Theta oscillation-coupled dendritic spiking integrates inputs on a long time scale

From Topological Analyses to Functional Modeling: The Case of Hippocampus

Topological data analyses are widely used for describing and conceptualizing large volumes of neurobiological data, e.g., for quantifying spiking outputs of large neuronal ensembles and thus understanding the functions of the corresponding networks. Below we discuss an approach in which convergent topological analyses produce insights into how information may be processed in mammalian hippocampus—a brain part that plays a key role in learning and memory. The resulting functional model provides a unifying framework for integrating spiking data at different timescales and following the course of spatial learning at different levels of spatiotemporal granularity. This approach allows accounting for contributions from various physiological phenomena into spatial cognition—the neuronal spiking statistics, the effects of spiking synchronization by different brain waves, the roles played by synaptic efficacies and so forth. In particular, it is possible to demonstrate that networks with plastic and transient synaptic architectures can encode stable cognitive maps, revealing the characteristic timescales of memory processing.

A model of topological mapping of space in bat hippocampus

The mammalian hippocampus plays a key role in spatial learning and memory, but the exact nature of the hippocampal representation of space is still being explored. Recently, there has been a fair amount of success in modeling hippocampal spatial maps in rats, assuming a topological perspective on spatial information processing. In this article, we use the topological approach to study the formation of a 3D spatial map in bats, which produces several insights into neurophysiological mechanisms of the hippocampal spatial leaning. First, we demonstrate that, in order to produce accurate maps of the environment, place cell should be organized into functional groups, which can be interpreted as cell assemblies. Second, the model suggests that the readout neurons in these cell assemblies should function as integrators of synaptic inputs, rather than detectors of place cells' coactivity, which allows estimating the integration time window. Lastly, the model suggests that, in contrast with relatively slow moving rats, suppressing θ-precession in bats improves the place cells capacity to encode spatial maps, which is consistent with the experimental observations. © 2016 Wiley Periodicals, Inc.

Electrophysiological aberrations associated with negative symptoms in schizophrenia

Clinical heterogeneity is a confound common to all of schizophrenia research. Deficit schizophrenia has been proposed as a homogeneous disease entity within the schizophrenia syndrome. The use of the Schedule for the Deficit Syndrome (SDS) has allowed the definition of a subgroup dominated by persistent and primary negative symptoms. While a number of studies have appeared over the years examining the electrophysiological correlates of the cluster of negative symptoms in schizophrenia, only a few studies have actually focused on the Deficit Syndrome (DS). In this chapter, electrophysiological investigations utilizing EEG, Evoked Potentials (EPs), polysomnography (PSG), or magnetoencephalography (MEG) to probe "negative symptoms," or "Deficit Syndrome" are reviewed. While this line of research is evidently in its infancy, two significant trends emerge. First, spectral EEG studies link increased slow wave activity during wakefulness to the prevalence of negative symptoms. Second, sleep studies point to an association between decrease in slow wave sleep and prevalence of negative symptoms. Several studies also indicate a relationship of negative symptoms with reduced alpha activity. A host of other abnormalities including sensory gating and P300 attenuation are less consistently reported. Three studies specifically addressed electrophysiology of the DS. Two of the three studies provided evidence suggesting that the DS may be a separate disease entity and not simply a severe form of schizophrenia.

Emergence in the central nervous system

"Emergence" is an idea that has received much attention in consciousness literature, but it is difficult to find characterizations of that concept which are both specific and useful. I will precisely define and characterize a type of epistemic ("weak") emergence and show that it is a property of some neural circuits throughout the CNS, on micro-, meso- and macroscopic levels. I will argue that possession of this property can result in profoundly altered neural dynamics on multiple levels in cortex and other systems. I will first describe emergent neural entities (ENEs) abstractly. I will then show how ENEs function specifically and concretely, and demonstrate some implications of this type of emergence for the CNS.

Models of grid cell spatial firing published 2005-2011

Since the discovery of grid cells in rat entorhinal cortex, many models of their hexagonally arrayed spatial firing fields have been suggested. We review the models and organize them according to the mechanisms they use to encode position, update the positional code, read it out in the spatial grid pattern, and learn any patterned synaptic connections needed. We mention biological implementations of the models, but focus on the models on Marr’s algorithmic level, where they are not things to individually prove or disprove, but rather are a valuable collection of metaphors of the grid cell system for guiding research that are all likely true to some degree, with each simply emphasizing different aspects of the system. For the convenience of interested researchers, MATLAB implementations of the discussed grid cell models are provided at ModelDB accession 144006 or http://people.bu.edu/zilli/gridmodels.html.

Coupled noisy spiking neurons as velocity-controlled oscillators in a model of grid cell spatial firing

One of the two primary classes of models of grid cell spatial firing uses interference between oscillators at dynamically modulated frequencies. Generally, these models are presented in terms of idealized oscillators (modeled as sinusoids), which differ from biological oscillators in multiple important ways. Here we show that two more realistic, noisy neural models (Izhikevich's simple model and a biophysical model of an entorhinal cortex stellate cell) can be successfully used as oscillators in a model of this type. When additive noise is included in the models such that uncoupled or sparsely coupled cells show realistic interspike interval variance, both synaptic and gap-junction coupling can synchronize networks of cells to produce comparatively less variable network-level oscillations. We show that the frequency of these oscillatory networks can be controlled sufficiently well to produce stable grid cell spatial firing on the order of at least 2-5 min, despite the high noise level. Our results suggest that the basic principles of oscillatory interference models work with more realistic models of noisy neurons. Nevertheless, a number of simplifications were still made and future work should examine increasingly realistic models.

Binding by asynchrony: the neuronal phase code

Neurons display continuous subthreshold oscillations and discrete action potentials (APs). When APs are phase-locked to the subthreshold oscillation, we hypothesize they represent two types of information: the presence/absence of a sensory feature and the phase of subthreshold oscillation. If subthreshold oscillation phases are neuron-specific, then the sources of APs can be recovered based on the AP times. If the spatial information about the stimulus is converted to AP phases, then APs from multiple neurons can be combined into a single axon and the spatial configuration reconstructed elsewhere. For the reconstruction to be successful, we introduce two assumptions: that a subthreshold oscillation field has a constant phase gradient and that coincidences between APs and intracellular subthreshold oscillations are neuron-specific as defined by the "interference principle." Under these assumptions, a phase-coding model enables information transfer between structures and reproduces experimental phenomenons such as phase precession, grid cell architecture, and phase modulation of cortical spikes. This article reviews a recently proposed neuronal algorithm for information encoding and decoding from the phase of APs (Nadasdy, 2009). The focus is given to the principles common across different systems instead of emphasizing system specific differences.

Democracy-independence trade-off in oscillating dendrites and its implications for grid cells

Dendritic democracy and independence have been characterized for near-instantaneous processing of synaptic inputs. However, a wide class of neuronal computations requires input integration on long timescales. As a paradigmatic example, entorhinal grid fields have been thought to be generated by the democratic summation of independent dendritic oscillations performing direction-selective path integration. We analyzed how multiple dendritic oscillators embedded in the same neuron integrate inputs separately and determine somatic membrane voltage jointly. We found that the interaction of dendritic oscillations leads to phase locking, which sets an upper limit on the timescale for independent input integration. Factors that increase this timescale also decrease the influence that the dendritic oscillations exert on somatic voltage. In entorhinal stellate cells, interdendritic coupling dominates and causes these cells to act as single oscillators. Our results suggest a fundamental trade-off between local and global processing in dendritic trees integrating ongoing signals.

Independence of the unimodal tuning of firing rate from theta phase precession in hippocampal place cells

There are two prominent features for place cells in rat hippocampus. The firing rate remarkably increases when rat enters the cell's place field and reaches a maximum around the center of place field, and it decreases when the animal approaches the end of the place field. Simultaneously the spikes gradually and monotonically advance to earlier phase relative to hippocampal theta rhythm as the rat traverses along the cell's place field, known as temporal coding. In this paper, we investigate whether two main characteristics of place cell firing are independent or not by mainly focusing on the generation mechanism of the unimodal tuning of firing rate by using a reduced CA1 two-compartment neuron model. Based on recent evidences, we hypothesize that the coupling of dendritic with the somatic compartment is not constant but dynamically regulated as the animal moves further along the place field, in contrast to previous two-compartment modeling. Simulations show that the regulable coupling is critically responsible for the generation of unimodal firing rate profile in place cells, independent of phase precession. Predictions of our model accord well with recent observations like occurrence of phase precession with very low as well as high firing rate (Huxter et al. Nature 425:828-832, 2003) and persistency of phase precession after transient silence of hippocampus activity (Zugaro et al. Nat Neurosci 8:67-71, 2005.

Storage of Phase-Coded Patterns via STDP in Fully-Connected and Sparse Network: A Study of the Network Capacity

We study the storage and retrieval of phase-coded patterns as stable dynamical attractors in recurrent neural networks, for both an analog and a integrate and fire spiking model. The synaptic strength is determined by a learning rule based on spike-time-dependent plasticity, with an asymmetric time window depending on the relative timing between pre and postsynaptic activity. We store multiple patterns and study the network capacity. For the analog model, we find that the network capacity scales linearly with the network size, and that both capacity and the oscillation frequency of the retrieval state depend on the asymmetry of the learning time window. In addition to fully connected networks, we study sparse networks, where each neuron is connected only to a small number z ≪ N of other neurons. Connections can be short range, between neighboring neurons placed on a regular lattice, or long range, between randomly chosen pairs of neurons. We find that a small fraction of long range connections is able to amplify the capacity of the network. This imply that a small-world-network topology is optimal, as a compromise between the cost of long range connections and the capacity increase. Also in the spiking integrate and fire model the crucial result of storing and retrieval of multiple phase-coded patterns is observed. The capacity of the fully-connected spiking network is investigated, together with the relation between oscillation frequency of retrieval state and window asymmetry.

The role of ongoing dendritic oscillations in single-neuron dynamics

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.

A central issue in biology is how local processes yield global consequences. This is especially relevant for neurons since these spatially extended cells process local synaptic inputs to generate global action potential output. The dendritic tree of a neuron, which receives most of the inputs, expresses ion channels that can generate nonlinear dynamics. A prominent phenomenon resulting from such ion channels are voltage oscillations. The distribution of the active membrane channels throughout the cell is often highly non-uniform. This can turn the dendritic tree into a network of sparsely spaced local oscillators. Here we analyze whether local dendritic oscillators can produce cell-wide voltage oscillations. Our mathematical theory shows that indeed even when the dendritic oscillators are weakly coupled, they lock their phases and give global oscillations. We show how the biophysical properties of the dendrites determine the global locking and how it can be controlled by synaptic inputs. As a consequence of global locking, even individual synaptic inputs can affect the timing of action potentials. In fact, dendrites locking in synchrony can lead to sustained firing of the cell. We show that dendritic trees can be bistable, with dendrites locking in either synchrony or asynchrony, which may provide a novel mechanism for single cell-based memory.

The first second: models of short-term memory traces in the brain

Many network models in computational neuroscience rise to the challenge of explaining behavioural phenomena ranging from microseconds to tens of seconds using components operating mostly on a time-scale of milliseconds. These models have in common that the underlying system has a memory, which implies that its output depends on its past input history. In this review we compare how such memory traces or delayed responses may be implemented in different brain areas supporting a diversity of functions.

Distance coding strategies based on the entorhinal grid cell system

Estimating and keeping track of the distance from salient points of the environment are important constituents of the spatial awareness and navigation. In rodents, the majority of principal cells in the hippocampus are known to be correlated with the position of the animal. However, the lack of topography in the hippocampal cognitive map does not support the assumption that connections between these cells are able to store and recall distances between coded positions. In contrast, the firing fields of the grid cells in the medial entorhinal cortex form triangular grids and are organized on metrical principles. We suggest a model in which a hypothesized 'distance cell' population is able to extract metrics from the activity of grid cells. We show that storing the momentary activity pattern of the grid cell system in a freely chosen position by one-shot learning and comparing it to the actual grid activity at other positions results in a distance dependent activity of these cells. The actual distance of the animal from the origin can be decoded directly by selecting the distance cell receiving the largest excitation or indirectly via transmission of local interneurons. We found that direct decoding works up to the longest grid spacing, but fails on smaller scales, while the indirect way provides precise distance determination up to the half of the longest grid spacing. In both cases, simulated distance cells have a multi-peaked, patchy spatial activity pattern consistent with the experimentally observed behavior of granule cells in the dentate gyrus.

Grid cells and theta as oscillatory interference: theory and predictions

The oscillatory interference model [Burgess et al. (2007) Hippocampus 17:801-802] of grid cell firing is reviewed as an algorithmic level description of path integration and as an implementation level description of grid cells and their inputs. New analyses concern the relationships between the variables in the model and the theta rhythm, running speed, and the intrinsic firing frequencies of grid cells. New simulations concern the implementation of velocity-controlled oscillators (VCOs) with different preferred directions in different neurons. To summarize the model, the distance traveled along a specific direction is encoded by the phase of a VCO relative to a baseline frequency. Each VCO is an intrinsic membrane potential oscillation whose frequency increases from baseline as a result of depolarization by synaptic input from speed modulated head-direction cells. Grid cell firing is driven by the VCOs whose preferred directions match the current direction of motion. VCOs are phase-reset by location-specific input from place cells to prevent accumulation of error. The baseline frequency is identified with the local average of VCO frequencies, while EEG theta frequency is identified with the global average VCO frequency and comprises two components: the frequency at zero speed and a linear response to running speed. Quantitative predictions are given for the inter-relationships between a grid cell's intrinsic firing frequency and grid scale, the two components of theta frequency, and the running speed of the animal. Qualitative predictions are given for the properties of the VCOs, and the relationship between environmental novelty, the two components of theta, grid scale and place cell remapping.

Phase Precession Through Synaptic Facilitation

Phase precession is a relational code that is thought to be important for episodic-like memory, for instance, the learning of a sequence of places. In the hippocampus, places are encoded through bursting activity of so-called place cells. The spikes in such a burst exhibit a precession of their firing phases relative to field potential theta oscillations (4–12 Hz); the theta phase of action potentials in successive theta cycles progressively decreases toward earlier phases. The mechanisms underlying the generation of phase precession are, however, unknown. In this letter, we show through mathematical analysis and numerical simulations that synaptic facilitation in combination with membrane potential oscillations of a neuron gives rise to phase precession. This biologically plausible model reproduces experimentally observed features of phase precession, such as (1) the progressive decrease of spike phases, (2) the nonlinear and often also bimodal relation between spike phases and the animal's place, (3) the range of phase precession being smaller than one theta cycle, and (4) the dependence of phase jitter on the animal's location within the place field. The model suggests that the peculiar features of the hippocampal mossy fiber synapse, such as its large efficacy, long-lasting and strong facilitation, and its phase-locked activation, are essential for phase precession in the CA3 region of the hippocampus.

Hippocampal place cell assemblies are speed-controlled oscillators

The phase of spikes of hippocampal pyramidal cells relative to the local field theta oscillation shifts forward ("phase precession") over a full theta cycle as the animal crosses the cell's receptive field ("place field"). The linear relationship between the phase of the spikes and the travel distance within the place field is independent of the animal's running speed. This invariance of the phase-distance relationship is likely to be important for coordinated activity of hippocampal cells and space coding, yet the mechanism responsible for it is not known. Here we show that at faster running speeds place cells are active for fewer theta cycles but oscillate at a higher frequency and emit more spikes per cycle. As a result, the phase shift of spikes from cycle to cycle (i.e., temporal precession slope) is faster, yet spatial-phase precession stays unchanged. Interneurons can also show transient-phase precession and contribute to the formation of coherently precessing assemblies. We hypothesize that the speed-correlated acceleration of place cell assembly oscillation is responsible for the phase-distance invariance of hippocampal place cells.

Input source and strength influences overall firing phase of model hippocampal CA1 pyramidal cells during theta: relevance to REM sleep reactivation and memory consolidation

In simulation studies using a realistic model CA1 pyramidal cell, we accounted for the shift in mean firing phase from theta cycle peaks to theta cycle troughs during rapid-eye movement (REM) sleep reactivation of hippocampal CA1 place cells over several days of growing familiarization with an environment (Brain Res 855:176-180). Changes in the theta drive phase and amplitude between proximal and distal dendritic regions of the cell modulated the theta phase of firing when stimuli were presented at proximal and distal dendritic locations. Stimuli at proximal dendritic sites (proximal to 100 microm from the soma) invoked firing with a significant phase preference at the depolarizing theta peaks, while distal stimuli (>290 microm from the soma) invoked firing at hyperpolarizing theta troughs. The input location-related phase preference depended on active dendritic conductances, a sufficient electrotonic separation between input sites and theta-induced subthreshold membrane potential oscillations in the cell. The simulation results predict that the shift in mean theta phase during REM sleep cellular reactivation could occur through potentiation of distal dendritic (temporo-ammonic) synapses and depotentiation of proximal dendritic (Schaffer collateral) synapses over the course of familiarization.

Matching storage and recall: hippocampal spike timing-dependent plasticity and phase response curves

Hippocampal area CA3 is widely considered to function as an autoassociative memory. However, it is insufficiently understood how it does so. In particular, the extensive experimental evidence for the importance of carefully regulated spiking times poses the question as to how spike timing-based dynamics may support memory functions. Here, we develop a normative theory of autoassociative memory encompassing such network dynamics. Our theory specifies the way that the synaptic plasticity rule of a memory constrains the form of neuronal interactions that will retrieve memories optimally. If memories are stored by spike timing-dependent plasticity, neuronal interactions should be formalized in terms of a phase response curve, indicating the effect of presynaptic spikes on the timing of postsynaptic spikes. We show through simulation that such memories are competent analog autoassociators and demonstrate directly that the attributes of phase response curves of CA3 pyramidal cells recorded in vitro qualitatively conform with the theory.