Speaker
Description
Regulatory networks in cell biology specify monotonicity structure of interactions between genes and proteins, but do not specify the interactions between multiple inputs.
We describe several classes of models compatible with a given regulatory network:
$\mathbf{(A)}$ a collection of all monotone Boolean networks (MBF) whose influence graph matches the network;
$\mathbf{(B)}$ a collection of MBFs where influence graph is a subgraph of the network;
$\mathbf{(C)}$ a collection of all ODE models with monotone steep nonlinearities.
We show that these collection of models are strict subsets of each other [\mathbf{(A) \subsetneq (B) \subsetneq (C)}] and describe precise embedding of each smaller class into the larger class.
While the dynamics of protein and mRNA abundance is stochastic, it is usually well approximated by dynamics that is continuous in time and space generated i.e. by models in class $\mathbf{(C)}$.
We illustrate on the set of examples which dynamics is reliably captured by the smaller class(es)of models, and where the set of dynamics of the larger class(es) is significantly richer than that of a smaller class(es).
Our results begin to illuminate the gap between dynamics observed by monotone Boolean models in class $\mathbf{(A)}$ and continuous dynamics of ODE models in class $\mathbf{(C)}$.
