Temporal pattern sensitivity of long-term potentiation in hippocampal CA1 neurons

Synaptic Plasticity in the Injured Brain Depends on the Temporal Pattern of Stimulation

Neurostimulation protocols are increasingly used as therapeutic interventions, including for brain injury. In addition to the direct activation of neurons, these stimulation protocols are also likely to have downstream effects on those neurons' synaptic outputs. It is well known that alterations in the strength of synaptic connections (long-term potentiation, LTP; long-term depression, LTD) are sensitive to the frequency of stimulation used for induction; however, little is known about the contribution of the temporal pattern of stimulation to the downstream synaptic plasticity that may be induced by neurostimulation in the injured brain. We explored interactions of the temporal pattern and frequency of neurostimulation in the normal cerebral cortex and after mild traumatic brain injury (mTBI), to inform therapies to strengthen or weaken neural circuits in injured brains, as well as to better understand the role of these factors in normal brain plasticity. Whole-cell (WC) patch-clamp recordings of evoked postsynaptic potentials in individual neurons, as well as field potential (FP) recordings, were made from layer 2/3 of visual cortex in response to stimulation of layer 4, in acute slices from control (naive), sham operated, and mTBI rats. We compared synaptic plasticity induced by different stimulation protocols, each consisting of a specific frequency (1 Hz, 10 Hz, or 100 Hz), continuity (continuous or discontinuous), and temporal pattern (perfectly regular, slightly irregular, or highly irregular). At the individual neuron level, dramatic differences in plasticity outcome occurred when the highly irregular stimulation protocol was used at 1 Hz or 10 Hz, producing an overall LTD in controls and shams, but a robust overall LTP after mTBI. Consistent with the individual neuron results, the plasticity outcomes for simultaneous FP recordings were similar, indicative of our results generalizing to a larger scale synaptic network than can be sampled by individual WC recordings alone. In addition to the differences in plasticity outcome between control (naive or sham) and injured brains, the dynamics of the changes in synaptic responses that developed during stimulation were predictive of the final plasticity outcome. Our results demonstrate that the temporal pattern of stimulation plays a role in the polarity and magnitude of synaptic plasticity induced in the cerebral cortex while highlighting differences between normal and injured brain responses. Moreover, these results may be useful for optimization of neurostimulation therapies to treat mTBI and other brain disorders, in addition to providing new insights into downstream plasticity signaling mechanisms in the normal brain.

Comparison of Pattern Discrimination Mechanisms of Hebbian and Spatiotemporal Learning Rules in Self-Organization

The spatiotemporal learning rule (STLR) proposed based on hippocampal neurophysiological experiments is essentially different from the Hebbian learning rule (HEBLR) in terms of the self-organization mechanism. The difference is the self-organization of information from the external world by firing (HEBLR) or not firing (STLR) output neurons. Here, we describe the differences of the self-organization mechanism between the two learning rules by simulating neural network models trained on relatively similar spatiotemporal context information. Comparing the weight distributions after training, the HEBLR shows a unimodal distribution near the training vector, whereas the STLR shows a multimodal distribution. We analyzed the shape of the weight distribution in response to temporal changes in contextual information and found that the HEBLR does not change the shape of the weight distribution for time-varying spatiotemporal contextual information, whereas the STLR is sensitive to slight differences in spatiotemporal contexts and produces a multimodal distribution. These results suggest a critical difference in the dynamic change of synaptic weight distributions between the HEBLR and STLR in contextual learning. They also capture the characteristics of the pattern completion in the HEBLR and the pattern discrimination in the STLR, which adequately explain the self-organization mechanism of contextual information learning.

Further Work on the Shaping of Cortical Development and Function by Synchrony and Metabolic Competition

This paper furthers our attempts to resolve two major controversies-whether gamma synchrony plays a role in cognition, and whether cortical columns are functionally important. We have previously argued that the configuration of cortical cells that emerges in development is that which maximizes the magnitude of synchronous oscillation and minimizes metabolic cost. Here we analyze the separate effects in development of minimization of axonal lengths, and of early Hebbian learning and selective distribution of resources to growing synapses, by showing in simulations that these effects are partially antagonistic, but their interaction during development produces accurate anatomical and functional properties for both columnar and non-columnar cortex. The resulting embryonic anatomical order can provide a cortex-wide scaffold for postnatal learning that is dimensionally consistent with the representation of moving sensory objects, and, as learning progressively overwrites the embryonic order, further associations also occur in a dimensionally consistent framework. The role ascribed to cortical synchrony does not demand specific frequency, amplitude or phase variation of pulses to mediate "feature linking." Instead, the concerted interactions of pulse synchrony with short-term synaptic dynamics, and synaptic resource competition can further explain cortical information processing in analogy to Hopfield networks and quantum computation.

A context-sensitive mechanism in hippocampal CA1 networks

This paper presents a possible context-sensitive mechanism in a neural network and at single neuron levels based on the experiments of hippocampal CA1 and their theoretical models. First, the spatiotemporal learning rule (STLR, non-Hebbian) and the Hebbian rule (HEBB) are experimentally shown to coexist in dendrite-soma interactions in single hippocampal pyramidal cells of CA1. Second, the functional differences between STLR and HEBB are theoretically shown in pattern separation and pattern completion. Third, the interaction between STLR and HEBB in neural levels is proposed to play an important role in forming a selective context determined by value information, which is related to expected reward and behavioral estimation.

Dual synaptic plasticity in the hippocampus: Hebbian and spatiotemporal learning dynamics

We assume that Hebbian learning dynamics (HLD) and spatiotemporal learning dynamics (SLD) are involved in the mechanism of synaptic plasticity in the hippocampal neurons. While HLD is driven by pre- and postsynaptic spike timings through the backpropagating action potential, SLD is evoked by presynaptic spike timings alone. Since the backpropagation attenuates as it nears the distal dendrites, we assume an extreme case as a neuron model where HLD exists only at proximal dendrites and SLD exists only at the distal dendrites. We examined how the synaptic weights change in response to three types of synaptic inputs in computer simulations. First, in response to a Poisson train having a constant mean frequency, the synaptic weights in HLD and SLD are qualitatively similar. Second, SLD responds more rapidly than HLD to synchronous input patterns, while each responds to them. Third, HLD responds more rapidly to more frequent inputs, while SLD shows fluctuating synaptic weights. These results suggest an encoding hypothesis in that a transient synchronous structure in spatiotemporal input patterns will be encoded into distal dendrites through SLD and that persistent synchrony or firing rate information will be encoded into proximal dendrites through HLD.

The rate of intravenous cocaine administration alters c-fos mRNA expression and the temporal dynamics of dopamine, but not glutamate, overflow in the striatum

The rapid entry of drugs into the brain is thought to increase the propensity for addiction. The mechanisms that underlie this effect are not known, but variation in the rate of intravenous cocaine delivery does influence its ability to induce immediate early gene expression (IEG) in the striatum, and to produce psychomotor sensitization. Both IEG induction and psychomotor sensitization are dependent upon dopamine and glutamate neurotransmission within the striatum. We hypothesized, therefore, that varying the rate of intravenous cocaine delivery might influence dopamine and/or glutamate overflow in the striatum. To test this we used microdialysis coupled to on-line capillary electrophoresis and laser-induced fluorescence, which allows for very rapid sampling, to compare the effects of a rapid (5 s) versus a slow (100 s) intravenous cocaine infusion on extracellular dopamine and glutamate levels in the striatum of freely moving rats. An acute injection of cocaine had no effect on extracellular glutamate, at either rate tested. In contrast, although peak levels of dopamine were unaffected by infusion rate, dopamine levels increased more rapidly when cocaine was administered over 5 versus 100 s. Moreover, c-fos mRNA expression in the region of the striatum sampled was greater when cocaine was administered rapidly than when given slowly. These data suggest that small differences in the temporal dynamics of dopamine neurotransmission may have a large effect on the subsequent induction of intracellular signalling cascades that lead to immediate early gene expression, and in this way influence the ability of cocaine to produce long-lasting changes in brain and behavior.

Spatial clustering property and its self-similarity in membrane potentials of hippocampal CA1 pyramidal neurons for a spatio-temporal input sequence

To clarify how the information of spatiotemporal sequence of the hippocampal CA3 affects the postsynaptic membrane potentials of single pyramidal cells in the hippocampal CA1, the spatio-temporal stimuli was delivered to Schaffer collaterals of the CA3 through a pair of electrodes and the post-synaptic membrane potentials were recorded using the patch-clamp recording method. The input-output relations were sequentially analyzed by applying two measures; "spatial clustering" and its "self-similarity" index. The membrane potentials were hierarchically clustered in a self-similar manner to the input sequences. The property was significantly observed at two and three time-history steps. In addition, the properties were maintained under two different stimulus conditions, weak and strong current stimulation. The experimental results are discussed in relation to theoretical results of Cantor coding, reported by Tsuda (Behav Brain Sci 24(5):793-847, 2001) and Tsuda and Kuroda (Jpn J Indust Appl Math 18:249-258, 2001; Cortical dynamics, pp 129-139, Springer-Verlag, 2004).

Interaction between the Spatiotemporal Learning Rule (STLR) and Hebb type (HEBB) in single pyramidal cells in the hippocampal CA1 Area

The spatiotemporal learning rule (STLR), proposed as a non-Hebb type by Tsukada et al. (Neural Networks 9 (1996) 1357 and Tsukada and Pan (Biol. cyberm 92 (2005) 139), 2005), consists of two distinctive factors; "cooperative plasticity without a cell spike," and "its temporal summation". On the other hand, Hebb (The organization of behavior. John Wiley, New York, 1949) proposed the idea (HEBB) that synaptic modification is strengthened only if the pre- and post-cell are activated simultaneously. We have shown, experimentally, that both STLR and HEBB coexist in single pyramidal cells of the hippocampal CA1 area. The functional differences between STLR and HEBB in dendrite (local)-soma (global) interactions in single pyramidal cells of CA1 and the possibility of pattern separation, pattern completion and reinforcement learning were discussed.

Separation of the convulsions and antidepressant-like effects produced by the delta-opioid agonist SNC80 in rats

RATIONALE

Delta-opioid agonists produce a number of behavioral effects, including convulsions, antinociception, locomotor stimulation, and antidepressant-like effects. The development of these compounds as treatments for depression is limited by their convulsive effects. Therefore, determining how to separate the convulsive and antidepressant-like characteristics of these compounds is essential for their potential clinical use.

OBJECTIVE

The present study tests the hypothesis that the rate of delta-opioid agonist administration greatly contributes to the convulsive properties, but not the antidepressant-like effects, of delta-opioid agonists.

MATERIALS AND METHODS

The delta-opioid agonist SNC80 (1, 3.2, and 10 mg kg-1 or vehicle) was administered to Sprague-Dawley rats by intravenous infusion over different durations of time (20 s, 20, or 60 min). Convulsions were measured by observation prior to determining antidepressant-like effects in the forced swim test.

RESULTS

Slowing the rate of SNC80 administration minimized delta agonist-induced convulsions without altering the effects of SNC80 in the forced swim test.

CONCLUSIONS

These data suggest that delta agonist-induced antidepressant properties are independent of convulsive effects, and that it may be possible to eliminate the convulsions produced by delta agonists, further promoting their potential clinical utility.

Spatiotemporal visualization of long-term potentiation and depression in the hippocampal CA1 area

Long-term potentiation (LTP) in the CA1 area of the hippocampus depends critically on the statistical characteristics of its stimulus. The ability of optical imaging to record spatial distribution has made it possible to examine systematically the effect of higher-order statistical characteristics, such as the correlation between successive pairs of inter-stimulus intervals (ISIs) on the induction of LTP. Therefore, the function of frequency (first-order) and temporal pattern (second-order) was examined using this imaging technique. To investigate the dependence of LTP on frequency, periodic stimuli with the same number of pulses were applied at different frequencies (1-10 Hz, n=200) to Schaffer commissural-collateral fibers. While stimulus frequencies from 2-10 Hz induced LTP of varying magnitudes and low-frequency stimuli (1 Hz) induced long-term depression (LTD), spatial distribution remained consistent. These results suggest that induction frequency has a greater effect on the magnitude of LTP than on its spatial distribution. By employing nonperiodic stimuli at the same mean frequency (2 Hz), the effect of varying the temporal structure of a stimulus was also investigated. As the correlation of successive ISIs was increased from negative to positive, not only did the magnitude of LTP increase, there was also a statistically significant change in the spatial distribution of LTP. Interestingly, when a strong negatively correlated stimulus was applied, both LTP and LTD were simultaneously observed in the CA1 area. It was also found that the magnitude of LTP 200-300 mum distal to the cellular layer was larger than that of the LTP induced proximal (<100 microm) to that layer. These results support the hypothesis that the spatial distribution of LTP throughout the hippocampus relies principally on the temporal patterning of input stimulation. This insight into the structure of the CA1 neural network may reveal the importance of stimulus timing events in the spatial encoding of memories.

The spatiotemporal learning rule and its efficiency in separating spatiotemporal patterns

The hippocampus plays an important role in the course of establishing long-term memory, i.e., to make short-term memory of spatially and temporally associated input information. In 1996 (Tsukada et al. 1996), the spatiotemporal learning rule was proposed based on differences observed in hippocampal long-term potentiation (LTP) induced by various spatiotemporal pattern stimuli. One essential point of this learning rule is that the change of synaptic weight depends on both spatial coincidence and the temporal summation of input pulses. We applied this rule to a single-layered neural network and compared its ability to separate spatiotemporal patterns with that of other rules, including the Hebbian learning rule and its extended rules. The simulated results showed that the spatiotemporal learning rule had the highest efficiency in discriminating spatiotemporal pattern sequences, while the Hebbian learning rule (including its extended rules) was sensitive to differences in spatial patterns.

Control of secretion by temporal patterns of action potentials in adrenal chromaffin cells

Action potentials (APs) are the principal physiological stimuli for neurotransmitter secretion in neurons. Most studies on stimulus-secretion coupling have been performed under voltage clamp using artificial electrical stimuli. To investigate the modulatory effects of AP codes on neural secretion, we introduce a capacitance method to study AP-induced secretion in single cells. The action potential pattern was defined by a four-parameter "code function:" F(n, m, f, d). With this method, cell secretion evoked by stimulation with an AP code was quantified in real time by membrane capacitance (Cm) in adrenal chromaffin cells. We found, in addition to AP frequency (f), for a given number of APs, another parameter of the AP code, the number of AP bursts (m) in which the set of APs occurs, can effectively modulate cell secretion. Possible mechanisms of the m effect are depletion of the readily releasable pool and inactivation of Ca2+ channels during a burst of APs. The physiological m effect may play a key role in AP-mediated neural information transfer within a single neuron and among the elements of a neural network.

A model synapse that incorporates the properties of short- and long-term synaptic plasticity

We propose a general computer model of a synapse, which incorporates mechanisms responsible for the realization of both short- and long-term synaptic plasticity-the two forms of experimentally observed plasticity that seem to be very significant for the performance of neuronal networks. The model consists of a presynaptic part based on the earlier 'double barrier synapse' model, and a postsynaptic compartment which is connected to the presynaptic terminal via a feedback, the sign and magnitude of which depend on postsynaptic Ca(2+) concentration. The feedback increases or decreases the amount of neurotransmitter which is in a ready for release state. The model adequately reproduced the phenomena of short- and long-term plasticity observed experimentally in hippocampal slices for CA3-CA1 synapses. The proposed model may be used in the investigation of certain real synapses to estimate their physiological parameters, and in the construction of realistic neuronal networks.

The rate of intravenous cocaine administration determines susceptibility to sensitization

The potential for addiction is thought to be greatest when drugs of abuse reach the brain rapidly, because this produces intense subjective pleasurable effects. However, the ability of drugs to induce forms of cellular plasticity related to behavioral sensitization may also contribute to addiction. Therefore, we studied the influence of rate of intravenous cocaine delivery on its ability to induce psychomotor sensitization. In one experiment, rotational behavior in rats with a unilateral 6-hydroxydopamine lesion was used as an index of psychomotor activation, and in a second experiment, locomotor activity in neurologically intact rats was used. Rapid (5-16 sec) intravenous infusions of cocaine induced robust psychomotor sensitization at all doses tested (0.5-2.0 mg/kg). Treatments given over 25 sec failed to induce sensitization at all doses tested. Treatments given over 50 or 100 sec induced sensitization only at the highest dose tested. Thus, the rate of intravenous cocaine delivery has profound effects on the ability of cocaine to induce psychomotor sensitization. This suggests that the temporal dynamics of drug delivery to the brain is a critical factor in the ability of cocaine to induce forms of neuronal plasticity that may contribute to addiction.

Sequence dependence of post-tetanic potentiation after sequential heterosynaptic stimulation in the rat auditory cortex

1. To investigate the mechanisms for the coding stimulus sequence in the auditory cortex (AC), post-tetanic potentiation (PTP) was recorded after sequentially combined heterosynaptic stimulation was applied in rat AC slices. 2. Brief tetanic stimulation (TS) was applied at two sites on AC slices at intervals of 0.5-10 s. PTP of field potentials was induced by the earlier TS, rather than the later TS. PTP was followed by sequence-dependent long-term potentiation (LTP). 3. Using Ca(2+) imaging in the slices loaded with rhod-2, a Ca(2+) indicator, a sequence-dependent distribution of PTP was found in AC slices. 4. The sequence-dependent PTP in excitatory postsynaptic potentials (EPSPs) was observed in supragranular pyramidal neurons. 5. The sequence dependence of PTP was not significantly affected by 1 microM bicuculline, an antagonist of GABA(A) receptors, or 100 microM 2-hydroxysaclofen, an antagonist of GABA(B) receptors. 6. Depolarization and firing recorded in pyramidal neurons during the later TS were less vigorous than when the slices were incubated in the control medium. However, this suppression of the responses during the later TS was not observed in the presence of 50 microM atropine, an antagonist of muscarinic receptors. 7. PTP was induced by the earlier and later TS in the presence of 50 microM atropine, so that the sequence dependence of PTP was abolished. Pirenzepine (50 microM), an antagonist of muscarinic M1 receptors, but not methoctramine (30 microM), an antagonist of M2 receptors, eliminated the sequence dependence of PTP. 8. These findings suggest that the sequence dependence of PTP in AC might have a role in the temporal processing of auditory information on the scale of seconds.

Chaotic stimulus dependent long-term potentiation in the hippocampal CA1 area

In our previous report [Tsukada, M., Aihara, T., Saito, H., Kato, H., 1996. Neural Netw. 9, 1357-1365], the temporal pattern sensitivity of long-term potentiation (LTP) in hippocampal CA1 neurons was estimated by using Markov chain stimuli (MS) with different values of the serial correlation coefficient rho1 between successive interstimulus-intervals. In this paper, the effect of chaotic stimuli (CS) on induction of LTP in the hippocampal CA1 area was investigated in comparison with that of MS and periodic pattern stimuli (PS). The CS were produced by a modified Bernoulli map, so that interstimulus sequences with various values of rho1 can be generated by changing the parameter B. These stimuli had an identical first order statistics (mean interstimulus-interval), but their higher order statistics such as the serial correlation coefficients were different. The LTP induced by CS at B = 2 was significantly larger in magnitude than that of PS and MS, and also depended on the initial value of CS at B = 2 and 3. These results suggest that chaotic signals play an important role for memory coding in the hippocampal CA1 network.

Long-term potentiation and depression induced by a stochastic conditioning of a model synapse

Protracted presynaptic activity can induce long-term potentiation (LTP) or long-term depression (LTD) of the synaptic strength. However, virtually all the experiments testing how LTP and LTD depend on the conditioning input are carried out with trains of stimuli at constant frequencies, whereas neurons in vivo most likely experience a stochastic variation of interstimulus intervals. We used a computational model of synaptic transmission to test if and to what extent the stochastic fluctuations of an input signal could alter the probability to change the state of a synapse. We found that, even if the mean stimulation frequency was maintained constant, the probability to induce LTD and LTP could be a function of the temporal variation of the input activity. This mechanism, which depends only on the statistical properties of the input and not on the onset of additional biochemical mechanisms, is not usually considered in the experiments, but it could have an important role to determine the amount of LTP/LTD induction in vivo. In response to a change in the distribution of the interstimulus intervals, as measured by the coefficient of variation, a synapse could be easily adapted to inputs that might require immediate attention, with a shift of the input thresholds required to elicit LTD or LTP, which are restored to their initial conditions as soon as the input pattern returns to the original temporal distribution.

Periodically-modulated inhibition of living pacemaker neurons--III. The heterogeneity of the postsynaptic spike trains, and how control parameters affect it

Codings involving spike trains at synapses with inhibitory postsynaptic potentials on pacemakers were examined in crayfish stretch receptor organs by modulating presynaptic instantaneous rates periodically (triangles or sines; frequencies, slopes and depths under, respectively, 5.0 Hz, 40.0/s/s and 25.0/s). Timings were described by interspike and cross-intervals ("phases"); patterns (dispersions, sequences) and forms (timing classes) were identified using pooled graphs (instant along the cycle when a spike occurs vs preceding interval) and return maps (plots of successive intervals). A remarkable heterogeneity of postsynaptic intervals and phases characterizes each modulation. All cycles separate into the same portions: each contains a particular form and switches abruptly to the next. Forms differ in irregularity and predictability: they are (see text) "p:q alternations", "intermittent", "phase walk-throughs", "messy erratic" and "messy stammering". Postsynaptic cycles are asymmetric (hysteresis). This contrasts with the presynaptic homogeneity, smoothness and symmetry. All control parameters are, individually and jointly, strongly influential. Presynaptic slopes, say, act through a postsynaptic sensitivity to their magnitude and sign; when increasing, hysteresis augments and forms change or disappear. Appropriate noise attenuates between-train contrasts, providing modulations are under 0.5 Hz. Postsynaptic natural intervals impose critical time bases, separating presynaptic intervals (around, above or below them) with dissimilar consequences. Coding rules are numerous and have restricted domains; generalizations are misleading. Modulation-driven forms are trendy pacemaker-driven forms. However, dissimilarities, slight when patterns are almost pacemaker, increase as inhibition departs from pacemaker and incorporate unpredictable features. Physiological significance-(1) Pacemaker-driven forms, simple and ubiquitous, appear to be elementary building blocks of synaptic codings, present always but in each case distorted typically. (2) Synapses are prototype: similar behaviours should be widespread, and networks simulations benefit by nonlinear units generating all forms. (3) Relevant to periodic functions are that few variables need be involved in form selection, that distortions are susceptible to noise levels and, if periods are heterogeneous, that simple input cycles impose heterogeneous outputs. (4) Slow Na inactivations are necessary for obtaining complex forms and hysteresis. Formal significance--(1) Pacemaker-driven forms and presumably their modulation-driven counterparts, pertain to universal periodic, intermittent, quasiperiodic and chaotic categories whose formal properties carry physiological connotations. (2) Only relatively elaborate, nonlinear geometric models show all forms; simpler ones, show only alternations and walk-throughs. (3) Bifurcations resemble those of simple maps that can provide useful guidelines. (4) Heterogeneity poses the unanswered question of whether or not the entire cycle and all portions have the same behaviours: therefore, whether trajectories are continuous or have discontinuities and/or singular points.

Induction of long-term potentiation at spinal synapses by noxious stimulation or nerve injury

Use-dependent long-term potentiation of synaptic strength (LTP) is an intensively studied model for learning and memory in vertebrates. Induction of LTP critically depends on the stimulation parameters of presynaptic fibres with synchronous high-frequency bursts being most effective at many central synapses. It is, however, not known whether naturally occurring discharge patterns may induce LTP and whether LTP has any biological function in sensory systems. Here we have investigated the LTP of excitatory synaptic transmission between primary afferent C-fibres, many of which are nociceptors, and neurons in rat superficial spinal dorsal horn. LTP that lasted for 4-6 h could not only be induced by electrical stimulation of sural nerve but also by natural stimulation of heat-, mechano- or chemosensitive nociceptors in the skin or by acute nerve injury. Maintenance of LTP was not affected when afferent nerves were cut 1 h or 5 min after noxious skin stimulation, indicating that an ongoing afferent barrage is not required. Natural noxious stimuli induced LTP in animals which were spinalized but were ineffective in intact animals. Thus, induction of LTP is suppressed by tonically active supraspinal descending systems. We conclude that the natural non-synchronized discharge patterns that are evoked by noxious stimulation may induce LTP and that this new form of LTP may be an underlying mechanism of afferent induced hyperalgesia.

Stimulus-dependent induction of long-term potentiation in CA1 area of the hippocampus: experiment and model

In the CA1 area of the hippocampus, the magnitude of long-term potentiation (LTP) depends not only on the frequency of applied stimuli, but also on their number. With a slice preparation using extracellular recording in the hippocampus CA1 of a guinea pig, we investigate the magnitude of LTP induced by electrical stimuli with a range of frequencies and the number of applied stimuli. We find that the magnitude of the saturated potentiation obtained with periodic stimuli largely depends on the frequency and is insensitive to the number of stimuli, once the saturation level has been obtained. Furthermore, we investigated nonperiodic stimuli and found that the magnitude of the saturated potentiation is also sensitive to the statistical correlation between successive interstimulus intervals, even when their average frequency is held constant. In order to explain the LTP dependence on these various experimental parameters, we propose a simple mathematical model for the induction of LTP. In the model, an exponentially decaying element released as a result of previous stimuli is coupled with a new stimulus to act as the potentiation force, and the magnitude of potentiation is determined by this potentiation force. We can determine the decaying time constant of this hypothetical element as a model parameter by fitting the model to the experimental data. The time scale is found to be of the order of 200 msc. A molecular or cellular factor with this decaying time constant is likely to be induced in LTP induction.

Hippocampal LTP Depends on Spatial and Temporal Correlation of Inputs

We studied the LTP inducing factors using temporally and spatially modulated stimuli given to the hippocampal neural network. It was found that when the spatial factors were maintained to be constant the positive correlation in the successive inter-stimulus intervals contributes to produce larger LTP. On the other hand, if the temporal factors are kept constant, the spatial coincidence contributes to produce larger LTP. We propose a learning rule by which these experimental results can be consistently interpreted. Copyright 1996 Elsevier Science Ltd.

Chaotic and phase-locked responses of the somatosensory cortex to a periodic medial lemniscus stimulation in the anesthetized rat

Field potential responses of the somatosensory cortex to a periodic medial lemniscus (ML) fiber stimulation were investigated in anesthetized rats. Since the field potential responses of the cortex depend on the depth of anesthesia, two criteria were introduced to control the depth of anesthesia. One criterion is that spindle oscillations are caused by a single shock to ML fibers, and the other is that the dominant frequency of spontaneous field potential rhythm is in the frequency range of the delta wave. Phase-lockings and chaotic responses occurred depending on stimulus parameters under the above conditions. Trajectories of the chaotic responses in the two-dimensional phase space (V, dV/dt) reconstruct strange attractors, and stroboscopic cross-sections of each attractor show stretching and folding process. Each one-dimensional strobomap of the chaotic responses is a noninvertible function with an unstable fixed point. This is undoubted evidence for chaotic responses of the somatosensory cortex in vivo. Power spectra well characterize the periodic and the chaotic responses. Positive Lyapunov exponents and low, noninteger correlation dimensions of the chaotic responses are consistent with the above evidence. Consequently, four kinds of chaotic responses were classified. A periodic-chaotic transition sequence was observed at a relatively low stimulus current when the frequency of the stimulation was varied. A cascade of period-doubling bifurcations was also observed on a route from the region of the 1:1 phase-locking to one of the regions of the chaotic responses.