Chaotic neural network applied to two-dimensional motion control

Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.     

Neural network mechanisms underlying stimulus driven variability reduction

It is well established that the variability of the neural activity across trials, as measured by the Fano factor, is elevated. This fact poses limits on information encoding by the neural activity. However, a series of recent neurophysiological experiments have changed this traditional view. Single cell recordings across a variety of species, brain areas, brain states and stimulus conditions demonstrate a remarkable reduction of the neural variability when an external stimulation is applied and when attention is allocated towards a stimulus within a neuron's receptive field, suggesting an enhancement of information encoding. Using an heterogeneously connected neural network model whose dynamics exhibits multiple attractors, we demonstrate here how this variability reduction can arise from a network effect. In the spontaneous state, we show that the high degree of neural variability is mainly due to fluctuation-driven excursions from attractor to attractor. This occurs when, in the parameter space, the network working point is around the bifurcation allowing multistable attractors. The application of an external excitatory drive by stimulation or attention stabilizes one specific attractor, eliminating in this way the transitions between the different attractors and resulting in a net decrease in neural variability over trials. Importantly, non-responsive neurons also exhibit a reduction of variability. Finally, this reduced variability is found to arise from an increased regularity of the neural spike trains. In conclusion, these results suggest that the variability reduction under stimulation and attention is a property of neural circuits.     

Analysis of Discrete Bioregulatory Networks Using Symbolic Steady States

A discrete model of a biological regulatory network can be represented by a discrete function that contains all available information on interactions between network components and the rules governing the evolution of the network in a finite state space. Since the state space size grows exponentially with the number of network components, analysis of large networks is a complex problem. In this paper, we introduce the notion of symbolic steady state that allows us to identify subnetworks that govern the dynamics of the original network in some region of state space. We state rules to explicitly construct attractors of the system from subnetwork attractors. Using the results, we formulate sufficient conditions for the existence of multiple attractors resp. a cyclic attractor based on the existence of positive resp. negative feedback circuits in the graph representing the structure of the system. In addition, we discuss approaches to finding symbolic steady states. We focus both on dynamics derived via synchronous as well as asynchronous update rules. Lastly, we illustrate the results by analyzing a model of T helper cell differentiation.     

Representational switching by dynamical reorganization of attractor structure in a network model of the prefrontal cortex

The prefrontal cortex (PFC) plays a crucial role in flexible cognitive behavior by representing task relevant information with its working memory. The working memory with sustained neural activity is described as a neural dynamical system composed of multiple attractors, each attractor of which corresponds to an active state of a cell assembly, representing a fragment of information. Recent studies have revealed that the PFC not only represents multiple sets of information but also switches multiple representations and transforms a set of information to another set depending on a given task context. This representational switching between different sets of information is possibly generated endogenously by flexible network dynamics but details of underlying mechanisms are unclear. Here we propose a dynamically reorganizable attractor network model based on certain internal changes in synaptic connectivity, or short-term plasticity. We construct a network model based on a spiking neuron model with dynamical synapses, which can qualitatively reproduce experimentally demonstrated representational switching in the PFC when a monkey was performing a goal-oriented action-planning task. The model holds multiple sets of information that are required for action planning before and after representational switching by reconfiguration of functional cell assemblies. Furthermore, we analyzed population dynamics of this model with a mean field model and show that the changes in cell assemblies' configuration correspond to those in attractor structure that can be viewed as a bifurcation process of the dynamical system. This dynamical reorganization of a neural network could be a key to uncovering the mechanism of flexible information processing in the PFC.     

Learning shapes spontaneous activity itinerating over memorized states

Learning is a process that helps create neural dynamical systems so that an appropriate output pattern is generated for a given input. Often, such a memory is considered to be included in one of the attractors in neural dynamical systems, depending on the initial neural state specified by an input. Neither neural activities observed in the absence of inputs nor changes caused in the neural activity when an input is provided were studied extensively in the past. However, recent experimental studies have reported existence of structured spontaneous neural activity and its changes when an input is provided. With this background, we propose that memory recall occurs when the spontaneous neural activity changes to an appropriate output activity upon the application of an input, and this phenomenon is known as bifurcation in the dynamical systems theory. We introduce a reinforcement-learning-based layered neural network model with two synaptic time scales; in this network, I/O relations are successively memorized when the difference between the time scales is appropriate. After the learning process is complete, the neural dynamics are shaped so that it changes appropriately with each input. As the number of memorized patterns is increased, the generated spontaneous neural activity after learning shows itineration over the previously learned output patterns. This theoretical finding also shows remarkable agreement with recent experimental reports, where spontaneous neural activity in the visual cortex without stimuli itinerate over evoked patterns by previously applied signals. Our results suggest that itinerant spontaneous activity can be a natural outcome of successive learning of several patterns, and it facilitates bifurcation of the network when an input is provided.     

An Efficient Algorithm for Computing Attractors of Synchronous And Asynchronous Boolean Networks

Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD), we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly faster in computing attractors for empirical experimental systems.

Availability

The software package is available at https://sites.google.com/site/desheng619/download.     

The Problem of Colliding Networks and its Relation to Cell Fusion and?Cancer

Cell fusion, a process that merges two or more cells into one, is required for normal development and has been explored as a tool for stem cell therapy. It has also been proposed that cell fusion causes cancer and contributes to its progression. These functions rely on a poorly understood ability of cell fusion to create new cell types. We suggest that this ability can be understood by considering cells as attractor networks whose basic property is to adopt a set of distinct, stable, self-maintaining states called attractors. According to this view, fusion of two cell types is a collision of two networks that have adopted distinct attractors. To learn how these networks reach a consensus, we model cell fusion computationally. To do so, we simulate patterns of gene activities using a formalism developed to simulate patterns of memory in neural networks. We find that the hybrid networks can assume attractors that are unrelated to parental attractors, implying that cell fusion can create new cell types by nearly instantaneously moving cells between attractors. We also show that hybrid networks are prone to assume spurious attractors, which are emergent and sporadic network states. This finding means that cell fusion can produce abnormal cell types, including cancerous types, by placing cells into normally inaccessible spurious states. Finally, we suggest that the problem of colliding networks has general significance in many processes represented by attractor networks, including biological, social, and political phenomena.     

Dynamics of excitable neural networks with heterogeneous connectivity

A central issue of neuroscience is to understand how neural units integrates internal and external signals to create coherent states. Recently, it has been shown that the sensitivity and dynamic range of neural assemblies are optimal at a critical coupling among its elements. Complex architectures of connections seem to play a constructive role on the reliable coordination of neural units. Here we show that, the synchronizability and sensitivity of excitable neural networks can be tuned by diversity in the connections strengths. We illustrate our findings for weighted networks with regular, random and complex topologies. Additional comparisons of real brain networks support previous studies suggesting that heterogeneity in the connectivity may play a constructive role on information processing. These findings provide insights into the relationship between structure and function of neural circuits.     

Embedding Responses in Spontaneous Neural Activity Shaped through Sequential Learning

Recent experimental measurements have demonstrated that spontaneous neural activity in the absence of explicit external stimuli has remarkable spatiotemporal structure. This spontaneous activity has also been shown to play a key role in the response to external stimuli. To better understand this role, we proposed a viewpoint, “memories-as-bifurcations,” that differs from the traditional “memories-as-attractors” viewpoint. Memory recall from the memories-as-bifurcations viewpoint occurs when the spontaneous neural activity is changed to an appropriate output activity upon application of an input, known as a bifurcation in dynamical systems theory, wherein the input modifies the flow structure of the neural dynamics. Learning, then, is a process that helps create neural dynamical systems such that a target output pattern is generated as an attractor upon a given input. Based on this novel viewpoint, we introduce in this paper an associative memory model with a sequential learning process. Using a simple Hebbian-type learning, the model is able to memorize a large number of input/output mappings. The neural dynamics shaped through the learning exhibit different bifurcations to make the requested targets stable upon an increase in the input, and the neural activity in the absence of input shows chaotic dynamics with occasional approaches to the memorized target patterns. These results suggest that these dynamics facilitate the bifurcations to each target attractor upon application of the corresponding input, which thus increases the capacity for learning. This theoretical finding about the behavior of the spontaneous neural activity is consistent with recent experimental observations in which the neural activity without stimuli wanders among patterns evoked by previously applied signals. In addition, the neural networks shaped by learning properly reflect the correlations of input and target-output patterns in a similar manner to those designed in our previous study.     

Language models based on Hebbian cell assemblies.

This paper demonstrates how associative neural networks as standard models for Hebbian cell assemblies can be extended to implement language processes in large-scale brain simulations. To this end the classical auto- and hetero-associative paradigms of attractor nets and synfire chains (SFCs) are combined and complemented by conditioned associations as a third principle which allows for the implementation of complex graph-like transition structures between assemblies. We show example simulations of a multiple area network for object-naming, which categorises objects in a visual hierarchy and generates different specific syntactic motor sequences ("words") in response. The formation of cell assemblies due to ongoing plasticity in a multiple area network for word learning is studied afterwards. Simulations show how assemblies can form by means of percolating activity across auditory and motor-related language areas, a process supported by rhythmic, synchronized propagating waves through the network. Simulations further reproduce differences in own EEG&MEG experiments between responses to word- versus non-word stimuli in human subjects.     

Stability switches,oscillatory multistability,and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks

A model of time-delay recurrently coupled spatially segregated neural assemblies is here proposed. We show that it operates like some of the hierarchical architectures of the brain. Each assembly is a neural network with no delay in the local couplings between the units. The delay appears in the long range feedforward and feedback inter-assemblies communications. Bifurcation analysis of a simple four-units system in the autonomous case shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multistability, hysteresis, and stability switches of the rest state provoked by the time delay. Then we investigate the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric local Hopf bifurcation theory of delay differential equations and derive the equation describing the flow on the center manifold that enables us determining the direction of Hopf bifurcations and stability of the bifurcating periodic orbits. We also discuss computational properties of the system due to the delay when an external drive of the network mimicks external sensory input.     

Floral morphogenesis: stochastic explorations of a gene network epigenetic landscape

In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical temporal pattern in gene expression during flower development. We modeled the regulatory network of organ identity genes in the Arabidopsis thaliana flower as a stochastic system. This network has previously been shown to converge to ten fixed-point attractors, each with gene expression arrays that characterize inflorescence cells and primordial cells of sepals, petals, stamens, and carpels. The network used is binary, and the logical rules that govern its dynamics are grounded in experimental evidence. We introduced different levels of uncertainty in the updating rules of the network. Interestingly, for a level of noise of around 0.5-10%, the system exhibited a sequence of transitions among attractors that mimics the sequence of gene activation configurations observed in real flowers. We also implemented the gene regulatory network as a continuous system using the Glass model of differential equations, that can be considered as a first approximation of kinetic-reaction equations, but which are not necessarily equivalent to the Boolean model. Interestingly, the Glass dynamics recover a temporal sequence of attractors, that is qualitatively similar, although not identical, to that obtained using the Boolean model. Thus, time ordering in the emergence of cell-fate patterns is not an artifact of synchronous updating in the Boolean model. Therefore, our model provides a novel explanation for the emergence and robustness of the ubiquitous temporal pattern of floral organ specification. It also constitutes a new approach to understanding morphogenesis, providing predictions on the population dynamics of cells with different genetic configurations during development.     

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 (100ms). 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.     

A comparison of two cell regulatory models entailing high dimensional attractors representing phenotype

Two models for mammalian cell regulation that invoke the concept of cellular phenotype represented by high dimensional dynamic attractor states are compared. In one model the attractors are derived from an experimentally determined genetic regulatory network (GRN) for the cell type. As the state space architecture within which the attractors are embedded is determined by the binding sites on proteins and the recognition sites on DNA the attractors can be described as “hard-wired” in the genome through the genomic DNA sequence. In the second model attractors arising from the interactions between active gene products (mainly proteins) and independent of the genomic sequence, are descended from a pre-cellular state from which life originated. As this model is based on the cell as an open system the attractor acts as the interface between the cell and its environment. Environmental sources of stress can serve to trigger attractor and therefore phenotypic, transitions without entailing genotypic sequence changes.It is asserted that the evidence from cell and molecular biological research and logic, favours the second model. If correct there are important implications for understanding how environmental factors impact on evolution and may be implicated in hereditary and somatic disease.     

The Potential Landscape of Genetic Circuits Imposes the Arrow of Time in Stem Cell Differentiation

Differentiation from a multipotent stem or progenitor state to a mature cell is an essentially irreversible process. The associated changes in gene expression patterns exhibit time-directionality. This “arrow of time” in the collective change of gene expression across multiple stable gene expression patterns (attractors) is not explained by the regulated activation, the suppression of individual genes which are bidirectional molecular processes, or by the standard dynamical models of the underlying gene circuit which only account for local stability of attractors. To capture the global dynamics of this nonequilibrium system and gain insight in the time-asymmetry of state transitions, we computed the quasipotential landscape of the stochastic dynamics of a canonical gene circuit that governs branching cell fate commitment. The potential landscape reveals the global dynamics and permits the calculation of potential barriers between cell phenotypes imposed by the circuit architecture. The generic asymmetry of barrier heights indicates that the transition from the uncommitted multipotent state to differentiated states is inherently unidirectional. The model agrees with observations and predicts the extreme conditions for reprogramming cells back to the undifferentiated state.     

Embryonic stem cells assume a primitive neural stem cell fate in the absence of extrinsic influences

The mechanisms governing the emergence of the earliest mammalian neural cells during development remain incompletely characterized. A default mechanism has been suggested to underlie neural fate acquisition; however, an instructive process has also been proposed. We used mouse embryonic stem (ES) cells to explore the fundamental issue of how an uncommitted, pluripotent mammalian cell will self-organize in the absence of extrinsic signals and what cellular fate will result. To assess this default state, ES cells were placed in conditions that minimize external influences. Individual ES cells were found to rapidly transition directly into neural cells, a process shown to be independent of suggested instructive factors (e.g., fibroblast growth factors). Further, we provide evidence that the default neural identity is that of a primitive neural stem cell (NSC). The exiguous conditions used to reveal the default state were found to present primitive NSCs with a survival challenge (limiting their persistence and proliferation), which could be mitigated by survival factors or genetic interference with apoptosis.     

A synchronization-desynchronization code for natural communication signals

Synchronous spiking of neural populations is hypothesized to play important computational roles in forming neural assemblies and solving the binding problem. Although the opposite phenomenon of desynchronization is well known from EEG studies, it is largely neglected on the neuronal level. We here provide an example of in vivo recordings from weakly electric fish demonstrating that, depending on the social context, different types of natural communication signals elicit transient desynchronization as well as synchronization of the electroreceptor population without changing the mean firing rate. We conclude that, in general, both positive and negative changes in the degree of synchrony can be the relevant signals for neural information processing.     

From Genes to Flower Patterns and Evolution: Dynamic Models of Gene Regulatory Networks

Genes and proteins form complex dynamical systems or gene regulatory networks (GRN) that can reach several steady states (attractors). These may be associated with distinct cell types. In plants, the ABC combinatorial model establishes the necessary gene combinations for floral organ cell specification. We have developed dynamic gene regulatory network (GRN) models to understand how the combinatorial selection of gene activity is established during floral organ primordia specification as a result of the concerted action of ABC and non-ABC genes. Our analyses have shown that the floral organ specification GRN reaches six attractors with gene configurations observed in primordial cell types during early stages of flower development and four that correspond to regions of the inflorescence meristem. This suggests that it is the overall GRN dynamics rather than precise signals that underlie the ABC model. Furthermore, our analyses suggest that the steady states of the GRN are robust to random alterations of the logical functions that define the gene interactions. Here we have updated the GRN model and have systematically altered the outputs of all the logical functions and addressed in which cases the original attractors are recovered. We then reduced the original three-state GRN to a two-state (Boolean) GRN and performed the same systematic perturbation analysis. Interestingly, the Boolean GRN reaches the same number and type of attractors as reached by the three-state GRN, and it responds to perturbations in a qualitatively identical manner as the original GRN. These results suggest that a Boolean model is sufficient to capture the dynamical features of the floral network and provide additional support for the robustness of the floral GRN. These findings further support that the GRN model provides a dynamical explanation for the ABC model and that the floral GRN robustness could be behind the widespread conservation of the floral plan among eudicotyledoneous plants. Other aspects of evolution of flower organ arrangement and ABC gene expression patterns are discussed in the context of the approach proposed here. álvaro Chaos, Max Aldana and Elena Alvarez-Buylla contributed equally to this work.     

Functional interactions in hierarchically organized neural networks studied with spatiotemporal firing patterns and phase-coupling frequencies

A scalable hardware/software hybrid module--called Ubidule--endowed with bio-inspired ontogenetic and epigenetic features is configured to run a neural networks simulation with developmental and evolvable capabilities. We simulated the activity of hierarchically organized spiking neural networks characterized by an initial developmental phase featuring cell death followed by spike timing dependent synaptic plasticity in presence of background noise. An upstream 'sensory' network received a spatiotemporally organized external input and downstream networks were activated only via the upstream network. Precise firing sequences, formed by recurrent patterns of spikes intervals above chance levels, were observed in all recording conditions, thus suggesting the build-up of a connectivity able to sustain temporal information processing. The activity of a Ubinet--a network of Ubidules--is analyzed by means of virtual electrodes that recorded neural signals similar to EEG. The analysis of these signals was compared with a small set of human recordings and revealed common patterns of shift in quadratic phase coupling. The results suggest some interpretations of changes and plasticity of functional interactions between cortical areas driven by external stimuli and by learning/cognitive     

Uncovering operational interactions in genetic networks using asynchronous Boolean dynamics

Biological networks of large dimensions, with their diagram of interactions, are often well represented by a Boolean model with a family of logical rules. The state space of a Boolean model is finite, and its asynchronous dynamics are fully described by a transition graph in the state space. In this context, a model reduction method will be developed for identifying the active or operational interactions responsible for a given dynamic behaviour. The first step in this procedure is the decomposition of the asynchronous transition graph into its strongly connected components, to obtain a “reduced” and hierarchically organized graph of transitions. The second step consists of the identification of a partial graph of interactions and a sub-family of logical rules that remain operational in a given region of the state space. This model reduction method and its usefulness are illustrated by an application to a model of programmed cell death. The method identifies two mechanisms used by the cell to respond to death-receptor stimulation and decide between the survival and apoptotic pathways.