Engineered internal noise stochastic resonator in gene network: a model study

Based on a genetic bistable switch model coupled with a gene oscillator model, we have constructed a mesoscopic stochastic model for the coupled synthetic gene network, and studied how internal noise would influence the oscillation of such a system. We found that the state-to-state transitions can occur if the internal noise is taken into account, and the performance of resulting oscillation can reach a maximum in a certain internal noise level, which indicates the occurrence of internal noise stochastic resonance (SR) and makes the coupled gene network work as a stochastic resonator. The potential role of such an effect on gene expression systems is also discussed.     

A self-organising neural network model of image velocity encoding

A self-organising neural network has been developed which maps the image velocities of rigid objects, moving in the fronto-parallel plane, topologically over a neural layer. The input is information in the Fourier domain about the spatial components of the image. The computation performed by the network may be viewed as a neural instantiation of the Intersection of Constraints solution to the aperture problem. The model has biological plausibility in that the connectivity develops simply as a result of exposure to inputs derived from rigid translation of textures and its overall organisation is consistent with psychophysical evidence.     

Estimating three synaptic conductances in a stochastic neural model

We present a method for the reconstruction of three stimulus-evoked time-varying synaptic input conductances from voltage recordings. Our approach is based on exploiting the stochastic nature of synaptic conductances and membrane voltage. Starting with the assumption that the variances of the conductances are known, we use a stochastic differential equation to model dynamics of membrane potential and derive equations for first and second moments that can be solved to find conductances. We successfully apply the new reconstruction method to simulated data. We also explore the robustness of the method as the assumptions of the underlying model are relaxed. We vary the noise levels, the reversal potentials, the number of stimulus repetitions, and the accuracy of conductance variance estimation to quantify the robustness of reconstruction. These studies pave the way for the application of the method to experimental data.     

Effects of demographic parameters on metapopulation size and persistence: an analytical stochastic model

An analytical stochastic metapopulation model is developed. It describes how individuals will be distributed among patches as a function of density-dependent birth, death and emigration rates, and the probability of successful dispersal. The model includes demographic stochasticity, but not catastrophes, environmental stochasticity or variation in patch size and suitability. All patches are equally likely to be colonized by migrants. The model predicts: (a) mean and variance of the number of individuals per patch; (b) probability distribution of individuals per patch; (c) mean number of individuals in transit; and (d) turn-over rate and expected persistence time of a single patch. The model shows that (a) dispersal rates must be intermediate in order to ensure metapopulation persistence; (b) the mean number of individuals per patch is often well below the carrying capacity; (c) long transit times and/or high mortality during dispersal reduce the mean number of individuals per patch; (d) density-dependent emigration responses will usually increase metapopulation size and persistence compared with density-independent dispersal; (e) an increase in the per capita net growth rate can both increase and decrease metapopulation size and persistence depending on whether dispersal rates are high or low; (f) density-independent birth, death, and emigration rates lead to a spatial pattern described by the negative binomial distribution.     

Principles of evolutionary learning design for a stochastic neural network

The authors develop principles for evolutionary learning typical of biological systems and demonstrate how these principles can be realized with a formal stochastic network.     

Synaptic transmission in a model for stochastic neural activity.

A stochastic model equation for nerve membrane depolarization is derived which incorporates properties of synaptic transmission with a Rail-Eccles circuit for a trigger zone. If input processes are Poisson the depolarization is a Markov process for which equations for the moments of the interspike interval can be written down. An analytic result for the mean interval is obtained in a special case. The effect of the excitatory reversal potential is considerable if it is not too far from threshold and if the interspike interval is long. Computer simulations were performed when inhibitory and excitatory inputs are active. A substantial amount of inhibition leads to an exceedingly long tail in the density of the interspike time. With excitation only the interspike interval is often an approximately lognormal random variable. A coefficient of variation greater than one is often a consequence of relatively strong inhibition. Inferences can be made on the nature of the synaptic input from the statistics and density of the time between spikes. The inhibitory reversal potential usually has a relatively small effect except when the frequency of inhibition is large. An appendix contains the model equations in the case of an arbitrary distribution of postsynaptic potential amplitudes.     

Bifurcation analysis of a neural network model

This paper describes the analysis of the well known neural network model by Wilson and Cowan. The neural network is modeled by a system of two ordinary differential equations that describe the evolution of average activities of excitatory and inhibitory populations of neurons. We analyze the dependence of the model's behavior on two parameters. The parameter plane is partitioned into regions of equivalent behavior bounded by bifurcation curves, and the representative phase diagram is constructed for each region. This allows us to describe qualitatively the behavior of the model in each region and to predict changes in the model dynamics as parameters are varied. In particular, we show that for some parameter values the system can exhibit long-period oscillations. A new type of dynamical behavior is also found when the system settles down either to a stationary state or to a limit cycle depending on the initial point.     

Multisensory integration in the superior colliculus: a neural network model

Neurons in the superior colliculus (SC) are known to integrate stimuli of different modalities (e.g., visual and auditory) following specific properties. In this work, we present a mathematical model of the integrative response of SC neurons, in order to suggest a possible physiological mechanism underlying multisensory integration in SC. The model includes three distinct neural areas: two unimodal areas (auditory and visual) are devoted to a topological representation of external stimuli, and communicate via synaptic connections with a third downstream area (in the SC) responsible for multisensory integration. The present simulations show that the model, with a single set of parameters, can mimic various responses to different combinations of external stimuli including the inverse effectiveness, both in terms of multisensory enhancement and contrast, the existence of within- and cross-modality suppression between spatially disparate stimuli, a reduction of network settling time in response to cross-modal stimuli compared with individual stimuli. The model suggests that non-linearities in neural responses and synaptic (excitatory and inhibitory) connections can explain several aspects of multisensory integration.     

Recognition of partly occluded patterns: a neural network model

 Human beings are often able to read a letter or word partly occluded by contaminating ink stains. However, if the stains are completely erased and the occluded areas of the letter are changed to white, we usually have difficulty in reading the letter. In this article I propose a hypothesis explaining why a pattern is easier to recognize when it is occluded by visible objects than by invisible opaque objects. A neural network model is constructed based on this hypothesis. The visual system extracts various visual features from the input pattern and then attempts to recognize it. If the occluding objects are not visible, the visual system will have difficulty in distinguishing which features are relevant to the original pattern and which are newly generated by the occlusion. If the occluding objects are visible, however, the visual system can easily discriminate between relevant and irrelevant features and recognize the occluded pattern correctly. The proposed model is an extended version of the neocognitron model. The activity of the feature-extracting cells whose receptive fields cover the occluding objects is suppressed in an early stage of the hierarchical network. Since the irrelevant features generated by the occlusion are thus eliminated, the model can recognize occluded patterns correctly, provided the occlusion is not so large as to prevent recognition even by human beings. Received: 21 February 2000 / Accepted in revised form: 11 September 2000     

Purposive behavior and cognitive mapping: a neural network model

This study presents a real-time, biologically plausible neural network approach to purposive behavior and cognitive mapping. The system is composed of (a) an action system, consisting of a goal-seeking neural mechanism controlled by a motivational system; and (b) a cognitive system, involving a neural cognitive map. The goal-seeking mechanism displays exploratory behavior until either (a) the goal is found or (b) an adequate prediction of the goal is generated. The cognitive map built by the network is a top logical map, i.e., it represents only the adjacency, but not distances or directions, between places. The network has recurrent and non-recurrent properties that allow the reading of the cognitive map without modifying it. Two types of predictions are introduced: fast-time and real-time predictions. Fast-time predictions are produced in advance of what occurs in real time, when the information stored in the cognitive map is used to predict the remote future. Real-time predictions are generated simultaneously with the occurrence of environmental events, when the information stored in the cognitive map is being updated. Computer simulations show that the network successfully describes latent learning and detour behavior in rats. In addition, simulations demonstrate that the network can be applied to problem-solving paradigms such as the Tower of Hanoi puzzle.     

Timing in the absence of clocks: encoding time in neural network states

Decisions based on the timing of sensory events are fundamental to sensory processing. However, the mechanisms by which the brain measures time over ranges of milliseconds to seconds remain unclear. The dominant model of temporal processing proposes that an oscillator emits events that are integrated to provide a linear metric of time. We examine an alternate model in which cortical networks are inherently able to tell time as a result of time-dependent changes in network state. Using computer simulations we show that within this framework, there is no linear metric of time, and that a given interval is encoded in the context of preceding events. Human psychophysical studies were used to examine the predictions of the model. Our results provide theoretical and experimental evidence that, for short intervals, there is no linear metric of time, and that time may be encoded in the high-dimensional state of local neural networks.     

Structural study of the development of ocularity domains using a neural network model

We present a model for the development of ocularity domains in the visual cortex of mammals during the embryonic stage. We model the thalamo-cortical pathway with a self-organising neural network with two source layers, each of them serving different retinae, and one target layer, where the connections end. The connectivity between the source layers and the target layer is driven by Hebbian learning. In both the source layers and the target layer we assume excitatory lateral signal diffusion between proximal neurons that causes them to be correlated. According to the developmental state being modelled, we do not consider either correlation or anti-correlation between the signals originated in neurons of different retinae. The basic assumptions made are proved to be sufficient to attain a distribution of connections arranged in ocularity domains. The dependence of the geometry of the ocularity domains on the parameters of the model is analysed and a correlation between the width of the signal diffusion and the extent of the domains is found. The generality of the assumptions made allows an easy translation of the model to explain the development of other elements of the sensory nervous system.     

Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis

Journal of Mathematical Biology - We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and...     

Distribution of births in an abrupt sequence: a stochastic model

A probability model for the distribution of number of births in a time segment (T0, T0 + T), where T0 is a distant time point since the start of the process, has been derived. The provision that birth propensities in the process of human reproduction may change over time has been considered. The model is illustrated with a set of observed data.     

Transitory memory retrieval in a biologically plausible neural network model

A number of memory models have been proposed. These all have the basic structure that excitatory neurons are reciprocally connected by recurrent connections together with the connections with inhibitory neurons, which yields associative memory (i.e., pattern completion) and successive retrieval of memory. In most of the models, a simple mathematical model for a neuron in the form of a discrete map is adopted. It has not, however, been clarified whether behaviors like associative memory and successive retrieval of memory appear when a biologically plausible neuron model is used. In this paper, we propose a network model for associative memory and successive retrieval of memory based on Pinsky-Rinzel neurons. The state of pattern completion in associative memory can be observed with an appropriate balance of excitatory and inhibitory connection strengths. Increasing of the connection strength of inhibitory interneurons changes the state of memory retrieval from associative memory to successive retrieval of memory. We investigate this transition.     

Applying a neural network to predict the thermodynamic parameters for an expanded nearest-neighbor model

Predicting the secondary and tertiary structure of RNAs largely depends on our capabilities in estimating the thermodynamics of RNA duplexes. In this work, an expanded nearest-neighbor model, designated INN-48, is established. The thermodynamic parameters of this model are predicted using both multiple linear regression analysis and neural network analysis. It is suggested that due to the increase in the number of parameters and the insufficiency of the existing data, neural network analysis results in more reliable predictions. Furthermore, it is suggested that INN-48 can be used to estimate the thermodynamics of RNA duplex formation for longer sequences, whereas INN-HB, the previous model on which INN-48 is based, can be used for short sequences.     

Computational antisense oligo prediction with a neural network model

MOTIVATION: The expression of a gene can be selectively inhibited by antisense oligonucleotides (AOs) targeting the mRNA. However, if the target site in the mRNA is picked randomly, typically 20% or less of the AOs are effective inhibitors in vivo. The sequence properties that make an AO effective are not well understood, thus many AOs need to be tested to find good inhibitors, which is time consuming and costly. So far computational models have been based exclusively on RNA structure prediction or motif searches while ignoring information from other aspects of AO design into the model. RESULTS: We present a computational model for AO prediction based on a neural network approach using a broad range of input parameters. Collecting sequence and efficacy data from AO scanning experiments in the literature generated a database of 490 AO molecules. Using a set of derived parameters based on AO sequence properties we trained a neural network model. The best model, an ensemble of 10 networks, gave an overall correlation coefficient of 0.30 (p=10(-8)). This model can predict effective AOs (>50% inhibition of gene expression) with a success rate of 92%. Using these thresholds the model predicts on average 12 effective AOs per 1000 base pairs, making it a stringent yet practical method for AO prediction.