Analyzing pharmacological intervention points: A method to calculate external stimuli to switch between steady states in regulatory networks

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.
Author summary Organisms can be seen as molecular networks being able to react on external stimuli. Experiments are performed to understand the underlying regulating mechanisms within the molecular network. A common purpose for these efforts is to reveal mechanisms with which the molecular networks can be affected to achieve a desired behavior. To cover the complexity of life these models of molecular networks often need to be quite huge and need to have many cross connections between the different agents of the network that regulate the behavior of the network. A useful tool to structure this complexity are mathematical methods. Once the model based on experiments is set up the experimental data can be further processed by mathematical methods. As experiments are cumbersome, the present work provides a framework that can be used to systematically figure out intervention points in molecular networks to cause a desired effect. In this way promising intervention strategies can be obtained. For instance the process of obtaining new drugs for pharmacological modulation can be shortened as in the best case the calculated intervention strategy just has to be validated with one experiment and the time consuming procedure of searching an intervention strategy with several experiments can be saved.