Abstract
BackgroundBoolean networks capture switching behavior of many naturally occurring regulatory networks. For semi-quantitative modeling, interpolation between ON and OFF states is necessary. The high degree polynomial interpolation of Boolean genetic regulatory networks (GRNs) in cellular processes such as apoptosis or proliferation allows for the modeling of a wider range of node interactions than continuous activator-inhibitor models, but suffers from scaling problems for networks which contain nodes with more than ~10 inputs. Many GRNs from literature or new gene expression experiments exceed those limitations and a new approach was developed.Results(i) As a part of our new GRN simulation framework Jimena we introduce and setup Boolean-tree-based data structures; (ii) corresponding algorithms greatly expedite the calculation of the polynomial interpolation in almost all cases, thereby expanding the range of networks which can be simulated by this model in reasonable time. (iii) Stable states for discrete models are efficiently counted and identified using binary decision diagrams. As application example, we show how system states can now be sampled efficiently in small up to large scale hormone disease networks (Arabidopsis thaliana development and immunity, pathogen Pseudomonas syringae and modulation by cytokinins and plant hormones).ConclusionsJimena simulates currently available GRNs about 10-100 times faster than the previous implementation of the polynomial interpolation model and even greater gains are achieved for large scale-free networks. This speed-up also facilitates a much more thorough sampling of continuous state spaces which may lead to the identification of new stable states. Mutants of large networks can be constructed and analyzed very quickly enabling new insights into network robustness and behavior.
Highlights
Introduction to random Boolean networksIn Workshop and tutorial proceedings, ninth International conference on the simulation and synthesis of living systems (ALife IX). 2004:160–173. 2
For the simulation of genetic regulatory networks (GRNs) two important paradigms have been used: Discrete models, where each node has a value of either 0 or 1 and Boolean expressions are used to update the values of the nodes in each simulation step using an updating scheme like CRBN or ARBN [1], and continuous models where nodes have values in the interval [0,1] and real-valued ODEs determine the behavior of the network
Two commonly used continuous modeling paradigms for GRNs are activator-inhibitor-models such as the exponential standardized qualitative dynamical systems model [2], which is implemented in the SQUAD [3] simulation package, and real-valued interpolations of Boolean functions which allow for more complex node interactions
Summary
Jimena simulates currently available GRNs about 10-100 times faster than the previous implementation of the polynomial interpolation model and even greater gains are achieved for large scale-free networks. This speed-up facilitates a much more thorough sampling of continuous state spaces which may lead to the identification of new stable states. Mutants of large networks can be constructed and analyzed very quickly enabling new insights into network robustness and behavior
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