Directional spike propagation in a recurrent network: dynamical firewall as anisotropic recurrent inhibition.

It has been demonstrated that theta rhythm propagates along the septotemporal axis of the hippocampal CA1 of the rat running on a track, and it has been suggested that directional spike propagation in the hippocampal CA3 is reflected in CA1. In this paper, we show that directional spike propagation occurs in a recurrent network model in which neurons are connected locally and connection weights are modified through STDP. The recurrent network model consists of excitatory and inhibitory neurons, which are intrinsic bursting and fast spiking neurons developed by Izhikevich, respectively. The maximum length of connections from excitatory neurons is shorter in the horizontal direction than the vertical direction. Connections from inhibitory neurons have the same maximum length in both directions, and the maximum length of inhibitory connections is the same as that of excitatory connections in the vertical direction. When connection weights between excitatory neurons (E→E) were modified through STDP and those from excitatory neurons to inhibitory neurons (E→I) were constant, spikes propagated in the vertical direction as expected from the network structure. However, when E→I connection weights were modified through STDP, as well as E→E connection weights, spikes propagated in the horizontal direction against the above expectation. This paradoxical propagation was produced by strengthened E→I connections which shifted the timing of inhibition forward. When E→I connections are enhanced, the direction of effective inhibition changes from horizontal to vertical, as if a gate for spike propagation is opened in the horizontal direction and firewalls come out in the vertical direction. These results suggest that the advance of timing of inhibition caused by potentiation of E→I connections is influential in network activity and is an important element in determining the direction of spike propagation.

Cooperation and competition between lateral and medial perforant path synapses in the dentate gyrus.

It has been suggested that non-spatial and spatial pieces of information are transmitted to the dentate gyrus from entorhinal cortex layer II through the lateral and medial perforant paths (LPP and MPP), which establish synapses on granule cell dendrites in the outer and middle one-thirds of the dentate molecular layer, respectively. In the present paper, we first investigated cooperation and competition between MPP and LPP synapses being subject to STDP rules, using a four-compartmental granule cell model. MPP and LPP were stimulated simultaneously by periodic and random pulse trains, respectively. Both synapses were gradually enhanced by cooperation between those synapses in the early stage, and then either the MPP or the LPP synapse was rapidly enhanced through synaptic competition in the following stage, depending on their initial synaptic conductances. The dominant cause of synaptic competition is that the distance between the MPP synapse and the soma is shorter than that between the LPP synapse and the soma. These results suggest that the LPP and MPP synapses tend to be enhanced in the dentate supra- and infrapyramidal blades, respectively, taking account of the thickness of each of the LPP and MPP fiber laminae in the blades. The dentate gyrus may select spatial and non-spatial pieces of information through synaptic cooperation, and may open a gate for each piece of information through synaptic competition. Then we investigated the role of inhibitory local circuits in synaptic competition in the dentate gyrus. The feed-forward GABA(B) inhibition suppressed unusual high-frequency firing of the granule cell, and consequently prevented excessive synaptic depression due to synaptic competition through STDP. The feed-forward and feedback GABA(A) inhibitions tend to reduce synaptic conductance fluctuations resulting from large increments and decrements due to very small spike-timings happening occasionally.

LTD windows of the STDP learning rule and synaptic connections having a large transmission delay enable robust sequence learning amid background noise.

Spike-timing-dependent synaptic plasticity (STDP) is a simple and effective learning rule for sequence learning. However, synapses being subject to STDP rules are readily influenced in noisy circumstances because synaptic conductances are modified by pre- and postsynaptic spikes elicited within a few tens of milliseconds, regardless of whether those spikes convey information or not. Noisy firing existing everywhere in the brain may induce irrelevant enhancement of synaptic connections through STDP rules and would result in uncertain memory encoding and obscure memory patterns. We will here show that the LTD windows of the STDP rules enable robust sequence learning amid background noise in cooperation with a large signal transmission delay between neurons and a theta rhythm, using a network model of the entorhinal cortex layer II with entorhinal-hippocampal loop connections. The important element of the present model for robust sequence learning amid background noise is the symmetric STDP rule having LTD windows on both sides of the LTP window, in addition to the loop connections having a large signal transmission delay and the theta rhythm pacing activities of stellate cells. Above all, the LTD window in the range of positive spike-timing is important to prevent influences of noise with the progress of sequence learning.

Emergence of sequence sensitivity in a hippocampal CA3-CA1 model.

Recent studies have shown that place cells in the hippocampal CA1 region fire in a sequence sensitive manner. In this study we tested if hippocampal CA3 and CA1 regions can give rise to the sequence sensitivity. We used a two-layer CA3-CA1 hippocampal model that consisted of Hodgkin-Huxley style neuron models. Sequential input signals that mimicked signals projected from the entorhinal cortex gradually modified the synaptic conductances between CA3 pyramidal cells through spike-timing-dependent plasticity (STDP) and produced propagations of neuronal activity in the radial direction from stimulated pyramidal cells. This sequence dependent spatio-temporal activity was picked up by specific CA1 pyramidal cells through modification of Schaffer collateral synapses with STDP. After learning, these CA1 pyramidal cells responded with the highest probability to the learned sequence, while responding with a lower probability to different sequences. These results demonstrate that sequence sensitivity of CA1 place cells would emerge through computation in the CA3 and CA1 regions.

Theta phase coding in a network model of the entorhinal cortex layer II with entorhinal-hippocampal loop connections.

We investigated successive firing of the stellate cells within a theta cycle, which replicates the phase coding of place information, using a network model of the entorhinal cortex layer II with loop connections. Layer II of the entorhinal cortex (ECII) sends signals to the hippocampus, and the hippocampus sends signals back to layer V of the entorhinal cortex (ECV). In addition to this major pathway, projection from ECV to ECII also exists. It is, therefore, inferred that reverberation activity readily appears if projections from ECV to ECII are potentiated. The frequency of the reverberation would be in a gamma range because it takes signals 20-30 ms to go around the entorhinal-hippocampal loop circuits. On the other hand, it has been suggested that ECII is a theta rhythm generator. If the reverberation activity appears in the entorhinal-hippocampal loop circuits, gamma oscillation would be superimposed on a theta rhythm in ECII like a gamma-theta oscillation. This is a reminiscence of the theta phase coding of place information. In this paper, first, a network model of ECII will be developed in order to reproduce a theta rhythm. Secondly, we will show that loop connections from one stellate cell to the other one are selectively potentiated by afferent signals to ECII. Frequencies of those afferent signals are different, and transmission delay of the loop connections is 20 ms. As a result, stellate cells fire successively within one cycle of the theta rhythm. This resembles gamma-theta oscillation underlying the phase coding. Our model also replicates the phase precession of stellate cell firing within a cycle of subthreshold oscillation (theta rhythm).

Analog VLSI implementation of resonate-and-fire neuron.

We propose an analog integrated circuit that implements a resonate-and-fire neuron (RFN) model based on the Lotka-Volterra (LV) system. The RFN model is a spiking neuron model that has second-order membrane dynamics, and thus exhibits fast damped subthreshold oscillation, resulting in the coincidence detection, frequency preference, and post-inhibitory rebound. The RFN circuit has been derived from the LV system to mimic such dynamical behavior of the RFN model. Through circuit simulations, we demonstrate that the RFN circuit can act as a coincidence detector and a band-pass filter at circuit level even in the presence of additive white noise and background random activity. These results show that our circuit is expected to be useful for very large-scale integration (VLSI) implementation of functional spiking neural networks.

Regulation of spontaneous rhythmic activity and organization of pacemakers as memory traces by spike-timing-dependent synaptic plasticity in a hippocampal model.

It is widely believed that memory traces can be stored through synaptic conductance modification of dense excitatory recurrent connections (ERCs) in the hippocampal CA3 region, namely associative memory. ERCs, on the other hand, are crucial to maintain spontaneous rhythmic activity in CA3. Since it is experimentally suggested that synaptic conductances of ERCs are modified through spike-timing-dependent synaptic plasticity (STDP), rhythmic activity might modify ERCs with the presence of STDP because rhythmic activity involves discharges of pyramidal cells. Memory patterns that are stored using ERCs might thus be modified or even destroyed. Rhythmic activity itself might also be modified. In this study, we assumed that the synaptic modification in the hippocampal CA3 was subject to STDP, and examined the coexistence of memory traces and rhythmic activity. The activity of the network was dominated by radially propagating burst activities (radial activities) that initiated at local regions and acted as pacemakers. The frequency of the rhythmic activity converged into one specific frequency with time, depending on the shape of the STDP functions. This indicates that rhythmic activity could be regulated by STDP. By applying theta burst stimulation locally to the network, we found that the stimulation whose frequency was higher than that of the spontaneous rhythmic activity could organize a new radial activity at the stimulus site. Newly organized radial activities were preserved for seconds after the termination of the stimulation. These results imply that CA3 with STDP has an ability to self-regulate rhythmic activity and that memory traces can coexist with the rhythmic activity by means of radial activity.

Stochastic resonance in the hippocampal CA3-CA1 model: a possible memory recall mechanism.

Stochastic resonance (SR) in a hippocampal network model was investigated. The hippocampal model consists of two layers, CA3 and CA1. Pyramidal cells in CA3 are connected to pyramidal cells in CA1 through Schaffer collateral synapses. The CA3 network causes spontaneous irregular activity (broadband spectrum peaking at around 3 Hz), while the CA1 network does not. The activity of CA3 causes membrane potential fluctuations in CA1 pyramidal cells. The CA1 network also receives a subthreshold signal (2.5 or 50 Hz) through the perforant path (PP). The subthreshold PP signals can fire CA1 pyramidal cells in cooperation with the membrane potential fluctuations that work as noise. The firing of the CA1 network shows typical features of SR. When the frequency of the PP signal is in the gamma range (50 Hz), SR that takes place in the present model shows distinctive features. 50 Hz firing of CA1 pyramidal cells is modulated by the membrane potential fluctuations, resulting in bursts. Such burst firing in the CA1 network, which resembles the firing patterns observed in the real hippocampal CA1, improves performance of subthreshold signal detection in CA1. Moreover, memory embedded at Schaffer collateral synapses can be recalled by means of SR. When Schaffer collateral synapses in subregions of CA1 are augmented three-fold as a memory pattern. pyramidal cells in the subregions respond to the subthreshold PP signal due to SR, while pyramidal cells in the rest of CA1 do not fire.

Complexity of spatiotemporal activity of a neural network model which depends on the degree of synchronization.

Spatiotemporal activity of a hippocampal CA3 model and its dynamic features were investigated. The CA3 model consists of 256 pyramidal cells and 25 inhibitory interneurons. Each pyramidal cell is a single-compartment model which was reduced from the 19-compartment cable model of the CA3 pyramidal cell developed by [Traub et al. (1991)]. Each interneuron is a model which causes tonic responses to constant depolarizing currents. The hippocampal model spontaneously causes four kinds of rhythms, A-D, which depend on the degree of synchronization of neuronal activity. The rhythm A (about 2Hz) which occurs in a range of strong mutual excitation is spatially coherent, though epileptiform bursts of pyramidal cells propagate from one end of the network to the other in a short period of time. The rhythm B (about 3Hz) occurs in an intermediate range of the strength of mutual excitation; synchronization of bursts is incomplete and the spatiotemporal pattern is complex. When the mutual excitation is relatively weak, the rhythm C (about 6Hz) occurs. Burst propagation is not uniform in direction, and the spatiotemporal activity is irregular. The rhythm D (10-35Hz) occurs in a range of weak mutual excitation when the recurrent inhibition is relatively strong. In this parameter region, pyramidal cells do not cause bursting discharges but irregular beating discharges. The hippocampal model causes phase-lockings and irregular responses to periodic synaptic stimulation depending on its own rhythmic activity and stimulus parameters. Bursting discharges of pyramidal cells are well synchronized in phase-locked responses. Several irregular responses of the rhythms A and B are evidently chaotic; each one-dimensional strobomap of chaotic responses is a non-invertible function with an unstable fixed point. Attractors reconstructed from chaotic responses demonstrate the stretching and folding mechanism.