Two-Layer Mathematical Modeling of Gene Expression: Incorporating DNA-Level Information and System Dynamics

Abstract

High-throughput genome sequencing and transcriptome analysis have provided researchers with a quantitative basis for detailed modeling of gene expression using a wide variety of mathematical models. Two of the most commonly employed approaches used to model eukaryotic gene regulation are systems of differential equations, which describe time-dependent interactions of gene networks, and thermodynamic equilibrium approaches that can explore DNA-level transcriptional regulation. To combine the strengths of these approaches, we have constructed a new two-layer mathematical model that provides a dynamical description of gene regulatory systems, using detailed DNA-based information, as well as spatial and temporal transcription factor concentration data. We also developed a semi-implicit numerical algorithm for solving the model equations and demonstrate here the efficiency of this algorithm through stability and convergence analyses. To test the model, we used it together with the semi-implicit algorithm to simulate a Drosophila gene regulatory circuit that drives development in the dorsal-ventral axis of the blastoderm-stage embryo, involving three genes. For model validation, we have done both mathematical and statistical comparisons between the experimental data and the model’s simulated data. Where protein and cis-regulatory information is available, our two-layer model provides a method for recapitulating and predicting dynamic aspects of eukaryotic transcriptional systems that will greatly improve our understanding of gene regulation at a global level.

Sig2GRN: a software tool linking signaling pathway with gene regulatory network for dynamic simulation

“…The goal of the upstream simulation is to generate the dynamical trends of the transcription factors under the perturbations. Then the simulated transcription factor activities are employed to predict the gene expression patterns over time, using either a Boolean model or a thermodynamic-based model [21], which can be selected by users. Therefore, the two layers of network are linked together by the transcription factors, and the cellular responses can be predicted given the extracellular perturbations.…”

“…Once the time-series data of the transcription factor activities (value ∈[0,1] at each simulation iteration) are generated, users can select either a Boolean model [30] or a thermodynamic model [21] to predict the subsequent gene expression patterns.…”

“…Since the Boolean simulation only refers to whether a gene up-regulated or down-regulated without revealing to what extent they will be expressed or not, we implement a thermodynamic (also termed fractional occupancy ) model [21] to describe the gradual responses of gene expression to signal transduction. The thermodynamic model is derived under the assumption that the system is in the thermodynamic equilibrium.…”

“…If the underlying biochemical mechanisms are known, biochemical kinetic modeling [17–20] is a well-established strategy for describing the dynamic sub-cellular systems using a set of mathematical equations. In the field of gene regulation, thermodynamic models have also been successfully applied [21–23] besides the aforementioned methods.…”

“…A generalized logical model, which we proposed previously in [13] and is based on network topology, is employed here to capture the dynamical trends of transcription factors in cellular signaling pathways. Then two different models, i.e., a Boolean model and a thermodynamics-based model [21], are integrated to predict the downstream gene expression patterns based on the predicted transcription factor activities. As a Java plugin for Cytoscape [29] (version 2.8.3), Sig2GRN is able to simulate the dynamics of the signaling pathways and the subsequent time-series gene expression data.…”