In-phase waves and echo waves are commonly existing in coupled systems. In Physica D 151 (2001) 199 we proved existence of echo waves in linearly coupled oregonators and showed that the echo waves may coexist with the stable homogeneous positive steady state. This Letter develops a different approach (so-called "reducing dimension") compared with our "mode decomposition" method of stability of in-phase waves in Phys. Lett. A 301 (2002) 231, and rigorously proves stability of the echo waves. The method can be easily applied to other similar systems.

Motivation: Protein structure alignment is one of the most important computational problems in molecular biology and plays a key role in protein structure prediction, fold family classification, motif finding, phylogenetic tree reconstruction and so on. From the viewpoint of computational complexity, a pairwise structure alignment is also a NP-hard problem, in contrast to the polynomial time algorithm for a pairwise sequence alignment. Results: We propose a method for solving the structure alignment problem in an accurate manner at the amino acid level, based on a mean field annealing technique. We define the structure alignment as a mixed integer-programming (MIP) problem. By avoiding complicated combinatorial computation and exploiting the special structure of the continuous partial problem, we transform the MIP into a reduced non-linear continuous optimization problem (NCOP) with a much simpler form. To optimize the reduced NCOP, a mean field annealing procedure is adopted with a modified Potts model, whose solution is generally identical to that of the MIP. There is no 'soft constraint' in our mean field model and all constraints are automatically satisfied throughout the annealing process, thereby not only making the optimization more efficient but also eliminating many unnecessary parameters that depend on problems and usually require careful tuning. A number of benchmark examples are tested by the proposed method with comparisons to several existing approaches.

All cell components exhibit intracellular noise due to random births and deaths of individual molecules, and extracellular noise due to environment perturbations. In particular, gene regulation is an inherently noisy process with transcriptional control, alternative splicing, translation, diffusion and chemical modification reactions, which all involve stochastic fluctuations. Such stochastic noises may not only affect the dynamics of the entire system but may also be exploited by living organisms to actively facilitate certain functions, such as cooperative behavior and communication. Results: We have provided a general model and an analytic tool to examine the cooperative behavior of a multi-cell system with both intracellular and extracellular stochastic fluctuations. A multi-cell system with a synthetic gene network is adopted to demonstrate the effects of noises and coupling on collective dynamics. These results establish not only a theoretical foundation but also a quantitative basis for understanding essential roles of noises on cooperative dynamics, such as synchronization and communication among cells.

We model a synthetic gene regulatory network in a microbial cell, and investigate the effect of noises on cell-cell communication in a well-mixed multicellular system. A biologically plausible model is developed for cellular communication in an indirectly coupled multicellular system.Without extracellular noises, all cells, in spite of interaction among them, behave irregularly due to independent intracellular noises. On the other hand, extracellular noises that are common to all cells can induce collective dynamics and stochastically synchronize the multicellular system by actively enhancing the integrated interchange of signaling molecules.