Stability analysis of a dynamical model representing gene regulatory networks

In this paper we perform stability analysis of a class of cyclic biological processes involving time delayed feedback. More precisely, we analyze the genetic regulatory network having nonlinearities with negative Schwarzian derivatives. We derive a set of conditions implying global stability of the genetic regulatory network under positive feedback. As a special case, we also consider homogenous genetic regulatory networks and obtain an appropriate stability condition which depends only on the parameters of the nonlinearity function. © 2012 IFAC

Stability and chaos in coupled two-dimensional maps on Gene Regulatory Network of bacterium E.Coli

The collective dynamics of coupled two-dimensional chaotic maps on complex networks is known to exhibit a rich variety of emergent properties which crucially depend on the underlying network topology. We investigate the collective motion of Chirikov standard maps interacting with time delay through directed links of Gene Regulatory Network of bacterium Escherichia Coli. Departures from strongly chaotic behavior of the isolated maps are studied in relation to different coupling forms and strengths. At smaller coupling intensities the network induces stable and coherent emergent dynamics. The unstable behavior appearing with increase of coupling strength remains confined within a connected sub-network. For the appropriate coupling, network exhibits statistically robust self-organized dynamics in a weakly chaotic regime

Relative Stability of Network States in Boolean Network Models of Gene Regulation in Development

Progress in cell type reprogramming has revived the interest in Waddington's concept of the epigenetic landscape. Recently researchers developed the quasi-potential theory to represent the Waddington's landscape. The Quasi-potential U(x), derived from interactions in the gene regulatory network (GRN) of a cell, quantifies the relative stability of network states, which determine the effort required for state transitions in a multi-stable dynamical system. However, quasi-potential landscapes, originally developed for continuous systems, are not suitable for discrete-valued networks which are important tools to study complex systems. In this paper, we provide a framework to quantify the landscape for discrete Boolean networks (BNs). We apply our framework to study pancreas cell differentiation where an ensemble of BN models is considered based on the structure of a minimal GRN for pancreas development. We impose biologically motivated structural constraints (corresponding to specific type of Boolean functions) and dynamical constraints (corresponding to stable attractor states) to limit the space of BN models for pancreas development. In addition, we enforce a novel functional constraint corresponding to the relative ordering of attractor states in BN models to restrict the space of BN models to the biological relevant class. We find that BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics of pancreas cell differentiation. This framework can also determine the genes' influence on cell state transitions, and thus can facilitate the rational design of cell reprogramming protocols.Comment: 24 pages, 6 figures, 1 tabl

Dynamical Properties of a Two-gene Network with Hysteresis

A mathematical model for a two-gene regulatory network is derived and several of their properties analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we employ a hybrid systems model to capture the dynamics of the system. The proposed model incorporates binary hysteresis with different thresholds capturing the interaction between the genes. We analyze properties of the solutions and asymptotic stability of equilibria in the system as a function of its parameters. Our analysis reveals the presence of limit cycles for a certain range of parameters, behavior that is associated with hysteresis. The set of points defining the limit cycle is characterized and its asymptotic stability properties are studied. Furthermore, the stability property of the limit cycle is robust to small perturbations. Numerical simulations are presented to illustrate the results.Comment: 55 pages, 31 figures.Expanded version of paper in Special Issue on Hybrid Systems and Biology, Elsevier Information and Computation, 201

Homogeneous and Scalable Gene Expression Regulatory Networks with Random Layouts of Switching Parameters

We consider a model of large regulatory gene expression networks where the thresholds activating the sigmoidal interactions between genes and the signs of these interactions are shuffled randomly. Such an approach allows for a qualitative understanding of network dynamics in a lack of empirical data concerning the large genomes of living organisms. Local dynamics of network nodes exhibits the multistationarity and oscillations and depends crucially upon the global topology of a "maximal" graph (comprising of all possible interactions between genes in the network). The long time behavior observed in the network defined on the homogeneous "maximal" graphs is featured by the fraction of positive interactions ($0\leq \eta\leq 1$) allowed between genes. There exists a critical value $\eta_c<1$ such that if $\eta<\eta_c$, the oscillations persist in the system, otherwise, when $\eta>\eta_c,$ it tends to a fixed point (which position in the phase space is determined by the initial conditions and the certain layout of switching parameters). In networks defined on the inhomogeneous directed graphs depleted in cycles, no oscillations arise in the system even if the negative interactions in between genes present therein in abundance ($\eta_c=0$). For such networks, the bidirectional edges (if occur) influence on the dynamics essentially. In particular, if a number of edges in the "maximal" graph is bidirectional, oscillations can arise and persist in the system at any low rate of negative interactions between genes ($\eta_c=1$). Local dynamics observed in the inhomogeneous scalable regulatory networks is less sensitive to the choice of initial conditions. The scale free networks demonstrate their high error tolerance.Comment: LaTeX, 30 pages, 20 picture

Gene autoregulation via intronic microRNAs and its functions

Background: MicroRNAs, post-transcriptional repressors of gene expression, play a pivotal role in gene regulatory networks. They are involved in core cellular processes and their dysregulation is associated to a broad range of human diseases. This paper focus on a minimal microRNA-mediated regulatory circuit, in which a protein-coding gene (host gene) is targeted by a microRNA located inside one of its introns. Results: Autoregulation via intronic microRNAs is widespread in the human regulatory network, as confirmed by our bioinformatic analysis, and can perform several regulatory tasks despite its simple topology. Our analysis, based on analytical calculations and simulations, indicates that this circuitry alters the dynamics of the host gene expression, can induce complex responses implementing adaptation and Weber's law, and efficiently filters fluctuations propagating from the upstream network to the host gene. A fine-tuning of the circuit parameters can optimize each of these functions. Interestingly, they are all related to gene expression homeostasis, in agreement with the increasing evidence suggesting a role of microRNA regulation in conferring robustness to biological processes. In addition to model analysis, we present a list of bioinformatically predicted candidate circuits in human for future experimental tests. Conclusions: The results presented here suggest a potentially relevant functional role for negative self-regulation via intronic microRNAs, in particular as a homeostatic control mechanism of gene expression. Moreover, the map of circuit functions in terms of experimentally measurable parameters, resulting from our analysis, can be a useful guideline for possible applications in synthetic biology.Comment: 29 pages and 7 figures in the main text, 18 pages of Supporting Informatio