The formation of neural codes in the hippocampus: trace conditioning as a prototypical paradigm for studying the random recoding hypothesis.

The trace version of classical conditioning is used as a prototypical hippocampal-dependent task to study the recoding sequence prediction theory of hippocampal function. This theory conjectures that the hippocampus is a random recoder of sequences and that, once formed, the neuronal codes are suitable for prediction. As such, a trace conditioning paradigm, which requires a timely prediction, seems by far the simplest of the behaviorally-relevant paradigms for studying hippocampal recoding. Parameters that affect the formation of these random codes include the temporal aspects of the behavioral/cognitive paradigm and certain basic characteristics of hippocampal region CA3 anatomy and physiology such as connectivity and activity. Here we describe some of the dynamics of code formation and describe how biological and paradigmatic parameters affect the neural codes that are formed. In addition to a backward cascade of coding neurons, we point out, for the first time, a higher-order dynamic growing out of the backward cascade-a particular forward and backward stabilization of codes as training progresses. We also observe that there is a performance compromise involved in the setting of activity levels due to the existence of three behavioral failure modes. Each of these behavioral failure modes exists in the computational model and, presumably, natural selection produced the compromise performance observed by psychologists. Thus, examining the parametric sensitivities of the codes and their dynamic formation gives insight into the constraints on natural computation and into the computational compromises ensuing from these constraints.

Estradiol increases delayed, N-methyl-D-aspartate receptor-mediated excitation in the hippocampal CA1 region.

Hippocampal functions, e.g. synaptic plasticity and hippocampal-dependent behavior, are influenced by the circulating levels of ovarian steroids in adult, female rats. The mechanisms underlying this estradiol-dependent modulation, however, are poorly understood. One possibility is that estradiol alters N-methyl-D-aspartate (NMDA)-receptor functioning in the hippocampus. Here, using the in vitro hippocampal slice preparation, we evaluate estradiol-dependent changes in the NMDA receptor- and the alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor-mediated components of excitatory postsynaptic potentials (EPSPs) evoked in CA1 by Schaffer collateral test stimulation. Using established experimental conditions [J Neurosci 17 (1997) 1848], we replicate the observation that estradiol pretreatment of ovariectomized rats increases a pharmacologically isolated NMDA receptor-mediated EPSP evoked by Schaffer collateral stimulation. However, using different conditions that optimize study of this evoked response, the estradiol-dependent increase in the monosynaptic NMDA receptor-mediated EPSP is eliminated. Low-intensity test stimulation of the Schaffer collaterals in this optimized medium reveals a novel, late NMDA receptor-mediated EPSP in CA1 from estradiol-pretreated rats. The mechanism(s) underlying this estradiol-dependent increase in a late, NMDA receptor-mediated EPSP is not known, but enhanced CA1-CA1 excitatory circuitry and glutamate spillover could contribute to this response. We conclude that estradiol pretreatment enhances NMDA receptor function in the female hippocampus by increasing not the monosynaptic, but rather a late NMDA receptor-mediated response. Variations in the magnitude of this late response may well contribute to ovarian steroid-dependent modulation of hippocampal synaptic plasticity.

Quantal synaptic failures enhance performance in a minimal hippocampal model.

Despite the fact that animals are not optimal, natural selection is an optimizing process that can readily control small bits and pieces of organisms. It is for this reason that we need to explain certain parameters as found in Nature (e.g., number of neurons and their average activity) to fully understand the biological basis of cognition. In this optimizing sense, the failure of quantal synaptic transmission is problematic because this process incurs information loss at each synapse which seems like a bad thing for information processing. However, recent work based on an information-theoretic analysis of a single neuron suggests that such losses can be tolerated and lead to energy savings. Here we study computational simulations of a hippocampal model as a function of failure rate. We find that the failure process actually enhances some indices of performance when the model is required to solve the hippocampally dependent task of transverse patterning or when it is required to learn a simple sequence. Adding the random process of synaptic failures to the recurrent CA3-to-CA3 excitatory connections results in simulations that are more robust to parametric settings. Not only is the model more robust when synaptic failures are part of the model but there is a notable increase of sequence length memory capacity. Also, the failure process combined with additional neurons allows lower activity settings while still remaining compatible with learning the transverse patterning task. Indeed, as neuron number tended towards the biological numbers (nearly 5 x 10(4) in the simulations), it was not only possible to achieve biological failure rates (55-85%) at the minimally tolerated activity setting but these appropriately high failure rates were required for successful learning. The results are interpreted in terms of previous research demonstrating that randomization during training can enhance performance by facilitating implicit state-space search for interconnected neurons.

Initial state randomness improves sequence learning in a model hippocampal network.

Randomness can be a useful component of computation. Using a computationally minimal, but still biologically based model of the hippocampus, we evaluate the effects of initial state randomization on learning a cognitive problem that requires this brain structure. Greater randomness of initial states leads to more robust performance in simulations of the cognitive task called transverse patterning, a context-dependent discrimination task that we code as a sequence prediction problem. At the conclusion of training, greater initial randomness during training trials also correlates with increased, repetitive firing of select individual neurons, previously named local context neurons. In essence, such repetitively firing neurons recognize subsequences, and previously their presence has been correlated with solving the transverse patterning problem. A more detailed analysis of the simulations across training trials reveals more about initial state randomization. The beneficial effects of initial state randomization derive from enhanced variation, across training trials, of the sequential states of a network. This greater variation is not uniformly present during training; it is largely restricted to the beginning of training and when novel sequences are introduced. Little such variation occurs after extensive or even moderate amounts of training. We explain why variation is high early in training, but not later. This automatic modulation of the initial-state-driven random variation through state space is reminiscent of simulated annealing where modulated randomization encourages a selectively broad search through state space. In contrast to an annealing schedule, the selective occurrence of such a random search here is an emergent property, and the critical randomization occurs during training rather than testing.

Relational learning with and without awareness: transitive inference using nonverbal stimuli in humans.

Learning complex relationships among items and representing them flexibly have been shown to be highly similar in function and structure to conscious forms of learning. However, it is unclear whether conscious learning is essential for the exhibition of flexibility in learning. Successful performance on the transitive inference task requires representational flexibility. Participants learned four overlapping premise pairs (A > B, B > C, C > D, D > E) that could be encoded separately or as a sequential hierarchy (A > B > C > D > E). Some participants (informed) were told prior to training that the task required an inference made from premise pairs. Other participants (uninformed) were told simply that they were to learn a series of pairs by trial and error. Testing consisted of unreinforced trials that included the non-adjacent pair, B versus D, to assess capacity for transitive inference. Not surprisingly, those in the informed condition outperformed those in the uninformed condition. After completion of training and testing, uninformed participants were given a postexperimental questionnaire to assess awareness of the task structure. In contrast with expectations, successful performance on the transitive inference task for uninformed participants does not depend on or correlate with postexperimental awareness. The present results suggest that relational learning tasks do not necessarily require conscious processes.

A model of hippocampal activity in trace conditioning: where's the trace?

The hippocampus is generally thought to play a modulating role in the timing of conditioned responses in classical trace conditioning. One hypothesis is that the hippocampus stores a memory trace of the conditioned stimulus (CS) during the stimulus-free period. Cellular recordings, however, do not show any obvious CS storage. This article examines this issue by using a biologically plausible model of the CA3 region of the hippocampus. Simulations of the model reproduce both behavioral and physiological experimental data. On the basis of neural codes that develop in the model, the authors hypothesize that the hippocampus functions as a time-indexed encoding device for the CS and not as a CS storage buffer. Specifically, the CS initiates a sequence of neural activity during the trace interval that only indirectly represents the CS. The model yields 2 predictions: Some cells will increase in activity only during the trace interval, and some unconditioned stimulus (US)-coding cells will shift in time and fire before US onset.

Estradiol modulates long-term synaptic depression in female rat hippocampus.

Fluctuating estradiol levels in the adult, female rat modify the anatomical and functional organization of the hippocampal CA1 region. When systemic levels of estradiol are low, e.g., on estrus or in ovariectomized (OVX) rats, long-term synaptic potentiation is difficult to induce in vivo. However, little is known about the role of this ovarian hormone in long-term synaptic depression. Using multiple conditioning paradigms, we assess the magnitude of long-term depression (LTD) at CA3-CA1 synapses in vitro from adult, ovariectomized rats as a function of systemic estradiol replacement. In hippocampal slices from control OVX rats with low levels of estradiol, a low-frequency (2 Hz), asynchronous conditioning stimulation protocol does not produce LTD at 1 h postconditioning. However, this same protocol induces robust LTD in slices from estradiol-treated OVX rats. When the conditioning frequency is increased to 4 Hz, slices from both groups of rats show robust LTD in vitro. At an even higher conditioning frequency (10 Hz), the 2-Hz-based observations are reversed; no consistent changes in synaptic transmission are observed in slices from estradiol-treated OVX rats, but those from control rats (OVX + oil) show robust LTD. Thus estradiol reduces the frequency threshold for LTD induction at the CA3-CA1 synapses. Further, regardless of the conditioning frequency employed, where robust LTD is seen, its induction depends on normally functioning N-methyl-D-aspartate (NMDA) receptors during conditioning. The shift in conditioning frequency needed to elicit LTD is consistent with a decrease in NMDA receptor activation with decreasing estradiol levels.

Estradiol enhances the induction of homosynaptic long-term depression in the CA1 region of the adult, ovariectomized rat.

An ovarian steroid-dependent cycle of synaptogenesis and synapse shedding occurs naturally in the hippocampus of the adult female rat. The newly formed axospinous synapses in CA1 may differ functionally from extant axospinous synapses, e.g., in terms of their modifiability. Here we assess whether estradiol alters the induction of homosynaptic long-term depression of the Schaffer collateral-CA1 synapses in vitro. Sprague-Dawley rats were bilaterally ovariectomized and, beginning 6-8 days later, received a series of injections of either 17beta-estradiol or sesame oil sc. Field potentials were recorded in hippocampal slices. In estradiol-treated animals, asynchronous, low-frequency stimulation led to significant long-term depression of the activated synapses in CA1 s. radiatum and no change of the inactive synapses in s. oriens. In contrast, this conditioning stimulation did not significantly alter any CA1 responses in oil-treated control animals. Subsequent high-frequency conditioning stimulation significantly potentiated the activated s. radiatum synapses in both estradiol- and oil-treated animals. Thus, given the stimulation conditions used here, estradiol enables the induction of homosynaptic long-term depression at the CA3-CA1 synapses in adult females.

Primacy versus recency in a quantitative model: activity is the critical distinction.

Behavioral and neurobiological evidence shows that primacy and recency are subserved by memory systems for intermediate- and short-term memory, respectively. A widely accepted explanation of recency is that in short-term memory, new learning overwrites old learning. Primacy is not as well understood, but many hypotheses contend that initial items are better encoded into long-term memory because they have had more opportunity to be rehearsed. A simple, biologically motivated neural network model supports an alternative hypothesis of the distinct processing requirements for primacy and recency given single-trial learning without rehearsal. Simulations of the model exhibit either primacy or recency, but not both simultaneously. The incompatibility of primacy and recency clarifies possible reasons for two neurologically distinct systems. Inhibition, and its control of activity, determines those list items that are acquired and retained. Activity levels that are too low do not provide sufficient connections for learning to occur, while higher activity diminishes capacity. High recurrent inhibition, and progressively diminishing activity, allows acquisition and retention of early items, while later items are never acquired. Conversely, low recurrent inhibition, and the resulting high activity, allows continuous acquisition such that acquisition of later items eventually interferes with the retention of early items.

Controlling activity fluctuations in large, sparsely connected random networks.

Controlling activity in recurrent neural network models of brain regions is essential both to enable effective learning and to reproduce the low activities that exist in some cortical regions such as hippocampal region CA3. Previous studies of sparse, random, recurrent networks constructed with McCulloch-Pitts neurons used probabilistic arguments to set the parameters that control activity. Here, we extend this work by adding an additional, biologically appropriate, parameter to control the magnitude and stability of activity oscillations. The new constant can be considered to be the rest conductance in a shunting model or the threshold when subtractive inhibition is used. This new parameter is critical for large networks run at low activity levels. Importantly, extreme activity fluctuations that act to turn large networks totally on or totally off can now be avoided. We also show how the size of external input activity interacts with this parameter to affect network activity. Then the model based on fixed weights is extended to estimate activities in networks with distributed weights. Because the theory provides accurate control of activity fluctuations, the approach can be used to design a predictable amount of pseudorandomness into deterministic networks. Such nonminimal fluctuations improve learning in simulations trained on the transitive inference problem.

Temporal sequence compression by an integrate-and-fire model of hippocampal area CA3.

Cells in the rat hippocampus fire as a function of the animal's location in space. Thus, a rat moving through the world produces a statistically reproducible sequence of "place cell" firings. With this perspective, spatial navigation can be viewed as a sequence learning problem for the hippocampus. That is, learning entails associating the relationships among a sequence of places that are represented by a sequence of place cell firing. Recent experiments by McNaughton and colleagues suggest the hippocampus can recall a sequence of place cell firings at a faster rate than it was experienced. This speedup, which occurs during slow-wave sleep, is called temporal compression. Here, we show that a simplified model of hippocampal area CA3, based on integrate-and-fire cells and unsupervised Hebbian learning, reproduces this temporal compression. The amount of compression is proportional to the activity level during recall and to the relative timespan of associativity during learning. Compression seems to arise from an alteration of network dynamics between learning and recall. During learning, the dynamics are paced by external input and slowed by a low overall level of activity. During recall, however, external input is absent, and the dynamics are controlled by intrinsic network properties. Raising the activity level by lowering inhibition increases the rate at which the network can transition between previously learned states and thereby produces temporal compression. The tendency for speeding up future activations, however, is limited by the temporal range of associations that were present during learning.

The statistical relationship between connectivity and neural activity in fractionally connected feed-forward networks.

It is desirable to have a statistical description of neuronal connectivity in developing tractable theories on the development of biological neural networks and in designing artificial neural networks. In this paper, we bring out a relationship between the statistics of the input environment, the degree of network connectivity, and the average postsynaptic activity. These relationships are derived using simple neurons whose inputs are only feed-forward, excitatory and whose activity is a linear function of its inputs. In particular, we show that only the empirical mean of the pairwise input correlations, rather than the full matrix of all such correlations, is needed to produce an accurate estimate of the number of inputs necessary to attain a prespecified average postsynaptic activity level. Predictions from this work also include distributional aspects of connectivity and activity as shown by a combination of analysis and simulations.

A neural network solution to the transverse patterning problem depends on repetition of the input code.

Using computer simulations, this paper investigates how input codes affect a minimal computational model of the hippocampal region CA3. Because encoding context seems to be a function of the hippocampus, we have studied problems that require learning context for their solution. Here we study a hippocampally dependent, configural learning problem called transverse patterning. Previously, we showed that the network does not produce long local context codings when the sequential input patterns are orthogonal, and it fails to solve many context-dependent problems in such situations. Here we show that this need not be the case if we assume that the input changes more slowly than a processing interval. Stuttering, i.e., repeating inputs, allows the network to create long local context firings even for orthogonal inputs. With these long local context firings, the network is able to solve the transverse patterning problem. Without stuttering, transverse patterning is not learned. Because stuttering is so useful, we investigate the relationship between the stuttering repetition length and relative context length in a simple, idealized sequence prediction problem. The relative context length, defined as the average length of the local context codes divided by the stuttering length, interacts with activity levels and has an optimal stuttering repetition length. Moreover, the increase in average context length can reach this maximum without loss of relative capacity. Finally, we note that stuttering is an example of maintained or introduced redundancy that can improve neural computations.

Free postsynaptic densities in the hippocampus of the female rat.

The number of synapses in the adult, female hippocampal CA1 region fluctuates naturally across the estrous cycle in an ovarian steroid-dependent manner. This phasic variation in synapse number occurs without identifiable degenerating synapses. Ultrastructural correlates of the dynamic aspect of this synapse loss and synapse formation thus remain undescribed. During early development, one hallmark of synaptogenesis is the presence of free postsynaptic densities (PSDs). Here we report that the incidence of free PSDs in CA1 fluctuates across the rat estrous cycle. The number of free PSDs is greatest on the afternoon of proestrus and is significantly decreased on the afternoon of estrus, 24 h later. We hypothesize that these free PSDs reflect synapse turnover in the adult CA1 region.

Homosynaptic long-term depression of CA3-CA3 synapses in the in vivo hippocampus.

We tested the hypothesis that homosynaptic long-term depression (LTD) can be induced at the CA3-CA3 synapses in the adult, in vivo hippocampus while the CA3-CA1 synapses remain unchanged. Low-frequency conditioning stimulation of the contralateral fimbria significantly depressed the CA3 population response but did not change the simultaneously recorded CA3 response to angular bundle test stimulation. Similarly, in another group of animals, low-frequency conditioning stimulation of the contralateral fimbria depressed the CA3 synaptic response and left the collateral CA1 synaptic response unchanged. Among the possible explanations for this differential induction of homosynaptic LTD at the CA3-CA3 and CA3-CA1 synapses are differential control of intracellular calcium, differing levels of inhibition in these two regions, and the recency of 'natural' long-term potentiation in the two regions.

Predicting the distribution of synaptic strengths and cell firing correlations in a self-organizing, sequence prediction model.

This article investigates the synaptic weight distribution of a self-supervised, sparse, and randomly connected recurrent network inspired by hippocampal region CA3. This network solves nontrivial sequence prediction problems by creating, on a neuron-by-neuron basis, special patterns of cell firing called local context units. These specialized patterns of cell firing--possibly an analog of hippocampal place cells--allow accurate prediction of the statistical distribution of synaptic weights, and this distribution is not at all gaussian. Aside from the majority of synapses that are, at least functionally, lost due to synaptic depression, the distribution is approximately uniform. Unexpectedly, this result is relatively independent of the input environment, and the uniform distribution of synaptic weights can be approximately parameterized based solely on the average activity level. Next, the results are generalized to other cell firing types (frequency codes and stochastic firing) and place cell-like firing distributions. Finally, we note that our predictions concerning the synaptic strength distribution can be extended to the distribution of correlated cell firings. Recent published neurophysiological results are consistent with this extension.

Perforant path activation modulates the induction of long-term potentiation of the schaffer collateral--hippocampal CA1 response: theoretical and experimental analyses.

In one computational model of hippocampal function, the entorhinal cortical input to CA1 is hypothesized to play a key role in the ability of CA1 to decode CA3 recodings. Here, we develop a modification of this CA1 decoder hypothesis that is applicable to several computational theories of hippocampal function, and then we electrophysiologically investigate one assumption of this new hypothesis. First, using biologically realistic estimates, we calculate that CA3-induced CA1 excitation is too high and that inhibition plausibly plays a role in this CA1 decoder model. Thus motivated, we turn to a physiological demonstration to substantiate the plausibility of the proposed mechanism. Using the rat hippocampal slice, we examine an interlaminar interaction between the distal perforant path input to hippocampal CA1 stratum moleculare and the more proximal Schaffer collateral input to stratum radiatum. Perforant path activation provides sufficient inhibition to block homosynaptic long-term potentiation elicited by a suitably strong stratum radiatum input. For this interlaminar interaction to be most effective, perforant path activation must both precede and follow Schaffer collateral activation. Perforant path-evoked inhibition in CA1 can thus serve as a viable mechanism in the learned decoder theory of hippocampal CA1.

Quantifying the role of inhibition in associative long-term potentiation in dentate granule cells with computational models.

In the dentate gyrus, coactivation of a mildly strong ipsilateral perforant path (pp) input with a weak contralateral pp input will not induce associative long-term potentiation in the weak input path unless both inputs project to the same part of the molecular layer. This "spatial convergence requirement" is thought to arise from either voltage attenuation between input locations or inhibition. Simulations with a detailed model of a dentate granule cell were performed to rule out voltage attenuation and to quantify the inhibition necessary to obtain the spatial convergence requirement. Strong lateral and weak medial or strong medial and weak lateral pp input were activated eight times at 400 Hz. Calcium current through N-methyl-D-aspartate receptor channels and subsequent changes in calcium concentration and the concentration of calmodulin bound with four calcium ions ([Cal-Ca4]) in the spine head were computed for a medial and a lateral pp synapse. To satisfy the spatial convergence requirement, peak [Cal-Ca4] had to be much larger in the strongly activated path synapse than in the weakly activated path synapse. With no inhibition in the model, differences in peak [Cal-Cal4] at the two synapses were small, ruling out voltage attenuation as the explanation of the spatial convergence requirement. However, with shunting inhibition, modeled by reducing membrane resistivity to 1,600 omega cm2 in the distal two-thirds of the dendritic tree, peak [Cal-Ca4] was 3-5 times larger in the strongly activated path synapse than in the weakly activated path synapse. The magnitude of shunting inhibition was varied to determine the level that maximized this difference in peak [Cal-Ca4]. For strong lateral and weak medial pp input, the optimal level was one that prevented the cell from firing an action potential. For strong medial and weak lateral pp input, the optimal level was one at which the cell fired two action potentials. The distribution of shunting inhibition that best satisfied the spatial convergence requirement was inhibition on the distal two-thirds of the dendritic tree with or without inhibition at the soma, with inhibition stronger in the distal third than in the middle third. It was estimated that the number of inhibitory synapses involved in the shunting inhibition should be 25-50% of the number of excitatory synapses activated by the eight-pulse, 400-Hz tetanus. This number could be 20-50% of the total number of inhibitory synapses in the distal two-thirds of the dendritic tree. The addition of a single inhibitory synapse on a dendrite had a significant effect on peak spine head [Cal-Ca4] in nearby spines. Inhibitory synapses had to be activated four or more times at 100 Hz for effective shunting to take place, and the inhibition had to begin no later than 2-5 ms after the first excitatory input. The results suggest that inhibition can isolate potentiated synapses to particular dendritic domains and that the location of activated inhibitory synapses may affect potentiation of individual synapses on individual dendrites.

Ovarian steroidal control of connectivity in the female hippocampus: an overview of recent experimental findings and speculations on its functional consequences.

Experimental evidence accumulated over the past 5 years clearly indicates that ovarian steroids regulate the number of synapses in the rat hippocampal CA1 region. When estradiol levels are high such as during proestrus and ovulation, the number of synapses is high; when estradiol levels are low such as during estrus, the number of synapses is low. Here we address three questions that are frequently raised by these phasic fluctuations in synapse number in a brain region to which cognitive functions are classically attributed. First, what neuronal signals might produce the changes in synapse number? Second, how are the hippocampal functions of memory encoding and cognitive mapping affected by fluctuating levels of ovarian steroids? Third, for mammals in general, what might be the ecological/cognitive significance of such changes? In this last section, we integrate some of the relevant human and rodent cognitive/behavioral literature and propose a hypothesis. Namely, by altering its quantitative connectivity, the female hippocampus is optimized for different cognitive/behavioral functions when the female is sexually receptive and ovarian steroid levels are high rather than when she is not receptive and steroid levels are low. The hippocampus thus shifts its optimal computational functions across the estrous/menstrual cycle.

The relationship of local context codes to sequence length memory capacity.

This paper pursues part of a theory to understand sequence prediction networks that use local context neuron encodings. In particular, a previously described neural network model of hippocampal CA3 is studied. General expressions relating CA3 interpattern distances (which reflect local context codes) to sequence length memory capacity are created and verified by computer simulations. As a result, we confirm a very simple relationship between the sequence length memory capacity and a combination of average activity level and the average local context lifetimes. Sequence length memory capacity is also bounded for networks using such local context neuronal codes. Thus, this simple theory quantifies an important limitation on a fully adaptive (i.e. self-supervising) neural model capable of creating context-dependent learning and memory.