Adaptive group consensus of coupled harmonic oscillators with multiple leaders

In this paper, we investigate the group consensus of coupled harmonic oscillators with multiple leaders in an undirected fixed network. Unlike many existing algorithms for group consensus of multi-agent systems or cluster synchronization of complex dynamical networks, which require global information of the underlying network such as the eigenvalues of the coupling matrix or centralized control protocols, we propose a novel decentralized adaptive group consensus algorithm for coupled harmonic oscillators. By using the decentralized adaptive group consensus algorithm and without using any global information of the underlying network, all agents in the same group asymptotically synchronize with the corresponding leader even when only one agent in each group has access to the information of the corresponding leader. Numerical simulation results are presented to illustrate the theoretical results. © 2012 IEEE.published_or_final_versio

A systems model of phosphorylation for inflammatory signaling events

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Kinetic regulation of multi-ligand binding proteins

Background: Second messengers, such as calcium, regulate the activity of multisite binding proteins in a concentration-dependent manner. For example, calcium binding has been shown to induce conformational transitions in the calcium-dependent protein calmodulin, under steady state conditions. However, intracellular concentrations of these second messengers are often subject to rapid change. The mechanisms underlying dynamic ligand-dependent regulation of multisite proteins require further elucidation. Results: In this study, a computational analysis of multisite protein kinetics in response to rapid changes in ligand concentrations is presented. Two major physiological scenarios are investigated: i) Ligand concentration is abundant and the ligand-multisite protein binding does not affect free ligand concentration, ii) Ligand concentration is of the same order of magnitude as the interacting multisite protein concentration and does not change. Therefore, buffering effects significantly influence the amounts of free ligands. For each of these scenarios the influence of the number of binding sites, the temporal effects on intermediate apo- and fully saturated conformations and the multisite regulatory effects on target proteins are investigated. Conclusions: The developed models allow for a novel and accurate interpretation of concentration and pressure jump-dependent kinetic experiments. The presented model makes predictions for the temporal distribution of multisite protein conformations in complex with variable numbers of ligands. Furthermore, it derives the characteristic time and the dynamics for the kinetic responses elicited by a ligand concentration change as a function of ligand concentration and the number of ligand binding sites. Effector proteins regulated by multisite ligand binding are shown to depend on ligand concentration in a highly nonlinear fashion

A calcium dependent de-adhesion mechanism regulates the direction and rate of cell migration: a mathematical model.

Cell migration has long been studied by a variety of techniques and many proteins have been implicated in its regulation. Integrins, key proteins that link the cell to the extracellular matrix, are central to adhesion complexes whose turnover defines the rate of cell locomotion. The formation and disassembly of these adhesions is regulated by both intracellular and extracellular factors. In this study we have focused on the Ca2+-dependent protein network (module) that disassembles the adhesion complexes. We have developed a mathematical model that includes the Ca2+-dependent enzymes micro-calpain and phospholipase C (PLC) as well as IP3 receptors and stretch activated Ca2+ channels, all of which have been reported to regulate migration. The model also considers the spatial effects of Ca2+ propagation into lamella. Our model predicts differential activation of calpain at the leading and trailing edges of the cell. Since disassembly of integrin adhesive contacts is proportional to the degree of calpain activation, this leads to cell migration in a preferred direction. We show how the dynamics of Ca2+ spiking affects calpain activation and thus changes the disassembly rate of adhesions. The spiking is controlled by PLC activity and currents through stretch-activated Ca2+ channels. Our model thus combines the effects of various molecular factors and leads to a consistent explanation of the regulation of the rate and direction of cell migration

Solution structure and dynamics of a prototypical chordin-like cysteine-rich repeat (von Willebrand Factor type C module) from collagen IIA.

Chordin-like cysteine-rich (CR) repeats (also referred to as von Willebrand factor type C (VWC) modules) have been identified in approximately 200 extracellular matrix proteins. These repeats, named on the basis of amino acid conservation of 10 cysteine residues, have been shown to bind members of the transforming growth factor-beta (TGF-beta) superfamily and are proposed to regulate growth factor signaling. Here we describe the intramolecular disulfide bonding, solution structure, and dynamics of a prototypical chordin-like CR repeat from procollagen IIA (CR(ColIIA)), which has been previously shown to bind TGF-beta1 and bone morphogenetic protein-2. The CR(ColIIA) structure manifests a two sub-domain architecture tethered by a flexible linkage. Initial structures were calculated using RosettaNMR, a de novo prediction method, and final structure calculations were performed using CANDID within CYANA. The N-terminal region contains mainly beta-sheet and the C-terminal region is more irregular with the fold constrained by disulfide bonds. Mobility between the N- and C-terminal sub-domains on a fast timescale was confirmed using NMR relaxation measurements. We speculate that the mobility between the two sub-domains may decrease upon ligand binding. Structure and sequence comparisons have revealed an evolutionary relationship between the N-terminal sub-domain of the CR module and the fibronectin type 1 domain, suggesting that these domains share a common ancestry. Based on the previously reported mapping of fibronectin binding sites for vascular endothelial growth factor to regions containing fibronectin type 1 domains, we discuss the possibility that this structural homology might also have functional relevance