Glucose-Potential Simulation for Hardware

To verify the feasibility of the Protato kit design proposed by the hardware team, we investigated the theoretical basis of enzymatic and electrode reactions, constructed a three-electrode system in COMSOL software for simulation, and obtained the relationship between glucose concentration and potential, thus completing the verification process.

The Biological Basis of Sensors

Our amperometric sensor-based quantitative detection tool, typically immobilized with glucose oxidase on the electrode surface or in its vicinity, employs this highly specific catalyst to selectively oxidize glucose into gluconolactone, while the enzyme's own cofactor flavin adenine dinucleotide ($FAD$) is reduced to $FADH_2$. ¹

For electron acceptors, we use an artificial electron mediator, namely potassium ferricyanide/potassium ferrocyanide ($[Fe(CN)6]^{3−}/[Fe(CN)6]^{4−}$) redox mediator. The ferricyanide ion $[Fe(CN)6]^{3−}$ can rapidly receive electrons from the reduced enzyme $GOx(FADH₂)$, being reduced itself to ferrocyanide ion $[Fe(CN)6]^{4−}$, while regenerating the enzyme to its oxidized state ($GOx(FAD$)) and preparing it for the next catalytic cycle.

The entire biochemical reaction chain can be summarized in the following two steps:

a.Enzymatic Oxidation Reaction

b. Mediator Regeneration Reaction

The enzymatic reaction produces ferrocyanide ions that diffuse to the working electrode surface under a specific applied potential. At this potential, the ferrocyanide ions are electrochemically oxidized back to ferricyanide ions, releasing electrons and generating a measurable Faradaic current at the electrode. Meanwhile, to maintain charge balance in the system, an equivalent reduction reaction occurs at the counter electrode, completing the electrochemical circuit.

We assume that the entire process follows: a. The Hill reaction occurs continuously, and b. Enzymatic reactions only take place near the electrode without any concentration gradient relationship. The measured steady-state current is proportional to the generation rate of ferrocyanide ions, which in turn shows a linear relationship with the glucose concentration in the bulk solution. ²

Mathematical and Physical Basis of Sensors

Due to the complex supporting electrolyte system formed by various ions released after leaf cell disruption. When the concentration of supporting electrolyte is much higher than that of the analyte and mediator, the resistance of electrolyte solution becomes very small, and the electric field gradient can be ignored, assuming the electrolyte potential is constant.

First, we present the fundamental equation for mass transfer near electrodes------the Nernst-Planck equation:

Based on the above assumptions, we optimize it as Fick's Second Law:

Among them, $c_i$ is the concentration of substance i, $D_i$ is its diffusion coefficient in the solution, $∇⋅$ is the divergence operator, and $R_i$ is the net production/consumption rate of this substance caused by chemical reactions). For the steady-state response analysis of amperometric sensors, we solve for the state that does not change with time, at which point:

The consumption of glucose and ferricyanide, as well as the formation of ferrocyanide, occur in the bulk electrolyte region as homogeneous reactions. The reaction rate ($R_i$) is determined by the catalytic properties of the enzyme. Enzyme-catalyzed reactions generally follow the Michaelis-Menten equation. And we assume that the reaction rate of ferricyanide and ferrocyanide can be correlated with the consumption rate of glucose, which is in a 2:1 ratio.

Near the electrode, a concentration gradient will form due to enzyme reaction consumption. When the rate of glucose diffusion from the solution to the electrode area is slower than the rate of enzyme consumption, assuming sufficient enzyme content, the overall sensor response will be controlled by the diffusion process. This is the ideal situation for achieving a wide linear detection range. $R_i$ can basically simulate the reaction rate.

The classic equation describing the relationship between electrode reaction rate, electrode potential, and reactant concentration is the Butler-Volmer equation.

Simulations in COMSOL

We assume that the substrate and enzyme only react near the electrode, and apply the Michaelis-Menten equation to this process, conducting simulations in COMSOL. the simulated function indeed appears as a straight line:

The previous simulation has validated our conclusion that the reaction potential indeed shows an increasing relationship with glucose concentration. This also provides basic proof for the practical theory of the hardware team. To more realistically simulate the conditions in the Kit, we divided the solution into two parts and introduced a concentration gradient for simulation.

So we conducted the second simulation, remove the assumption that the reaction can only occur near the electrode. The process of glucose diffusing from leaf blades into the electrode area was simulated, which better reflects the actual situation. Moreover, this simulates the diffusion process of glucose from leaf cells into the electrode area, better reflecting the actual situation.

Optimized enzymatic reaction equation:

b. Enzyme-Mediator Reaction

c. Electrochemical reaction

Table1. Relevant parameters (Ref ³,Ref ⁴)

The final result was a curve showing a gradual increase in potential with rising glucose concentration. Although not a linear function, it confirmed the rationality of the detection device.

Compared to the glucose added in our reaction system, the glucose concentration in leaves can be virtually ignored. The final result shows that under this reaction system, a current density of approximately $2✖10^{-4}$ $A/m^2$ will be generated and decay within a short period of time. Therefore, we Speculate that detecting this potential can determine whether a plant is infected or not. This provides a theoretical basis for the feasibility of simulation performed by the hardware team.

In summary, we have successfully simulated the actual reaction conditions in the Kit, laying a theoretical foundation for their practical testing work.

However, this system has relatively low sensitivity in measuring glucose concentration and a short response time, allowing it only to assist hardware in making qualitative judgments.

View our COMSOL files in igem gitlab.

References