Evaluation of the Oscillatory Interference Model of Grid Cell Firing through Analysis and Measured Period Variance of Some Biological Oscillators

Models of the hexagonally arrayed spatial activity pattern of grid cell firing in the literature generally fall into two main categories: continuous attractor models or oscillatory interference models. Burak and Fiete (2009, PLoS Comput Biol) recently examined noise in two continuous attractor models, but did not consider oscillatory interference models in detail. Here we analyze an oscillatory interference model to examine the effects of noise on its stability and spatial firing properties. We show analytically that the square of the drift in encoded position due to noise is proportional to time and inversely proportional to the number of oscillators. We also show there is a relatively fixed breakdown point, independent of many parameters of the model, past which noise overwhelms the spatial signal. Based on this result, we show that a pair of oscillators are expected to maintain a stable grid for approximately t = 5µ3/(4πσ)2 seconds where µ is the mean period of an oscillator in seconds and σ2 its variance in seconds2. We apply this criterion to recordings of individual persistent spiking neurons in postsubiculum (dorsal presubiculum) and layers III and V of entorhinal cortex, to subthreshold membrane potential oscillation recordings in layer II stellate cells of medial entorhinal cortex and to values from the literature regarding medial septum theta bursting cells. All oscillators examined have expected stability times far below those seen in experimental recordings of grid cells, suggesting the examined biological oscillators are unfit as a substrate for current implementations of oscillatory interference models. However, oscillatory interference models can tolerate small amounts of noise, suggesting the utility of circuit level effects which might reduce oscillator variability. Further implications for grid cell models are discussed

From A to Z: a potential role for grid cells in spatial navigation

Since their discovery, the strikingly regular and spatially stable firing of entorhinal grid cells has attracted the attention of experimentalists and theoreticians alike. The bulk of this work has focused either on the assumption that the principal role of grid cells is to support path integration or the extent to which their multiple firing locations can drive the sparse activity of hippocampal place cells. Here, we propose that grid cells are best understood as part of a network that combines self-motion and environmental cues to accurately track an animal’s location in space. Furthermore, that grid cells - more so than place cells - efficiently encode self-location in allocentric coordinates. Finally, that the regular structure of grid firing fields represents information about the relative structure of space and, as such, may be used to guide goal directed navigation

Movement Dependence and Layer Specificity of Entorhinal Phase Precession in Two-Dimensional Environments

As a rat moves, grid cells in its entorhinal cortex (EC) discharge at multiple locations of the external world, and the firing fields of each grid cell span a hexagonal lattice. For movements on linear tracks, spikes tend to occur at successively earlier phases of the theta-band filtered local field potential during the traversal of a firing field - a phenomenon termed phase precession. The complex movement patterns observed in two-dimensional (2D) open-field environments may fundamentally alter phase precession. To study this question at the behaviorally relevant single-run level, we analyzed EC spike patterns as a function of the distance traveled by the rat along each trajectory. This analysis revealed that cells across all EC layers fire spikes that phase-precess;indeed, the rate and extent of phase precession were the same, only the correlation between spike phase and path length was weaker in EC layer III. Both slope and correlation of phase precession were surprisingly similar on linear tracks and in 2D open-field environments despite strong differences in the movement statistics, including running speed. While the phase-precession slope did not correlate with the average running speed, it did depend on specific properties of the animal's path. The longer a curving path through a grid-field in a 2D environment, the shallower was the rate of phase precession, while runs that grazed a grid field tangentially led to a steeper phase-precession slope than runs through the field center. Oscillatory interference models for grid cells do not reproduce the observed phenomena

Cellular properties of the medial entorhinal cortex as possible mechanisms of spatial processing

Cells of the rodent medial entorhinal cortex (EC) possess cellular properties hypothesized to underlie the spatially periodic firing behaviors of 'grid cells' (GC) observed in vivo. Computational models have simulated experimental GC data, but a consensus as to what mechanism(s) generate GC properties has not been reached. Using whole cell patch-clamp and computational modeling techniques this thesis investigates resonance, rebound spiking and persistent spiking properties of medial EC cells to test potential mechanisms generating GC firing. The first experiment tested the voltage dependence of resonance frequency in layer II medial EC stellate cells. Some GC models use interference between velocity-controlled oscillators to generate GCs. These interference mechanisms work best with a linear relationship between voltage and resonance frequency. Experimental results showed resonance frequency decreased linearly with membrane potential depolarization, suggesting resonance properties could support the generation of GCs. Resonance appeared in medial EC but not lateral EC consistent with location of GCs. The second experiment tested predictions of a recent network model that generates GCs using medial EC stellate cell resonance and rebound spiking properties. Sinusoidal oscillations superimposed with hyperpolarizing currents were delivered to layer II stellate cells. Results showed that relative to the sinusoid, a limited phase range of hyperpolarizing inputs elicited rebound spikes, and the phase range of rebound spikes was even narrower. Tuning model parameters of the stellate cell population to match experimental rebound spiking properties resulted in GC spatial periodicity, suggesting resonance and rebound spiking are viable mechanisms for GC generation. The third experiment tested whether short duration current inputs can induce persistent firing and afterdepolarization in layer V pyramidal cells. During muscarinic acetylcholine receptor activation 1-2 second long current injections have been shown to induce persistent firing in EC principal cells. Persistent firing may underlie working memory performance and has been used to model GCs. However, input stimuli during working memory and navigation may be much shorter than 1-2 seconds. Data showed that input durations of 10, 50 and 100 ms could elicit persistent firing, and revealed time courses and amplitude of afterdepolarization that could contribute to GC firing or maintenance of working memory

Theta oscillations, timing and cholinergic modulation in the rodent hippocampal circuit

The medial temporal lobe (MTL) is crucial for episodic and spatial memory, and shows rhythmicity in the local field potential and neuronal spiking. Gamma oscillations (>40Hz) are mediatepd by local circuitry and interact with slower theta oscillations (6-10 Hz). Both oscillation frequencies are modulated by cholinergic input from the medial septum. Entorhinal grid cells fire when an animal visits particular locations in the environment arranged on the corners of tightly packed, equilateral triangles. Grid cells show phase precession, in which neurons fire at progressively earlier phases relative to theta oscillation as animals move through firing fields. This work focuses on the temporal organization of spiking and network rhythms, and their modulation by septal inputs, which are thought to be involved in MTL function. First, I recorded grid cells as rats explored open spaces and examined precession, previously only characterized on linear tracks, and compared it to predictions from models. I identified precession, including in conjunctive head-direction-by-grid cells and on passes that clipped the edge of the firing field. Secondly, I studied problems of measuring single neuron theta rhythmicity and developed an improved approach. Using the novel approach, I identified diverse modulation of rat medial entorhinal neurons’ rhythmic frequencies by running speed, independent from the modulation of firing rate by speed. Under pharmacological inactivation of the septum, rhythmic tuning was disrupted while rate tuning was enhanced. The approach also showed that available data is insufficient to prove that bat grid cells are arrhythmic due to low firing rates. In the final project, I optogenetically silenced cholinergic septal cells while recording from hippocampal area CA1. I identified changes in theta rhythmic currents and in theta-gamma coupling. This silencing disrupted performance when applied during the encoding phase of a delayed match to position task. These data support hypothetical roles of these rhythms in encoding and retrieval and suggest possible mechanisms for their modulation. Together, evidence from these projects suggests a role for theta in the function of spatial and episodic memory. These oscillations have important implications for communication and computation, and they can provide a substrate for efficient brain function

Models of spatial representation in the medial entorhinal cortex

Komplexe kognitive Funktionen wie Gedächtnisbildung, Navigation und Entscheidungsprozesse hängen von der Kommunikation zwischen Hippocampus und Neokortex ab. An der Schnittstelle dieser beiden Gehirnregionen liegt der entorhinale Kortex - ein Areal, das Neurone mit bemerkenswerten räumlichen Repräsentationen enthält: Gitterzellen. Gitterzellen sind Neurone, die abhängig von der Position eines Tieres in seiner Umgebung feuern und deren Feuerfelder ein dreieckiges Muster bilden. Man vermutet, dass Gitterzellen Navigation und räumliches Gedächtnis unterstützen, aber die Mechanismen, die diese Muster erzeugen, sind noch immer unbekannt. In dieser Dissertation untersuche ich mathematische Modelle neuronaler Schaltkreise, um die Entstehung, Weitervererbung und Verstärkung von Gitterzellaktivität zu erklären. Zuerst konzentriere ich mich auf die Entstehung von Gittermustern. Ich folge der Idee, dass periodische Repräsentationen des Raumes durch Konkurrenz zwischen dauerhaft aktiven, räumlichen Inputs und der Tendenz eines Neurons, durchgängiges Feuern zu vermeiden, entstehen könnten. Aufbauend auf vorangegangenen theoretischen Arbeiten stelle ich ein Einzelzell-Modell vor, das gitterartige Aktivität allein durch räumlich-irreguläre Inputs, Feuerratenadaptation und Hebbsche synaptische Plastizität erzeugt. Im zweiten Teil der Dissertation untersuche ich den Einfluss von Netzwerkdynamik auf das Gitter-Tuning. Ich zeige, dass Gittermuster zwischen neuronalen Populationen weitervererbt werden können und dass sowohl vorwärts gerichtete als auch rekurrente Verbindungen die Regelmäßigkeit von räumlichen Feuermustern verbessern können. Schließlich zeige ich, dass eine entsprechende Konnektivität, die diese Funktionen unterstützt, auf unüberwachte Weise entstehen könnte. Insgesamt trägt diese Arbeit zu einem besseren Verständnis der Prinzipien der neuronalen Repräsentation des Raumes im medialen entorhinalen Kortex bei.High-level cognitive abilities such as memory, navigation, and decision making rely on the communication between the hippocampal formation and the neocortex. At the interface between these two brain regions is the entorhinal cortex, a multimodal association area where neurons with remarkable representations of self-location have been discovered: the grid cells. Grid cells are neurons that fire according to the position of an animal in its environment and whose firing fields form a periodic triangular pattern. Grid cells are thought to support animal's navigation and spatial memory, but the cellular mechanisms that generate their tuning are still unknown. In this thesis, I study computational models of neural circuits to explain the emergence, inheritance, and amplification of grid-cell activity. In the first part of the thesis, I focus on the initial formation of grid-cell tuning. I embrace the idea that periodic representations of space could emerge via a competition between persistently-active spatial inputs and the reluctance of a neuron to fire for long stretches of time. Building upon previous theoretical work, I propose a single-cell model that generates grid-like activity solely form spatially-irregular inputs, spike-rate adaptation, and Hebbian synaptic plasticity. In the second part of the thesis, I study the inheritance and amplification of grid-cell activity. Motivated by the architecture of entorhinal microcircuits, I investigate how feed-forward and recurrent connections affect grid-cell tuning. I show that grids can be inherited across neuronal populations, and that both feed-forward and recurrent connections can improve the regularity of spatial firing. Finally, I show that a connectivity supporting these functions could self-organize in an unsupervised manner. Altogether, this thesis contributes to a better understanding of the principles governing the neuronal representation of space in the medial entorhinal cortex

Cholinergic modulation of the superficial layers of the parasubiculum.

ABSTRACT Cholinergic modulation of the superficial layers of the parasubiculum Stephen D. Glasgow, Ph.D. Concordia University, 2011 Recent evidence suggests that the parahippocampal area, including the entorhinal cortex and parasubiculum, may play a crucial role in spatial processing and memory formation. However, little is known about the basic cellular and network properties of the parasubiculum, an isocortical brain region that receives input from the hippocampus and other subcortical regions associated with spatial navigation, and projects exclusively to the superficial layers of the entorhinal cortex. Neurons in layer II of the parasubiculum demonstrate theta-frequency membrane potential oscillations at near-threshold voltages that are generated via an interplay between a persistent Na+ current and the hyperpolarization-activated cationic current Ih, and these rhythmic fluctuations in membrane potential may contribute to the generation of oscillatory local field potentials. Further, the parasubiculum receives strong cholinergic projections from the medial septum. Acetylcholine has been linked to theta-frequency oscillations via regulation of cellular and network dynamics through membrane depolarization, while concurrently suppressing excitatory synaptic transmission, and it is likely that cholinergic receptor activation has similar effects in the parasubiculum. I found that activation of cholinergic receptors depolarizes layer II cells of the parasubiculum by exerting numerous effects on K+ channels, including IM and IKir, however also suppresses incoming excitatory synaptic transmission from the CA1. These results indicate that increases in cholinergic tone during network-level theta-frequency oscillations in the parasubiculum may increase neuronal excitability by exerting strong effects on postsynaptic conductances, but may also regulate network dynamics by reducing the strength of incoming afferents