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# Dynamics of complex biological systems determined from minimal subsets of molecules in regulatory networks

Held by Dr. Atsushi Mochizuki (RIKEN Advanced Science Institute, Japan) for the seminar "Complex Nonlinear Processes in Chemistry and Biology".

Honorary Chairman: Gerhard Ertl

Organizers: M. Bär, C. Beta,
H. Engel, M. Falcke, M. J. B. Hauser, J. Kurths, A. S. Mikhailov, P.
Plath, L. Schimansky-Geier, and H. Stark

Abstract:

Modern biology provides series of large networks
describing regulations between many species of molecules. It is widely
believed that dynamics of molecular activities based on such
regulatory networks are the origin of biological functions. However,
we currently have a limited understanding of the relationship between
structure of a regulatory network and its dynamics. In this study we
develop a general theory to provide an important aspect of dynamics
from information of regulatory linkages alone. It shows that
"Feedback Vertex Set" of a regulatory network is
"Determining Set" of the dynamics of molecular activities.
The theory is practically powerful to study biological systems. First,
it assures that i) any dynamical behaviors of whole system, steady
states, periodic oscillations or quasi-periodic oscillations can be
identified by measurements of a subset of molecules in the network,
and that ii) the subset is determined from the regulatory linkage
alone. For example, all of the dynamical attractors possibly generated
by a signal transduction network with 113 molecules can be identified
by measurement of activity of 5 molecules, if the information of
network is correct. Second, our theory provides rational criterion to
select key molecules to control a system. We demonstrate the aspect
using a model for mammalian circadian rhythms with 6 informative
variables among 21 variables in the system. We show that controlling
the dynamics of informative molecules is sufficient to switch dynamics
of whole system from an attractor to others distinct from original. We
will show other examples of analysis for complex biological systems.

[1] Mochizuki A. and Saito D. (2010) Analyzing steady states of
dynamics of bio-molecules from the structure of regulatory networks J.
Theor. Biol. 266, 323-335.

[2] Fiedler B., Mochizuki A., Kurosawa
G. and Saito D. (In review) Feedback vertex sets as informative and
determining nodes of regulatory network dynamics, J. Math. Biol.