Abstract
Once biological systems are modeled by regulatory networks, the next step is to include external stimuli, which model the experimental possibilities to affect the activity level of certain network’s nodes, in a mathematical framework. Then, this framework can be interpreted as a mathematical optimal control framework such that optimization algorithms can be used to determine external stimuli which cause a desired switch from an initial state of the network to another final state. These external stimuli are the intervention points for the corresponding biological experiment to obtain the desired outcome of the considered experiment. In this work, the model of regulatory networks is extended to controlled regulatory networks. For this purpose, external stimuli are considered which can affect the activity of the network’s nodes by activation or inhibition. A method is presented how to calculate a selection of external stimuli which causes a switch between two different steady states of a regulatory network. A software solution based on Jimena and Mathworks Matlab is provided. Furthermore, numerical examples are presented to demonstrate application and scope of the software on networks of 4 nodes, 11 nodes and 36 nodes. Moreover, we analyze the aggregation of platelets and the behavior of a basic T-helper cell protein-protein interaction network and its maturation towards Th0, Th1, Th2, Th17 and Treg cells in accordance with experimental data.
Highlights
Biological networks are often formed by interacting proteins and molecules
To illustrate the broadness of our approach we examine two different areas of pharmacological interventions in detail: The results first focus on platelets: Here the fragile balance between platelet activation and blood clotting and platelet inhibition with resulting normal blood flow is critical for health and an imbalance in platelet regulation is central to pathological conditions such as stroke and heart failure, still the major causes of death
The considerations presented in the presented work hold for any model consisting of wellposed ordinary differential equations, like chemical reaction networks [13,14,15]
Summary
Biological networks are often formed by interacting proteins and molecules. Their change in time is often biologically regulated to adapt to different conditions. We analyze here in particular the question, how we can calculate the result of a pharmacological intervention and identify the best target points (receptors or downstream in the cascade or any other point in the network) to shift the network state into a new activity pattern as desired (either for medical or for research purpose). Our approach allows the user to define the intervention points of choice and we systematically calculate the optimal steering options the user has available to drive the network into the desired state. We include the information how well the objective can be met with this choice
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