysozymes downstream of the Pgad part so that they can selectively lyse at low pH. The model, however, replaces the lysis cassette with GFP for the purpose of comparing the model to results. The Pgad/GFP system is illustrated below:

The equations were solved with MATLAB’s ode15s, an ODE solver for ‘stiff’ functions. A full system plot can be seen below:

In the figure above, we can see GFP levels (marked green) rising once Pgad becomes activated. This also coincides with rising chloride levels, which continue to increase over time. In order for the Pgad/Lysis/Antiporter system to be plausible for our use, lysis enzyme concentration must reach appropriate levels before chelated iron in the stomach empties into the primary iron-absorbing area of the digestive system - the duodenum. The model predicts this target concentration (1uM) to be reached within 2.5 hours. Since the stomach typically takes 4 or more hours to fully empty, the model suggests plausible use of the pH-sensitive lysis construct for our nutritional purposes.

The pH of the cell quickly drops upon the modeled ‘entrance’ into the stomach. Interestingly, the pH of the cell quickly stabilizes to approximately its initial value (y0=7.5). This pattern is significant to the validity of the model, as pH in the modeled system nearly matches biological patterns of pH stability.