A discrete time neural network model with spiking neurons: II: Dynamics with noise

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.     

Coincidence detection of place and temporal context in a network model of spiking hippocampal neurons

Recent advances in single-neuron biophysics have enhanced our understanding of information processing on the cellular level, but how the detailed properties of individual neurons give rise to large-scale behavior remains unclear. Here, we present a model of the hippocampal network based on observed biophysical properties of hippocampal and entorhinal cortical neurons. We assembled our model to simulate spatial alternation, a task that requires memory of the previous path through the environment for correct selection of the current path to a reward site. The convergence of inputs from entorhinal cortex and hippocampal region CA3 onto CA1 pyramidal cells make them potentially important for integrating information about place and temporal context on the network level. Our model shows how place and temporal context information might be combined in CA1 pyramidal neurons to give rise to splitter cells, which fire selectively based on a combination of place and temporal context. The model leads to a number of experimentally testable predictions that may lead to a better understanding of the biophysical basis of information processing in the hippocampus.     

Evolution of robustness to noise and mutation in gene expression dynamics

Phenotype of biological systems needs to be robust against mutation in order to sustain themselves between generations. On the other hand, phenotype of an individual also needs to be robust against fluctuations of both internal and external origins that are encountered during growth and development. Is there a relationship between these two types of robustness, one during a single generation and the other during evolution? Could stochasticity in gene expression have any relevance to the evolution of these types of robustness? Robustness can be defined by the sharpness of the distribution of phenotype; the variance of phenotype distribution due to genetic variation gives a measure of 'genetic robustness', while that of isogenic individuals gives a measure of 'developmental robustness'. Through simulations of a simple stochastic gene expression network that undergoes mutation and selection, we show that in order for the network to acquire both types of robustness, the phenotypic variance induced by mutations must be smaller than that observed in an isogenic population. As the latter originates from noise in gene expression, this signifies that the genetic robustness evolves only when the noise strength in gene expression is larger than some threshold. In such a case, the two variances decrease throughout the evolutionary time course, indicating increase in robustness. The results reveal how noise that cells encounter during growth and development shapes networks' robustness to stochasticity in gene expression, which in turn shapes networks' robustness to mutation. The necessary condition for evolution of robustness, as well as the relationship between genetic and developmental robustness, is derived quantitatively through the variance of phenotypic fluctuations, which are directly measurable experimentally.     

Adaptive aging in the context of evolutionary theory

Compelling evidence for an adaptive origin of aging has clashed with traditional evolutionary theory based on exclusively individual selection. The consensus view has been to try to understand aging in the context of a narrow, restrictive evolutionary paradigm, called the Modern Synthesis, or neo-Darwinism. But neo-Darwinism has shown itself to be inadequate in other ways, failing to account for stable ecosystems, for the evolution of sex and the maintenance of diversity and the architecture of the genome, which appears to be optimized for evolvability. Thus aging is not the only reason to consider overhauling the standard theoretical framework. Selection for stable ecosystems is rapid and efficient, and so it is the easiest modification of the neo-Darwinian paradigm to understand and to model. Aging may be understood in this context. More profound and more mysterious are the ways in which the process of evolution itself has been transformed in a bootstrapping process of selection for evolvability. Evolving organisms have learned to channel their variation in ways that are likely to enhance their long-term prospects. This is an expanded notion of fitness. Only in this context can the full spectrum of sophisticated adaptations be understood, including aging, sex, diversity, ecological interdependence, and the structure of the genome.     

Metabolic robustness and network modularity: a model study

Background

Several studies have mentioned network modularity—that a network can easily be decomposed into subgraphs that are densely connected within and weakly connected between each other—as a factor affecting metabolic robustness. In this paper we measure the relation between network modularity and several aspects of robustness directly in a model system of metabolism.

Methodology/Principal Findings

By using a model for generating chemical reaction systems where one can tune the network modularity, we find that robustness increases with modularity for changes in the concentrations of metabolites, whereas it decreases with changes in the expression of enzymes. The same modularity scaling is true for the speed of relaxation after the perturbations.

Conclusions/Significance

Modularity is not a general principle for making metabolism either more or less robust; this question needs to be addressed specifically for different types of perturbations of the system.     

Adaptive neural encoder model with selfinhibition and threshold control

A general model for an adaptive neural encoder relating the output firing frequency to input stimulus is presented. The model is based on an integrate and fire at threshold scheme and includes cumulative inhibitory feedback as well as output rate dependent threshold control.     

Adaptive processing in electrosensory systems: Links to cerebellar plasticity and learning

The first central stage of electrosensory processing in fish takes place in structures with local circuitry that resembles the cerebellum. Cerebellum-like structures and the cerebellum itself share common patterns of gene expression and may also share developmental and evolutionary origins. Given these similarities it is natural to ask whether insights gleaned from the study of cerebellum-like structures might be useful for understanding aspects of cerebellar function and vice versa. Work from electrosensory systems has shown that cerebellum-like circuitry acts to generate learned predictions about the sensory consequences of the animals’ own behavior through a process of associative plasticity at parallel fiber synapses. Subtraction of these predictions from the actual sensory input serves to highlight unexpected and hence behaviorally relevant features. Learning and prediction are also central to many current ideas regarding the function of the cerebellum itself. The present review draws comparisons between cerebellum-like structures and the cerebellum focusing on the properties and sites of synaptic plasticity in these structures and on connections between plasticity and learning. Examples are drawn mainly from the electrosensory lobe (ELL) of mormyrid fish and from extensive work characterizing the role of the cerebellum in Pavlovian eyelid conditioning and vestibulo-ocular reflex (VOR) modification. Parallels with other cerebellum-like structures, including the gymnotid ELL, the elasmobranch dorsal octavolateral nucleus (DON), and the mammalian dorsal cochlear nucleus (DCN) are also discussed.     

Brain switching: studying evolutionary behavioral changes in the context of individual brain development

Working together at Nogent, Marie-Aimee Teillet, Nicole Le Douarin and the author successfully developed an extension of the quail-chick transplant technique for relating species brain cell differences to behavioral differences. This article reviews the application of the technique to species differences in motor behavior (crowing) and auditory perceptual preferences. Interspecies brain transplants provide a unique means for elucidating general cellular mechanisms which integrate evolutionary and individual experience during the development of complex brain circuitry.     

Closed loop control of human body temperature: results from a one-dimensional model

A one-dimensional model of human thermoregulation is used to solve a variety of basic problems in determining an adequate structure of the controller for metabolic heat production, skin blood flow and sweat production. Assuming one integrated central and one integrated peripheral afferent signal the controller parameters are evaluated by analysis of the control performance. Based on a validation by experimental results this allows the determination of a first optimized set of values for controller gains and weight of skin temperature feedback. Furthermove we analyse the effect of inhomogeneous distribution of heat production and blood flow, the influence of body fat content, of controller gains, of weight of skin temperature feedback and of depth of peripheral receptors on the dynamic performance. Increase of peripheral blood flow in particular evokes essentially both an increase of energy requirement in the cold and a quicker system response. Differing rates of increase of metabolic heat production are the consequence of differing body fat content. The weight of skin temperature feedback can be limited to 5...20%, because values outside this range evoke dynamic responses incompatible with the experiments. The actual value can only be determined if there is a correct assumption for the depth of the skin receptors. The use of measured superficial skin temperatures brings about an underestimation of the peripheral afferent signal. Of the controller gains it is primarily the gain of the metabolic controller which affects the dynamic response of the system. The experimental fact of a delayed onset of sweat production after a transition from cold to heat is the consequence of a high gain of the vasomotor system.     

Proportionality between variances in gene expression induced by noise and mutation: consequence of evolutionary robustness

Background  

Characterization of robustness and plasticity of phenotypes is a basic issue in evolutionary and developmental biology. The robustness and plasticity are concerned with changeability of a biological system against external perturbations. The perturbations are either genetic, i.e., due to mutations in genes in the population, or epigenetic, i.e., due to noise during development or environmental variations. Thus, the variances of phenotypes due to genetic and epigenetic perturbations provide quantitative measures for such changeability during evolution and development, respectively.     

A computational model of visual marking using an inter-connected network of spiking neurons: the spiking search over time & space model (sSoTS).

In the real world, visual information is selected over time as well as space, when we prioritise new stimuli for attention. Watson and Humphreys [Watson, D., Humphreys, G.W., 1997. Visual marking: prioritizing selection for new objects by top-down attentional inhibition of old objects. Psychological Review 104, 90-122] presented evidence that new information in search tasks is prioritised by (amongst other processes) active ignoring of old items - a process they termed visual marking. In this paper we present, for the first time, an explicit computational model of visual marking using biologically plausible activation functions. The "spiking search over time and space" model (sSoTS) incorporates different synaptic components (NMDA, AMPA, GABA) and a frequency adaptation mechanism based on [Ca(2+)] sensitive K(+) current. This frequency adaptation current can act as a mechanism that suppresses the previously attended items. We show that, when coupled with a process of active inhibition applied to old items, frequency adaptation leads to old items being de-prioritised (and new items prioritised) across time in search. Furthermore, the time course of these processes mimics the time course of the preview effect in human search. The results indicate that the sSoTS model can provide a biologically plausible account of human search over time as well as space.     

The role of spiking and bursting pacemakers in the neuronal control of breathing

Breathing is controlled by a distributed network involving areas in the neocortex, cerebellum, pons, medulla, spinal cord, and various other subcortical regions. However, only one area seems to be essential and sufficient for generating the respiratory rhythm: the preBötzinger complex (preBötC). Lesioning this area abolishes breathing and following isolation in a brain slice the preBötC continues to generate different forms of respiratory activities. The use of slice preparations led to a thorough understanding of the cellular mechanisms that underlie the generation of inspiratory activity within this network. Two types of inward currents, the persistent sodium current (I_NaP) and the calcium-activated non-specific cation current (I_CAN), play important roles in respiratory rhythm generation. These currents give rise to autonomous pacemaker activity within respiratory neurons, leading to the generation of intrinsic spiking and bursting activity. These membrane properties amplify as well as activate synaptic mechanisms that are critical for the initiation and maintenance of inspiratory activity. In this review, we describe the dynamic interplay between synaptic and intrinsic membrane properties in the generation of the respiratory rhythm and we relate these mechanisms to rhythm generating networks involved in other behaviors.     

Feedback loop between kinship and dominance: the macaque model

There is growing evidence that macaque social systems represent sets of coadapted traits in which strength of hierarchies and degree of nepotism covary. A framework is developed to explain the link between dominance and kinship phenomena, assuming that power brought by alliances among non-kin is allometrically related to those involving relatives. This can account for the type of social relationships observed in "despotic" systems vs. "egalitarian" ones. When social bonds are mostly founded on kinship, lineages are closed and social power generated by coalitions among relatives may reach high levels; social power frequently outweighs the fighting abilities of single individuals, and asymmetry of dominance between group members may be marked. When lineages are more open, social bonds and alliances are less kin-biased, social relationships are more equal, and as the influence of coalitions is less important, the individual retains a certain degree of freedom in relation to the power of kin-networks. Acknowledging that the balance between individual and social power is not set at the same level across different species can explain a number of variations in rules of rank inheritance and relative dominance of males and females among macaques. The framework illustrates how epigenetic processes may shape complex features of primate social systems, and offers opportunities for testing.     

Intercellular coupling confers robustness against mutations in the SCN circadian clock network

Molecular mechanisms of the mammalian circadian clock have been studied primarily by genetic perturbation and behavioral analysis. Here, we used bioluminescence imaging to monitor Per2 gene expression in tissues and cells from clock mutant mice. We discovered that Per1 and Cry1 are required for sustained rhythms in peripheral tissues and cells, and in neurons dissociated from the suprachiasmatic nuclei (SCN). Per2 is also required for sustained rhythms, whereas Cry2 and Per3 deficiencies cause only period length defects. However, oscillator network interactions in the SCN can compensate for Per1 or Cry1 deficiency, preserving sustained rhythmicity in mutant SCN slices and behavior. Thus, behavior does not necessarily reflect cell-autonomous clock phenotypes. Our studies reveal previously unappreciated requirements for Per1, Per2, and Cry1 in sustaining cellular circadian rhythmicity and demonstrate that SCN intercellular coupling is essential not only to synchronize component cellular oscillators but also for robustness against genetic perturbations.     

Death wins against life in a spatially extended model of the caspase-3/8 feedback loop

Apoptosis is an important physiological process which enables organisms to remove unwanted or damaged cells. A mathematical model of the extrinsic pro-apoptotic signaling pathway has been introduced by Eissing et al. (2007) and a bistable behavior with a stable death state and a stable life state of the reaction system has been established. In this paper, we consider a spatial extension of the extrinsic pro-apoptotic signaling pathway incorporating diffusion terms and make a model-based, numerical analysis of the apoptotic switch in the spatial dimension. For the parameter regimes under consideration it turns out that for this model diffusion homogenizes rapidly the concentrations which afterward are governed by the original reaction system. The activation of effector-caspase 3 depends on the space averaged initial concentration of pro-caspase 8 and pro-caspase 3 at the beginning of the process.