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At least 1,153 records · Page 64Linked to original sources
PubMed1996

Synaptic organizations and dynamical properties of weakly connected neural oscillators. I. Analysis of a canonical model.

We study weakly connected networks of neural oscillators near multiple Andronov-Hopf bifurcation points. We analyze relationships between synaptic organizations (anatomy) of the networks and their dynamical properties (function). Our principal assumptions are: (1) Each neural oscillator comprises two populations of neurons; excitatory and inhibitory ones; (2) activity of each population of neurons is described by a scalar (one-dimensional) variable; (3) each neural oscillator is near a nondegenerate supercritical Andronov-Hopf bifurcation point; (4) the synaptic connections between the neural oscillators are weak. All neural networks satisfying these hypotheses are governed by the same dynamical system, which we call the canonical model. Studying the canonical model shows that: (1) A neural oscillator can communicate only with those oscillators which have roughly the same natural frequency. That is, synaptic connections between a pair of oscillators having different natural frequencies are functionally insignificant. (2) Two neural oscillators having the same natural frequencies might not communicate if the connections between them are from among a class of pathological synaptic configurations. In both cases the anatomical presence of synaptic connections between neural oscillators does not necessarily guarantee that the connections are functionally significant. (3) There can be substantial phase differences (time delays) between the neural oscillators, which result from the synaptic organization of the network, not from the transmission delays. Using the canonical model we can illustrate self-ignition and autonomous quiescence (oscillator death) phenomena. That is, a network of passive elements can exhibit active properties and vice versa. We also study how Dale's principle affects dynamics of the networks, in particular, the phase differences that the network can reproduce. We present a complete classification of all possible synaptic organizations from this point of view. The theory developed here casts some light on relations between synaptic organization and functional properties of oscillatory networks. The major advantage of our approach is that we obtain results about all networks of neural oscillators, including the real brain. The major drawback is that our findings are valid only when the brain operates near a critical regime, viz. for a multiple Andronov-Hopf bifurcation.

Cell Death↗
PubMed1991

A neural network model of the cerebellar cortex performing dynamic associations.

The present paper proposes a model which applies formal neural network modeling techniques to construct a theoretical representation of the cerebellar cortex and its performances in motor control. A schema that makes explicit use of propagation delays of neural signals, is introduced to describe the ability to store temporal sequences of patterns in the Golgi-granule cell system. A perceptron association is then performed on these sequences of patterns by the Purkinje cell layer. The model conforms with important biological constraints, such as the known excitatory or inhibitory nature of the various synapses. Also, as suggested by experimental evidence, the synaptic plasticity underlying the learning ability of the model, is confined to the parallel fiber--Purkinje cell synapses, and takes place under the control of the climbing fibers. The result is a neural network model, constructed according to the anatomy of the cerebellar cortex, and capable of learning and retrieval of temporal sequences of patterns. It provides a framework to represent and interpret properties of learning and control of movements by the cerebellum, and to assess the capacity of formal neural network techniques for modeling of real neural systems.

Animals↗
PubMed2001

SPiD: a subtilis protein interaction database.

MOTIVATION: Protein-protein interactions are a potential source of valuable clues in determining the functional role of as yet uncharacterized gene products in metabolic pathways. Graph-like structures emerging from the accumulation of interaction data make it difficult to maintain a consistent and global overview by hand. Bioinformatics tools are needed to perform this graph visualization while maintaining a link to the experimental data. RESULTS: "SPiD" is an online database for exploring networks of interacting proteins in Bacillus subtilis characterized by the two-hybrid system. Graphical displays of interaction networks are created dynamically as users interactively navigate through these networks. Third party applications can interface the database through a Common Object Request Broker Architecture (CORBA) tier. AVAILABILITY: SPiD is available through its web site at http://www-mig.versailles.inra.fr/bdsi/SPiD, and through an Interoperable Object Reference (IOR) and its associated Interface Definition Language (IDL). CONTACT: hoebeke@versailles.inra.fr

Bacillus subtilis↗
PubMedDate not supplied

A neural model of cerebellar learning for arm movement control: cortico-spino-cerebellar dynamics.

A neural network model of opponent cerebellar learning for arm movement control is proposed. The model illustrates how a central pattern generator in cortex and basal ganglia, a neuromuscular force controller in spinal cord, and an adaptive cerebellum cooperate to reduce motor variability during multijoint arm movements using mono- and bi-articular muscles. Cerebellar learning modifies velocity commands to produce phasic antagonist bursts at interpositus nucleus cells whose feed-forward action overcomes inherent limitations of spinal feedback control of tracking. Excitation of alpha motoneuron pools, combined with inhibition of their Renshaw cells by the cerebellum, facilitate movement initiation and optimal execution. Transcerebellar pathways are opened by learning through long-term depression (LTD) of parallel fiber-Purkinje cell synapses in response to conjunctive stimulation of parallel fibers and climbing fiber discharges that signal muscle stretch errors. The cerebellar circuitry also learns to control opponent muscles pairs, allowing cocontraction and reciprocal inhibition of muscles. Learning is stable, exhibits load compensation properties, and generalizes better across movement speeds if motoneuron pools obey the size principle. The intermittency of climbing fiber discharges maintains stable learning. Long-term potentiation (LTP) in response to uncorrelated parallel fiber signals enables previously weakened synapses to recover. Loss of climbing fibers, in the presence of LTP, can erode normal opponent signal processing. Simulated lesions of the cerebellar network reproduce symptoms of cerebellar disease, including sluggish movement onsets, poor execution of multijoint plans, and abnormally prolonged endpoint oscillations.

Adaptation, Physiological↗
PubMed2002

Network topology of a potential energy landscape: a static scale-free network.

Here we analyze the topology of the network formed by the minima and transition states on the potential energy landscape of small clusters. We find that this network has both a small-world and scale-free character. In contrast to other scale-free networks, where the topology results from the dynamics of the network growth, the potential energy landscape is a static entity. Therefore, a fundamentally different organizing principle underlies this behavior: The potential energy landscape is highly heterogeneous with the low-energy minima having large basins of attraction and acting as the highly connected hubs in the network.

Models, Theoretical↗
PubMed2004

Canonical sensitivities: a useful tool to deal with large perturbations in metabolic network modeling.

The dynamic range of metabolic models can be extended to deal with large perturbations by introducing the related concepts of "generalized" kinetic order and "canonical" sensitivities. Generalized kinetic orders are built as a well-defined non linear combination of the canonical sensitivities coefficients, which in turn are obtained by a least-squares regression on central composite factorial design data. In a such way, the whole domain of the operating variables is mapped without need to determine locally neither the first nor the second order model derivatives. The method was validated through numerical simulations, its predictions being compared with those coming from a Michaelis-Menten formalism taken as reference. In parallel, two variants of the Power-law formalism (S-system, least-squares GMA) also were tested. The canonical sensitivities method produced the widest range to predict metabolite concentrations and metabolic fluxes at the steady states. In addition, the variation pattern for the logarithmic gains and for the characteristic eigenvalues have been accurately determined from a unique overall model, being both required to make realistic analysis in metabolic engineering. The achieved information also can be expressed in terms of those typical coefficients derived from the Metabolic Control Analysis (MCA). Even if current first order Power-law or MCA formalisms were used, the canonical sensitivities approach provides a significant advantage, since complete sets of homologous, accurate, locally valid metabolic coefficients can be simultaneously recovered from the array proposed, being representative of the whole range of the operating variables instead of a unique nominal condition as is usual.

Algorithms↗
PubMed1997

Threshold-dependent Limit Cycles in a Nonlinear Network Model.

A mathematical model of the dynamics of a neural network, in which synaptic strength varies simultaneously with activation, is analyzed. This feedback network, with infinite-gain transfer function, is described by a system of ordinary differential equations. It is shown that the resulting discontinuous nonlinear dynamical system has multiple stable periodic solutions. The existence of these periodic attractors depends critically on the value of the threshold parameter; and by varying the threshold the network can be made to cycle through a sequence of attracting states. Copyright 1997 Elsevier Science Ltd.

Journal Article↗
PubMed1998

Chaos in a dynamic model of traffic flows in an origin-destination network.

In this paper we investigate the dynamic behavior of road traffic flows in an area represented by an origin-destination (O-D) network. Probably the most widely used model for estimating the distribution of O-D flows is the gravity model, [J. de D. Ortuzar and L. G. Willumsen, Modelling Transport (Wiley, New York, 1990)] which originated from an analogy with Newton's gravitational law. The conventional gravity model, however, is static. The investigation in this paper is based on a dynamic version of the gravity model proposed by Dendrinos and Sonis by modifying the conventional gravity model [D. S. Dendrinos and M. Sonis, Chaos and Social-Spatial Dynamics (Springer-Verlag, Berlin, 1990)]. The dynamic model describes the variations of O-D flows over discrete-time periods, such as each day, each week, and so on. It is shown that when the dimension of the system is one or two, the O-D flow pattern either approaches an equilibrium or oscillates. When the dimension is higher, the behavior found in the model includes equilibria, oscillations, periodic doubling, and chaos. Chaotic attractors are characterized by (positive) Liapunov exponents and fractal dimensions.(c) 1998 American Institute of Physics.

Journal Article↗
PubMed2005

Dynamics of a temporo-fronto-parietal network during sustained spatial or spectral auditory processing.

Animal and human studies have suggested that posterior temporal, parietal, and frontal regions are specifically involved in auditory spatial (location and motion) processing, forming a putative dorsal "where" pathway. We used scalp EEG and current density mapping to investigate the dynamics of this network in human subjects presented with a varying acoustic stream in a two-factor paradigm: spatial versus pitch variations, focused versus diverted attention. The main findings were: (i) a temporo-parieto-frontal network was activated during the whole duration of the stream in all conditions and modulated by attention; (ii) the left superior temporal cortex was the only region showing different activations for pitch and spatial variations. Therefore, parietal and frontal regions would be involved in task-related processes (attention and motor preparation), whereas the differential processing of acoustic spatial and object-related features seems to take place at the temporal level.

Acoustic Stimulation↗
PubMed1998

Genomic regulation modeled as a network with basins of attraction.

Many natural processes consist of networks of interacting elements which affect each other's state over time, the dynamics depending on the pattern of connections and the updating rules for each element. Genomic regulatory networks are arguably networks of this sort. An attempt to understand genomic networks would benefit from the context of a general theory of discrete dynamical networks which is currently emerging. A key notion here is global dynamics, whereby state-space is organized into basins of attraction, objects that have only recently become accessible by computer simulation of idealized models, in particular "random Boolean networks". Cell types have been explained as attractors in genomic networks, where the network architecture is biased to achieve a balance between stability and adaptability in response to perturbation. Based on computer simulations using the software Discrete Dynamics Lab (DDLab), these ideas are described, as well as order-chaos measures on typical trajectories that further characterize network dynamics.

Algorithms↗
PubMed1991

Morphogenesis in shape-space. Elementary meta-dynamics in a model of the immune network.

A unique feature of the immune system is that it possesses meta-dynamics: the process governing the removal of certain clones from the active population and the recruitment of new clones from the pool of lymphocytes freshly produced by the bone marrow. In this paper, we present a computer model which focuses on those aspects of the system that characteristically derive from the meta-dynamics as such. We observe that when a region of shape-space is densely populated, there is an emergence of dynamically quasi-stable configurations. Moreover, when the system develops in the presence of permanent self-antigens, the latter are systematically incorporated into such coherent configurations. We conclude that the meta-dynamics of the biological immune system may be such that it gives rise to the emergence of a connected, self-sustaining network that we call the Central Immune System: a coherent self-identity which incorporates the molecules of the somatic self and, more generally, reflects the history of its own development.

Autoantigens↗
PubMed2005

Neural network adaptive control for nonlinear nonnegative dynamical systems.

Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous. In this paper, we develop a full-state feedback neural adaptive control framework for adaptive set-point regulation of nonlinear uncertain nonnegative and compartmental systems. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains. In addition, the neural adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state-space for nonnegative initial conditions.

Adaptation, Physiological↗
PubMed2006

Dynamics analysis and analog associative memory of networks with LT neurons.

The additive recurrent network structure of linear threshold neurons represents a class of biologically-motivated models, where nonsaturating transfer functions are necessary for representing neuronal activities, such as that of cortical neurons. This paper extends the existing results of dynamics analysis of such linear threshold networks by establishing new and milder conditions for boundedness and asymptotical stability, while allowing for multistability. As a condition for asymptotical stability, it is found that boundedness does not require a deterministic matrix to be symmetric or possess positive off-diagonal entries. The conditions put forward an explicit way to design and analyze such networks. Based on the established theory, an alternate approach to study such networks is through permitted and forbidden sets. An application of the linear threshold (LT) network is analog associative memory, for which a simple design method describing the associative memory is suggested in this paper. The proposed design method is similar to a generalized Hebbian approach, but with distinctions of additional network parameters for normalization, excitation and inhibition, both on a global and local scale. The computational abilities of the network are dependent on its nonlinear dynamics, which in turn is reliant upon the sparsity of the memory vectors.

Algorithms↗
PubMed1992

Nuclear-cytoskeletal interactions: evidence for physical connections between the nucleus and cell periphery and their alteration by transformation.

The overall coordination of cell structure and function that results in gene expression requires a spatial and temporal precision that would be unobtainable in the absence of structural order within the cell. Cells contain extensive and elaborate three-dimensional skeletal networks that form integral structural components of the plasma membrane, cytoplasm, and nucleus. These skeletal networks form a dynamic tissue matrix are composed of the nuclear matrix, cytoskeleton, and extracellular matrix. The tissue matrix is an interactive network which undergoes dynamic changes as cells move and change shape. Pathologists have long recognized cancer in pathologic specimens based on the altered morphology of tumor cells compared to their normal counterparts. The structural order of cells appears to be altered in transformed cells. This structural order is reflected in the altered morphology and motility observed in transformed cells compared to their normal counterparts, however, it is unclear whether the structural changes observed in cancer cells have any functional significance. We report here on the nature of the physical connections between the nucleus and cell periphery in nontransformed cells and demonstrate that the nucleus is dynamically coupled to the cell periphery via actin microfilaments. We also demonstrate that the dynamic coupling of the nucleus to the cell periphery via actin microfilaments is altered in Kirsten-ras transformed rat kidney epithelial cells. This loss of structure-function relationship may be an important factor in the process of cell transformation.

Acrylamide↗
PubMed2006

Habitat loss and the structure of plant-animal mutualistic networks.

Recent papers have described the structure of plant-animal mutualistic networks. However, no study has yet explored the dynamical implications of network structure for the persistence of such mutualistic communities. Here, we develop a patch-model of a whole plant-animal community and explore its persistence. To assess the role of network structure, we build three versions of the model. In the first version, we use the exact network of interactions of two real mutualistic communities. In the other versions, we randomize the observed network of interactions using two different null models. We show that the community response to habitat loss is affected by network structure. Real communities start to decay sooner than random communities, but persist for higher destruction levels. There is a destruction threshold at which the community collapses. Our model is the first attempt to describe the dynamics of whole mutualistic metacommunities interacting in realistic ways.

Animal Population Groups↗
PubMed1991

Modifications of the intermediate filament and nuclear matrix networks by the extracellular matrix.

The tissue matrix system is a dynamic, interacting structural network directly linking the nuclear matrix, cytoskeleton and the extracellular matrix. We report here that interaction of normal rat kidney epithelial cells (NRK) and Kirsten-ras transformed rat kidney cells, with an extracellular matrix secreted by tumor cells, causes modifications to the protein composition of the intermediate filament and nuclear matrix networks. The matrix networks are different between normal and transformed cells; however, these alterations by the tumor extracellular matrix are similar in both cell types. These data represent the first report that modification of the extracellular matrix environment can have an effect on the protein composition of the nuclear matrix.

Animals↗
PubMed2006

Bringing metabolic networks to life: integration of kinetic, metabolic, and proteomic data.

BACKGROUND: Translating a known metabolic network into a dynamic model requires reasonable guesses of all enzyme parameters. In Bayesian parameter estimation, model parameters are described by a posterior probability distribution, which scores the potential parameter sets, showing how well each of them agrees with the data and with the prior assumptions made. RESULTS: We compute posterior distributions of kinetic parameters within a Bayesian framework, based on integration of kinetic, thermodynamic, metabolic, and proteomic data. The structure of the metabolic system (i.e., stoichiometries and enzyme regulation) needs to be known, and the reactions are modelled by convenience kinetics with thermodynamically independent parameters. The parameter posterior is computed in two separate steps: a first posterior summarises the available data on enzyme kinetic parameters; an improved second posterior is obtained by integrating metabolic fluxes, concentrations, and enzyme concentrations for one or more steady states. The data can be heterogeneous, incomplete, and uncertain, and the posterior is approximated by a multivariate log-normal distribution. We apply the method to a model of the threonine synthesis pathway: the integration of metabolic data has little effect on the marginal posterior distributions of individual model parameters. Nevertheless, it leads to strong correlations between the parameters in the joint posterior distribution, which greatly improve the model predictions by the following Monte-Carlo simulations. CONCLUSION: We present a standardised method to translate metabolic networks into dynamic models. To determine the model parameters, evidence from various experimental data is combined and weighted using Bayesian parameter estimation. The resulting posterior parameter distribution describes a statistical ensemble of parameter sets; the parameter variances and correlations can account for missing knowledge, measurement uncertainties, or biological variability. The posterior distribution can be used to sample model instances and to obtain probabilistic statements about the model's dynamic behaviour.

Bayes Theorem↗
PubMed1999

Fast global oscillations in networks of integrate-and-fire neurons with low firing rates.

We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons --> infinity, the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized. The activity becomes oscillatory when the inhibitory feedback is strong enough. The period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input. In large but finite networks, the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters in these two different regions. The results are found to be in good agreement with numerical simulations.

Algorithms↗