Iterated function systems in the hippocampal CA1

Functional differentiations in evolutionary reservoir computing networks

We propose an extended reservoir computer that shows the functional differentiation of neurons. The reservoir computer is developed to enable changing of the internal reservoir using evolutionary dynamics, and we call it an evolutionary reservoir computer. To develop neuronal units to show specificity, depending on the input information, the internal dynamics should be controlled to produce contracting dynamics after expanding dynamics. Expanding dynamics magnifies the difference of input information, while contracting dynamics contributes to forming clusters of input information, thereby producing multiple attractors. The simultaneous appearance of both dynamics indicates the existence of chaos. In contrast, the sequential appearance of these dynamics during finite time intervals may induce functional differentiations. In this paper, we show how specific neuronal units are yielded in the evolutionary reservoir computer.

Physiological properties of Cantor coding-like iterated function system in the hippocampal CA1 network

Cantor coding provides an information coding scheme for temporal sequences of events. In the hippocampal CA3-CA1 network, Cantor coding-like mechanism was observed in pyramidal neurons and the relationship between input pattern and recorded responses could be described as an iterated function system. However, detailed physiological properties of the system in CA1 remain unclear. Here, we performed a detailed analysis of the properties of the system related to the physiological basis of learning and memory. First, we investigated whether the system could be simply based on a series of on-off responses of excitatory postsynaptic potential (EPSP) amplitudes. We applied a series of three spatially distinct input patterns with similar EPSP peak amplitudes. The membrane responses showed significant differences in spatial clustering properties related to the iterated function system. These results suggest that existence of some factors, which do not simply depend on a series of on-off responses but on spatial patterns in the system. Second, to confirm whether the system is dependent on the interval of sequential input, we applied spatiotemporal sequential inputs at several intervals. The optimal interval was 30 ms, similar to the physiological input from CA3 to CA1. Third, we analyzed the inhibitory network dependency of the system. After GABA_A receptor blocker (gabazine) application, quality of code discrimination in the system was lower under subthreshold conditions and higher under suprathreshold conditions. These results suggest that the inhibitory network increase the difference between the responses under sub- and suprathreshold conditions. In summary, Cantor coding-like iterated function system appears to be suitable for information expression in relation to learning and memory in CA1 network.

Recovery of vesicular storage and release parameters after high frequency stimulation in rat hippocampus

The replenishment rates estimated from the recovery of synaptic efficacy following synaptic depression are known to be widely scattered. Given the importance of the replenishment during stimulation, especially if it is prolonged, it is important to better understand what influences the recovery of the synaptic efficacy following stimulation. We fit a two-pool model of vesicular secretion to the changes of the excitatory post-synaptic currents recorded in CA1 neurons of rat hippocampal slices to determine how the model parameters change during, and following, long stimulation. The replenishment rate at the end of stimulation inducing synaptic depression differs greatly from that at the beginning of stimulation. It decreases progressively and rapidly (by ~75 % and with a time constant of <10 s) during stimulation, and this is followed by a similarly fast recovery (time constant of ~10 s), but to a steady-state that is approximately twice as large as its pre-stimulation value. Both [Ca(++)]o and the duration of long stimulation influence the recovery of the replenishment rate. Its new steady-state is significantly higher, if either [Ca(++)]o is higher or stimulation longer, but the recovery of the replenishment rate becomes clearly slower if [Ca(++)]o is higher, and faster if stimulation is longer. Many factors thus influence the recovery of the replenishment rate and of the synaptic efficacy, but the stimulation induced [Ca(++)]i accumulation cannot explain the change of the replenishment rate during recovery. Finally, okadaic acid, which speeds up vesicular trafficking, does not alter the recovery of the replenishment rate. The vesicular replenishment of the RRP following stimulation is thus not likely to be associated with significant vesicular movement.

A MODEL OF HIPPOCAMPAL MEMORY BASED ON AN ADAPTIVE LEARNING RULE OF SYNAPSES

We constructed a neural network of the hippocampus and proposed an adaptive learning rule of synapses to simulate the storing and retrieving processes of memory in the hippocampus by a mechanism of resonance. The hippocampus network consists of CA1, CA3 and DG, in particular, CA1 is a storage of memory, which receives inputs from both EC through perforant path (PP) and CA3 through Schaffer collaterals (SC). The stimulated results showed that the memory trace was unable to be encoded in CA1 when only a single subthreshold signal from EC or CA3 was inputted, of which the main reason might be lack of the resonance of the two signals. We calculated signal-to-noise ratio (SNR) of the network, and found it reached a peak value at appropriate SC connection strength, indicating that a typical stochastic resonance phenomenon appeared in PP signal detection. The inputs from EC and CA3 were able to enhance the memory representation in CA1, although still incomplete. We used a learning rule to modify synaptic weights by which the network could learn an external pattern. The hippocampus network tended to be stable after sufficient evolution. Some CA1 neurons show synchronized firings which are used to represent memory and are clearer than observed memory traces before learning. The model and results provide a good guidance to our understanding of the mechanism of the hippocampus memory.