Turbulent fields and their recurrences

We introduce a new variational method for finding periodic orbits of flows and spatio-temporally periodic solutions of classical field theories, a generalization of the Newton method to a flow in the space of loops. The feasibility of the method is demonstrated by its application to several dynamical systems, including the Kuramoto-Sivashinsky system.Comment: 14 pages, 13 figures; in N. Antoniou, ed., Proceed. of 10. Intern. Workshop on Multiparticle Production: Correlations and Fluctuations in QCD (World Scientific, Singapore 2003

The interplay between discrete noise and nonlinear chemical kinetics in a signal amplification cascade

We used various analytical and numerical techniques to elucidate signal propagation in a small enzymatic cascade which is subjected to external and internal noise. The nonlinear character of catalytic reactions, which underlie protein signal transduction cascades, renders stochastic signaling dynamics in cytosol biochemical networks distinct from the usual description of stochastic dynamics in gene regulatory networks. For a simple 2-step enzymatic cascade which underlies many important protein signaling pathways, we demonstrated that the commonly used techniques such as the linear noise approximation and the Langevin equation become inadequate when the number of proteins becomes too low. Consequently, we developed a new analytical approximation, based on mixing the generating function and distribution function approaches, to the solution of the master equation that describes nonlinear chemical signaling kinetics for this important class of biochemical reactions. Our techniques work in a much wider range of protein number fluctuations than the methods used previously. We found that under certain conditions the burst-phase noise may be injected into the downstream signaling network dynamics, resulting possibly in unusually large macroscopic fluctuations. In addition to computing first and second moments, which is the goal of commonly used analytical techniques, our new approach provides the full time-dependent probability distributions of the colored non-Gaussian processes in a nonlinear signal transduction cascade.Comment: 16 pages, 9 figure

Variational method for locating invariant tori

We formulate a variational fictitious-time flow which drives an initial guess torus to a torus invariant under given dynamics. The method is general and applies in principle to continuous time flows and discrete time maps in arbitrary dimension, and to both Hamiltonian and dissipative systems.Comment: 10 page

On the architecture of cell regulation networks

<p>Abstract</p> <p>Background</p> <p>With the rapid development of high-throughput experiments, detecting functional modules has become increasingly important in analyzing biological networks. However, the growing size and complexity of these networks preclude structural breaking in terms of simplest units. We propose a novel graph theoretic decomposition scheme combined with dynamics consideration for probing the architecture of complex biological networks.</p> <p>Results</p> <p>Our approach allows us to identify two structurally important components: the "minimal production unit"(MPU) which responds quickly and robustly to external signals, and the feedback controllers which adjust the output of the MPU to desired values usually at a larger time scale. The successful application of our technique to several of the most common cell regulation networks indicates that such architectural feature could be universal. Detailed illustration and discussion are made to explain the network structures and how they are tied to biological functions.</p> <p>Conclusions</p> <p>The proposed scheme may be potentially applied to various large-scale cell regulation networks to identify functional modules that play essential roles and thus provide handles for analyzing and understanding cell activity from basic biochemical processes.</p