A method to visualize pseudo-potential landscape of high-dimensional Boolean networks

Boolean networks (BNs) are a successful mathematical framework to represent thedynamical behavior of molecular networks. For the BNs, a pseudo-potential function can be defined toassign a numerical value to each state such that its value is minimum for the stable states or attractorsof the system. Visualization of the pseudo-potential landscape of the BNs helps us gain insight into thestate space of the BNs. However, plotting the pseudo-potential landscape for the BNs in the case ofhaving three or more variables is a challenging task [۱]. Since the state space of the BNs growsexponentially with the number of variables, calculating and storing the pseudo-potential values for allstates is not feasible. Here, we present a method to visualize the pseudo-potential landscape of a possiblyhigh-dimensional BN (having three or more variables) by choosing a representative subset of the statesand placing them over a ۱D or ۲D plane, such that the consecutive states are placed as close together aspossible [۲]. Consequently, the second axis in the case of a ۱D plane (or alternatively, the third axis inthe case of a ۲D plane) shows the pseudo-potential values associated with different states. We presentthe results for some BNs and then discuss the performance of the proposed visualization approach.Keywords: Boolean network; Pseudo-potential landscape; Visualization

کلیدواژه ها:

Boolean network ، Pseudo-potential landscape ، Visualization