Gheorghe Craciun, Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin-Madison, USA.
Persistence, Permanence, and Global Stability in Biological Interaction Networks
Complex interaction networks are present in all areas of biology, and manifest themselves at very different spatial and temporal scales. Persistence, permanence and global stability are emergent properties of complex networks, and play key roles in the dynamics of living systems. Mathematically, a dynamical system is called persistent if, for all positive solutions, no variable approaches zero. In addition, for a permanent system, all variables are uniformly bounded. We describe criteria for persistence and permanence of solutions, and for global convergence of solutions to an unique equilibrium, in a manner that is robust with respect to initial conditions and parameter values. A thorough understanding of these properties will allow for a better understanding of essential biological processes, such as homeostasis and adaptability.
Fabian Theis, Institute of Computational Biology, Neuherberg, Germany. Institute of Computational Biology, Helmholtz Zentrum München and Department of Mathematics, Technical University München, Germany.
Model reduction for the efficient moment-closure based simulation of
stochastic chemical reaction kinetics
Atefeh Kazeroonian, Jan Hasenauer and Fabian J. Theis
Stochastic chemical reaction kinetics can be modeled by multivariate discrete Markov jump processes, summarized by the chemical master equation. Efficient simulation in biologically meaningful dimensions however needs approximations. Here we study moment-based descriptions of the underlying stochastic system after moment-closure. We show that we can select a subset of moments to be simulated dynamically by analyzing the reaction kinetics. We will finish by outlining application of the simulation method for efficient parameter estimation in stochastic reaction kinetics with application to signaling or gene regulation