Abstract : Biological systems have been identified as complex networks consisting of many biomolecules and interactions between them. The dynamics of molecular activities based on such networks are considered to be the origin of biological functions. In the recent progress of mathematical sciences, various methods have been developed to determine important aspects of dynamical properties based on network topologies. Such theories may become breakthroughs to solve the dynamics of complex biological systems. In this symposium, we introduce a wide variety of topological approaches and discuss their future perspectives from both mathematical and biological points of view.
[01956] Controlling cell fate specification system based on network structure
Format : Talk at Waseda University
Author(s) :
Atsushi Mochizuki (Institute for Life and Medical Sciences, Kyoto University)
Kenji Kobayashi (Department of Zoology, Graduate School of Science, Kyoto University)
Kazuki Maeda (Faculty of Informatics, The University of Fukuchiyama)
Miki Tokuoka (Department of Zoology, Graduate School of Science, Kyoto University)
Yutaka Satou (Department of Zoology, Graduate School of Science, Kyoto University)
Abstract : Modern biology provided large networks describing regulatory interactions between biomolecules. We developed Linkage Logic theory, which ensures observability and controllability of any long-term dynamics of the whole system by a subset of nodes, that is identified from the network alone as a feedback vertex set (FVS). We applied the theory to gene network for cell-fate specification in ascidian, including 92 genes. By manipulating 6 genes in FVS, all the seven tissues could be induced experimentally.
[01938] An extension of the Fiedler-Mochizuki theory to time-delay systems
Format : Talk at Waseda University
Author(s) :
Atsushi Kondo (Department of Mathematics, Kyoto University)
Abstract : We consider the dynamics of a system of differential equations called a Regulatory Network, which represents complex regulatory relationships such as gene regulatory networks. The paper by Fiedler-Mochizuki et al. (JDDE 2013) showed that it is possible to identify a set of determining nodes that determines the asymptotic dynamics of the Regulatory Network from its network structure alone. We extend this theory to the case where the regulatory network contains time delays.
[01727] Structure-based and dynamics-based control of biological network models
Format : Talk at Waseda University
Author(s) :
Jorge Gomez Tejeda Zanudo (Harvard Medical School)
Reka Albert (Pennsylvania State University)
Eli Newby (Pennsylvania State University)
Abstract : A task of interest when analyzing mathematical models of intracellular networks is to identify nodes that can provide attractor control in these systems. I will introduce stable motif control and feedback vertex set (FVS) control, two methods we have used to provide control strategies in multiple systems. I will discuss how we used FVS control and structure-based metrics based on signal propagation to identify high-ranking manipulations involving only 1-3 nodes that can provide attractor control.
[01991] Universal structural requirements for maximal robust perfect-adaptation in biomolecular networks
Format : Talk at Waseda University
Author(s) :
Ankit Gupta (ETH Zürich)
Mustafa Khammash (ETH Zürich)
Abstract : Living systems survive in unpredictable environments by maintaining key physiological variables at their desired levels through tight regulation. This property is called robust perfect adaptation (RPA) and the aim of this talk is to mathematically characterize the structural requirements for biomolecular networks to attain a form of maximal RPA, whereby the network is simultaneously robust to the largest set of disturbances. These results provide a new Internal Model Principle for biomolecular RPA networks.
[01961] Network topology determines robustness and flexibility in chemical reaction systems
Format : Talk at Waseda University
Author(s) :
TAKASHI OKADA (Kyoto Univ)
Abstract : In living cells, biochemical reactions form complex networks. Conventional sensitivity analysis is limited by the need for detailed reaction kinetics and parameters, which are often not available for living systems. Our new method, structural sensitivity analysis, determines qualitative sensitivity solely from network structures. Based on this framework, we established a topological theorem that determines the extent to which the perturbation of a parameter affects chemical concentrations and fluxes within the network.
[01937] Simplifying complex chemical reaction networks
Format : Talk at Waseda University
Author(s) :
Yuji Hirono (Asia Pacific Center for Theoretical Physics)
Abstract : Understanding the behavior of complex biochemical reaction networks is an important and challenging problem. To ease the analysis, it is desirable if we can simplify a complex reaction network while preserving its important features. In this talk, we discuss a method for the reduction of chemical reaction networks. We identify topological conditions on its subnetworks, reduction of which preserves the original steady state exactly.
[01907] Multistationarity conditions for polynomial systems in biology
Format : Talk at Waseda University
Author(s) :
Carsten Conradi (HTW Berlin)
Abstract : Polynomial Ordinary Differential Equations are an important tool in quantitative biology. Often parameters vary in large intervals. Consequently one is interested in parameter conditions that guarantee multistationarity and further constrain parameter values. The focus of this talk are mass action ODEs that admit a monomial parameterization of positive steady states. For such systems it is straightforward to derive a parameterization of rate constants where multistationarity exists. Multisite phosphorylation systems are of this type.
[02165] Global Attractor Conjecture, Persistence Conjecture, and Toric Differential Inclusions
Format : Talk at Waseda University
Author(s) :
Gheorghe Craciun (University of Wisconsin-Madison)
Abstract : The Global Attractor Conjecture can be regarded as a far-reaching generalization of Boltzmann’s H-theorem for finite dimensional systems. The related Persistence Conjecture is even more general, and essentially says that solutions of weakly reversible systems cannot go extinct. We will discuss some of these connections, and we focus especially on introducing Toric Differential Inclusions as a tool for proving these conjectures. We also describe implications for biochemical mechanisms for noise filtering and cellular homeostasis.
