A minimal synaptic architecture is proposed for how the brain might perform path integration by computing the next internal representation of self-location from the current representation and from the perceived velocity of motion. In the model, a place-cell assembly called a “chart ” contains a twodimensional attractor set called an “attractor map ” that can be used to represent coordinates in any arbitrary environment, once associative binding has occurred between chart locations and sensory inputs. In hippocampus, there are different spatial relations among place fields in different environments and behavioral contexts. Thus, the same units may participate in many charts, and it is shown that the number of uncorrelated charts that can be encoded in the same recurrent network is potentially quite large. According to this theory, the firing of a given place cell is primarily a cooperative effect of the activity of its

The problem of predicting the position of a freely foraging rat based on the ensemble firing patterns of place cells recorded from the CA1 region of its hippocampus is used to develop a two-stage statistical paradigm for neural spike train decoding. In the first,or encoding stage,place cell spiking activity is modeled as an inhomogeneous Poisson process whose instantaneous rate is a function of the animal’s position in space and phase of its theta rhythm. The animal’s path is modeled as a Gaussian random walk. In the second,or decoding stage,a Bayesian statistical paradigm is used to derive a nonlinear recursive causal filter algorithm for predicting the position of the animal from the place cell ensemble firing patterns. The algebra of the decoding algorithm defines an explicit map of the discrete spike trains into the position prediction. The confidence regions for the position predictions quantify spike train infor-

ABSTRACT: This paper presents a model of how hippocampal place cells might be used for spatial navigation in two watermaze tasks: the standard reference memory task and a delayed matching-to-place task. In the reference memory task, the escape platform occupies a single location and rats gradually learn relatively direct paths to the goal over the course of days, in each of which they perform a fixed number of trials. In the delayed matching-to-place task, the escape platform occupies a novel location on each day, and rats gradually acquire one-trial learning, i.e., direct paths on the second trial of each day. The model uses a local, incremental, and statistically efficient connectionist algorithm called temporal difference learning in two distinct components. The first is a reinforcement-based ‘‘actor-critic’ ’ network that is a general model of classical and instrumental conditioning. In this case, it is applied to navigation, using place cells to provide information about state. By itself, the actor-critic can learn the reference memory task, but this learning is inflexible to changes to the platform location. We argue that one-trial learning in the delayed matching-to-place task demands a goal-independent representation of space. This is provided by the second component of the model: a network that uses temporal difference learning and selfmotion information to acquire consistent spatial coordinates in the environment. Each component of the model is necessary at a different stage of the task; the actor-critic provides a way of transferring control to the component that performs best. The model successfully captures gradual acquisition in both tasks, and, in particular, the ultimate development of one-trial learning in the delayed matching-to-place task. Place cells report a form of stable, allocentric information that is well-suited to the various kinds of learning in the model. Hippocampus 2000;10:1–16.

Our model of the spatial and temporal aspects of place cell firing, and their role in rat navigation is reviewed. The model provides a can- didate mechanism, at the level of individual cells, by which place cell information concerning self-localization could be used to guide navi- gation to previously visited reward sites. The model embodies specific predictions regarding the formation of place fields, the phase coding of place cell firing with respect to the hippocampal theta rhythm, and the formation of neuronal population vectors downstream from the place cells that code for the directions of goals during navigation. Re- cent experiments regarding the spatial distribution of place cell firing have confirmed our initial modeling hypothesis, that place fields are formed from Gaussian tuning curve inputs coding for the distances from environmental features, and enabled us to further specify the functional form of these inputs. Other recent experiments regarding the temporal distribution of place cell firing in 2-dimensional environ- ments have confirmed our predictions based on the temporal aspects of place cell firing on linear tracks. Directions for further experiments and refinements to the model are outlined for the future.

Information in neuronal networks may be represented by the spatiotemporal patterns of spikes. Here we examined the temporal coordination of pyramidal cell spikes in the rat hippocampus during slow-wave sleep. In addition, rats were trained to run in a defined position in space (running wheel) to activate a selected group of pyramidal cells. A template-matching method and a joint probability map method were used for sequence search. Repeating spike sequences in excess of chance occurrence were examined by comparing the number of repeating sequences in the original spike trains and in surrogate trains after Monte Carlo shuffling of the spikes. Four different shuffling procedures were used to control for the population dynamics of Although it is a widely accepted notion that information is distributed in cell assemblies rather than encoded by single cells, the nature of coding in cell assembly has remained a major challenge for neuroscience research. Several explanations have been proposed on theoretical grounds, including frequency coding

Cortical neurons are typically driven by thousands of synaptic inputs. The arrival of a spike from one input may or may not be correlated with the arrival of other spikes from different inputs. How does this interdependence alter the probability that the postsynaptic neuron will fire? We constructed a simple random walk model in which the membrane potential of a target neuron fluctuates stochastically, driven by excitatory and inhibitory spikes arriving at random times. An analytic expression was derived for the mean output firing rate as a function of the firing rates and pairwise correlations of the inputs. This stochastic model made three quantitative predictions. (1) Correlations between pairs of excitatory or inhibitory inputs increase the fluctuations in synaptic drive, whereas correlations between excitatory–inhibitory pairs decrease them. (2) When excitation and inhibition are fully balanced (the mean net synaptic drive is zero),

ABSTRACT: Firing of place cells in the exploring rat conveys doubly coded spatial information: both the rate of spikes and their timing relative to the phase of the ongoing field theta oscillation are correlated with the location of the animal. Specifically, the firing rate of a place cell waxes and wanes, while the timing of spikes precesses monotonically as the animal traverses the portion of the environment preferred by the cell. We propose a mechanism for the generation of this firing pattern that can be applied for place cells in all three hippocampal subfields and that encodes spatial information in the output of the cell without relying on topographical connections or topographical input. A single pyramidal cell was modeled so that the cell received rhythmic inhibition in phase with theta field potential oscillation on the soma and was excited on the dendrite with input depending on the speed of the rat. The dendrite sustained an intrinsic membrane potential oscillation, frequency modulated by its input. Firing probability of the cell was determined jointly by somatic and

The firing characteristics of 1437 CA1 pyramidal neurons were studied in relation to both spatial location and the phase of the theta rhythm in healthy young and old rats performing a simple spatial task on a rectangular track. The old rats had previously been found to be deficient on the Morris spatial learning task. Age effects on the theta rhythm per se were minimal. Theta amplitude and frequency during rapid eye movement sleep were virtually identical. During behavior, theta frequency was slightly reduced with age. In both groups, cell firing occurred at progressively earlier phases of the theta rhythm as the rat traversed the place field of the cell (i.e., there was “phase precession, ” as reported by others). The net phase shift did not differ between age groups. The main finding of the study was a Because effective spatial learning requires an intact hippocampus (e.g., O’Keefe and Nadel, 1978; Morris et al., 1982; Sutherland et al., 1982; Barnes, 1988; Jarrard, 1993), and because this crucial cognitive function is significantly impaired during normal aging, the study of how neuronal information processing in the hippocampus is altered with age is of considerable interest. In rodents, age deficits are observed in a variety of spatial learning

The neocortex, hippocampus, and several other brain regions contain populations of excitatory principal cells with recurrent connections and strong interactions with local inhibitory interneurons. To improve our understanding of the interactions among these cell types, we modeled the dynamic behavior of this type of network, including external inputs. A surprising finding was that increasing the direct external inhibitory input to the inhibitory interneurons, without directly affecting any other part of the network, can, in some circumstances, cause the interneurons to increase their firing rates. The main prerequisite for this paradoxical response to external input is that the recurrent connections among the excitatory cells are strong enough to make the excitatory network unstable when feedback inhibition is removed. Because this requirement is met in the neocortex and several regions of the hippocampus, these observations

ABSTRACT: This article presents a model of grid cell firing based on the intrinsic persistent firing shown experimentally in neurons of entorhinal cortex. In this model, the mechanism of persistent firing allows individual neurons to hold a stable baseline firing frequency. Depolarizing input from speed-modulated head direction cells transiently shifts the frequency of firing from baseline, resulting in a shift in spiking phase in proportion to the integral of velocity. The convergence of input from different persistent firing neurons causes spiking in a grid cell only when the persistent firing neurons are within similar phase ranges. This model effectively simulates the two-dimensional firing of grid cells in open field environments, as well as the properties of theta phase precession. This model provides an alternate implementation of oscillatory interference models. The persistent firing could also interact on a circuit level with rhythmic inhibition and neurons showing membrane potential oscillations to code position with spiking phase. These mechanisms could operate in parallel with computation of position from visual angle and distance of stimuli. In addition to simulating two-dimensional grid patterns, models of phase interference can account for context-dependent firing in other tasks. In network simulations of entorhinal cortex, hippocampus, and postsubiculum, the reset of phase effectively replicates context-dependent firing by entorhinal and hippocampal neurons during performance of a continuous spatial alternation task, a delayed spatial alternation task with running in a wheel during the delay period (Pastalkova et al., Science, 2008), and a hairpin maze task. VC 2008 Wiley-Liss, Inc. KEY WORDS: grid cells; place cells; persistent spiking; membrane potential oscillations; theta rhythm; neuromodulation; stellate cells;