Team:IISc-Bangalore/Model Supplementary
Model: Supplementary information
Model for OP Degradation:
Equations and Definitions
The enzymatic hydrolysis of organophosphates is described by Michaelis-Menten kinetics, which states that the rate of loss of the substrate is given by:
\[ k = \frac{d[S]}{dt} = -k_{cat} [E_0] \left(\frac{[S]}{K_M + [S]}\right) \]Here:
- \( [S] \): concentration of substrate
- \( k_{cat} \): catayltic rate constant
- \( [E_0] \): initial concentration of enzyme
- \( K_M \): Michaelis constant; half-saturation constant
The prototypical enzyme-substrate reaction scheme that the model assumes is:
\[ E + S \rightleftharpoons ES \rightarrow E + P \]Where \( E \) is the enzyme, \( S \) is the substrate, \( ES \) is the intermediate enzyme-substrate complex and \( P \) is the product.
Model for OP Degradation: Sample Values
To estimate the profile of the substrate gradient, sample values were plugged into the model.
- Organophosphates such as methyl chlorpyrifos thion, methyl parathion and methyl paraoxon all have \( k_{cat} \) values ranging from \( 1200-2500 \ s^{-1} \). We therefore used \( k_{cat} = 2000 \ s^{-1} \).
- The Michaelis constant ranges from \( 100 - 230 \ \mu M \), and we use a value of \( K_M = 150 \ \mu M \).
- For \( \eta \), an order of magnitude estimate is made. Since the PDMS tube is quite small (\(\sim 10 \ \mu M\)), we estimate \( \eta \approx 0.1 \).
- For the initial concentrations of OP and OPH, we take them to the same order as the value of \( K_M \) to clearly see how the shape of the profile changes when constants are tweaked. \( [S_0] = [E_0] = 100 \ \mu M \).
Please do keep in mind that these values are motivated from literature and on the underlying assumptions of the model and are meant for the purpose of observing how the model changes with change in parameters. The values will be refined in subsequent stages of our project, once a functioning filter is implemented.