| Abstract: |
| We consider general systems of differential equations derived from chemical reaction
networks,
$$\dot x = S\textbf{r}(x).$$
Here, $x$ is interpreted as the vector of the concentrations of chemicals, $S$ is
the stoichiometric matrix and $\textbf{r}(x)$ is the vector of reaction functions,
which we consider as \textbf{positive given parameters}. From an abstract
network point of view: the vector $x$ represents the vertices, the matrix $S$ is the
incidence matrix and the vector $\textbf{r}(x)$ refers to the directed arrows.\\
Sensitivity studies the response of equilibrium solutions to the perturbation of a single
reaction function.\\
In previous work, Fiedler, Matano, the author et al., were able to present
systematic criteria, which distinguish zero response from nonzero response, for any
other reaction function or metabolite concentration. Importantly, these results were only based on the network structure.\
Based on these works, we give here an overview of the results and techniques developed through this structural approach. In particular, we will focus on an extension of these results, which provides for the first time criteria for predicting the sign of any nonzero response, without requiring any additional input information. |
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