Category Archives: Modeling

Smallest Chemical Reactions Systems that is Bistable

A while back Thomas Wilhelm, published a paper that described the smallest chemical network that could display bistability. The paper that describes this result is: Wilhelm, T. (2009). The smallest chemical reaction system with bistability. BMC systems biology, 3(1), 90. … Continue reading

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Smallest Chemical Reaction System with Hopf Bifurcation

A while back Wilhelm, and Heinrich published a paper that described the smallest chemical network that could display a Hopf bifurcation. That is, the chemical species oscillated. The paper that describes this result is: Wilhelm, Thomas, and Reinhart Heinrich. “Smallest … Continue reading

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C Based Reduce Row Echelon Code

I recently needed some code to compute the reduced row echelon of a matrix. Applications such as Matlab, Mathematics, sympy and R support this functionality out of the box. Libraries such as LAPACK do not, including the linear algebra package … Continue reading

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Plotting Bar graph of Species Concentations in Tellurium

I had a model with 27 flaoting species and I wanted to plot the steady state concentrations on a histogram where the labels were the names of the different species. Here is a general purpose script that will do that: … Continue reading

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Drawing a Pathway Fragment with Inhibition using Tikz

Here is another quick pathway fragment I needed today. This won’t scale well because I’ve used some fixed dimensions eg the width of the lines and the size of the text. But these are easily adjusted if you want to … Continue reading

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Plotting 3D graphs using Python and Tellurium

As an example I wanted to show how one could plot a 3D phase plot. A great example to use for this is the Lorenz Attractor. This system is interesting because it displays chaotic behavior. The differential equations for the … Continue reading

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How do I change the simulation tolerances in Tellurium?

For very complicated and large models it may be necessary to adjust the simulator tolerances in order to get the correct simulation results. Sometimes the simulator will terminate a simulation because it was unable to proceed due to numerical errors. … Continue reading

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How do I plot phase plots using Tellurium?

Phase plots are a common way to visualize the dynamics of models where time courses are generated and one variable is plotted against the other. For example consider the following model that can show oscillations:

In this model S2 … Continue reading

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How to get the Stoichiometry Matrix using Tellurium

Here is a simple need, given a reaction model how do we get hold of the stoichiometry matrix? Consider the following simple model:

Running this script by clicking on the green arrow in the tool bar will yield:

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How to do a simple simulation using Tellurium

The most common requirement is the ability to carry out a simple time course simulation of a model. Consider the model:     Two reactions and three metabolites, S1, S2 and S3. We can describe this system using an Antimony … Continue reading

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