Boolean network simulations for life scientists

Abstract

Modern life sciences research increasingly relies on computational solutions, from large scale data analyses to theoretical modeling. Within the theoretical models Boolean networks occupy an increasing role as they are eminently suited at mapping biological observations and hypotheses into a mathematical formalism. The conceptual underpinnings of Boolean modeling are very accessible even without a background in quantitative sciences, yet it allows life scientists to describe and explore a wide range of surprisingly complex phenomena. In this paper we provide a clear overview of the concepts used in Boolean simulations, present a software library that can perform these simulations based on simple text inputs and give three case studies. The large scale simulations in these case studies demonstrate the Boolean paradigms and their applicability as well as the advanced features and complex use cases that our software package allows. Our software is distributed via a liberal Open Source license and is freely accessible from http://booleannet.googlecode.com.

Figure 1

Abscisic Acid signaling simulations: a) Effect of mutations on closure in asynchronous Boolean simulation of ABA induced closure. Blue line indicates the closure response (percentage of simulations with Closure = 1) in wild type (WT). Three other knockout mutants: S1P (green line), PA (red line) and pH_c (light-blue line) were shown experimentally to be less sensitive to ABA in term of ABA-induced stomatal closure. b) Variability of closure in WT, pH_c knockout and PA knockouts in a piece-wise linear simulation. The mean of the continuous variable corresponding to the node Closure in 300 simulations is plotted as a solid line and dashed lines indicate the mean plus or minus standard deviation. In the WT simulation the variation of closure (blue lines) is small during the first 20 time steps, increases from 20 to 50 time steps and gradually decreases to 0 after 50 time steps. In PA (red lines) and pH_c (light blue lines) knockout mutants, although the mean closure responses are similar to that of WT, the variances are not decreasing after 50 time steps.

Figure 2

Representative outputs of simulating the long-term survival of leukemic T-LGL cells. (a). Inhibition of AICD by constitutive overexpression of MCL1 and sFas. Chronic antigen stimulation will induce the depletion of reactive CTL through AICD, as suggested by the asymptotic increase to 1 of apoptosis percentage in the output "Normal-Apop". Constitutive overexpression of MCL1 or sFas alone does not rescue reactive CTL from AICD, as suggested by the output "MCL1-Apop" and "sFas-Apop". However, when simulating the simultaneous overexpression of MCL1 and sFas, resistance to AICD was achieved, see output "LGL-like-Apop", as observed in leukemic T-LGL cells. (b). Additional characterization of the effect of simultaneous overexpression of MCL1 and sFas. In addition to the inhibition of AICD, simulations under conditions mimicking the constitutive overexpression of MCL1 and sFas also reproduced the known deregulated signaling pathway components in leukemic T-LGL cells, such as constitutively overexpressed FasL ("LGL-like-FasL") and constitutively activated Ras ("LGL-like-Ras"), were reproduced compared to simulations mimicking normal CTL activation ("Normal-FasL" and "Normal-Ras").

Figure 3

The time course of (a) innate and (b) adaptive immune response to B. bronchiseptica is shown by plotting the dynamics of the following representative nodes: EC: Epithelial cells, PIC: pro-inflammatory cytokines, C: Complement, IL12: Interleukin-12 (I and II indicate concentrations in different compartments) and PH: phagocytosis. Colors demonstrate the difference in the behavior of the nodes in case of normal (blue: wild type simulation) and perturbed (red: deletion simulation) host immunity. The perturbation is modeled by turning off the node representing B cells. The figure shows that innate immune responses are active for a longer period in the deletion simulation due to the persistence of bacteria. Plot b shows that complement is activated in normal simulations but not in the deletion simulation. The figure also shows the coupled fluctuations of the concentrations of IL12 in the two compartments. We can also see that the rate of phagocytosis is much slower in the deletion simulation.