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PubMed2000

Mode dynamics of interacting neural populations by bi-orthogonal spectral decomposition.

A system of coupled bistable Hopf oscillators with an external periodic input source was used to model the ability of interacting neural populations to synchronize and desynchronize in response to variations of the input signal. We propose that, in biological systems, the settings of internal and external coupling strengths will affect the behaviour of the system to a greater degree than the input frequency. While input frequency and coupling strength were varied, the spatio-temporal dynamics of the network was examined by the bi-orthogonal decomposition technique. Within this method, effects of variation of input frequency and coupling strength were analyzed in terms of global, spatial and temporal mode entropy and energy, using the spatio-temporal data of the system. We observed a discontinuous evolution of spatio-temporal patterns depending sensitively on both the input frequency and the internal and external coupling strengths of the network.

Animals↗
PubMedDate not supplied

The messages in optic nerve fibers and their interpretation.

Spike discharges are the principal carriers of information in the nervous system. Although both the ionic and the molecular mechanisms of spike generation have been studied extensively, the methods for analyzing a spike train that are currently employed have not changed much from those in use 20 years ago. There is an apparent need for a refinement of the methods used to analyze spike trains. We present here a summary of our recent results of an analysis of spike trains from retinal ganglion cells that is based on Wiener's theory of non-linear analysis or white-noise analysis. We found that spike trains carry, at least to a second-order approximation, as much information as is carried by the ganglion cell's postsynaptic potential (PSP). There is no loss of information when an analog signal, PSP, is converted into a point process, namely, spike discharges. It is indeed possible to predict the cell's PSP from a spike train. This finding has two important implications. First, the neuron network in the retina produces a PSP, the dynamics of which are optimal for triggering a spike discharge, or conversely, the spike-generation mechanism is optimized to match the dynamics of the network. The external stimulus that is optimal for production of a ganglion-cell discharge is represented as the cell's PSP. Second, there is structure encoded within the spike train; information on a second-order non-linearity is encoded by the relative timing of two consecutive spike discharges. Coding of non-linearity into a spike train is an efficient means of signal compression and is an important aspect of neurophysiology.

Animals↗
PubMed1996

Modeling of the three-dimensional structure of luffin-alpha and its simulated reaction with the substrate oligoribonucleotide GAGA.

A fundamental problem in biochemistry and molecular biology is understanding the spatial structure of macromolecules and then analyzing their functions. In this study, the three-dimensional structure of a ribosome-inactivating protein luffin-alpha was predicted using a neural network method and molecular dynamics simulation. A feedforward neural network with the backpropagation learning algorithm were trained on model class of homologous proteins including trichosanthin and alpha-momorcharin. The distance constraints for the C alpha atoms in the protein backbone were utilized to generate a folded crude conformation of luffin-alpha by model building and the steepest descent minimization approach. The crude conformation was refined by molecular dynamics techniques and a simulated annealing procedure. The interaction between luffin-alpha and its analogous substrate GAGA was also simulated to understand its action mechanism.

Algorithms↗
PubMed2004

Reverse engineering of linking preferences from network restructuring.

We provide a method to deduce the preferences governing the restructuring dynamics of a network from the observed rewiring of the edges. Our approach is applicable for systems in which the preferences can be formulated in terms of a single-vertex energy function with f (k) being the contribution of a node of degree k to the total energy, and the dynamics obeys the detailed balance. The method is first tested by Monte Carlo simulations of restructuring graphs with known energies; then it is used to study variations of real network systems ranging from the coauthorship network of scientific publications to the asset graphs of the New York Stock Exchange. The empirical energies obtained from the restructuring can be described by a universal function f (k) approximately -k ln k , which is consistent with and justifies the validity of the preferential attachment rule proposed for growing networks.

Journal Article↗
PubMed2003

Disease evolution on networks: the role of contact structure.

Owing to their rapid reproductive rate and the severe penalties for reduced fitness, diseases are under immense evolutionary pressure. Understanding the evolutionary response of diseases in new situations has clear public-health consequences, given the changes in social and movement patterns over recent decades and the increased use of antibiotics. This paper investigates how a disease may adapt in response to the routes of transmission available between infected and susceptible individuals. The potential transmission routes are defined by a computer-generated contact network, which we describe as either local (highly clustered networks where connected individuals are likely to share common contacts) or global (unclustered networks with a high proportion of long-range connections). Evolution towards stable strategies operates through the gradual random mutation of disease traits (transmission rate and infectious period) whenever new infections occur. In contrast to mean-field models, the use of contact networks greatly constrains the evolutionary dynamics. In the local networks, high transmission rates are selected for, as there is intense competition for susceptible hosts between disease progeny. By contrast, global networks select for moderate transmission rates because direct competition between progeny is minimal and a premium is placed upon persistence. All networks show a very slow but steady rise in the infectious period.

Biological Evolution↗
PubMed2001

Dynamic simulation of the human red blood cell metabolic network.

We have developed a Mathematica application package to perform dynamic simulations of the red blood cell (RBC) metabolic network. The package relies on, and integrates, many years of mathematical modeling and biochemical work on red blood cell metabolism. The extensive data regarding the red blood cell metabolic network and the previous kinetic analysis of all the individual components makes the human RBC an ideal 'model' system for mathematical metabolic models. The Mathematica package can be used to understand the dynamics and regulatory characteristics of the red blood cell.

Computer Simulation↗
PubMed2006

The use of neural networks in evaluation of the direction and dynamics of changes in lipid parameters in kidney transplant patients on the Mediterranean diet.

OBJECTIVE: The objective of the study was to assess whether neural networks can be a tool useful in the evaluation of the effect of the Mediterranean diet (MD) on the direction and dynamics of selected parameters. DESIGN: Randomized, prospective study. SETTING: Outpatient Clinic of the Department of Nephrology, Transplantology, and Internal Medicine. PATIENTS AND INTERVENTION: The study group consisted of 21 patients after kidney transplantation whose diet complied with the MD; the control group included 16 patients (also after transplantation) on a low-fat diet, isocaloric with the study diet. MAIN OUTCOME MEASURES: Anthropometry, plasma lipids, chromatography of triacylglycerols and fatty acids, and activity of superoxide dismutase and catalase were measured in both groups. Statistical analysis was done with the SNN (Statistica Neural Networks) StatSoft software package. RESULTS: The advantage of neural networks is the possibility of the dynamic presentation of a process taking place in a biological system. In the MD group in the first months of use of the diet, the cholesterol level was reduced only in the group of young and middle-aged patients. This tendency was not observed among elderly patients, among whom a small reduction of the total cholesterol level was noted only at the end of the observation period. In control group at the beginning of the observation, the plasma total cholesterol level was proportional to the patient's age. After 6 months, the total cholesterol increased in young patients and redacted in the group of elderly patients. CONCLUSIONS: We concluded that the MD diet would be ideal for posttransplantation patients without serious pathologic dyslipidemia. In the case of patients with substantial dyslipidemia, appropriate pharmacologic treatment lowering proatherosclerotic lipid levels should be used in combination with the MD. Artificial neural networks (ANNs) were a useful tool in modeling biological parameters, showing dynamics of the studied interactions in a very detailed way. ANN is the most suitable method for investigations with many variables, interconnected nonlinearly; therefore, this method allows for a more general approach to biological problems. However, it should be noted that considerable data sets are required to obtain a satisfactory fit to the data. Moreover, to ensure the predictive power of this method for new cases, the representative database is indispensable. In spite of these demands, ANN is a prospective tool for reliable, quick assessments and predictions.

Adult↗
PubMed2006

Classification of epilepsy types through global network analysis of scalp electroencephalograms.

Epilepsy is a dynamic disease in which self-organization and emergent structures occur dynamically at multiple levels of neuronal integration. Therefore, the transient relationship within multichannel electroencephalograms (EEGs) is crucial for understanding epileptic processes. In this paper, we show that the global relationship within multichannel EEGs provides us with more useful information in classifying two different epilepsy types than pairwise relationships such as cross correlation. To demonstrate this, we determine the global network structure within channels of the scalp EEG based on the minimum spanning tree method. The topological dissimilarity of the network structures from different types of temporal lobe epilepsy is described in the form of the divergence rate and is computed for 11 patients with left (LTLE) and right temporal lobe epilepsy (RTLE). We find that patients with LTLE and RTLE exhibit different large scale network structures, which emerge at the epoch immediately before the seizure onset, not in the preceding epochs. Our results suggest that patients with the two different epilepsy types display distinct large scale dynamical networks with characteristic epileptic network structures.

Artificial Intelligence↗
PubMed2004

Anomalous diffusion probes microstructure dynamics of entangled F-actin networks.

We study the thermal motion of colloidal tracer particles in entangled actin filament (F-actin) networks, where the particle radius is comparable to the mesh size of the F-actin network. In this regime, the ensemble-averaged mean-squared displacement of the particles is proportional to tau(gamma), where 0<gamma<1 from 0.1<tau<100 s and depends only on the ratio of the probe radius to mesh size. By directly imaging hundreds of particles over 20 min, we determine this anomalous subdiffusion is due to the dynamics of infrequent and large jumps particles make between distinct pores in the network.

Actins↗
PubMed2002

Self-selected modular recurrent neural networks with postural and inertial subnetworks applied to complex movements.

It has been shown that dynamic recurrent neural networks are successful in identifying the complex mapping relationship between full-wave-rectified electromyographic (EMG) signals and limb trajectories during complex movements. These connectionist models include two types of adaptive parameters: the interconnection weights between the units and the time constants associated to each neuron-like unit; they are governed by continuous-time equations. Due to their internal structure, these models are particularly appropriate to solve dynamical tasks (with time-varying input and output signals). We show in this paper that the introduction of a modular organization dedicated to different aspects of the dynamical mapping including privileged communication channels can refine the architecture of these recurrent networks. We first divide the initial individual network into two communicating subnetworks. These two modules receive the same EMG signals as input but are involved in different identification tasks related to position and acceleration. We then show that the introduction of an artificial distance in the model (using a Gaussian modulation factor of weights) induces a reduced modular architecture based on a self-elimination of null synaptic weights. Moreover, this self-selected reduced model based on two subnetworks performs the identification task better than the original single network while using fewer free parameters (better learning curve and better identification quality). We also show that this modular network exhibits several features that can be considered as biologically plausible after the learning process: self-selection of a specific inhibitory communicating path between both subnetworks after the learning process, appearance of tonic and phasic neurons, and coherent distribution of the values of the time constants within each subnetwork.

Adult↗
PubMed2003

Theory of time-resolved somatic complementation and its use to explore the sporulation control network in Physarum polycephalum.

Mutants of Physarum polycephalum can be complemented by fusion of plasmodial cells followed by cytoplasmic mixing. Complementation between strains carrying different mutational defects in the sporulation control network may depend on the signaling state of the network components. We have previously suggested that time-resolved somatic complementation (TRSC) analysis with such mutants may be used to probe network architecture and dynamics. By computer simulation it is now shown how and under which conditions the regulatory hierarchy of genes can be determined experimentally. A kinetic model of the sporulation control network is developed, which is then used to demonstrate how the mechanisms of TRSC can be understood and simulated at the kinetic level. On the basis of theoretical considerations, experimental parameters that determine whether functional complementation of two mutations will occur are identified. It is also shown how gene dosage-effect relationships can be employed for network analysis. The theoretical framework provided may be used to systematically analyze network structure and dynamics through time-resolved somatic complementation studies. The conclusions drawn are of general relevance in that they do not depend on the validity of the model from which they were derived.

Animals↗
PubMed1996

Counting and classifying attractors in high dimensional dynamical systems.

Randomly connected Boolean networks have been used as mathematical models of neural, genetic, and immune systems. A key quantity of such networks is the number of basins of attraction in the state space. The number of basins of attraction changes as a function of the size of the network, its connectivity and its transition rules. In discrete networks, a simple count of the number of attractors does not reveal the combinatorial structure of the attractors. These points are illustrated in a reexamination of dynamics in a class of random Boolean networks considered previously by Kauffman. We also consider comparisons between dynamics in discrete networks and continuous analogues. A continuous analogue of a discrete network may have a different number of attractors for many different reasons. Some attractors in discrete networks may be associated with unstable dynamics, and several different attractors in a discrete network may be associated with a single attractor in the continuous case. Special problems in determining attractors in continuous systems arise when there is aperiodic dynamics associated with quasiperiodicity of deterministic chaos.

Animals↗
PubMed2005

The role of log-normal dynamics in the evolution of biochemical pathways.

The study of the scale-free topology in non-biological and biological networks and the dynamics that can explain this fascinating property of complex systems have captured the attention of the scientific community in the last years. Here, we analyze the biochemical pathways of three organisms (Methanococcus jannaschii, Escherichia coli, Saccharomyces cerevisiae) which are representatives of the main kingdoms Archaea, Bacteria and Eukaryotes during the course of the biological evolution. We can consider two complementary representations of the biochemical pathways: the enzymes network and the chemical compounds network. In this article, we propose a stochastic model that explains that the scale-free topology with exponent in the vicinity of gamma approximately 3/2 found across these three organisms is governed by the log-normal dynamics in the evolution of the enzymes network. Precisely, the fluctuations of the connectivity degree of enzymes in the biochemical pathways between evolutionary distant organisms follow the same conserved dynamical principle, which in the end is the origin of the stationary scale-free distribution observed among species, from Archaea to Eukaryotes. In particular, the log-normal dynamics guarantees the conservation of the scale-free distribution in evolving networks. Furthermore, the log-normal dynamics also gives a possible explanation for the restricted range of observed exponents gamma in the scale-free networks (i.e., gamma > or = 3/2). Finally, our model is also applied to the chemical compounds network of biochemical pathways and the Internet network.

Biological Evolution↗
PubMed2006

Estimating topology of networks.

We suggest a method for estimating the topology of a network based on the dynamical evolution supported on the network. Our method is robust and can be also applied when disturbances and/or modeling errors are presented. Several examples with networks of phase oscillators, pulse-coupled Hindmarch-Rose neurons, and Lorenz oscillators are provided to illustrate our approach.

Journal Article↗
PubMed2003

Network capacity analysis for latent attractor computation.

Attractor networks have been one of the most successful paradigms in neural computation, and have been used as models of computation in the nervous system. Recently, we proposed a paradigm called 'latent attractors' where attractors embedded in a recurrent network via Hebbian learning are used to channel network response to external input rather than becoming manifest themselves. This allows the network to generate context-sensitive internal codes in complex situations. Latent attractors are particularly helpful in explaining computations within the hippocampus--a brain region of fundamental significance for memory and spatial learning. Latent attractor networks are a special case of associative memory networks. The model studied here consists of a two-layer recurrent network with attractors stored in the recurrent connections using a clipped Hebbian learning rule. The firing in both layers is competitive--K winners take all firing. The number of neurons allowed to fire, K, is smaller than the size of the active set of the stored attractors. The performance of latent attractor networks depends on the number of such attractors that a network can sustain. In this paper, we use signal-to-noise methods developed for standard associative memory networks to do a theoretical and computational analysis of the capacity and dynamics of latent attractor networks. This is an important first step in making latent attractors a viable tool in the repertoire of neural computation. The method developed here leads to numerical estimates of capacity limits and dynamics of latent attractor networks. The technique represents a general approach to analyse standard associative memory networks with competitive firing. The theoretical analysis is based on estimates of the dendritic sum distributions using Gaussian approximation. Because of the competitive firing property, the capacity results are estimated only numerically by iteratively computing the probability of erroneous firings. The analysis contains two cases: the simple case analysis which accounts for the correlations between weights due to shared patterns and the detailed case analysis which includes also the temporal correlations between the network's present and previous state. The latter case predicts better the dynamics of the network state for non-zero initial spurious firing. The theoretical analysis also shows the influence of the main parameters of the model on the storage capacity.

Animals↗
PubMed2006

Synchronization in complex networks with a modular structure.

Networks with a community (or modular) structure arise in social and biological sciences. In such a network individuals tend to form local communities, each having dense internal connections. The linkage among the communities is, however, much more sparse. The dynamics on modular networks, for instance synchronization, may be of great social or biological interest. (Here by synchronization we mean some synchronous behavior among the nodes in the network, not, for example, partially synchronous behavior in the network or the synchronizability of the network with some external dynamics.) By using a recent theoretical framework, the master-stability approach originally introduced by Pecora and Carroll in the context of synchronization in coupled nonlinear oscillators, we address synchronization in complex modular networks. We use a prototype model and develop scaling relations for the network synchronizability with respect to variations of some key network structural parameters. Our results indicate that random, long-range links among distant modules is the key to synchronization. As an application we suggest a viable strategy to achieve synchronous behavior in social networks.

Action Potentials↗
PubMed1997

Complex dynamics of mass-closed coupled autocatalytic systems in response to minute asymmetric perturbations.

The role of kinetic coupling in catering to a remote-control mechanism for the onset and regulation of self-organization phenomena in a multicompartmental biochemical system has been examined. Using two cyclic autocatalytic reaction networks operating in two chambers separated by a membrane and coupled through a common cofactor, it has been demonstrated that (i) in response to asymmetric perturbations, the coupled reaction networks exhibit a variety of temporal self-organization phenomena such as bistability, multiple periodicity, hard excitation and coexistence of aperiodic oscillation with limit cycle even in mass-closed conditions; (ii) without disturbing a network directly, its dynamic behaviour can be regulated by perturbing some other network kinetically coupled to it and (iii) the dynamics of two coupled networks can be made to flip-flop between oscillatory and steady-states simply by modulating the time of application of external perturbations. The extreme sensitivity of this model to minute asymmetric fluctuations in the environment can predict how the impact of local changes in physico-chemical conditions can be transmitted from one compartment to another through coupled biochemical pathways in a living cell.

Journal Article↗
PubMed2004

Spike synchronization in the cortex/basal-ganglia networks of Parkinsonian primates reflects global dynamics of the local field potentials.

Cortical local field potentials (LFPs) reflect synaptic potentials and accordingly correlate with neuronal discharge. Because LFPs are coherent across substantial cortical areas, we hypothesized that cortical spike correlations could be predicted from them. Because LFPs recorded in the basal ganglia (BG) are also correlated with neuronal discharge and are clinically accessible in Parkinson's disease patients, we were interested in testing this hypothesis in the BG, as well. We recorded LFPs and unit discharge from multiple electrodes, which were placed in primary motor cortex or in the basal ganglia (striatum and pallidum) of two monkeys before and after rendering them parkinsonian with 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine. We used the method of partial spectra to construct LFP predictors of the spike cross-correlation functions (CCFs). The predicted CCF is an estimate of the correlation between two neurons under the assumption that their association is explained solely by the association of each with the LFP recorded on a third electrode. In the normal condition, the predictors account for cortical rate covariations but not for the association among the tonically active neurons of the striatum. In the parkinsonian condition, with the appearance of 10 Hz oscillations throughout the cortex-basal ganglia networks, the LFP predictors account remarkably better for the CCFs in both the cortex and the basal ganglia. We propose that, in the parkinsonian condition, the cortex-basal ganglia networks are more tightly related to global modes of brain dynamics that are echoed in the LFP.

Action Potentials↗