A Semiquantitative Framework for Gene Regulatory Networks: Increasing the Time and Quantitative Resolution of Boolean Networks

RESEARCH ARTICLE A Semiquantitative Framework for Gene Regulatory Networks: Increasing the Time and Quantitative Resolution of Boolean Networks Johan Kerkhofs1,2,3, Liesbet Geris1,2,3* 1 Biomechanics Research Unit, University of Liège, Liège, Belgium, 2 Biomechanics section, KU Leuven, Leuven, Belgium, 3 Prometheus, the Leuven R&D division of skeletal tissue engineering, KU Leuven, Leuven, Belgium * Abstract OPEN ACCESS Citation: Kerkhofs J, Geris L (2015) A Semiquantitative Framework for Gene Regulatory Networks: Increasing the Time and Quantitative Resolution of Boolean Networks. PLoS ONE 10(6): e0130033. doi:10.1371/journal.pone.0130033 Academic Editor: Manuela Helmer-Citterich, University of Rome Tor Vergata, ITALY Received: January 12, 2015 Accepted: May 15, 2015 Published: June 11, 2015 Copyright: © 2015 Kerkhofs, Geris. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: Johan Kerkhofs is a PhD fellow of the research Foundation Flanders (FWO-Vlaanderen). This work is part of Prometheus, the KU Leuven R&D division for skeletal tissue engineering (http://www. kuleuven.be/prometheus). The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 279100. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Boolean models have been instrumental in predicting general features of gene networks and more recently also as explorative tools in specific biological applications. In this study we introduce a basic quantitative and a limited time resolution to a discrete (Boolean) framework. Quantitative resolution is improved through the employ of normalized variables in unison with an additive approach. Increased time resolution stems from the introduction of two distinct priority classes. Through the implementation of a previously published chondrocyte network and T helper cell network, we show that this addition of quantitative and time resolution broadens the scope of biological behaviour that can be captured by the models. Specifically, the quantitative resolution readily allows models to discern qualitative differences in dosage response to growth factors. The limited time resolution, in turn, can influence the reachability of attractors, delineating the likely long term system behaviour. Importantly, the information required for implementation of these features, such as the nature of an interaction, is typically obtainable from the literature. Nonetheless, a trade-off is always present between additional computational cost of this approach and the likelihood of extending the model’s scope. Indeed, in some cases the inclusion of these features does not yield additional insight. This framework, incorporating increased and readily available time and semiquantitative resolution, can help in substantiating the litmus test of dynamics for gene networks, firstly by excluding unlikely dynamics and secondly by refining falsifiable predictions on qualitative behaviour. Introduction As molecular biology gradually shifted away from its reductionist framework towards integrative thinking and helped spawn the field of systems biology, network modelling gained more and more thrust as a pivot to formally tackle the complexity of biological systems [1]. Since the PLOS ONE | DOI:10.1371/journal.pone.0130033 June 11, 2015 1 / 23 A Semiquantitative Framework for Gene Regulatory Networks Competing Interests: The authors have declared that no competing interests exist. dynamical analysis of elaborate and intricate biological networks is impeded by a scarcity in kinetic information on the biochemical reactions that form them, a focus in systems biology, pioneered by the work of Kauffman [2] and Thomas [3], lies on the development of discrete and logic-based dynamical models that are better equipped to deal with the qualitative information that is typically at the modeller’s disposal. The model representations of the biochemical species and their interactions that direct biological function at the cellular scale are dubbed gene regulatory networks (GRNs), henceforth called gene networks for brevity, or protein-protein interaction (PPIs) networks. In spite of their names, both types of network often combine interactions on the gene and protein level. These qualitative models are suitable for exploratory modelling, since they do not require kinetic information or detailed mechanisms. This lack of detail also simplifies the addition of additional pathways to an existing model, potentially leading to a more global understanding of the process under investigation [4,5]. However, the relative simplicity in dynamics in the discrete models may cause them to miss behaviours that more advanced models do pick up (an example would be substrate competition), hence amounting to a clear quid pro quo. Indeed, as the maxim goes in genetics, ‘no genotype is superior in all environments’ [6], neither is any model type optimal for each and every type of problem or aspect of it. The best choice of model is determined by multiple factors, including the specific research question, the type of data and available computational power. In this paper we focus on gene networks involved in cellular fate decisions, particularly in the case where no detailed quantitative information, such as time series data, is available. The model input is thus limited to topological information on the network itself and some basic information on the nature of the reactions that it represents. The type of data then lends itself to a qualitative modelling approach. The quintessential qualitative model in this context is the Boolean network model, requiring the network dynamics to be cast in ON/OFF terms. Briefly, each gene is represented by a node, that has a 0 (OFF) or 1 (ON) value for every gene. The dynamics are simulated in discrete steps using Boolean functions that describe a set of logical rules for each node [7–9]. The updating scheme determines the order in which the nodes are updated. One possible scheme is the synchronous scheme, where all nodes are updated at the same time [10]. While Boolean functions present an intuitive approach to capture interactions, they become increasingly harder to specify as the number of interaction partners of a particular gene increases, starting with the choice between AND/OR gates at 2 inputs [11]. At the same time, with the exponentially increasing number of input combinations it becomes progressively limiting to mould all output into all or nothing responses. Another issue arising in Boolean m (...truncated)