Using computers to simulate chemical kinetics

1 Example simulating Michaelis-Menten enzyme kinetics 

As we have pointed out in the introduction, our focus in this chapter is on how to build models of biochemical systems, and not on mathematical analysis of models. As an example, consider the system of Equations (3.27), which represents a model for the reactions of Equation (3.25). It is possible to analyze these equations using a number of mathematical techniques. For example Murray [146] presents an elegant asymptotic analysis of a model of an irreversible (with 2 = 0) Michaelis-Menten enzyme. Such analyses invariably yield mathematical insights into the behavior of 

1 Although the irreversible approximation successfully simulates the enzymatic flux in the range in which the reverse flux is small compared to the forward flux, the impact of approximating nearly irreversible reactions as entirely irreversible in simulations of reaction systems can be significant. It has been shown that feedback of product concentration in nearly irreversible reactions, either through reverse flux or product inhibition, is necessary for models of certain reaction networks to reach realistic steady states [36]. 

For large-scale problems, the most widely useful mathematical tool available is computational/numerical simulation. A great number of computer tools are available for simulation of ordinary differential equation (ODE) based models, such as Equations (3.27). Here we demonstrate how this system may be simulated using the ubiquitous Matlab software package. 

The major requirement to simulate an ODE-based model using Matlab (or most other packages) is to supply a code that computes the time derivatives of the state variables - the right-hand side of Equations (3.27). An example of a function that computes the time derivatives for this model using Matlab syntax is given below.2 

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