Modeling gene regulatory networks with piecewise linear differential equations

A fundamental step in synthetic biology and systems biology is to derive appropriate mathematical models for the purposes of analysis and design. For example, to synthesize a gene regulatory network, the derivation of a mathematical model is important in order to carry out in silico investigations of the network dynamics and to investigate parameter variations and robustness issues. Different mathematical frameworks have been proposed to derive such models. In particular, the use of sets of nonlinear ordinary differential equations (ODEs) has been proposed to model the dynamics of the concentrations of mRNAs and proteins. These models are usually characterized by the presence of highly nonlinear Hill function terms. A typical simplification is to reduce the number of equations by means of a quasi-steady-state assumption on the mRNA concentrations. This yields a class of simplified ODE models. A radically different approach is to replace the Hill functions by piecewise-linear approximations [5]. A further modelling approach is the use of discretetime maps [7] where the evolution of the system is modelled in discrete, rather than continuous, time. The aim of this paper is to discuss and compare these different modelling approaches, using a representative gene regulatory network. We will show that different models often lead to conflicting conclusions concerning the existence and stability of equilibria and stable oscillatory behaviours. Moreover, we shall discuss, where possible, the viability of making certain modelling approximations (e.g. quasi-steady-state mRNA dynamics or piecewise-linear approximations of Hill functions) and their effects on the overall system dynamics.

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“…In particular, in the work originated by Plahte et al [36], and also in [3,4,19] the following PWL function for activation is used:…”

Section: Ordinary Differential Equationsmentioning

confidence: 99%

Comparing different ODE modelling approaches for gene regulatory networks

Polynikis

Hogan

Bernardo

2009

Journal of Theoretical Biology

154

103

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“…The nonlinearity functions in the proposed model are either Hill functions or tangent hyperbolic function; hence, they are bounded and monotonic. Therefore, these assumptions do not impose any constraints on our analysis of the GRN, and they are compatible with various modeling studies, e.g., [37]. Also note that g In the next two chapters, we will investigate the GRN under both negative and positive feedback conditions.…”

Section: Model Transformation and Simplificationmentioning

confidence: 66%

“…Another challenge for such networks is the estimation of the network parameters from time series data. A work in this direction is [37], where Hill functions are taken as nonlinearities, and the coefficients of specific Hill functions are estimated from experimental data. Apart from the GRN literature, 1.3 Models for Gene Regulatory Networks 11 models similar to (1.4) are also found in the neural networks literature.…”

Section: Continuous-time Modelsmentioning

confidence: 99%

Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays

Ahsen¹,

Özbay²,

Niculescu³

2015

SpringerBriefs in Electrical and Computer Engineering

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“…Flexibility of ordinary deferential equations allows the description of complex relations between components of the net. Differential equations can describe complex dynamic behaviour like oscillations, cyclical patterns, multistationary and switch-like behaviour (Gebert et al, 2007). According to Hecker et al, 2009 the dynamic of gene regulatory networks can be described with (Eq.3.…”

Section: Difference and Differential Equation Modelsmentioning

confidence: 99%

“…8. Model of gene regulation (Gebert et al, 2007) Model was based on assumption that regulation between genes can be described using piecewise linear differential equations (Eq 7-9). …”

Section: Difference and Differential Equation Modelsmentioning

confidence: 99%