Self-organized two-state membrane potential transitions in a network of realistically modeled cortical neurons

Emergence of spatially periodic diffusive waves in small-world neuronal networks

It has been observed in experiment that the anatomical structure of neuronal networks in the brain possesses the feature of small-world networks. Yet how the small-world structure affects network dynamics remains to be fully clarified. Here we study the dynamics of a class of small-world networks consisting of pulse-coupled integrate-and-fire (I&F) neurons. Under stochastic Poisson drive, we find that the activity of the entire network resembles diffusive waves. To understand its underlying mechanism, we analyze the simplified regular-lattice network consisting of firing-rate-based neurons as an approximation to the original I&F small-world network. We demonstrate both analytically and numerically that, with strongly coupled connections, in the absence of noise, the activity of the firing-rate-based regular-lattice network spatially forms a static grating pattern that corresponds to the spatial distribution of the firing rate observed in the I&F small-world neuronal network. We further show that the spatial grating pattern with different phases comprise the continuous attractor of both the I&F small-world and firing-rate-based regular-lattice network dynamics. In the presence of input noise, the activity of both networks is perturbed along the continuous attractor, which gives rise to the diffusive waves. Our numerical simulations and theoretical analysis may potentially provide insights into the understanding of the generation of wave patterns observed in cortical networks.

Potentiation decay of synapses and length distributions of synfire chains self-organized in recurrent neural networks

Synfire chains are thought to underlie precisely timed sequences of spikes observed in various brain regions and across species. How they are formed is not understood. Here we analyze self-organization of synfire chains through the spike-timing dependent plasticity (STDP) of the synapses, axon remodeling, and potentiation decay of synaptic weights in networks of neurons driven by noisy external inputs and subject to dominant feedback inhibition. Potentiation decay is the gradual, activity-independent reduction of synaptic weights over time. We show that potentiation decay enables a dynamic and statistically stable network connectivity when neurons spike spontaneously. Periodic stimulation of a subset of neurons leads to formation of synfire chains through a random recruitment process, which terminates when the chain connects to itself and forms a loop. We demonstrate that chain length distributions depend on the potentiation decay. Fast potentiation decay leads to long chains with wide distributions, while slow potentiation decay leads to short chains with narrow distributions. We suggest that the potentiation decay, which corresponds to the decay of early long-term potentiation of synapses, is an important synaptic plasticity rule in regulating formation of neural circuity through STDP.

A spontaneous state of weakly correlated synaptic excitation and inhibition in visual cortex

Cortical spontaneous activity reflects an animal's behavioral state and affects neural responses to sensory stimuli. The correlation between excitatory and inhibitory synaptic input to single neurons is a key parameter in models of cortical circuitry. Recent measurements demonstrated highly correlated synaptic excitation and inhibition during spontaneous "up-and-down" states, during which excitation accounted for approximately 80% of inhibitory variance (Shu et al., 2003; Haider et al., 2006). Here we report in vivo whole-cell estimates of the correlation between excitation and inhibition in the rat visual cortex under pentobarbital anesthesia, during which up-and-down states are absent. Excitation and inhibition are weakly correlated, relative to the up-and-down state: excitation accounts for less than 40% of inhibitory variance. Although these correlations are lower than when the circuit cycles between up-and-down states, both behaviors may arise from the same circuitry. Our observations provide evidence that different correlational patterns of excitation and inhibition underlie different cortical states.

Dynamics of coupled adaptive elements: bursting and intermittent oscillations generated by frustration in networks

Adaptation to environmental change is a common property of biological systems. Cells initially respond to external changes in the environment, but after some time, they regain their original state. By considering an element consisting of two variables that show such adaptation dynamics, we studied a coupled dynamical system containing such elements to examine the diverse dynamics in the system and classified the behaviors on the basis of the network structure that determined the interaction among elements. For a system with two elements, two types of behaviors, perfect adaptation and simple oscillation, were observed. For a system with three elements, in addition to these two types of dynamics, rapid-burst-type oscillation and a slow cycle were discovered; depending on the initial conditions, these two types of dynamics coexisted. These behaviors are a result of the characteristic dynamics of each element, i.e., fast response and slow adaptation processes. The behaviors depend on the network structure (in specific, a combination of positive or negative feedback among elements). Cooperativity among elements due to a positive feedback loop leads to simple oscillation, whereas frustration involving alternating positive and negative interactions among elements leads to the coexistence of rapid bursting oscillation and a slow cycle. These behaviors are classified on the basis of the frustration indices defined by the network structure. The period of the slow cycle is much longer than the original adaptation time scale, while the burst-type oscillation is a continued response that does not involve any adaptation. We briefly discuss the universal applicability of our results to a network of a larger number of elements and their possible relevance to biological systems.

Self-organization of a neural network with heterogeneous neurons enhances coherence and stochastic resonance

Most network models for neural behavior assume a predefined network topology and consist of almost identical elements exhibiting little heterogeneity. In this paper, we propose a self-organized network consisting of heterogeneous neurons with different behaviors or degrees of excitability. The synaptic connections evolve according to the spike-timing dependent plasticity mechanism and finally a sparse and active-neuron-dominant structure is observed. That is, strong connections are mainly distributed to the synapses from active neurons to inactive ones. We argue that this self-emergent topology essentially reflects the competition of different neurons and encodes the heterogeneity. This structure is shown to significantly enhance the coherence resonance and stochastic resonance of the entire network, indicating its high efficiency in information processing.

Structure of spontaneous UP and DOWN transitions self-organizing in a cortical network model

Synaptic plasticity is considered to play a crucial role in the experience-dependent self-organization of local cortical networks. In the absence of sensory stimuli, cerebral cortex exhibits spontaneous membrane potential transitions between an UP and a DOWN state. To reveal how cortical networks develop spontaneous activity, or conversely, how spontaneous activity structures cortical networks, we analyze the self-organization of a recurrent network model of excitatory and inhibitory neurons, which is realistic enough to replicate UP-DOWN states, with spike-timing-dependent plasticity (STDP). The individual neurons in the self-organized network exhibit a variety of temporal patterns in the two-state transitions. In addition, the model develops a feed-forward network-like structure that produces a diverse repertoire of precise sequences of the UP state. Our model shows that the self-organized activity well resembles the spontaneous activity of cortical networks if STDP is accompanied by the pruning of weak synapses. These results suggest that the two-state membrane potential transitions play an active role in structuring local cortical circuits.

Network model of spontaneous activity exhibiting synchronous transitions between up and down States

Both in vivo and in vitro recordings indicate that neuronal membrane potentials can make spontaneous transitions between distinct up and down states. At the network level, populations of neurons have been observed to make these transitions synchronously. Although synaptic activity and intrinsic neuron properties play an important role, the precise nature of the processes responsible for these phenomena is not known. Using a computational model, we explore the interplay between intrinsic neuronal properties and synaptic fluctuations. Model neurons of the integrate-and-fire type were extended by adding a nonlinear membrane current. Networks of these neurons exhibit large amplitude synchronous spontaneous fluctuations that make the neurons jump between up and down states, thereby producing bimodal membrane potential distributions. The effect of sensory stimulation on network responses depends on whether the stimulus is applied during an up state or deeply inside a down state. External noise can be varied to modulate the network continuously between two extreme regimes in which it remains permanently in either the up or the down state.

Stability of discrete memory states to stochastic fluctuations in neuronal systems

Noise can degrade memories by causing transitions from one memory state to another. For any biological memory system to be useful, the time scale of such noise-induced transitions must be much longer than the required duration for memory retention. Using biophysically-realistic modeling, we consider two types of memory in the brain: short-term memories maintained by reverberating neuronal activity for a few seconds, and long-term memories maintained by a molecular switch for years. Both systems require persistence of (neuronal or molecular) activity self-sustained by an autocatalytic process and, we argue, that both have limited memory lifetimes because of significant fluctuations. We will first discuss a strongly recurrent cortical network model endowed with feedback loops, for short-term memory. Fluctuations are due to highly irregular spike firing, a salient characteristic of cortical neurons. Then, we will analyze a model for long-term memory, based on an autophosphorylation mechanism of calcium/calmodulin-dependent protein kinase II (CaMKII) molecules. There, fluctuations arise from the fact that there are only a small number of CaMKII molecules at each postsynaptic density (putative synaptic memory unit). Our results are twofold. First, we demonstrate analytically and computationally the exponential dependence of stability on the number of neurons in a self-excitatory network, and on the number of CaMKII proteins in a molecular switch. Second, for each of the two systems, we implement graded memory consisting of a group of bistable switches. For the neuronal network we report interesting ramping temporal dynamics as a result of sequentially switching an increasing number of discrete, bistable, units. The general observation of an exponential increase in memory stability with the system size leads to a trade-off between the robustness of memories (which increases with the size of each bistable unit) and the total amount of information storage (which decreases with increasing unit size), which may be optimized in the brain through biological evolution.

Correlated transition between two activity states of neurons

In order to understand the dynamical properties of a neural network, it is important to characterize the relation between spike trains of two neurons in the network. In this study, we show that in some neuron pairs in inferior temporal cortices of macaque monkeys, spike trains of a pair are described by a two-dimensional Poisson process whose means are modulated by a common two-state Markov process. The common two-state Markov process describes a correlated state transition between firing and nonfiring states of the constituent neurons of the pair.