Abstract
The in silico study and reverse engineering of regulatory networks has gained in recognition as an insightful tool for the qualitative study of biological mechanisms that underlie a broad range of complex illness. In the creation of reliable network models, the integration of prior mechanistic knowledge with experimentally observed behavior is hampered by the disparate nature and widespread sparsity of such measurements. The former challenges conventional regression-based parameter fitting while the latter leads to large sets of highly variable network models that are equally compliant with the data. In this paper, we propose a bounded Constraint Satisfaction (CS) based model checking framework for parameter set identification that readily accommodates partial records and the exponential complexity of this problem. We introduce specific criteria to describe the biological plausibility of competing multi-valued regulatory networks that satisfy all the constraints and formulate model identification as a multi-objective optimization problem. Optimization is directed at maximizing structural parsimony of the regulatory network by mitigating excessive control action selectivity while also favoring increased state transition efficiency and robustness of the network's dynamic response. The framework's scalability, computational time and validity is demonstrated on several well-established and well-studied biological networks.
Highlights
With the rapid advances in broad-spectrum biological assays and corresponding algorithmic developments in the computational sciences, the in silico analysis of regulatory networks has become an increasingly valuable tool in creating new insight into the underpinnings of complex biological phenomena
While the significant inroads have been made in the study of biological networks with platforms like CellNOptR (Terfve et al, 2012) and Optimusqual (Dorier et al, 2016) these pioneering tools apply global goal-seeking approaches like genetic algorithms to reconcile experimental data with prior knowledge network dynamics based on Boolean logic and extensions such as constrained fuzzy logic and logic-based ODEs
We have proposed an extended framework based on multi-level logic where we apply bounded model checking using Constraint Satisfaction Problem (CSP) in order to provide an exhaustive search of the parameter space while addressing the super-exponential nature of this problem in a multi-objective setting, both of which are novel
Summary
With the rapid advances in broad-spectrum biological assays and corresponding algorithmic developments in the computational sciences, the in silico analysis of regulatory networks has become an increasingly valuable tool in creating new insight into the underpinnings of complex biological phenomena. Klarner et al (2012a) proposed a model identification method for multi-valued regulatory graphs based on a colored model-checking (Barnat et al, 2012) of general Linear Temporal Logic (LTL) to handle the combinatorial complexity of the parameter space Their approach consists of first identifying those parameter sets that satisfy a set of observed experimental data and second ranking them based on Length Cost and Robustness. The framework formulates the parameter identification problem as a bounded constraint satisfaction problem, enabling one to parametrize larger models by reducing the corresponding bound, something which remains daunting (NP-hard) in a conventional OBDD-based framework (Bollig and Wegener, 1996) It ranks models satisfying these constraints based on their goodness-of-fit and complexity which in this discrete logic framework are denoted as path-length, robustness, number of interactions, and their threshold of action. The whole framework is implemented in a unified standard constraint programming syntax which enables it to benefit from the latest state-of-the-art solvers which are wellsupported and frequently updated
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