大脑中的抉择神经元

近年来神经科学领域的进展表明,大脑中不仅存在如位置神经元之类的特异性编码感觉信息的神经元,也存在能够特异性地反映动物思考过程的神经元。在一系列以侧内顶叶(LIP)为目标的猕猴电生理实验中,人们发现LIP神经元的动作电位发放率可以反映抉择思考的过程。抉择的研究为我们打开了一个研究大脑高级认知功能的窗口。抉择神经元的发现表明了大脑的高级认知功能是基于与感觉信息处理类似的神经计算原理。     

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.     

Persistent activity in neural networks with dynamic synapses

Persistent activity states (attractors), observed in several neocortical areas after the removal of a sensory stimulus, are believed to be the neuronal basis of working memory. One of the possible mechanisms that can underlie persistent activity is recurrent excitation mediated by intracortical synaptic connections. A recent experimental study revealed that connections between pyramidal cells in prefrontal cortex exhibit various degrees of synaptic depression and facilitation. Here we analyze the effect of synaptic dynamics on the emergence and persistence of attractor states in interconnected neural networks. We show that different combinations of synaptic depression and facilitation result in qualitatively different network dynamics with respect to the emergence of the attractor states. This analysis raises the possibility that the framework of attractor neural networks can be extended to represent time-dependent stimuli.     

Memory Capacity of Networks with Stochastic Binary Synapses

In standard attractor neural network models, specific patterns of activity are stored in the synaptic matrix, so that they become fixed point attractors of the network dynamics. The storage capacity of such networks has been quantified in two ways: the maximal number of patterns that can be stored, and the stored information measured in bits per synapse. In this paper, we compute both quantities in fully connected networks of N binary neurons with binary synapses, storing patterns with coding level , in the large and sparse coding limits (). We also derive finite-size corrections that accurately reproduce the results of simulations in networks of tens of thousands of neurons. These methods are applied to three different scenarios: (1) the classic Willshaw model, (2) networks with stochastic learning in which patterns are shown only once (one shot learning), (3) networks with stochastic learning in which patterns are shown multiple times. The storage capacities are optimized over network parameters, which allows us to compare the performance of the different models. We show that finite-size effects strongly reduce the capacity, even for networks of realistic sizes. We discuss the implications of these results for memory storage in the hippocampus and cerebral cortex.     

Multistability in Large Scale Models of Brain Activity

Noise driven exploration of a brain network’s dynamic repertoire has been hypothesized to be causally involved in cognitive function, aging and neurodegeneration. The dynamic repertoire crucially depends on the network’s capacity to store patterns, as well as their stability. Here we systematically explore the capacity of networks derived from human connectomes to store attractor states, as well as various network mechanisms to control the brain’s dynamic repertoire. Using a deterministic graded response Hopfield model with connectome-based interactions, we reconstruct the system’s attractor space through a uniform sampling of the initial conditions. Large fixed-point attractor sets are obtained in the low temperature condition, with a bigger number of attractors than ever reported so far. Different variants of the initial model, including (i) a uniform activation threshold or (ii) a global negative feedback, produce a similarly robust multistability in a limited parameter range. A numerical analysis of the distribution of the attractors identifies spatially-segregated components, with a centro-medial core and several well-delineated regional patches. Those different modes share similarity with the fMRI independent components observed in the “resting state” condition. We demonstrate non-stationary behavior in noise-driven generalizations of the models, with different meta-stable attractors visited along the same time course. Only the model with a global dynamic density control is found to display robust and long-lasting non-stationarity with no tendency toward either overactivity or extinction. The best fit with empirical signals is observed at the edge of multistability, a parameter region that also corresponds to the highest entropy of the attractors.     

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 diluted attractor neural networks with delays

We present an analysis of the attractors of a deterministic dynamics in formal neural networks characterized by binary threshold units and a nonsymmetric connectivity. It is shown that in these networks a stored pattern or a pattern sequence is represented by a cloud of attractors rather than by a single attractor. Dilution, which we describe by a power-law scaling, and delayed couplings are shown to equip this type of network with a dynamic behaviour that is interesting enough for simplified models of biological motor systems. Received: 27 November 1992/Accepted in revised form: 22 September 1993     

Synaptic plasticity and connectivity requirements to produce stimulus-pair specific responses in recurrent networks of spiking neurons

Animals must respond selectively to specific combinations of salient environmental stimuli in order to survive in complex environments. A task with these features, biconditional discrimination, requires responses to select pairs of stimuli that are opposite to responses to those stimuli in another combination. We investigate the characteristics of synaptic plasticity and network connectivity needed to produce stimulus-pair neural responses within randomly connected model networks of spiking neurons trained in biconditional discrimination. Using reward-based plasticity for synapses from the random associative network onto a winner-takes-all decision-making network representing perceptual decision-making, we find that reliably correct decision making requires upstream neurons with strong stimulus-pair selectivity. By chance, selective neurons were present in initial networks; appropriate plasticity mechanisms improved task performance by enhancing the initial diversity of responses. We find long-term potentiation of inhibition to be the most beneficial plasticity rule by suppressing weak responses to produce reliably correct decisions across an extensive range of networks.     

Synaptic Potentiation Facilitates Memory-like Attractor Dynamics in Cultured In Vitro Hippocampal Networks

Collective rhythmic dynamics from neurons is vital for cognitive functions such as memory formation but how neurons self-organize to produce such activity is not well understood. Attractor-based computational models have been successfully implemented as a theoretical framework for memory storage in networks of neurons. Additionally, activity-dependent modification of synaptic transmission is thought to be the physiological basis of learning and memory. The goal of this study is to demonstrate that using a pharmacological treatment that has been shown to increase synaptic strength within in vitro networks of hippocampal neurons follows the dynamical postulates theorized by attractor models. We use a grid of extracellular electrodes to study changes in network activity after this perturbation and show that there is a persistent increase in overall spiking and bursting activity after treatment. This increase in activity appears to recruit more “errant” spikes into bursts. Phase plots indicate a conserved activity pattern suggesting that a synaptic potentiation perturbation to the attractor leaves it unchanged. Lastly, we construct a computational model to demonstrate that these synaptic perturbations can account for the dynamical changes seen within the network.     

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.     

Artificial astrocytes improve neural network performance

Compelling evidence indicates the existence of bidirectional communication between astrocytes and neurons. Astrocytes, a type of glial cells classically considered to be passive supportive cells, have been recently demonstrated to be actively involved in the processing and regulation of synaptic information, suggesting that brain function arises from the activity of neuron-glia networks. However, the actual impact of astrocytes in neural network function is largely unknown and its application in artificial intelligence remains untested. We have investigated the consequences of including artificial astrocytes, which present the biologically defined properties involved in astrocyte-neuron communication, on artificial neural network performance. Using connectionist systems and evolutionary algorithms, we have compared the performance of artificial neural networks (NN) and artificial neuron-glia networks (NGN) to solve classification problems. We show that the degree of success of NGN is superior to NN. Analysis of performances of NN with different number of neurons or different architectures indicate that the effects of NGN cannot be accounted for an increased number of network elements, but rather they are specifically due to astrocytes. Furthermore, the relative efficacy of NGN vs. NN increases as the complexity of the network increases. These results indicate that artificial astrocytes improve neural network performance, and established the concept of Artificial Neuron-Glia Networks, which represents a novel concept in Artificial Intelligence with implications in computational science as well as in the understanding of brain function.     

Probabilistic decision making by slow reverberation in cortical circuits

Recent physiological studies of alert primates have revealed cortical neural correlates of key steps in a perceptual decision-making process. To elucidate synaptic mechanisms of decision making, I investigated a biophysically realistic cortical network model for a visual discrimination experiment. In the model, slow recurrent excitation and feedback inhibition produce attractor dynamics that amplify the difference between conflicting inputs and generates a binary choice. The model is shown to account for salient characteristics of the observed decision-correlated neural activity, as well as the animal's psychometric function and reaction times. These results suggest that recurrent excitation mediated by NMDA receptors provides a candidate cellular mechanism for the slow time integration of sensory stimuli and the formation of categorical choices in a decision-making neocortical network.     

Is Payoff Necessarily Weighted by Probability When Making a Risky Choice? Evidence from Functional Connectivity Analysis

How people make decisions under risk remains an as-yet-unresolved but fundamental question. Mainstream theories about risky decision making assume that the core processes involved in reaching a risky decision include weighting each payoff or reward magnitude by its probability and then summing the outcomes. However, recently developed theories question whether payoffs are necessarily weighted by probability when making a risky choice. Using functional connectivity analysis, we aimed to provide neural evidence to answer whether this key assumption of computing expectations holds when making a risky choice. We contrasted a trade-off instruction choice that required participants to integrate probability and payoff information with a preferential choice that did not. Based on the functional connectivity patterns between regions in which activity was detected during both of the decision-making tasks, we classified the regions into two networks. One network includes primarily the left and right lateral prefrontal cortices and posterior parietal cortices, which were found to be related to probability in previous reports, and the other network is composed of the bilateral basal ganglia, which have been implicated in payoff. We also found that connectivity between the payoff network and some regions in the probability network (including the left lateral prefrontal cortices and bilateral inferior parietal lobes) were stronger during the trade-off instruction choice task than during the preferential choice task. This indicates that the functional integration between the probability and payoff networks during preferential choice was not as strong as the integration during trade-off instruction choice. Our results provide neural evidence that the weighting process uniformly predicted by the mainstream theory is unnecessary during preferential choice. Thus, our functional integration findings can provide a new direction for the investigation of the principles of risky decision making.     

A dynamical systems hypothesis of schizophrenia

We propose a top-down approach to the symptoms of schizophrenia based on a statistical dynamical framework. We show that a reduced depth in the basins of attraction of cortical attractor states destabilizes the activity at the network level due to the constant statistical fluctuations caused by the stochastic spiking of neurons. In integrate-and-fire network simulations, a decrease in the NMDA receptor conductances, which reduces the depth of the attractor basins, decreases the stability of short-term memory states and increases distractibility. The cognitive symptoms of schizophrenia such as distractibility, working memory deficits, or poor attention could be caused by this instability of attractor states in prefrontal cortical networks. Lower firing rates are also produced, and in the orbitofrontal and anterior cingulate cortex could account for the negative symptoms, including a reduction of emotions. Decreasing the GABA as well as the NMDA conductances produces not only switches between the attractor states, but also jumps from spontaneous activity into one of the attractors. We relate this to the positive symptoms of schizophrenia, including delusions, paranoia, and hallucinations, which may arise because the basins of attraction are shallow and there is instability in temporal lobe semantic memory networks, leading thoughts to move too freely round the attractor energy landscape.     

An efficient algorithm for identifying primary phenotype attractors of a large-scale Boolean network

Background

Boolean network modeling has been widely used to model large-scale biomolecular regulatory networks as it can describe the essential dynamical characteristics of complicated networks in a relatively simple way. When we analyze such Boolean network models, we often need to find out attractor states to investigate the converging state features that represent particular cell phenotypes. This is, however, very difficult (often impossible) for a large network due to computational complexity.

Results

There have been some attempts to resolve this problem by partitioning the original network into smaller subnetworks and reconstructing the attractor states by integrating the local attractors obtained from each subnetwork. But, in many cases, the partitioned subnetworks are still too large and such an approach is no longer useful. So, we have investigated the fundamental reason underlying this problem and proposed a novel efficient way of hierarchically partitioning a given large network into smaller subnetworks by focusing on some attractors corresponding to a particular phenotype of interest instead of considering all attractors at the same time. Using the definition of attractors, we can have a simplified update rule with fixed state values for some nodes. The resulting subnetworks were small enough to find out the corresponding local attractors which can be integrated for reconstruction of the global attractor states of the original large network.

Conclusions

The proposed approach can substantially extend the current limit of Boolean network modeling for converging state analysis of biological networks.

     

Robustness and state-space structure of Boolean gene regulatory models

Robustness to perturbation is an important characteristic of genetic regulatory systems, but the relationship between robustness and model dynamics has not been clearly quantified. We propose a method for quantifying both robustness and dynamics in terms of state-space structures, for Boolean models of genetic regulatory systems. By investigating existing models of the Drosophila melanogaster segment polarity network and the Saccharomyces cerevisiae cell-cycle network, we show that the structure of attractor basins can yield insight into the underlying decision making required of the system, and also the way in which the system maximises its robustness. In particular, gene networks implementing decisions based on a few genes have simple state-space structures, and their attractors are robust by virtue of their simplicity. Gene networks with decisions that involve many interacting genes have correspondingly more complicated state-space structures, and robustness cannot be achieved through the structure of the attractor basins, but is achieved by larger attractor basins that dominate the state space. These different types of robustness are demonstrated by the two models: the D. melanogaster segment polarity network is robust due to simple attractor basins that implement decisions based on spatial signals; the S. cerevisiae cell-cycle network has a complicated state-space structure, and is robust only due to a giant attractor basin that dominates the state space.     

Fluctuations and synchronizations of neural activities during sleep: Neural basis of possible sleep functions?

Physiological and psychological evidence have been accumulated concerning the function of sleep in development and learning/memory. Many conceptual ideas have been proposed to elucidate the mechanisms underlying them. Sleep consists of a wide variety of physiological processes. It has not yet been clarified which processes are involved in development and learning/memory processes. We have found that single neuronal activity exhibits a slowly fluctuating rate of discharge during rapid eye movement (REM) sleep and a random low discharge rate during non-rapid eye movement (NREM) sleep. It is suggested that a structural change of the neural network attractor underlies this neuronal dynamics-alternation by mathematical modeling. Functional interpretation of the neuronal dynamics-alternation was provided in combination with the phase locking of ponto-geniculo-occipital (PGO)/pontine (P) wave to the hippocampal theta wave, each of which is known to be involved in learning/memory processes. More directly, by the long-term sensory deprivation, the dynamics of neural activity during sleep was found to progressively change in a non-monotonic way. This finding reveals a possible interaction between sleep and reorganization of neural network in the matured brain. Here, in addition to the related findings, we described our idea about how sleep contributes to the learning/memory processes and reorganization of neural network of the matured brain through characteristic neural activities during sleep.

     

Roles of dynamic linkage of stable attractors across cortical networks in recalling long-term memory

 We propose a neural network model for a category-association task. By simulating the model, neuronal relevance of cortical interactions to recalling long-term memory was investigated. The model consists of the left and right hemispheres, each of which has IT (inferotemporal cortex) and PC (prefrontal cortex) networks. Information about visual features and their categories were encoded into point attractors of the IT and PC networks, respectively. In the task, the IT network of the right hemisphere was stimulated with a cue feature. After a delay period, the IT network of the left hemisphere was simultaneously stimulated with the choice feature and an irrelevant feature. The cue and choice features belong to the same category, while the irrelevant feature belongs to another category. To complete the task, the IT network must select the point attractor corresponding to the choice feature. We demonstrate that the top-down pathway (PC-to-IT) triggers the retrieval of long-term memory of the choice feature from the IT, and the bottom-up pathway (IT-to-PC) contributes to the maintenance of the retrieved memory during the delay period. The key mechanism for the retrieval and maintenance of that memory is the dynamic linkage of attractors across separate cortical networks. We show that a single hemisphere is sufficient for the memory retrieval, but it is advantageous to use the two hemispheres because the retrieved memory is thereby retained with greater reliability until the brain chooses the choice feature. Received: 4 April 2001 / Accepted in revised form: 17 September 2002 / Published online: 20 January 2003 Correspondence to: O. Hoshino (e-mail: hoshino@cc.oita-u.ac.jp, Tel.: +81-97-554-7301, Fax: +81-97-554-7507)