Multistability refers to the capacity of a system to operate at several discrete, alternative stable steady-states, and is one of the most important features of biological dynamics. The phenomenon of multistability, which is the focus of much modern biomedical. research, is found at all scales, from the molecular and cellular, to tissues, organisms, populations, and ecosystems. In order to understand the role played by some of these interactions (for example the role of a gene regulatory network or a signaling pathway in a cell), one often faces great difficulties in trying to interpret the effect of positive and negative feedbacks, nonlinear interactions, and other complex signaling between the nodes of the biological interaction network. We propose to develop new theory and to significantly expand existing theory for understanding multistability in biological interaction networks, and identifying the key features of biological interaction networks that give rise to multistable behavior. Also, we will create software that implements our various existing multistability-related algorithms, and any newly discovered methods that result form this work. To guide and complement our theoretical work, we will investigate whether our mathematical techniques lead to predictions which can be validated experimentally. The long-term goal of the proposed work is to analyze multistability as a fundamental theoretical concept that traverses levels of biological complexity, and to develop theoretical, computational, and experimental tools to understand multistability in concrete biological interaction networks. Understanding multistability in gene regulatory networks and signaling pathways will play an important role in the study of key cellular processes deregulated during carcinogenesis. The analysis of multistability will also benefit research in cellular differentiation (relevant to tissue engineering), viral infections (e.g. HIV's dormant state), and the immune system. Our software tools and our experimental genetic systems will be made available to the biomedical research community.
| Knight, Daniel; Shinar, Guy; Feinberg, Martin (2015) Sharper graph-theoretical conditions for the stabilization of complex reaction networks. Math Biosci 262:10-27 |
| Anderson, David F; Craciun, Gheorghe; Gopalkrishnan, Manoj et al. (2015) Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks. Bull Math Biol 77:1744-67 |
| Paulevé, Loïc; Craciun, Gheorghe; Koeppl, Heinz (2014) Dynamical properties of Discrete Reaction Networks. J Math Biol 69:55-72 |
| Margaliot, Michael; Sontag, Eduardo D; Tuller, Tamir (2014) Entrainment to periodic initiation and transition rates in a computational model for gene translation. PLoS One 9:e96039 |
| Anderson, David F; Enciso, Germán A; Johnston, Matthew D (2014) Stochastic analysis of biochemical reaction networks with absolute concentration robustness. J R Soc Interface 11:20130943 |
| Johnston, Matthew D (2014) Translated chemical reaction networks. Bull Math Biol 76:1081-116 |
| Shinar, Guy; Feinberg, Martin (2013) Concordant chemical reaction networks and the Species-Reaction Graph. Math Biosci 241:1-23 |
| Craciun, Gheorghe (2013) MOST HOMEOMORPHISMS WITH A FIXED POINT HAVE A CANTOR SET OF FIXED POINTS. Arch Math 100:95-99 |
| Craciun, Gheorghe; Kim, Jaejik; Pantea, Casian et al. (2013) Statistical Model for Biochemical Network Inference. Commun Stat Simul Comput 42:121-137 |
| Barton, John P; Sontag, Eduardo D (2013) The energy costs of insulators in biochemical networks. Biophys J 104:1380-90 |
Showing the most recent 10 out of 27 publications
