The hypothesis for this project is that the voltage sensor can help increase the rate of reaction.
The aim of this simulation is to check the effect of change in structure of the voltage switch on the overall reaction rate. The commercial software COMSOL, which was made for finite element analysis, is used. The overall model is separated into three models. Model 1 is a simulation of the bending of the voltage switch by a piezoelectric model. Model 2 is a simulation of the reaction in a 0D environment. Model 3 is a simulation of the flow and diffusion of the fluid and reactants around the enzymes. Several areas of physics are touched upon, including piezoelectric devices, reaction engineering, laminar flow and transport of diluted species.

The physics module used here is Piezoelectric Devices. In this module, two equations used here are as following:


Where D is electric charge density displacement,  is stress,  is total electric charge density,  is deformation gradient.
The geometry of the model is two identical rectangular plates representing the voltage-sensing S4 protein (VS), each with a box at the bottom to represent the enzymes, laccase and dioxygenase. The bending of the voltage switch is simulated by the bending of piezoelectric material when there is a voltage applied across two surfaces. The angle of bending is set to be about 4 degree, as shown in literature[1]. As the two VS proteins are linked by PDZ domain and PDZ ligand, the top boundary of the proteins are set to be static. The “Form Union” function is used to link the VS-representing part and the enzyme-representing part together. Configuration 1, with the two plates bent, represents the structure of the protein when it is the natural position. Configuration 2, with the two plates straight, represents the structure of the protein when there is a change in membrane potential.
The material used to simulate the voltage switch is Lead Zirconate Titanate (PZT-5H). Voltage is applied across the x-y planes of the plates, with higher voltage applied on the inner side. We solved for a stationary solution.

The physics module used here is Reaction Engineering. Since the actual chemical equations for degradation of benzo(α)-pyrene (BaP) are not known, the overall reaction is represented by the following two step reaction.
BaP => I + S,
I => P,
where I represents intermediate, S represents the second product and P represents the final harmless product.
This is set to be an irreversible reaction with forward rate constant of 1. The temperature and pressure in which the reaction is carried out is 298K and 1atm respectively. It is a surface reaction with a constant volume of liquid mixture. We solved for a time-dependent solution.

The physics module used here is Transport of Diluted Species and Laminar Flow.
As membrane proteins “floats” tangentially to cell membrane, there is relative motion of the intracellular fluid to the proteins. Laminar Flow is chosen to include this phenomenon in the model. Transport of Diluted Species is used to include convection and diffusion of the molecules.
The geometry of this model is similar to that in Model 1, except that a rectangular box is added to represent the domain for diffusion and fluid flow. The two x-y plane of the model is set to be inlet and outlet. The surfaces of the enzyme-representing boxes are set to be the catalytic surfaces, with each box responsible for one reaction.

By integrating the three models, we can simulate the correlation of voltage switch and reaction rate. The concentration of the product can be checked at the output of the fluid flow domain while switching between the two configurations of the voltage-sensing proteins. A significant change in concentration of product when the voltage-sensing proteins are closer to each other validates the hypothesis.

[1] ANDERSSON Magnus, FREITES J. Alfredo, TOBIAS J. Douglas, WHITE H. Stephen. “Structural Dynamics of the S4 Voltage-Sensor Helix in Lipid Bilayers Lacking Phosphate Groups.” The Journal of Physical Chemistry B (2011) No. 115, pp. 8732-8738.