I'm trying to simulate time-series data for protein expression. I have a PPI network for which I want to simulate the data. Beside proteins, there are other proteins which we know as stimuli nodes. These nodes are connected to one or several proteins (like a drug molecule which is affecting a protein in our network).
I use formula 1 from this paper for simulating the relation between concentration of proteins.
I need this data to test my network inference algorithm.
Now my question is:
How can I simulate data in first time-step? For example can I just create random values and then apply the formula to get the data for the next time steps (of course I should ignore the random row)?
For example if I have an activator for EGFR, then if this activator is on, EGFR should be expressed, otherwise EGFR should be silent (no expression I mean). But if I just fix this, then the data would hardly be changed in next time steps. I mean any way I can't use a fix value for perturbed nodes, since in the formula itself the expression level is not fixed. I don't know how to calculate the concentrations for a node which is connected to an inhibitor or a stimuli node. It is already considered in the formula but using the formula it is possible that an inhibited node, gets a high value during next time steps.
I don't know how to set reasonable alpha and beta in the formula 1 (I solved the formula to get expression level in time t in terms of expression levels in time t-1).
Any help would be appreciated.