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At least 613 records · Page 34Linked to original sources
PubMed2005

Combinatorial complexity and dynamical restriction of network flows in signal transduction.

The activities and interactions of proteins that govern the cellular response to a signal generate a multitude of protein phosphorylation states and heterogeneous protein complexes. Here, using a computational model that accounts for 307 molecular species implied by specified interactions of four proteins involved in signalling by the immunoreceptor FcepsilonRI, we determine the relative importance of molecular species that can be generated during signalling, chemical transitions among these species, and reaction paths that lead to activation of the protein tyrosine kinase (PTK) Syk. By all of these measures and over two- and ten-fold ranges of model parameters--rate constants and initial concentrations--only a small portion of the biochemical network is active. The spectrum of active complexes, however, can be shifted dramatically, even by a change in the concentration of a single protein, which suggests that the network can produce qualitatively different responses under different cellular conditions and in response to different inputs. Reduced models that reproduce predictions of the full model for a particular set of parameters lose their predictive capacity when parameters are varied over two-fold ranges.

Animals↗
PubMed2001

Dynamics of neural networks: a proposed mechanism to account for changes in clinical symptomatology through time in patients with psychotic diseases.

The classical Kraepelinean dichotomy between manic depressive insanity and the schizophrenias has been recently challenged from clinical and neurobiological quarters. It is not so infrequent to see patients shift from a manic to a schizophrenic symptomatology and vice versa. This paper proposes neurobiological mechanisms as to how these changes may occur, based on recent data on the functioning of neural networks at different modes.

Humans↗
PubMed1992

Evolution of host-parasitoid network through homeochaotic dynamics.

Host-parasitoid systems with evolving mutation rates are studied. By increasing the growth rate of hosts, the diversity of both species is maintained dynamically. For the lower growth rate, diversity is brought about by mere parasitism. The average mutation rate for parasites is elevated to a high value, while that for hosts is suppressed at a low level. For the higher growth rate, the mutation rates for both hosts and parasites are elevated to form a symbiotic cluster connected by on-going mutation. This symbiotic state is sustained through a chaotic oscillation keeping some coherency among species. For a flat landscape for hosts, dynamical clustering of oscillation is observed. Lyapunov spectra of such oscillations show that high dimensional chaos with small positive exponents underlies in the symbiotic state. This weak high dimensional chaos, termed "homeochaos," is essential to the maintenance of symbiosis in ecosystems.

Journal Article↗
PubMed2000

More realistic models of sexually transmitted disease transmission dynamics: sexual partnership networks, pair models, and moment closure.

BACKGROUND: Mathematical models of sexually transmitted disease transmission have proven powerful tools for interpreting observed epidemiologic pattern. However, the most commonly used formulation of such models largely fail to capture the effect of partnership concurrency and contact network structure on transmission. GOAL: The development of a compartmental model of partnership formation and dissolution that includes approximations for the influence of the sexual-partner network. STUDY DESIGN: Theoretical analysis of ordinary differential equation models for sexually transmitted disease transmission within sex-partner networks. RESULTS: The approach developed advances earlier pair models, allows for the influence of concurrent sexual partnerships, and illustrates the importance of concurrency to the persistence of diseases with relatively short durations of infectiousness. The authors also illustrate that heterogeneity in risk is possible even in model populations in which all individuals follow the same behavioral rules. CONCLUSION: Deterministic extended pair models offer a powerful approach to modelling sexually transmitted disease transmission that usefully complement computationally intensive microsimulation models.

Female↗
PubMed2002

Information space dynamics for neural networks.

We propose a coupled map lattice defined on a hypercube in M dimensions, the information space, to model memory retrieval by a neural network. We consider that both neuronal activity and the spiking phase may carry information. In this model the state of the network at a given time t is completely determined by a function y(sigma-->,t) of the bit strings sigma-->=(sigma1,sigma2,...,sigmaM), where sigma(i)=+/-1 with i=1,2, ...,M, that gives the intensity with which the information sigma--> is being expressed by the network. As an example, we consider logistic maps, coupled in the information space, to describe the evolution of the intensity function y(sigma-->,t). We propose an interpretation of the maps in terms of the physiological state of the neurons and the coupling between them, obtain Hebb-like learning rules, show that the model works as an associative memory, numerically investigate the capacity of the network and the size of the basins of attraction, and estimate finite size effects. We finally show that the model, when exposed to sequences of uncorrelated stimuli, shows recency and latency effects that depend on the noise level, delay time of measurement, and stimulus intensity.

Journal Article↗
PubMed2004

Extreme fluctuations in small-world networks with relaxational dynamics.

We study the distribution and scaling of the extreme height fluctuations for Edwards-Wilkinson-type relaxation on small-world substrates. When random links are added to a one-dimensional lattice, the average size of the fluctuations becomes finite (synchronized state) and the extreme height diverges only logarithmically in the large system-size limit. This latter property ensures synchronization in a practical sense in small-world coupled multi-component autonomous systems. The statistics of the extreme heights is governed by the Fisher-Tippett-Gumbel distribution.

Journal Article↗
PubMed2004

Physics, stability, and dynamics of supply networks.

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed "bullwhip effect" in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.

Journal Article↗
PubMed2005

Extremal dynamics on complex networks: analytic solutions.

The Bak-Sneppen model displaying punctuated equilibria in biological evolution is studied on random complex networks. By using the rate equation and the random walk approaches, we obtain the analytic solution of the fitness threshold xc to be 1/((k)f+1), where (k)f=(k2)/(k) (=(k)) in the quenched (annealed) updating case, where kn is the nth moment of the degree distribution. Thus, the threshold is zero (finite) for the degree exponent gamma<3 (gamma>3) for the quenched case in the thermodynamic limit. The theoretical value xc fits well to the numerical simulation data in the annealed case only. Avalanche size, defined as the duration of successive mutations below the threshold, exhibits a critical behavior as its distribution follows a power law, Pa(s) approximately s(-3/2).

Journal Article↗
PubMed1987

Frequency modulation dynamics in neural networks.

The VCON model described here shares certain qualitative features of stimulus-response characteristics with the data in FIGURE 1 and TABLE 1. At the same time, it provides an uncomplicated methodology for modelling neural networks that emphasizes their frequency aspects. In particular, models based on VCONs are amenable to the rotation vector method, which can be used to uncover stable synchronization of firing within a network. This is described in the appendix, where it is shown that the stable firing patterns within the network correspond to minima of an associated (local) energy function. We have seen here how a model of a simple CPG for breathing can be constructed and analyzed. Similar models for rhythm splitting of small mammal activity cycles, sound location networks, and motility in the gastrointestinal tract have been constructed, and large networks of VCONs have been shown to have stable spatial patterns of synchronization.

Action Potentials↗