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PubMed2001

A model for a network of phosphorylation-dephosphorylation cycles displaying the dynamics of dominoes and clocks.

We consider a model for a network of phosphorylation-dephosphorylation cycles coupled through forward and backward regulatory interactions, such that a protein phosphorylated in a given cycle activates the phosphorylation of a protein by a kinase in the next cycle as well as the dephosphorylation of a protein by a phosphatase in a preceding cycle. The network is cyclically organized in such a way that the protein phosphorylated in the last cycle activates the kinase in the first cycle. We study the dynamics of the network in the presence of both forward and backward coupling, in conditions where a threshold exists in each cycle in the amount of protein phosphorylated as a function of the ratio of kinase to phosphatase maximum rates. We show that this system can display sustained (limit-cycle) oscillations in which each cycle in the pathway is successively turned on and off, in a sequence resembling the fall of a series of dominoes. The model thus provides an example of a biochemical system displaying the dynamics of dominoes and clocks (Murray & Kirschner, 1989). It also shows that a continuum of clock waveforms exists of which the fall of dominoes represents a limit. When the cycles in the network are linked through only forward (positive) coupling, bistability is observed, while in the presence of only backward (negative) coupling, the system can display multistability or oscillations, depending on the number of cycles in the network. Inhibition or activation of any kinase or phosphatase in the network immediately stops the oscillations by bringing the system into a stable steady state; oscillations resume when the initial value of the kinase or phosphatase rate is restored. The progression of the system on the limit cycle can thus be temporarily halted as long as an inhibitor is present, much as when a domino is held in place. These results suggest that the eukaryotic cell cycle, governed by a network of phosphorylation-dephosphorylation reactions in which the negative control of cyclin-dependent kinases plays a prominent role, behaves as a limit-cycle oscillator impeded in the presence of inhibitors. We contrast the case where the sequence of domino-like transitions constitutes the clock with the case where the sequence of transitions is passively coupled to a biochemical oscillator operating as an independent clock.

Animals↗
PubMed1993

Percolation phenomenon: the effect of capillary network rarefaction.

The relationship between microvascular network resistance and functional capillary density was investigated by computer simulation. A model of spinotrapezius muscle microcirculatory network was constructed from measured data of vessel length and diameter. Progressive rarefaction was simulated by random stepwise removal of capillaries from the network. The flow distribution in the network was calculated after each step of capillary removal. Network resistance increased little when decreases in functional capillary density were less than 30%. Furthermore, capillary flow did not decrease and its variance across the network was unchanged despite the gradual flow redistribution. However, with further decreases in capillary density, network resistance increased in a double exponential fashion. The resistance approached infinity at a critical value of functional capillary density termed the percolation threshold. The value of this parameter varied between 56 and 62% and it was lower when capillaries with the lowest flow were preferentially removed.

Animals↗
PubMed2003

Mapping of the neuronal networks of human cortical brain functions.

OBJECTIVE: The principles and methodology of event-related fMRI, electromagnetic source imaging and intracranial evoked potentials will be described along with some examples of the mapping of the neuronal networks of human cortical brain functions with the use of these techniques. INTRODUCTION: Functional brain mapping using PET or fMRI has provided clues on the functioning brain and notably on the functional neuroanatomy of cognitive functions. These mapping possibilities can be used to delineate in an individual patient the brain areas subserving a cerebral function that might be compromised by a surgery in a nearby location, or to target a functional neurosurgical procedure. BACKGROUND: Brain functions and notably "higher brain functions" are served by a complex network of interrelating brain regions. Deeper insights into the functioning of a neuronal network can be gained by adding dynamic, i.e. temporal, information to the functional maps. This will demonstrate the orchestration of the activation of the different brain areas constituting the network, which gives clues to the information processing and therefore to the functioning of the different modules of the network. In order to track the flow of information and the sequential activation of the different brain regions constituting the network, brain activity has to be recorded at the speed of transfer of activation from one neuronal population to the other. The temporal resolution needed to achieve this is not in the range of traditional subtractive or comparative PET or fMRI techniques. NEW DEVELOPMENTS: Novel fMRI methods that record haemodynamic signal changes after single events (event-related fMRI) are now able to determine sequential neural processing by distinguishing the relative onset-time of activity between different areas. The temporal resolution of event-related (ER) fMRI is sufficient to detect changes of mental activity within the order of several hundreds of milliseconds. This allows the exploration of a broad range of cognitive functions. Nevertheless, this technique is currently not rapid enough to observe the transient coordinations and oscillations of neuronal activities occurring across certain cortical areas during the performance of cognitive tasks. The temporal resolution needed for that is within the order of tens or a few milliseconds and is only accessible by EEG or MEG that allow true real-time measurements of the neuronal activity elicited by a stimulus. Surface recordings of multichannel EEG or MEG combined with novel electromagnetic source localisation algorithms allow a relatively precise estimation of the activated areas. A more direct localisation of electric activity is achieved by intracranial recordings in patients having implanted electrodes for diagnostic reasons. In these cases, a high temporal and spatial resolution is achieved but with a limited sampling of brain regions. CONCLUSION: Although the temporal resolution of ER fMRI is due to improve, the temporal measures provided by EEG, MEG or intracranial event-related potentials (ERPs) are absolute, which remains a unique feature of these techniques. Therefore, ER fMRI and electromagnetic source imaging are complementary. The maps obtained with ER fMRI may be refined by electromagnetic ERPs that provide further insights into the temporal coordination or orchestration between the cortical areas already detected by ER fMRI and constituting a neuronal network, and ER fMRI can be used to precisely locate the areas coarsely situated and delineated by electromagnetic source imaging. Thus, the combination of ER fMRI and electromagnetic ERPs is essential in order to produce a mapping method with a millimetre spatial resolution and a millisecond temporal resolution. Future applications should combine these techniques to localise precisely and non-invasively relevant sensory, motor and cognitive processes in order to adequately tailor any brain surgery.

Attention↗
PubMed1994

Immune networks modeled by replicator equations.

In order to evaluate the role of idiotypic networks in the operation of the immune system a number of mathematical models have been formulated. Here we examine a class of B-cell models in which cell proliferation is governed by a non-negative, unimodal, symmetric response function f (h), where the field h summarizes the effect of the network on a single clone. We show that by transforming into relative concentrations, the B-cell network equations can be brought into a form that closely resembles the replicator equation. We then show that when the total number of clones in a network is conserved, the dynamics of the network can be represented by the dynamics of a replicator equation. The number of equilibria and their stability are then characterized using methods developed for the study of second-order replicator equations. Analogies with standard Lotka-Volterra equations are also indicated. A particularly interesting result of our analysis is the fact that even though the immune network equations are not second-order, the number and stability of their equilibria can be obtained by a superposition of second-order replicator systems. As a consequence, the problem of finding all of the equilibrium points of the nonlinear network equations can be reduced to solving linear equations.

Animals↗
PubMed1990

Evolutionary optimization and neural network models of behavior.

One of the main challenges to the adaptionist program in general and the use of optimization models in behavioral and evolutionary ecology, in particular, is that organisms are so constrained by ontogeny and phylogeny that they may not be able to attain optimal solutions, however those are defined. This paper responds to the challenge through the comparison of optimality and neural network models for the behavior of an individual polychaete worm. The evolutionary optimization model is used to compute behaviors (movement in and out of a tube) that maximize a measure of Darwinian fitness based on individual survival and reproduction. The neural network involves motor, sensory, energetic reserve and clock neuronal groups. Ontogeny of the neural network is the change of connections of a single individual in response to its experiences in the environment. Evolution of the neural network is the natural selection of initial values of connections between groups and learning rules for changing connections. Taken together, these can be viewed as "design parameters". The best neural networks have fitnesses between 85% and 99% of the fitness of the evolutionary optimization model. More complicated models for polychaete worms are discussed. Formulation of a neural network model for host acceptance decisions by tephritid fruit flies leads to predictions about the neurobiology of the flies. The general conclusion is that neural networks appear to be sufficiently rich and plastic that even weak evolution of design parameters may be sufficient for organisms to achieve behaviors that give fitnesses close to the evolutionary optimal fitness, particularly if the behaviors are relatively simple.

Animals↗
PubMed1995

Secretory granule formation and membrane recycling by the trans-Golgi network in adipokinetic cells of Locusta migratoria in relation to flight and rest.

The influence of flight activity on the formation of secretory granules and the concomitant membrane recycling by the trans-Golgi network in the peptidergic neurosecretory adipokinetic cells of Locusta migratoria was investigated by means of ultrastructural morphometric methods. The patterns of labelling of the trans-Golgi network by the exogenous adsorptive endocytotic tracer wheat-germ agglutinin-conjugated horse-radish peroxidase and by the endogenous marker enzyme acid phosphatase were used as parameters and were measured by an automatic image analysis system. The results show that endocytosed fragments of plasma membrane with bound peroxidase label were transported to the trans-Golgi network and used to build new secretory granules. The amounts of peroxidase and especially of acid phosphatase within the trans-Golgi network showed a strong tendency to be smaller in flight-stimulated cells than in non-stimulated cells. The amounts of acid phosphatase in the immature secretory granules originating from the trans-Golgi network were significantly smaller in stimulated cells. The number of immature secretory granules positive for acid phosphatase tended to be higher in stimulated cells. Thus, flight stimulation of adipokinetic cells for 1 h influences the functioning of the trans-Golgi network; this most probably results in a slight enhancement of the production of secretory granules by the trans-Golgi network.

Animals↗
PubMed1986

Associative recognition and storage in a model network of physiological neurons.

We consider a neural network model in which the single neurons are chosen to closely resemble known physiological properties. The neurons are assumed to be linked by synapses which change their strength according to Hebbian rules on a short time scale (100 ms). The dynamics of the network--the time evolution of the cell potentials and the synapses--is investigated by computer simulation. As in more abstract network models (Cooper 1973; Hopfield 1982; Kohonen 1984) it is found that the local dynamics of the cell potentials and the synaptic strengths result in global cooperative properties of the network and enable the network to process an incoming flux of information and to learn and store patterns associatively. A trained net can associate missing details of a pattern, can correct wrong details and can suppress noise in a pattern. The network can further abstract the prototype from a series of patterns with variations. A suitable coupling constant connecting the dynamics of the cell potentials with the synaptic strengths is derived by a mean field approximation. This coupling constant controls the neural sensitivity and thereby avoids both extremes of the network state, the state of permanent inactivity and the state of epileptic hyperactivity.

Animals↗
PubMed1987

A model of neural network for spatiotemporal pattern recognition.

A model of neural network to recognize spatiotemporal patterns is presented. The network consists of two kinds of neural cells: P-cells and B-cells. A P-cell generates an impulse responding to more than one impulse and embodies two special functions: short term storage (STS) and heterosynaptic facilitation (HSF). A B-cell generates several impulses with high frequency as soon as it receives an impulse. In recognizing process, an impulse generated by a P-cell represents a recognition of stimulus pattern, and triggers the generation of impulses of a B-cell. Inhibitory impulses with high frequency generated by a B-cell reset the activities of all P-cells in the network. Two examples of spatiotemporal pattern recognition are presented. They are achieved by giving different values to the parameters of the network. In one example, the network recognizes both directional and non-directional patterns. The selectivities to directional and non-directional patterns are realized by only adjusting excitatory synaptic weights of P-cells. In the other example, the network recognizes time series of spatial patterns, where the lengths of the series are not necessarily the same and the transitional speeds of spatial patterns are not always the same. In both examples, the HSF signal controls the total activity of the network, which contributes to exact recognition and error recovery. In the latter example, it plays a role to trigger and execute the recognizing process. Finally, we discuss the correspondence between the model and physiological findings.

Brain↗
PubMed1986

Social networks and social competence: exploring the effects of early adolescent friendships.

This study explored the relationship between friendship social network variables and social competence indices using a sample of 98 young black lower SES adolescents. Analyses indicated that perceived emotional support received from friends and the number of reciprocated best friends in an adolescents' social network were related positively. Multivariate hierarchical regression analyses indicated that perceived friend emotional support and number of reciprocated best friends contributed independently to school competence, peer competence, and perceived self-competence measures. The friendship network's school achievement orientation was related positively to school competence but was unrelated to peer or perceived self-competence. Friendship network density did not add to the variance explained by the other network variables. Methodological contributions of this study include the development of a computer program to map friendship networks and the expansion of network analysis beyond the examination of social support functions.

Achievement↗
PubMedDate not supplied

Long-term changes, induced by microstimulation of the neocortex, in the efficiency of excitatory postsynaptic transmission in the thalamocortical networks.

Neuronal networks with synaptic plasticity, consisting of cells located in various loci of the AC and the MGB, were investigated. It was demonstrated that, as a result of MS applied in the region of cortical elements of the network, connections could alter between all elements of the cortex-thalamus-cortex neuronal network. Changes were manifested in the form of LTP and/or LTD of the efficiency of excitatory connections, as well as in the form of intensification or attenuation of the action of the "common source'; the changes were maintained for tens of minutes. The number of connections between stimulated and non-stimulated elements of the network increased. Neurons in which more favorable conditions for LTP developed were distinguished in the networks. The character of the modification of synapses formed by the axons of several cells on one of the elements of the network could vary. Synapses formed by axonal collaterals of one cell on several elements of the network could also be modified variously.

Animals↗
PubMed1997

Generic properties of combinatory maps: neutral networks of RNA secondary structures.

Random graph theory is used to model and analyse the relationships between sequences and secondary structures of RNA molecules, which are understood as mappings from sequence space into shape space. These maps are non-invertible since there are always many orders of magnitude more sequences than structures. Sequences folding into identical structures form neutral networks. A neutral network is embedded in the set of sequences that are compatible with the given structure. Networks are modeled as graphs and constructed by random choice of vertices from the space of compatible sequences. The theory characterizes neutral networks by the mean fraction of neutral neighbors (lambda). The networks are connected and percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value (lambda > lambda *). Below threshold (lambda < lambda *), the networks are partitioned into a largest "giant" component and several smaller components. Structures are classified as "common" or "rare" according to the sizes of their pre-images, i.e. according to the fractions of sequences folding into them. The neutral networks of any pair of two different common structures almost touch each other, and, as expressed by the conjecture of shape space covering sequences folding into almost all common structures, can be found in a small ball of an arbitrary location in sequence space. The results from random graph theory are compared to data obtained by folding large samples of RNA sequences. Differences are explained in terms of specific features of RNA molecular structures.

Base Sequence↗
PubMed2001

The immunoglobulin-like genetic predetermination of the brain: the protocadherins, blueprint of the neuronal network.

The morphogenesis of the brain is governed by synaptogenesis. Synaptogenesis in turn is determined by cell adhesion molecules, which bridge the synaptic cleft and, by homophilic contact, decide which neurons are connected and which are not. Because of their enormous diversification in specificities, protocadherins (pcdh alpha, pcdh beta, pcdh gamma), a new class of cadherins, play a decisive role. Surprisingly, the genetic control of the protocadherins is very similar to that of the immunoglobulins. There are three sets of variable (V) genes followed by a corresponding constant (C) gene. Applying the rules of the immunoglobulin genes to the protocadherin genes leads, despite of this similarity, to quite different results in the central nervous system. The lymphocyte expresses one single receptor molecule specifically directed against an outside stimulus. In contrast, there are three specific recognition sites in each neuron, each expressing a different protocadherin. In this way, 4,950 different neurons arising from one stem cell form a neuronal network, in which homophilic contacts can be formed in 52 layers, permitting an enormous number of different connections and restraints between neurons. This network is one module of the central computer of the brain. Since the V-genes are generated during evolution and V-gene translocation during embryogenesis, outside stimuli have no influence on this network. The network is an inborn property of the protocadherin genes. Every circuit produced, as well as learning and memory, has to be based on this genetically predetermined network. This network is so universal that it can cope with everything, even the unexpected. In this respect the neuronal network resembles the recognition sites of the immunoglobulins.

Animals↗
PubMed1998

Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior.

The oculomotor integrator is a network that is composed of neurons in the medial vestibular nuclei and nuclei prepositus hypoglossi in the brainstem. Those neurons act approximately as fractional integrators of various orders, converting eye velocity commands into signals that are intermediate between velocity and position. The oculomotor integrator has been modeled as a network of linear neural elements, the time constants of which are lengthened by positive feedback through reciprocal inhibition. In this model, in which each neuron reciprocally inhibits its neighbors with the same Gaussian profile, all model neurons behave as identical, first-order, low-pass filters with dynamics that do not match the variable, approximately fractional-order dynamics of the neurons that compose the actual oculomotor integrator. Fractional-order integrators can be approximated by weighted sums of first-order, low-pass filters with diverse, broadly distributed time constants. Dynamic systems analysis reveals that the model integrator indeed has many broadly distributed time constants. However, only one time constant is expressed in the model due to the uniformity of its network connections. If the model network is made nonuniform by removing the reciprocal connections to and from a small number of neurons, then many more time constants are expressed. The dynamics of the neurons in the nonuniform network model are variable, approximately fractional-order, and resemble those of the neurons that compose the actual oculomotor integrator. Completely removing the connections to and from a neuron is equivalent to eliminating it, an operation done previously to demonstrate the robustness of the integrator network model. Ironically, the resulting nonuniform network model, previously supposed to represent a pathological integrator, may in fact represent a healthy integrator containing neurons with realistically variable, approximately fractional-order dynamics.

Animals↗
PubMed1999

Testable predictions from realistic neural network simulations of vestibular compensation: integrating the behavioural and physiological data.

Neural network simulations have been used previously in the investigation of the horizontal vestibulo-ocular reflex (HVOR) and vestibular compensation. The simulations involved in the present research were based on known anatomy and physiology of the vestibular pathway. This enabled the straightforward comparison of the network response, both in terms of behavioural (eye movement) and physiological (neural activity) data to empirical data obtained from guinea pig. The network simulations matched the empirical data closely both in terms of the static symptoms (spontaneous nystagmus) of unilateral vestibular deafferentation (UVD) as well as in terms of the dynamic symptoms (decrease in VOR gain). The use of multiple versions of the basic network, trained to simulate individual guinea pigs, highlighted the importance of the particular connections: the vestibular ganglion to the type I medial vestibular nucleus (MVN) cells on the contralesional side. It also indicated the significance of the relative firing rate in type I MVN cells which make excitatory connections with abducens cells as contributors to the variability seen in the level of compensated response following UVD. There was an absence of any difference (both in terms of behavioural and neural response) between labyrinthectomised and neurectomised simulations. The fact that a dynamic VOR gain asymmetry remained following the elimination of the spontaneous nystagmus in the network suggested that the amelioration of both the static and dynamic symptoms of UVD may be mediated by a single network. The networks were trained on high acceleration impulse stimuli but displayed the ability to generalise to low frequency, low acceleration sinusoids and closely approximated the behavioural responses to those stimuli.

Models, Biological↗
PubMed1999

Three-dimensional structures of c-Kit-positive cellular networks in the guinea pig small intestine and colon.

Cryosections and whole-mount preparations of the guinea pig small intestine and colon were single or double immunolabeled using the anti-c-Kit and protein gene product 9.5 antibodies. Immunolabeled specimens were observed under a confocal laser scanning microscope. The main findings of the present study are: (1) the distribution and profiles of three-dimensional structures of c-Kit-positive cellular networks in the small intestine and colon, and (2) the anatomical relations of c-Kit-positive cells to the enteric nerves in the layers. In the small intestine, c-Kit-positive cellular networks were observed at levels of the deep muscular plexus and myenteric plexus. The c-Kit-positive cellular networks ran along or overlay the nerve fibers at the deep muscular plexus, while they showed the reticular structures intermingled with the nerve elements at the myenteric plexus. In the colon, c-Kit-positive cellular networks were observed at levels of the submuscular plexus and myenteric plexus, and were further identified within the circular and longitudinal muscle layers as well as in the subserosal layer. In the circular muscle layer, c-Kit-positive cells surrounded the associated nerve fibers and extended several long processes toward the adjacent c-Kit-positive cells. The c-Kit-positive cellular networks within the longitudinal muscle layer as well as in the subserosal layer were not associated with the nerve fibers. In the layers of the intestinal wall with c-Kit-positive cells, the cellular networks of the interstitial cells were identified in ultrastructure. The characteristic profiles of c-Kit-positive cellular networks provide a morphological basis upon which to investigate the mechanisms regulating intestinal movement.

Animals↗
PubMed2005

Social networks and quality of life for long-term survivors of leukemia and lymphoma.

GOALS: This study examined the relationship between personal and medical characteristics and quality of life (QOL) for long-term survivors (LTS) of leukemia and lymphoma, and how social networks influence this relationship. PATIENTS AND METHODS: Fifty three LTS, at least 10 years postdiagnosis, were administered a standardized psychometric instrument, the Quality of Life--Cancer Survivors, to assess multidimensional aspects of QOL. Social network characteristics were measured by items assessing social support satisfaction, use of supportive care services, network size, and reliance on formal and informal social ties. MAIN RESULTS: A hierarchical regression model explained 52.4% of the variance in QOL for the final model, including all important predictors. Social support satisfaction (beta=0.393, p=0.001) and the use of supportive care services (beta=-0.262, p=0.047) significantly predicted QOL after controlling for confounding variables. Social network structures (including network size and reliance on formal and informal social ties) were indirectly associated with QOL through the use of supportive care services. CONCLUSIONS: The results indicate that the use of supportive care services, satisfaction with social support, network size, and reliance on formal and informal social ties affect QOL for long-term cancer survivors. Enhancing cancer survivors' social networks may ultimately improve their QOL.

Adult↗
PubMed2006

The role of social networks and support in postpartum women's depression: a multiethnic urban sample.

OBJECTIVES: This study examined the relationship of social support, and of social networks, to symptoms of depression in a multiethnic sample of women having recently given birth. METHODS: Women at community health centers in a Northeastern city were randomly sampled from groups stratified by race/ethnicity (African American, Hispanic, and White) and postpartum interval. Mother's score on the Center for Epidemiologic Studies of Depression Scale (CES-D) was the dependent variable. Main independent variables included the Medical Outcomes Study (MOS) Social Support Survey and a social network item. Univariate statistics assessed the relationship between CES-D score and each of the independent variables. Multivariate linear regression models included core sociodemographic variables alone, the core model with each of the social support and social network variables added separately, and all variables together. We evaluated interactions between race and social support, race and social networks, and social support and social networks. RESULTS: The multivariate models with MOS Social Support and core variables indicated that each 10-point increase in the MOS Social Support Survey was related to a 2.1-unit lower score on the CES-D (95% CI -2.4, -1.7). The inclusion of the social network variable into the core model showed that having two or more friends or family members available was associated with a 13.6-point lower mean score on the CES-D (95% CI -17.5, -9.6), compared to women reporting none or only one available person. CONCLUSIONS: Both social support and social networks were statistically significant and independently related to depressive symptomatology.

Adult↗
PubMed1976

The application of network analysis to the study of branching patterns of large dendritic fields.

Network analysis of dendritic fields not only defines the topology and connectivity of segments of an arborescence, but offers a means of discovering how networks grow. An important theory has recently been formulated29 suggesting that dendritic branching patterns may be established by synaptogenic interaction of dendritic growth cones with growing axons. This thesis may be verified through network analysis since the theory predicts that growth at pendant vertices will predominate in dendritic networks, that dendritic growth will be directed into areas of maximal synaptogenic activity and that arc lengths will be inversely related, and the order of branching at vertices directly related, to the magnitude of the synaptogenic activity operating about growing dendritic terminals. The possibility of a preponderance of terminal growth may be detected by comparing the topologies in an observed dendritic network with those of a series of hypothetical growth models. This paper provides the frequency table for models grown by monochotomous, dichotomous and trichotomous branching on random pendant vertices and random arcs for large networks in which 'set theory' contingencies are included. The paper also describes a method of calculating branching probabilities from the measurement of segment lengths, which is a means of testing the last mentioned prediction of the synaptogenic theory of denddritic growth. The method of network analysis is then discussed in relation to probable dendritic growth patterns, the constancy of segment lengths and the interaction of extrinsic and intrinsic factors in determining branching probabilities.

Dendrites↗