Hippocampal network dynamics constrain the time lag between pyramidal cells across modified environments

Independent theta phase coding accounts for CA1 population sequences and enables flexible remapping

Hippocampal place cells encode an animal's past, current, and future location through sequences of action potentials generated within each cycle of the network theta rhythm. These sequential representations have been suggested to result from temporally coordinated synaptic interactions within and between cell assemblies. Instead, we find through simulations and analysis of experimental data that rate and phase coding in independent neurons is sufficient to explain the organization of CA1 population activity during theta states. We show that CA1 population activity can be described as an evolving traveling wave that exhibits phase coding, rate coding, spike sequences and that generates an emergent population theta rhythm. We identify measures of global remapping and intracellular theta dynamics as critical for distinguishing mechanisms for pacemaking and coordination of sequential population activity. Our analysis suggests that, unlike synaptically coupled assemblies, independent neurons flexibly generate sequential population activity within the duration of a single theta cycle.

DOI:http://dx.doi.org/10.7554/eLife.03542.001

When we explore a new place, we naturally create a mental map of the location as we go. This mental map is stored in a region of the brain called the hippocampus, which contains cells called place cells. These cells can carry information about our past, present, and future location in the form of electrical signals. They connect to each other to form networks and it has been proposed that these connections can store the information needed for the mental maps.

Real-time maps are represented in the information carried by the electrical signals themselves. A physical location is specified by the individual place cell that is activated, and by the timing of the electrical signal it produces relative to a ‘brain wave’ called the theta rhythm. Brain waves are patterns of electrical signals activated in sets of brain cells and the theta rhythm is produced in the hippocampus of an animal as it explores its surroundings.

Previous experiments suggested that when a rat explores an area, several sets of brain cells in the hippocampus are activated in sequence within each cycle of the theta rhythm. As the rat moves forward, the sequence shifts to different sets of cells to reflect the upcoming locations ahead of the rat. It has been thought that these sequences are triggered by the individual connections between the place cells.

Here, Chadwick et al. developed mathematical models of the electrical activity in the brains of rats as they explored. They used these models to analyze data from previous experiments and found that the sequences of electrical activity arise from the timing of each cell's activity relative to the theta rhythm, rather than from the connections between the cells.

Chadwick et al.'s findings suggest that the mental map may be highly flexible, allowing vast numbers of distinct memories to be stored within the same network of place cells without interference. Future studies will involve investigating the role of brain waves in the forming new mental maps and creating new memories.

DOI:http://dx.doi.org/10.7554/eLife.03542.002

Millisecond timescale synchrony among hippocampal neurons

Inhibitory neurons in cortical circuits play critical roles in composing spike timing and oscillatory patterns in neuronal activity. These roles in turn require coherent activation of interneurons at different timescales. To investigate how the local circuitry provides for these activities, we applied resampled cross-correlation analyses to large-scale recordings of neuronal populations in the cornu ammonis 1 (CA1) and CA3 regions of the hippocampus of freely moving rats. Significant counts in the cross-correlation of cell pairs, relative to jittered surrogate spike-trains, allowed us to identify the effective couplings between neurons in CA1 and CA3 hippocampal regions on the timescale of milliseconds. In addition to putative excitatory and inhibitory monosynaptic connections, we uncovered prominent millisecond timescale synchrony between cell pairs, observed as peaks in the central 0 ms bin of cross-correlograms. This millisecond timescale synchrony appeared to be independent of network state, excitatory input, and γ oscillations. Moreover, it was frequently observed between cells of differing putative interneuronal type, arguing against gap junctions as the sole underlying source. Our observations corroborate recent in vitro findings suggesting that inhibition alone is sufficient to synchronize interneurons at such fast timescales. Moreover, we show that this synchronous spiking may cause stronger inhibition and rebound spiking in target neurons, pointing toward a potential function for millisecond synchrony of interneurons in shaping and affecting timing in pyramidal populations within and downstream from the circuit.

Back to the future: preserved hippocampal network activity during reverse ambulation

During movement, there is a transition of activity across the population, such that place-field centers ahead of the rat are sequentially activated in the order that they will be encountered. Although the mechanisms responsible for this sequence updating are unknown, two classes of models can be considered. The first class involves head-direction information for activating neurons in the order that their place fields will be traversed. An alternative model contends that motion and turn-related information from the posterior parietal cortex shift the subset of active hippocampal cells across the population. To explicitly test these two models, rodents were trained to run backward on a linear track, placing movement in opposition with head orientation. Although head-direction did not change between running conditions, place-field activity remapped and there was an increase in place-field size during backward running compared with forward. The population activity, however, could still be used to reconstruct the location of the rat accurately. Moreover, theta phase precession was maintained in both running conditions, indicating preservation of place-field sequences on short-time scales. The observation that sequence encoding persists even when the animal is orientated away from the direction of movement favors the concept that posterior parietal cortical mechanisms may be partially responsible for updating hippocampal activity patterns.

Theta phase segregation of input-specific gamma patterns in entorhinal-hippocampal networks

Precisely how rhythms support neuronal communication remains obscure. We investigated interregional coordination of gamma oscillations using high-density electrophysiological recordings in the rat hippocampus and entorhinal cortex. We found that 30-80 Hz gamma dominated CA1 local field potentials (LFPs) on the descending phase of CA1 theta waves during navigation, with 60-120 Hz gamma at the theta peak. These signals corresponded to CA3 and entorhinal input, respectively. Above 50 Hz, interregional phase-synchronization of principal cell spikes occurred mostly for LFPs in the axonal target domain. CA1 pyramidal cells were phase-locked mainly to fast gamma (>100 Hz) LFP patterns restricted to CA1, which were strongest at the theta trough. While theta phase coordination of spiking across entorhinal-hippocampal regions depended on memory demands, LFP gamma patterns below 100 Hz in the hippocampus were consistently layer specific and largely reflected afferent activity. Gamma synchronization as a mechanism for interregional communication thus rapidly loses efficacy at higher frequencies.

Reconceiving the hippocampal map as a topological template

The role of the hippocampus in spatial cognition is incontrovertible yet controversial. Place cells, initially thought to be location-specifiers, turn out to respond promiscuously to a wide range of stimuli. Here we test the idea, which we have recently demonstrated in a computational model, that the hippocampal place cells may ultimately be interested in a space's topological qualities (its connectivity) more than its geometry (distances and angles); such higher-order functioning would be more consistent with other known hippocampal functions. We recorded place cell activity in rats exploring morphing linear tracks that allowed us to dissociate the geometry of the track from its topology. The resulting place fields preserved the relative sequence of places visited along the track but did not vary with the metrical features of the track or the direction of the rat's movement. These results suggest a reinterpretation of previous studies and new directions for future experiments.

The effects of theta precession on spatial learning and simplicial complex dynamics in a topological model of the hippocampal spatial map

Learning arises through the activity of large ensembles of cells, yet most of the data neuroscientists accumulate is at the level of individual neurons; we need models that can bridge this gap. We have taken spatial learning as our starting point, computationally modeling the activity of place cells using methods derived from algebraic topology, especially persistent homology. We previously showed that ensembles of hundreds of place cells could accurately encode topological information about different environments (“learn” the space) within certain values of place cell firing rate, place field size, and cell population; we called this parameter space the learning region. Here we advance the model both technically and conceptually. To make the model more physiological, we explored the effects of theta precession on spatial learning in our virtual ensembles. Theta precession, which is believed to influence learning and memory, did in fact enhance learning in our model, increasing both speed and the size of the learning region. Interestingly, theta precession also increased the number of spurious loops during simplicial complex formation. We next explored how downstream readout neurons might define co-firing by grouping together cells within different windows of time and thereby capturing different degrees of temporal overlap between spike trains. Our model's optimum coactivity window correlates well with experimental data, ranging from ∼150–200 msec. We further studied the relationship between learning time, window width, and theta precession. Our results validate our topological model for spatial learning and open new avenues for connecting data at the level of individual neurons to behavioral outcomes at the neuronal ensemble level. Finally, we analyzed the dynamics of simplicial complex formation and loop transience to propose that the simplicial complex provides a useful working description of the spatial learning process.

One of the challenges in contemporary neuroscience is that we have few ways to connect data about the features of individual neurons with effects (such as learning) that emerge only at the scale of large cell ensembles. We are tackling this problem using spatial learning as a starting point. In previous work we created a computational model of spatial learning using concepts from the field of algebraic topology, proposing that the hippocampal map encodes topological features of an environment (connectivity) rather than precise metrics (distances and angles between locations)—more akin to a subway map than a street map. Our model simulates the activity of place cells as a rat navigates the experimental space so that we can estimate the effect produced by specific electrophysiological components —cell firing rate, population size, etc.—on the net outcome. In this work, we show that θ phase precession significantly enhanced spatial learning, and that the way downstream neurons group cells together into coactivity windows exerts interesting effects on learning time. These findings strongly support the notion that theta phase precession enhances spatial learning. Finally, we propose that ideas from topological theory provide a conceptually elegant description of the actual learning process.

Learning-induced plasticity regulates hippocampal sharp wave-ripple drive

Hippocampal sharp wave-ripples (SPW-Rs) and associated place-cell reactivations are crucial for spatial memory consolidation during sleep and rest. However, it remains unclear how learning and consolidation requirements influence and regulate subsequent SPW-R activity. Indeed, SPW-R activity has been observed not only following complex behavioral tasks, but also after random foraging in familiar environments, despite markedly different learning requirements. Because transient increases in SPW-R rates have been reported following training on memory tasks, we hypothesized that SPW-R activity following learning (but not routine behavior) could involve specific regulatory processes related to ongoing consolidation. Interfering with ripples would then result in a dynamic compensatory response only when initial memory traces required consolidation. Here we trained rats on a spatial memory task, and showed that subsequent sleep periods where ripple activity was perturbed by timed electrical stimulation were indeed characterized by increased SPW-R occurrence rates compared with control sleep periods where stimulations were slightly delayed in time and did not interfere with ripples. Importantly, this did not occur following random foraging in a familiar environment. We next showed that this dynamic response was abolished following injection of an NMDA receptor blocker (MK-801) before, but not after training. Our results indicate that NMDA receptor-dependent processes occurring during learning, such as network "tagging" and plastic changes, regulate subsequent ripple-mediated consolidation of spatial memory during sleep.

Neurosharing: large-scale data sets (spike, LFP) recorded from the hippocampal-entorhinal system in behaving rats

Using silicon-based recording electrodes, we recorded neuronal activity of the dorsal hippocampus and dorsomedial entorhinal cortex from behaving rats. The entorhinal neurons were classified as principal neurons and interneurons based on monosynaptic interactions and wave-shapes. The hippocampal neurons were classified as principal neurons and interneurons based on monosynaptic interactions, wave-shapes and burstiness. The data set contains recordings from 7,736 neurons (6,100 classified as principal neurons, 1,132 as interneurons, and 504 cells that did not clearly fit into either category) obtained during 442 recording sessions from 11 rats (a total of 204.5 hours) while they were engaged in one of eight different behaviours/tasks. Both original and processed data (time stamp of spikes, spike waveforms, result of spike sorting and local field potential) are included, along with metadata of behavioural markers. Community-driven data sharing may offer cross-validation of findings, refinement of interpretations and facilitate discoveries.

Comparison of sleep spindles and theta oscillations in the hippocampus

Several network patterns allow for information exchange between the neocortex and the entorhinal-hippocampal complex, including theta oscillations and sleep spindles. How neurons are organized in these respective patterns is not well understood. We examined the cellular-synaptic generation of sleep spindles and theta oscillations in the waking rat and during rapid eye movement (REM) sleep by simultaneously recording local field and spikes in the regions and layers of the hippocampus and entorhinal cortex (EC). We show the following: (1) current source density analysis reveals that similar anatomical substrates underlie spindles and theta in the hippocampus, although the hippocampal subregions are more synchronized during spindles than theta; (2) the spiking of putative principal cells and interneurons in the CA1, CA3, and dentate gyrus subregions of the hippocampus, as well as layers 2, 3, and 5 of medial EC, are significantly phase locked to spindles detected in CA1; (3) the relationship between local field potential (LFP) phase and unit spiking differs between spindles and theta; (4) individual hippocampal principal cells generally do not fire in a rhythmic manner during spindles; (5) power in gamma (30-90 Hz) and epsilon (>90 Hz) bands of hippocampal LFP is modulated by the phase of spindle oscillations; and (6) unit firing rates during spindles were not significantly affected by whether spindles occurred during non-REM or transitions between non-REM and REM sleep. Thus, despite the similar current generator inputs and macroscopic appearance of the LFP, the organization of neuronal firing patterns during spindles bears little resemblance to that of theta oscillations.

Oscillatory multiplexing of population codes for selective communication in the mammalian brain

Mammalian brains exhibit population oscillations, the structures of which vary in time and space according to behavioural state. A proposed function of these oscillations is to control the flow of signals among anatomically connected networks. However, the nature of neural coding that may support selective communication that depends on oscillations has received relatively little attention. Here, we consider the role of multiplexing, whereby multiple information streams share a common neural substrate. We suggest that multiplexing implemented through periodic modulation of firing-rate population codes enables flexible reconfiguration of effective connectivity among brain areas.

Theta oscillations decrease spike synchrony in the hippocampus and entorhinal cortex

Oscillations and synchrony are often used synonymously. However, oscillatory mechanisms involving both excitation and inhibition can generate non-synchronous yet coordinated firing patterns. Using simultaneous recordings from multiple layers of the entorhinal-hippocampal loop, we found that coactivation of principal cell pairs (synchrony) was lowest during exploration and rapid-eye-movement (REM) sleep, associated with theta oscillations, and highest in slow wave sleep. Individual principal neurons had a wide range of theta phase preference. Thus, while theta oscillations reduce population synchrony, they nevertheless coordinate the phase (temporal) distribution of neurons. As a result, multiple cell assemblies can nest within the period of the theta cycle.

Temporal redistribution of inhibition over neuronal subcellular domains underlies state-dependent rhythmic change of excitability in the hippocampus

The behaviour-contingent rhythmic synchronization of neuronal activity is reported by local field potential oscillations in the theta, gamma and sharp wave-related ripple (SWR) frequency ranges. In the hippocampus, pyramidal cell assemblies representing temporal sequences are coordinated by GABAergic interneurons selectively innervating specific postsynaptic domains, and discharging phase locked to network oscillations. We compare the cellular network dynamics in the CA1 and CA3 areas recorded with or without anaesthesia. All parts of pyramidal cells, except the axon initial segment, receive GABA from multiple interneuron types, each with distinct firing dynamics. The axon initial segment is exclusively innervated by axo-axonic cells, preferentially firing after the peak of the pyramidal layer theta cycle, when pyramidal cells are least active. Axo-axonic cells are inhibited during SWRs, when many pyramidal cells fire synchronously. This dual inverse correlation demonstrates the key inhibitory role of axo-axonic cells. Parvalbumin-expressing basket cells fire phase locked to field gamma activity in both CA1 and CA3, and also strongly increase firing during SWRs, together with dendrite-innervating bistratified cells, phasing pyramidal cell discharge. Subcellular domain-specific GABAergic innervation probably developed for the coordination of multiple glutamatergic inputs on different parts of pyramidal cells through the temporally distinct activity of GABAergic interneurons, which differentially change their firing during different network states.

Hippocampal theta oscillations are slower in humans than in rodents: implications for models of spatial navigation and memory

The theta oscillation is a neuroscience enigma. When a rat runs through an environment, large-amplitude theta oscillations (4-10 Hz) reliably appear in the hippocampus's electrical activity. The consistency of this pattern led to theta playing a central role in theories on the neural basis of mammalian spatial navigation and memory. However, in fact, hippocampal oscillations at 4-10 Hz are rare in humans and in some other species. This presents a challenge for theories proposing theta as an essential component of the mammalian brain, including models of place and grid cells. Here, I examine this issue by reviewing recent research on human hippocampal oscillations using direct brain recordings from neurosurgical patients. This work indicates that the human hippocampus does indeed exhibit rhythms that are functionally similar to theta oscillations found in rodents, but that these signals have a slower frequency of approximately 1-4 Hz. I argue that oscillatory models of navigation and memory derived from rodent data are relevant for humans, but that they should be modified to account for the slower frequency of the human theta rhythm.

Theoretical foundations of the sound analog membrane potential that underlies coincidence detection in the barn owl

A wide variety of neurons encode temporal information via phase-locked spikes. In the avian auditory brainstem, neurons in the cochlear nucleus magnocellularis (NM) send phase-locked synaptic inputs to coincidence detector neurons in the nucleus laminaris (NL) that mediate sound localization. Previous modeling studies suggested that converging phase-locked synaptic inputs may give rise to a periodic oscillation in the membrane potential of their target neuron. Recent physiological recordings in vivo revealed that owl NL neurons changed their spike rates almost linearly with the amplitude of this oscillatory potential. The oscillatory potential was termed the sound analog potential, because of its resemblance to the waveform of the stimulus tone. The amplitude of the sound analog potential recorded in NL varied systematically with the interaural time difference (ITD), which is one of the most important cues for sound localization. In order to investigate the mechanisms underlying ITD computation in the NM-NL circuit, we provide detailed theoretical descriptions of how phase-locked inputs form oscillating membrane potentials. We derive analytical expressions that relate presynaptic, synaptic, and postsynaptic factors to the signal and noise components of the oscillation in both the synaptic conductance and the membrane potential. Numerical simulations demonstrate the validity of the theoretical formulations for the entire frequency ranges tested (1–8 kHz) and potential effects of higher harmonics on NL neurons with low best frequencies (<2 kHz).

Preconfigured, skewed distribution of firing rates in the hippocampus and entorhinal cortex

Despite the importance of the discharge frequency in neuronal communication, little is known about the firing-rate patterns of cortical populations. Using large-scale recordings from multiple layers of the entorhinal-hippocampal loop, we found that the firing rates of principal neurons showed a lognormal-like distribution in all brain states. Mean and peak rates within place fields of hippocampal neurons were also strongly skewed. Importantly, firing rates of the same neurons showed reliable correlations in different brain states and testing situations, as well as across familiar and novel environments. The fraction of neurons that participated in population oscillations displayed a lognormal pattern. Such skewed firing rates of individual neurons may be due to a skewed distribution of synaptic weights, which is supported by our observation of a lognormal distribution of the efficacy of spike transfer from principal neurons to interneurons. The persistent skewed distribution of firing rates implies that a preconfigured, highly active minority dominates information transmission in cortical networks.

Brain rhythms and neural syntax: implications for efficient coding of cognitive content and neuropsychiatric disease

The perpetual activity of the cerebral cortex is largely supported by the variety of oscillations the brain generates, spanning a number of frequencies and anatomical locations, as well as behavioral correlates. First, we review findings from animal studies showing that most forms of brain rhythms are inhibition-based, producing rhythmic volleys of inhibitory inputs to principal cell populations, thereby providing alternating temporal windows of relatively reduced and enhanced excitability in neuronal networks. These inhibition-based mechanisms offer natural temporal frames to group or "chunk" neuronal activity into cell assemblies and sequences of assemblies, with more complex multi-oscillation interactions creating syntactical rules for the effective exchange of information among cortical networks. We then review recent studies in human psychiatric patients demonstrating a variety alterations in neural oscillations across all major psychiatric diseases, and suggest possible future research directions and treatment approaches based on the fundamental properties of brain rhythms.

Prefrontal activity links nonoverlapping events in memory

The medial prefrontal cortex (mPFC) plays an important role in memory. By maintaining a working memory buffer, neurons in prelimbic (PL) mPFC may selectively contribute to learning associations between stimuli that are separated in time, as in trace fear conditioning (TFC). Until now, evidence for this bridging role was largely descriptive. Here we used optogenetics to silence neurons in the PL mPFC of rats during learning in TFC. Memory formation was prevented when mPFC was silenced specifically during the interval separating the cue and shock. Our results provide support for a working memory function for these cells and indicate that associating two noncontiguous stimuli requires bridging activity in PL mPFC.

Memory, navigation and theta rhythm in the hippocampal-entorhinal system

Theories on the functions of the hippocampal system are based largely on two fundamental discoveries: the amnestic consequences of removing the hippocampus and associated structures in the famous patient H.M. and the observation that spiking activity of hippocampal neurons is associated with the spatial position of the rat. In the footsteps of these discoveries, many attempts were made to reconcile these seemingly disparate functions. Here we propose that mechanisms of memory and planning have evolved from mechanisms of navigation in the physical world and hypothesize that the neuronal algorithms underlying navigation in real and mental space are fundamentally the same. We review experimental data in support of this hypothesis and discuss how specific firing patterns and oscillatory dynamics in the entorhinal cortex and hippocampus can support both navigation and memory.

A topological paradigm for hippocampal spatial map formation using persistent homology

An animal's ability to navigate through space rests on its ability to create a mental map of its environment. The hippocampus is the brain region centrally responsible for such maps, and it has been assumed to encode geometric information (distances, angles). Given, however, that hippocampal output consists of patterns of spiking across many neurons, and downstream regions must be able to translate those patterns into accurate information about an animal's spatial environment, we hypothesized that 1) the temporal pattern of neuronal firing, particularly co-firing, is key to decoding spatial information, and 2) since co-firing implies spatial overlap of place fields, a map encoded by co-firing will be based on connectivity and adjacency, i.e., it will be a topological map. Here we test this topological hypothesis with a simple model of hippocampal activity, varying three parameters (firing rate, place field size, and number of neurons) in computer simulations of rat trajectories in three topologically and geometrically distinct test environments. Using a computational algorithm based on recently developed tools from Persistent Homology theory in the field of algebraic topology, we find that the patterns of neuronal co-firing can, in fact, convey topological information about the environment in a biologically realistic length of time. Furthermore, our simulations reveal a "learning region" that highlights the interplay between the parameters in combining to produce hippocampal states that are more or less adept at map formation. For example, within the learning region a lower number of neurons firing can be compensated by adjustments in firing rate or place field size, but beyond a certain point map formation begins to fail. We propose that this learning region provides a coherent theoretical lens through which to view conditions that impair spatial learning by altering place cell firing rates or spatial specificity.

Running speed alters the frequency of hippocampal gamma oscillations

Successful spatial navigation is thought to employ a combination of at least two strategies: the following of landmark cues and path integration. Path integration requires that the brain use the speed and direction of movement in a meaningful way to continuously compute the position of the animal. Indeed, the running speed of rats modulates both the firing rate of neurons and the spectral properties of low frequency, theta oscillations seen in the local field potential (LFP) of the hippocampus, a region important for spatial memory formation. Higher frequency, gamma-band LFP oscillations are usually associated with decision-making, increased attention, and improved reaction times. Here, we show that increased running speed is accompanied by large, systematic increases in the frequency of hippocampal CA1 network oscillations spanning the entire gamma range (30-120 Hz) and beyond. These speed-dependent changes in frequency are seen on both linear tracks and two-dimensional platforms, and are thus independent of the behavioral task. Synchrony between anatomically distant CA1 regions also shifts to higher gamma frequencies as running speed increases. The changes in frequency are strongly correlated with changes in the firing rates of individual interneurons, consistent with models of gamma generation. Our results suggest that as a rat runs faster, there are faster gamma frequency transitions between sequential place cell-assemblies. This may help to preserve the spatial specificity of place cells and spatial memories at vastly different running speeds.

The neuroscience of learning: beyond the Hebbian synapse

From the traditional perspective of associative learning theory, the hypothesis linking modifications of synaptic transmission to learning and memory is plausible. It is less so from an information-processing perspective, in which learning is mediated by computations that make implicit commitments to physical and mathematical principles governing the domains where domain-specific cognitive mechanisms operate. We compare the properties of associative learning and memory to the properties of long-term potentiation, concluding that the properties of the latter do not explain the fundamental properties of the former. We briefly review the neuroscience of reinforcement learning, emphasizing the representational implications of the neuroscientific findings. We then review more extensively findings that confirm the existence of complex computations in three information-processing domains: probabilistic inference, the representation of uncertainty, and the representation of space. We argue for a change in the conceptual framework within which neuroscientists approach the study of learning mechanisms in the brain.

Quantifying circular-linear associations: hippocampal phase precession

When a rat crosses the place field of a hippocampal pyramidal cell, this cell typically fires a series of spikes. Spike phases, measured with respect to theta oscillations of the local field potential, on average decrease as a function of the spatial distance traveled. This relation between phase and position of spikes might be a neural basis for encoding and is called phase precession. The degree of association between the circular phase variable and the linear spatial variable is commonly quantified through, however, a linear-linear correlation coefficient where the circular variable is converted to a linear variable by restricting the phase to an arbitrarily chosen range, which may bias the estimated correlation. Here we introduce a new measure to quantify circular-linear associations. This measure leads to a robust estimate of the slope and phase offset of the regression line, and it provides a correlation coefficient for circular-linear data that is a natural analog of Pearson's product-moment correlation coefficient for linear-linear data. Using surrogate data, we show that the new method outperforms the standard linear-linear approach with respect to estimates of the regression line and the correlation, and that the new method is less dependent on noise and sample size. We confirm these findings in a large data set of experimental recordings from hippocampal place cells and theta oscillations, and we discuss remaining problems that are relevant for the analysis and interpretation of phase precession. In summary, we provide a new method for the quantification of circular-linear associations.

Cross-frequency phase-phase coupling between θ and γ oscillations in the hippocampus

Neuronal oscillations allow for temporal segmentation of neuronal spikes. Interdependent oscillators can integrate multiple layers of information. We examined phase-phase coupling of theta and gamma oscillators in the CA1 region of rat hippocampus during maze exploration and rapid eye movement sleep. Hippocampal theta waves were asymmetric, and estimation of the spatial position of the animal was improved by identifying the waveform-based phase of spiking, compared to traditional methods used for phase estimation. Using the waveform-based theta phase, three distinct gamma bands were identified: slow gamma(S) (gamma(S); 30-50 Hz), midfrequency gamma(M) (gamma(M); 50-90 Hz), and fast gamma(F) (gamma(F); 90-150 Hz or epsilon band). The amplitude of each sub-band was modulated by the theta phase. In addition, we found reliable phase-phase coupling between theta and both gamma(S) and gamma(M) but not gamma(F) oscillators. We suggest that cross-frequency phase coupling can support multiple time-scale control of neuronal spikes within and across structures.

A nonlinear model for hippocampal cognitive prosthesis: memory facilitation by hippocampal ensemble stimulation

Collaborative investigations have characterized how multineuron hippocampal ensembles encode memory necessary for subsequent successful performance by rodents in a delayed nonmatch to sample (DNMS) task and utilized that information to provide the basis for a memory prosthesis to enhance performance. By employing a unique nonlinear dynamic multi-input/multi-output (MIMO) model, developed and adapted to hippocampal neural ensemble firing patterns derived from simultaneous recorded CA1 and CA3 activity, it was possible to extract information encoded in the sample phase necessary for successful performance in the nonmatch phase of the task. The extension of this MIMO model to online delivery of electrical stimulation delivered to the same recording loci that mimicked successful CA1 firing patterns, provided the means to increase levels of performance on a trial-by-trial basis. Inclusion of several control procedures provides evidence for the specificity of effective MIMO model generated patterns of electrical stimulation. Increased utility of the MIMO model as a prosthesis device was exhibited by the demonstration of cumulative increases in DNMS task performance with repeated MIMO stimulation over many sessions on both stimulation and nonstimulation trials, suggesting overall system modification with continued exposure. Results reported here are compatible with and extend prior demonstrations and further support the candidacy of the MIMO model as an effective cortical prosthesis.

Activity dynamics and behavioral correlates of CA3 and CA1 hippocampal pyramidal neurons

The CA3 and CA1 pyramidal neurons are the major principal cell types of the hippocampus proper. The strongly recurrent collateral system of CA3 cells and the largely parallel-organized CA1 neurons suggest that these regions perform distinct computations. However, a comprehensive comparison between CA1 and CA3 pyramidal cells in terms of firing properties, network dynamics, and behavioral correlations is sparse in the intact animal. We performed large-scale recordings in the dorsal hippocampus of rats to quantify the similarities and differences between CA1 (n > 3,600) and CA3 (n > 2,200) pyramidal cells during sleep and exploration in multiple environments. CA1 and CA3 neurons differed significantly in firing rates, spike burst propensity, spike entrainment by the theta rhythm, and other aspects of spiking dynamics in a brain state-dependent manner. A smaller proportion of CA3 than CA1 cells displayed prominent place fields, but place fields of CA3 neurons were more compact, more stable, and carried more spatial information per spike than those of CA1 pyramidal cells. Several other features of the two cell types were specific to the testing environment. CA3 neurons showed less pronounced phase precession and a weaker position versus spike-phase relationship than CA1 cells. Our findings suggest that these distinct activity dynamics of CA1 and CA3 pyramidal cells support their distinct computational roles.

Interaction between long-term potentiation and depression in CA1 synapses: temporal constrains, functional compartmentalization and protein synthesis

Information arriving at a neuron via anatomically defined pathways undergoes spatial and temporal encoding. A proposed mechanism by which temporally and spatially segregated information is encoded at the cellular level is based on the interactive properties of synapses located within and across functional dendritic compartments. We examined cooperative and interfering interactions between long-term synaptic potentiation (LTP) and depression (LTD), two forms of synaptic plasticity thought to be key in the encoding of information in the brain. Two approaches were used in CA1 pyramidal neurons of the mouse hippocampus: (1) induction of LTP and LTD in two separate synaptic pathways within the same apical dendritic compartment and across the basal and apical dendritic compartments; (2) induction of LTP and LTD separated by various time intervals (0–90 min). Expression of LTP/LTD interactions was spatially and temporally regulated. While they were largely restricted within the same dendritic compartment (compartmentalized), the nature of the interaction (cooperation or interference) depended on the time interval between inductions. New protein synthesis was found to regulate the expression of the LTP/LTD interference. We speculate that mechanisms for compartmentalization and protein synthesis confer the spatial and temporal modulation by which neurons encode multiplex information in plastic synapses.

Cross-frequency phase-phase coupling between θ and γ oscillations in the hippocampus

Neuronal oscillations allow for temporal segmentation of neuronal spikes. Interdependent oscillators can integrate multiple layers of information. We examined phase-phase coupling of theta and gamma oscillators in the CA1 region of rat hippocampus during maze exploration and rapid eye movement sleep. Hippocampal theta waves were asymmetric, and estimation of the spatial position of the animal was improved by identifying the waveform-based phase of spiking, compared to traditional methods used for phase estimation. Using the waveform-based theta phase, three distinct gamma bands were identified: slow gamma(S) (gamma(S); 30-50 Hz), midfrequency gamma(M) (gamma(M); 50-90 Hz), and fast gamma(F) (gamma(F); 90-150 Hz or epsilon band). The amplitude of each sub-band was modulated by the theta phase. In addition, we found reliable phase-phase coupling between theta and both gamma(S) and gamma(M) but not gamma(F) oscillators. We suggest that cross-frequency phase coupling can support multiple time-scale control of neuronal spikes within and across structures.

Greater running speeds result in altered hippocampal phase sequence dynamics

Hebb (1949) described a "phase sequence" to be the sequential activation of sets of cell assemblies. Within the hippocampus, cell assemblies have been described as groups of coactive neurons whose place fields overlap. Membership of assemblies in a phase sequence changes systematically as a rat travels through an environment, serving to accelerate the temporal order that place fields are encountered during a single theta cycle. This sweeping forward of network activity ("look ahead"), results in locations in front of the animal being transiently represented. In this experiment, a population vector-based reconstruction method was used to capture the look ahead and reveals that the composition of the phase sequence changes with velocity, such that more cell assemblies are active within a theta cycle at higher running speeds. These results are consistent with hypotheses suggesting that hippocampal networks generate short time scale predictions of future events to optimize behavior.

Neural syntax: cell assemblies, synapsembles, and readers

A widely discussed hypothesis in neuroscience is that transiently active ensembles of neurons, known as "cell assemblies," underlie numerous operations of the brain, from encoding memories to reasoning. However, the mechanisms responsible for the formation and disbanding of cell assemblies and temporal evolution of cell assembly sequences are not well understood. I introduce and review three interconnected topics, which could facilitate progress in defining cell assemblies, identifying their neuronal organization, and revealing causal relationships between assembly organization and behavior. First, I hypothesize that cell assemblies are best understood in light of their output product, as detected by "reader-actuator" mechanisms. Second, I suggest that the hierarchical organization of cell assemblies may be regarded as a neural syntax. Third, constituents of the neural syntax are linked together by dynamically changing constellations of synaptic weights ("synapsembles"). The existing support for this tripartite framework is reviewed and strategies for experimental testing of its predictions are discussed.

Effect of sampling frequency on the measurement of phase-locked action potentials

Phase-locked spikes in various types of neurons encode temporal information. To quantify the degree of phase-locking, the metric called vector strength (VS) has been most widely used. Since VS is derived from spike timing information, error in measurement of spike occurrence should result in errors in VS calculation. In electrophysiological experiments, the timing of an action potential is detected with finite temporal precision, which is determined by the sampling frequency. In order to evaluate the effects of the sampling frequency on the measurement of VS, we derive theoretical upper and lower bounds of VS from spikes collected with finite sampling rates. We next estimate errors in VS assuming random sampling effects, and show that our theoretical calculation agrees with data from electrophysiological recordings in vivo. Our results provide a practical guide for choosing the appropriate sampling frequency in measuring VS.

Dynamic grouping of hippocampal neural activity during cognitive control of two spatial frames

Hippocampal neurons represent two concurrent streams of spatial information by transiently organizing into subpopulations of coactive neurons and can reflect the most behaviorally relevant information at any given time.

Cognitive control is the ability to coordinate multiple streams of information to prevent confusion and select appropriate behavioral responses, especially when presented with competing alternatives. Despite its theoretical and clinical significance, the neural mechanisms of cognitive control are poorly understood. Using a two-frame place avoidance task and partial hippocampal inactivation, we confirmed that intact hippocampal function is necessary for coordinating two streams of spatial information. Rats were placed on a continuously rotating arena and trained to organize their behavior according to two concurrently relevant spatial frames: one stationary, the other rotating. We then studied how information about locations in these two spatial frames is organized in the action potential discharge of ensembles of hippocampal cells. Both streams of information were represented in neuronal discharge—place cell activity was organized according to both spatial frames, but almost all cells preferentially represented locations in one of the two spatial frames. At any given time, most coactive cells tended to represent locations in the same spatial frame, reducing the risk of interference between the two information streams. An ensemble's preference to represent locations in one or the other spatial frame alternated within a session, but at each moment, location in the more behaviorally relevant spatial frame was more likely to be represented. This discharge organized into transient groups of coactive neurons that fired together within 25 ms to represent locations in the same spatial frame. These findings show that dynamic grouping, the transient coactivation of neural subpopulations that represent the same stream of information, can coordinate representations of concurrent information streams and avoid confusion, demonstrating neural-ensemble correlates of cognitive control in hippocampus.

Understanding the world and making optimal decisions requires using the most relevant information while at the same time ignoring irrelevant information, a psychological phenomenon known as “cognitive control.” How the same population of neurons deals with multiple streams of information simultaneously is poorly understood. In this study, we investigated the underlying neural mechanisms of cognitive control in a network of hippocampal neurons known to represent space. We implanted electrodes into the hippocampus of rats and recorded the action potential discharge of many neurons at the same time. The recordings were made while rats that were foraging on a rotating disk used cognitive control to coordinate spatial information from different spatial frames. We found that at each moment, discharge preferentially represented location in one or the other spatial frame. Importantly, we were able to influence the behavioral relevance of these spatial frames, and we found that discharge alternated between signaling location in one or the other frames in accord with its current behavioral importance. The timing of when these neurons were active was also related to their function, such that neurons collectively represented locations in the same spatial frame if they were coactive within a few tens of milliseconds to seconds. We conclude that cognitive control is mediated by a dynamic functional grouping. Neural activity distributed across many neurons transiently organizes into functional groups by coactive firing that represents a coherent stream of information.

Temporal delays among place cells determine the frequency of population theta oscillations in the hippocampus

Driven either by external landmarks or by internal dynamics, hippocampal neurons form sequences of cell assemblies. The coordinated firing of these active cells is organized by the prominent "theta" oscillations in the local field potential (LFP): place cells discharge at progressively earlier theta phases as the rat crosses the respective place field ("phase precession"). The faster oscillation frequency of active neurons and the slower theta LFP, underlying phase precession, creates a paradox. How can faster oscillating neurons comprise a slower population oscillation, as reflected by the LFP? We built a mathematical model that allowed us to calculate the population activity analytically from experimentally derived parameters of the single neuron oscillation frequency, firing field size (duration), and the relationship between within-theta delays of place cell pairs and their distance representations ("compression"). The appropriate combination of these parameters generated a constant frequency population rhythm along the septo-temporal axis of the hippocampus, while allowing individual neurons to vary their oscillation frequency and field size. Our results suggest that the faster-than-theta oscillations of pyramidal cells are inherent and that phase precession is a result of the coordinated activity of temporally shifted cell assemblies, relative to the population activity, reflected by the LFP.

Theta oscillations provide temporal windows for local circuit computation in the entorhinal-hippocampal loop

Theta oscillations are believed to play an important role in the coordination of neuronal firing in the entorhinal (EC)-hippocampal system but the underlying mechanisms are not known. We simultaneously recorded from neurons in multiple regions of the EC-hippocampal loop and examined their temporal relationships. Theta-coordinated synchronous spiking of EC neuronal populations predicted the timing of current sinks in target layers in the hippocampus. However, the temporal delays between population activities in successive anatomical stages were longer (typically by a half theta cycle) than expected from axon conduction velocities and passive synaptic integration of feed-forward excitatory inputs. We hypothesize that the temporal windows set by the theta cycles allow for local circuit interactions and thus a considerable degree of computational independence in subdivisions of the EC-hippocampal loop.

Alteration of theta timescale dynamics of hippocampal place cells by a cannabinoid is associated with memory impairment

The integrity of the hippocampus is critical for both spatial navigation and episodic memory, but how its neuronal firing patterns underlie those functions is not well understood. In particular, the modality by which hippocampal place cells contribute to spatial memory is debated. We found that administration of the cannabinoid receptor agonist CP55940 (2-[(1S,2R,5S)-5-hydroxy-2-(3-hydroxypropyl)cyclohexyl]-5-(2-methyloctan-2-yl)phenol) induced a profound and reversible behavioral deficit in the hippocampus-dependent delayed spatial alternation task. On the one hand, despite severe memory impairment, the location-dependent firing of CA1 hippocampal place cells remained mostly intact. On the other hand, both spike-timing coordination between place cells at the theta timescale and theta phase precession of spikes were reversibly reduced. These results raise the possibility that cannabinoids impair memory primarily by altering short-term temporal dynamics of hippocampal neurons. We hypothesize that precise temporal coordination of hippocampal neurons is necessary for guiding behavior in spatial memory tasks.

Single-trial phase precession in the hippocampus

During the crossing of the place field of a pyramidal cell in the rat hippocampus, the firing phase of the cell decreases with respect to the local theta rhythm. This phase precession is usually studied on the basis of data in which many place field traversals are pooled together. Here we study properties of phase precession in single trials. We found that single-trial and pooled-trial phase precession were different with respect to phase-position correlation, phase-time correlation, and phase range. Whereas pooled-trial phase precession may span 360 degrees , the most frequent single-trial phase range was only approximately 180 degrees. In pooled trials, the correlation between phase and position (r = -0.58) was stronger than the correlation between phase and time (r = -0.27), whereas in single trials these correlations (r = -0.61 for both) were not significantly different. Next, we demonstrated that phase precession exhibited a large trial-to-trial variability. Overall, only a small fraction of the trial-to-trial variability in measures of phase precession (e.g., slope or offset) could be explained by other single-trial properties (such as running speed or firing rate), whereas the larger part of the variability remains to be explained. Finally, we found that surrogate single trials, created by randomly drawing spikes from the pooled data, are not equivalent to experimental single trials: pooling over trials therefore changes basic measures of phase precession. These findings indicate that single trials may be better suited for encoding temporally structured events than is suggested by the pooled data.