Verification of multistability in gene regulation networks: A combinatorial approach

Abstract

Bi-or even multistable behavior is a recurrent phenomenon in gene regulation networks. These networks have the capacity to operate in two or more distinct modes in a stable manner. In this work, we consider gene regulation networks with known interaction structure but unknown reaction kinetics. Additionally, it is assumed that several distinct operation modes were observed experimentally whereby also the measurements of the individual protein concentrations are uncertain. For this setup, the important question of model validation is addressed: Can the given network structure in principle reproduce the observed operation modes? To approach this problem, the work builds on an existing modeling framework [4] which is appropriate to deal with uncertain gene regulation networks. By regarding each operation mode as a forward-invariant set in the state space and with the notion of compatible intervals, it is shown how the validation problem can be translated into a combinatorial one. An algorithm is developed which can efficiently solve the new problem. Finally, the well-known bistable lactose utilization network is analyzed with this new method.

Multistability equivalence between gene regulatory networks of different dimensionality

“…A central property of GRNs is that many of them exhibit multistability, thereby realizing the coexistence of several stable states of the system, of which a suitable one can be adopted under the respective biological circumstances ( [2], [5], [7], [8]). The analysis of multistability properties of such systems is of high interest and has attracted the development of new specially suited methods [3], [1], [9], [10].…”

Steady‐state robustness of qualitative gene regulation networks

“…As discussed in Section , transcription factors can activate or inhibit the production of other proteins. The first assumption is that now, this positive or negative influence can be modeled by monotonously increasing or decreasing activation or inhibition functions whose definitions are given next . Let .…”

“…Moreover, many experiments yield merely relative data as absolute values are hard to obtain.As the first goal of this paper, we therefore want to present a modeling framework that is able to deal with the measurement uncertainties and the uncertainties about the system itself. This framework has already been used in [8][9][10] and shall be recalled here.Considering the asymptotic behavior of gene regulation networks, multistability is a very common phenomenon. All example systems mentioned earlier indeed show this behavior, and in this work, we want to explicitly focus on multistable networks.…”

“…As the first goal of this paper, we therefore want to present a modeling framework that is able to deal with the measurement uncertainties and the uncertainties about the system itself. This framework has already been used in [8][9][10] and shall be recalled here.…”

Multistability equivalence between gene regulatory networks of different dimensionality with application to a differentiation network

“…Copyright MULTISTABILITY EQUIVALENCE BETWEEN GENE REGULATORY NETWORKS 4149 A central property of GRNs is that many of them exhibit multistability, thereby realizing the coexistence of several stable states of the system, of which a suitable one can be adopted under the respective biological circumstances ([2, 5, 7, 8]). The analysis of multistability properties of such systems is of high interest and has attracted the development of new specially suited methods [9][10][11][12].It is desired that the analysis of a conceptual, low-dimensional model should allow for conclusions about a higher-dimensional model. On the one hand, low-dimensional systems are amenable to systems-theoretic tools such as multistability and bifurcation analysis.…”