# Team:Imperial College London/Drylab/Enzyme

Kinetics of drug protein of interest

Both our proteins of interest, PAH and cellulase, are enzymes to be released in the small intestines, after degradation of the capsule. As part of the study for our system, we would like to calculate the amount of enzyme a capsule must contain so that a PAH-replacement therapy or a grass-based diet becomes a feasible prospect.

A necessary step for this calculation is the estimation of the enzymatic activity of our enzymes of interest.

The standard model for enzymatic action will be used to analyse the raw data (either the substrate concentration or the product concentration over time) gathered in the wetlab.

## Contents

### Our Goals

• Overview of system
• Characterise the general dynamics of the system, including its two main modus operandi.
• Assess how its various parameters can affect its output.
• Investigate the validity of the common Michaelis-Menten assumption of enzyme kinetics.

• Data analysis
• Show how the relation between the enzymatic activity of our protein of interest and the rate of breakdown of substrate, d[P]/dt can be exploited.
• Investigate ways to estimate the concentrations of enzyme or substrate if either is unknown as is the case in our experiments.

about the model assumptions and predictions!

### The System

The behaviour of the system (the single-substrate mechanism) can be described with four ordinary differential equations (ODEs). Each component is described by a simple rate term for each of the four species involved in the mechanism.

about the equations and what they mean!

### Summary of simulation results

• For lower values of [S0], the rate of formation of the product is directly proportional to the amount of [S0]. However, for higher values of [S0], rate of formation of product saturates at a maximum rate.
• Michaelis-Menten approximation only holds for very small values of [E0].
• Increasing K3 values will increase rate of formation of product.

### Conclusions

• Michaelis-Menten assumption can be applied to our system because for us, KM >> [E0]

### References

[1]Alon, U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits - Chapman & Hall/Crc Mathematical and Computational Biology
[2]Physica A: Statistical and Theoretical Physics, Vol. 188, No. 1-3. (1 September 1992), pp. 404-425. A rigorous derivation of the chemical master Equation