Progress in brain research, volume 219

Serial Editor

Vincent Walsh

Institute of Cognitive Neuroscience
University College London
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London WC1N 3AR UK


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Contributors
John P. Aggleton
School of Psychology, Cardiff University, Cardiff, Wales, UK
Jean-Christophe Cassel
Laboratoire de Neurosciences Cognitives et Adaptatives, UMR 7364, Universite´
de Strasbourg, CNRS, Faculte´ de Psychologie, Neuropoˆle de Strasbourg—GDR
2905 du CNRS, Strasbourg, France
Kat Christiansen
School of Psychology, Cardiff University, Cardiff, Wales, UK
Julie R. Dumont
Department of Psychological and Brain Sciences, Dartmouth College, Hanover,
NH, USA
Michael E. Hasselmo
Department of Psychological and Brain Sciences, Center for Memory and Brain,
Center for Systems Neuroscience, Graduate Program for Neuroscience, Boston
University, Boston, MA, USA
Matthew W. Jones
School of Physiology and Pharmacology, University of Bristol, University Walk,
Bristol, UK

Laura A. Libby
Center for Neuroscience, University of California, Davis, CA, USA
Sheri J.Y. Mizumori
Psychology Department, University of Washington, Seattle, WA, USA
Andrew J.D. Nelson
School of Psychology, Cardiff University, Cardiff, UK
Anne Pereira de Vasconcelos
Laboratoire de Neurosciences Cognitives et Adaptatives, UMR 7364, Universite´
de Strasbourg, CNRS, Faculte´ de Psychologie, Neuropoˆle de Strasbourg—GDR
2905 du CNRS, Strasbourg, France
Charan Ranganath
Center for Neuroscience, and Department of Psychology, University of California,
Davis, CA, USA
Maureen Ritchey
Center for Neuroscience, University of California, Davis, CA, USA
Edmund T. Rolls
Oxford Centre for Computational Neuroscience, Oxford, and Department of
Computer Science, University of Warwick, Coventry, UK

v


vi

Contributors

Jeffrey S. Taube
Department of Psychological and Brain Sciences, Dartmouth College, Hanover,
NH, USA
Valerie L. Tryon

Psychology Department, University of Washington, Seattle, WA, USA
Marian Tsanov
Trinity College Institute of Neuroscience, and School of Psychology, Trinity
College Dublin, Dublin, Ireland
Seralynne D. Vann
School of Psychology, Cardiff University, Cardiff, UK
Robert P. Vertes
Center for Complex Systems and Brain Sciences, Florida Atlantic University,
Boca Raton, FL, USA
Emilie Werlen
School of Physiology and Pharmacology, University of Bristol, University Walk,
Bristol, UK


Preface
The hippocampus is an intriguing and anatomically remarkable structure: it is
possessed of a remarkable curvilinear appearance in coronal section, and it is easy
to spot in anatomical section with the naked eye in just about any mammalian species. A special and important function has been ascribed to it as a result of the pioneering work of John O’Keefe (Nobel Laureate, 2014), who described the
remarkable “place cells,” which fire as a function of the location of the rat in the
environment. Two other important discoveries also give it great importance: longterm potentiation and amnesia. Long-term potentiation, the demonstration that synapses are plastic, was first described in the hippocampus by Tim Bliss and Terje
Lomo. The famous amnesic patient, HM, had a more-or-less complete surgical ablation of the hippocampus. Correspondingly, the hippocampus has been implicated
in many important neurocognitive functions, with a particular latter-day emphasis on
its role in spatial and cognitive mapping, and in declarative (or explicit) memory.
A substantial body of data suggests that the hippocampal formation plays a critical
role in the biological processes underlying at least some forms of memory. Sometimes, however, it feels when reading the many, many papers published annually
on the hippocampus that it sits apart from the brain, with its functions analyzed in
a narrow hippocampo-centric framework—as if the purpose of the rest of the brain
is to serve the information processing needs of the hippocampus! This point is made a
little facetiously and exaggeratedly, of course. Nonetheless, we felt the need to assuage these feelings by assembling this volume to encourage researchers to situate
the hippocampus as part of a network connected to the rest of the brain and not to

consider it in isolation. We therefore present a selection of chapters that concentrate
on understanding the functions of the hippocampus in terms of the connectivity of the
hippocampus itself: in other words, in terms of its cortical and subcortical inputs and
outputs. To take just one important illustrative example: the anterior thalamic and
rostral thalamic nuclei are abundantly connected with the hippocampal formation
and have the capacity to profoundly shape hippocampal spatial and mnemonic information processing, a key point sometimes be overlooked in analyses favoring of hippocampally directed cortical processing. We also know that damage to the anterior
thalamus results in episodic memory impairment more-or-less similarly severe as
that resulting from hippocampal lesions; this may be a function of lost thalamohippocampal information transfer. However, the textbooks and the primary literature
often heavily emphasize the lessons from patients with hippocampal damage, while
neglecting the similarly instructive patients with thalamic damage who also suffer
amnesia. The complexity of thalamic signals and their contribution to the encoding
of experience-dependent memory traces in hippocampal formation needs further investigation, as signal processing in the hippocampal formation does not always follow a corticofugal route, but is also affected profoundly by thalamofugal signals. We
should conclude that memory is not a specialized property of a limited set of cortical
areas; rather, all areas of the cortex as well as several subcortical structures are

xiii


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Preface

capable of experience-dependent change over a wide range of timescales. We therefore hope that we will correct the common misconception that the hippocampus is a
closed system, self-sufficiently responsible for the declarative memory formation.
We here would like to thank all the authors of the chapters presented in this
volume—there is a considerable body of work to savor here and the pleasant feeling
of having one’s pet prejudices tested and changed a little to be enjoyed.
Shane O’Mara and Marian Tsanov
Institute of Neuroscience
Trinity College, Dublin

CHAPTER

1

If I had a million neurons:
Potential tests of corticohippocampal theories

Michael E. Hasselmo1
Department of Psychological and Brain Sciences, Center for Memory and Brain, Center for Systems
Neuroscience, Graduate Program for Neuroscience, Boston University, Boston, MA, USA
1
Corresponding author: Tel.: +617-353-1397; Fax: +617-358-3296,
e-mail address:

Abstract
Considerable excitement surrounds new initiatives to develop techniques for simultaneous recording of large populations of neurons in cortical structures. This chapter focuses on the potential value of large-scale simultaneous recording for advancing research on current issues in
the function of cortical circuits, including the interaction of the hippocampus with cortical and
subcortical structures. The review describes specific research questions that could be answered
using large-scale population recording, including questions about the circuit dynamics underlying coding of dimensions of space and time for episodic memory, the role of GABAergic and
cholinergic innervation from the medial septum, the functional role of spatial representations
coded by grid cells, boundary cells, head direction cells, and place cells, and the fact that many
models require cells coding movement direction.

Keywords
Entorhinal cortex, Stellate cells, Medial septum, Time coding, Spatial coding, Oscillatory
interference, Population recording.

1 INTRODUCTION

The title of this chapter has a number of inspirations. The title was partly inspired by
a song entitled “If I had a million dollars” by the Canadian band Barenaked Ladies,
who humorously sing about the things they would do with a million dollars. This
inspiration explains the title, which is not referring to the author having only a
million neurons in his own brain, but to the usefulness of data from a million individual neurons recorded simultaneously in a behaving animal. This inspiration also
explains the ambitious focus on a million neurons. Obviously, research can benefit
tremendously from techniques for recording up to a thousand neurons (Dombeck
et al., 2010; Gee et al., 2014; Ghosh et al., 2011; Heys et al., 2014; Sheffield and
Progress in Brain Research, Volume 219, ISSN 0079-6123, />© 2015 Elsevier B.V. All rights reserved.

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CHAPTER 1 A million neurons

Dombeck, 2014), and further benefits will also arise from recording tens of
thousands of neurons or hundreds of thousands of neurons.
The scientific inspiration for the title comes as a response to a surprising comment that I have heard from other scientists over the years. This comment takes different forms, but the common gist is that recordings of thousands or millions of
neurons would not be any more useful than data from current technology. I find this
comment surprising because it seems obvious how expanding the numbers of neurons would be useful. But I have heard the comment multiple times, even from researchers who were instrumental in developing techniques for the current state of the
art for multiple single-unit recording in behaving animals. So I want to take the opportunity to answer the question in the context of my own area of research.
This chapter is also inspired by the announcement of the federal BRAIN initiative
(Brain Research through Advancing Innovative Neurotechnology). One component
of this initiative proposes support for recording of activity in large populations of
neurons, showing that many scientists recognize the importance of this type of data.
But I think the field can benefit from explicit examples of questions that can be answered if we had large populations of neurons in a well-structured data set obtained
from an awake, behaving rat with well-described behavior. Answering this question
not only supports the idea of funding innovative neurotechnology but also provides a

framework for presenting some of the interesting current questions in the field.
As long as I am moving beyond current technology in terms of the number of
recorded neurons, I will also assume additional highly desirable features about the
data. I will assume that the spiking activity of neurons can be observed at a high temporal resolution, such as that obtained with multiple single-unit recording. This contrasts with the slower time course of activation data obtained from current techniques
for calcium imaging in large populations of neurons. I will assume the data are
recorded simultaneously over at least 10 min in an awake, behaving rat actively moving around its environment. I will assume the data include tracking the head direction
and movement direction of the behaving rat in space and time. I will assume that we
can record in multiple different anatomical regions, and, in some cases, that we can
identify the individual molecular identity of the neurons in the population. I will not
initially make any assumptions about knowledge of the connectivity of the neurons,
though connectome data would be useful when coupled with data on physiology and
molecular identity of neurons and the behavior of the animal.

2 CORTICAL CODING OF SPACE
If I had data from a million neurons, one top priority would be to analyze how grid
cells and place cells are generated. Fundamental questions about the nature of spatial
representations in the cortex would be answered through an understanding of the
mechanisms of generation of the spatial firing patterns of grid cells. Extensive data
from multiple interacting brain regions should be able to elucidate the mechanism of


2 Cortical coding of space

generation of grid cells, and I think it is useful to consider the steps that could be
taken with such extensive data. The following sections focus on different aspects
of this fundamental question, including the possible rate coding of movement direction, the possible phase coding of movement direction and speed, and the coding of
sensory cues and boundaries.
The Nobel prize in physiology or medicine in 2014 acknowledged the importance
of grid cells and place cells by recognizing O’Keefe for the discovery of place cells
(O’Keefe, 1976; O’Keefe and Dostrovsky, 1971) and May-Britt and Moser for the

discovery of grid cells (Fyhn et al., 2004; Hafting et al., 2005; Moser and Moser,
2008). Initially, grid cells were proposed as a mechanism for driving place cells
(McNaughton et al., 2006; Solstad et al., 2006), but recent data showing loss of grid
cells with inactivation of the hippocampus suggest that place cells might be driving
grid cells (Bonnevie et al., 2013). In either case, understanding the generation of one
of these phenomena is important to understanding the other.
The highly regular pattern of grid cell firing gives a sense that they can be
accounted for by elegant theoretical principles, and numerous published models address the mechanism of grid cell generation. Grid cell models can be grouped into
categories based on some of their component features. One category of models uses
attractor dynamics to generate the characteristic firing pattern of grid cells (Bonnevie
et al., 2013; Burak and Fiete, 2009; Bush and Burgess, 2014; Couey et al., 2013; Fuhs
and Touretzky, 2006; Guanella et al., 2007; McNaughton et al., 2006). Most of the
attractor models use circularly symmetric inhibitory connectivity within a large population of grid cells to generate competition between grid cells coding nearby locations. This results in a pattern of neural activity across the population that matches
the characteristic hexagonal array of grid cell firing fields (also described as falling
on the vertices of tightly packed equilateral triangles). Large-scale recording of cells
particularly during first entry to a familiar environment would allow testing of
whether the population dynamics appear to settle into an attractor state or whether
individual neurons independently code location. As noted by the models, the shared
orientation and spacing of the firing fields of grid cells within individual modules
(Barry et al., 2007; Stensola et al., 2012) and the shared shifts of firing fields with
environmental manipulations (Barry et al., 2007; Stensola et al., 2012; Yoon et al.,
2013) already support the existence of attractor dynamics.
However, generating a grid-like pattern across a population is not sufficient for
modeling individual grid cells. Replicating the changes in firing of an individual grid
cell over time requires that the grid-like pattern in the population needs to be shifted
in proportion to the behavioral movement of the animal, that is, in proportion to its
running velocity. To generate this movement, most attractor models of grid cells explicitly cite a role for experimental data on conjunctive grid-by-head-direction cells
(Sargolini et al., 2006). In attractor models of grid cells (Burak and Fiete, 2009;
Couey et al., 2013; McNaughton et al., 2006), these grid-by-head-direction cells
are proposed to drive adjacent neurons within the population based on the movement

of the animal. However, there is a fundamental problem in using grid-by-headdirection cells to represent the movement direction of an animal, as described in

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CHAPTER 1 A million neurons

Section 2.1. A similar problem occurs for oscillatory interference models of grid cells
(Burgess, 2008; Burgess et al., 2007; Hasselmo, 2008) that also require velocity
as an input. Data show that the movement direction coding required by these models
cannot be provided by cells coding head direction.

2.1 CODING OF SPACE BASED ON CODING OF MOVEMENT DIRECTION
If I had data from a million neurons, I would look for coding of movement direction.
This would resolve an important paradox about many models of the formation of
spatial representations in the cortex. This paradox concerns the fact that most models
of location coding require movement direction as input, but experimental data show
that neurons in these structures primarily code head direction rather than movement
direction (Raudies et al., 2014).
Many theories of spatial coding by the hippocampus and associated structures
propose that the coding of space depends upon path integration (Etienne and
Jeffery, 2004; McNaughton and Nadel, 1990; McNaughton et al., 2006;
Samsonovich and McNaughton, 1997), which involves the integration of a selfmotion signal of velocity to generate a representation of spatial location. These theories are very appealing and have formed the basis for many models of grid cells,
including the attractor dynamic models that use a velocity signal to shift the grid cell
activity within a population (Burak and Fiete, 2009; Couey et al., 2013; McNaughton
et al., 2006) and the oscillatory interference models that use a velocity signal to shift
the frequency of velocity-controlled oscillators (Blair et al., 2008; Burgess et al.,
2007; Hasselmo, 2008).

The problem for these models is the representation of movement direction. Path
integration specifically requires a representation of a rat’s movement velocity—that
is the direction of movement and the speed of movement. Most models of this effect
cite neurophysiological data in support of this data being available. They appropriately cite the neural recordings showing systematic changes in firing rate with running speed (McNaughton et al., 1983; O’Keefe et al., 1998; Wills et al., 2012).
However, the problem occurs when justifying the use of movement direction in these
modeling studies (Bonnevie et al., 2013; Burak and Fiete, 2009; McNaughton et al.,
2006). For movement direction, these papers commonly cite studies showing neurons that respond on the basis of head direction ( Jankowski et al., 2014; Taube,
1995; Taube et al., 1990; Tsanov et al., 2011). Data show robust and welldocumented responses of neurons to head direction in the presubiculum (Taube
et al., 1990), anterior thalamus (Taube, 1995; Tsanov et al., 2011), and medial entorhinal cortex (Brandon et al., 2011, 2013; Sargolini et al., 2006). However, there
is a fundamental logical flaw to the citation of head direction data for a model requiring movement direction as part of a velocity signal. Analysis of behavioral tracking
data shows that the behavioral measures of head direction are not equivalent to
movement direction in the same rat (Raudies et al., 2014), even when performing
a running average over extended periods of different head direction.
This paradox could be resolved by an exhaustive analysis of the firing properties
of neurons in entorhinal cortex, presubiculum, and anterior thalamus relative to


2 Cortical coding of space

either the movement direction or the head direction of the rat. We previously analyzed a few hundred entorhinal neurons (from separate data sets presented by
Brandon et al., 2011; Hafting et al., 2005) during behavioral periods with a discrepancy between the animal’s movement direction and head direction (Raudies et al.,
2014). This analysis shows that many neurons are significantly modulated by head
direction alone, whereas none are modulated by movement direction alone, and only
a few are modulated by both movement direction and head direction. We initially
concluded that a movement direction signal is not readily available to drive grid cell
firing in medial entorhinal cortex, but reviewers objected that this movement direction signal could arise from as yet undiscovered neurons in other regions. Coding of
movement direction is not only important for models of grid cells but could also be
important for planning of goal-directed movement trajectories (Erdem and
Hasselmo, 2012, 2014) that could underlie neural activity correlated with planning
of spatial responses (Brown et al., 2010, 2014; Sherrill et al., 2013).

The problem of movement direction neurons could be solved by sampling a massive population of neurons, searching for the elusive movement direction signal.
Given the importance of the movement direction signal for most models of grid cell
generation, it seems reasonable to assume that a movement direction signal should be
present in medial entorhinal cortex or in regions providing input to medial entorhinal
cortex, such as the presubiculum, parasubiculum, or anterior thalamus. But there
might be a segregation of a movement direction signal to other regions such as
the medial septum, the lateral entorhinal cortex, the postrhinal cortex, the perirhinal
cortex, or the retrosplenial cortex. The medial septum is of particular interest for
this process as some data suggest its role in coding of velocity, as described in
Section 2.2.

2.2 POSSIBLE PHASE CODING OF MOVEMENT IN THE MEDIAL
SEPTUM AND ENTORHINAL CORTEX
If I had data from a million neurons, my own personal priority would be to test
models of movement coding by the medial septum. This may be seen as idiosyncratic, but emphasizes how important I feel this structure is for understanding the
representation of dimensions of episodic memory.
The medial septum plays an important role in spatial memory function, as demonstrated by early lesion studies showing that lesions of the medial septum cause
impairments in spatial memory tasks (Givens and Olton, 1994; Martin et al.,
2007; Winson, 1978). Temporary inactivation of the medial septum impairs the ability to perform the Morris water maze (Chrobak et al., 1989) and the 8-arm radial
maze (Brioni et al., 1990). These effects of lesions and inactivation are accompanied
by a loss of theta rhythm oscillations in the hippocampus (Givens and Olton, 1994;
Winson, 1978) and entorhinal cortex ( Jeffery et al., 1995), and with the loss of spatial
periodicity of grid cells (Brandon et al., 2011; Koenig et al., 2011) but notably without a loss of head direction selectivity in conjunctive grid-by-head-direction cells
(Brandon et al., 2011).

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CHAPTER 1 A million neurons

An important question about these results concerns the role of cholinergic
neurons in the medial septum. The loss of grid cell periodicity with medial septum
inactivation might be due to loss of cholinergic modulation in the entorhinal cortex.
This is supported by effects of systemic injections of the muscarinic cholinergic antagonist scopolamine on grid cells (Newman et al., 2014) and on spatial memory
function (Blokland et al., 1992; Whishaw, 1985). It is possible that the firing rate
of cholinergic neurons might directly code the movement velocity of a rat. These
questions could be addressed by effective recording of identified cholinergic versus
GABAergic neurons in the medial septum of a rat during locomotion.
As an alternative to the coding of velocity by the mean firing rate of neurons,
physiological data suggest that movement velocity may be coded by changes in frequency of theta rhythm oscillations in the medial septum. Different data sets show
that the frequency of theta rhythm oscillations in the rat field potential increases with
running speed (Hinman et al., 2011, 2013; Maurer et al., 2005; Rivas et al., 1996;
Whishaw & Vanderwolf, 1973) as well as the frequency of spiking rhythmicity
(Jeewajee et al., 2008a,b).
Large-scale population recording in the medial septum would allow testing of
an interesting alternate model of grid cells that focuses on the role of theta rhythm
oscillations (Blair et al., 2008, 2013; Burgess et al., 2007; Bush and Burgess, 2014;
Hasselmo, 2008). In this framework, the shift in frequency of theta rhythm oscillations with velocity would cause a shift in the relative phase of oscillations that would
correspond to the current location of the animal (because temporal phase is the
integral of temporal frequency). This idea formed the basis for the category of
oscillatory interference models of grid cells that use velocity-controlled oscillators
(Blair et al., 2008, 2013; Burgess, 2008; Burgess et al., 2007; Bush and Burgess,
2014; Hasselmo, 2008; Zilli and Hasselmo, 2010). Researchers have proposed that
velocity-controlled oscillators are in the medial septum (Blair et al., 2008, 2013;
Hasselmo, 2013).
This model has already been tested by analysis of individual theta rhythmic
neurons in the medial septum, anterior thalamus, and hippocampus (Welday
et al., 2011), supporting the idea that cells change their rhythmic frequency based

on the direction and speed of movement. Another important part of this model is
the proposal that neurons might be organized in ring attractors in which the spiking
activity loops through a ring of cells (Blair et al., 2008, 2013; Welday et al., 2011).
This activity corresponds to a traveling wave, and related models can use traveling
waves with different direction and wave number to generate grid cells (Hasselmo
and Brandon, 2012; Hasselmo and Shay, 2014). Large-scale population recording
would allow analysis of the relative phase of spikes in different cells in medial septum to determine whether activity appears to propagate through neurons as a traveling wave that codes different movement directions. Recordings could also show
whether differences in wave number could code nonuniform spatial dimensions
and could underlie differences in spatial scale of different grid cell modules. Recordings could also show whether these traveling waves shift in relative phase dependent


2 Cortical coding of space

upon the current speed and movement direction of the rat. These waves could
arise from the rebound properties arising from h-current in medial septal neurons
(Varga et al., 2008).

2.3 RELATIONSHIP TO CELLULAR CURRENTS IN THE ENTORHINAL
CORTEX
If I had a million neurons, I would address the intriguing relationship between the
properties of grid cell firing fields recorded in behaving animals (Hafting et al.,
2005; Sargolini et al., 2006) and the intrinsic properties of medial entorhinal neurons
recorded intracellularly (Boehlen et al., 2010; Giocomo and Hasselmo, 2008;
Giocomo et al., 2007; Pastoll et al., 2012, 2013; Shay et al., 2012). Medial entorhinal
stellate cells show intrinsic properties dependent upon a hyperpolarization-gated cation current (h-current) that include resonance (Canto and Witter, 2012; Erchova
et al., 2004; Fernandez and White, 2008; Fernandez et al., 2013; Giocomo et al.,
2007; Haas and White, 2002; Shay et al., 2012) as well as rebound spiking
(Alonso and Klink, 1993; Alonso and Llinas, 1989; Shay et al., 2012). The resonance
frequency is higher in stellate cells from dorsal anatomical locations compared to
ventral locations (Boehlen et al., 2010; Giocomo and Hasselmo, 2008; Giocomo

et al., 2007), resembling the higher spatial frequency (narrow spacing) of dorsal grid
cell firing fields compared to lower spatial frequency (wider spacing) in ventral grid
cells. Supporting this relationship to cellular currents, knockout of the HCN1 subunit
of the h-current results in a reduction in resonance frequency of entorhinal stellate
cells (Giocomo and Hasselmo, 2009) and results in wider spacing between grid cell
firing fields (Giocomo et al., 2011). Cholinergic modulation has also been shown to
regulate the intrinsic rhythmicity of neurons (Heys and Hasselmo, 2012; Heys et al.,
2010), which could underlie changes in the spacing between grid cell firing fields in
novel environments (Barry et al., 2012a,b).
Recent modeling suggests that the faster rebound spiking associated with higher
resonance frequency could underlie the narrower spacing of grid cell firing fields in
dorsal medial entorhinal cortex (Hasselmo, 2013; Hasselmo and Shay, 2014). Largescale recording of identified inhibitory interneurons in the medial entorhinal cortex
could determine if they show systematic shifts in phase based on spatial location, and
whether their summed input causes faster rebound spiking in stellate cells during
higher velocity (Hasselmo, 2013; Hasselmo and Shay, 2014).
Intracellular recordings of entorhinal grid cells have already been used to
evaluate predictions of grid cell models (Domnisoru et al., 2013; Schmidt-Hieber
and Hausser, 2013). These intracellular recordings show depolarizing shifts in
the membrane potential within the firing fields of grid cells that support the properties of attractor dynamic models (Burak and Fiete, 2009; Couey et al., 2013;
McNaughton et al., 2006; Pastoll et al., 2013). Intracellular data also show prominent subthreshold membrane potential oscillations, but these oscillations do not
systematically change in amplitude within firing fields (Domnisoru et al., 2013;

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CHAPTER 1 A million neurons

Schmidt-Hieber and Hausser, 2013), which has been used as an argument against

oscillatory interference models (Domnisoru et al., 2013). However, these effects
can be replicated in a recent hybrid model that combines oscillatory interference with
attractor dynamics to generate grid cell firing fields without a change in the magnitude of subthreshold oscillations within firing fields (Bush and Burgess, 2014). This
hybrid model effectively accounts for the clear precession of intracellular membrane
potential oscillations relative to theta rhythm oscillations in the extracellular field
potential in both entorhinal cortex (Schmidt-Hieber and Hausser, 2013) and hippocampus (Harvey et al., 2009). It is important to note that oscillatory interference
models of grid cells (Burgess et al., 2007) directly account for experimental data
on theta phase precession in grid cells (Climer et al., 2013; Hafting et al., 2008)
and grew out of models of theta phase precession in hippocampal place cells
(O’Keefe and Recce, 1993; Skaggs et al., 1996).

2.4 CODING OF SPACE BASED ON SENSORY FEATURES
If I had data from a million neurons, I would test theories about the coding of sensory
cues for self-localization. This could demonstrate alternate mechanisms that drive
the neural representations of location by grid cells and place cells. As noted above,
data do not yet show the movement direction coding necessary for models using path
integration. Path integration also suffers from the problem of accumulation of error
that could be overcome by recalibration based on sensory cues. There are also intriguing changes in the firing of grid cells and place cells associated with shifts in
the sensory cues associated with boundaries of the environment.
Grid cells and place cells show strong dependence on sensory cues. Rotation of a
white cue card on the wall of a circular environment causes rotations of the firing
location of place cells (Muller and Kubie, 1987) as well as grid cells (Hafting
et al., 2005). Movement of the boundaries of an environment cause shifts in the firing
location of place cells and grid cells (Barry et al., 2007; O’Keefe and Burgess, 1996,
2005). The shifts in firing of place cells were effectively modeled based on theoretical cells predicted to coding the direction and angle of boundaries (Burgess et al.,
2000; Hartley et al., 2000), and this explicit modeling prediction was supported by
the finding of boundary cells in the medial entorhinal cortex (Savelli et al., 2008;
Solstad et al., 2008) and subiculum (Lever et al., 2009). Another striking set of data
show that changing the open field environment to a zig-zag maze results in a dramatic change in the grid cell firing pattern to firing at specific intervals from turns
within the maze (Derdikman et al., 2009).

These data demonstrate that path integration of self-motion cannot account for
the changes in grid cell firing patterns due to sensory coding of boundaries. The compression or expansion occurs without contact with distant boundaries, indicating that
the influence of boundaries on grid cell firing must at least partly result from changes
in optic flow or visual features. Large-scale population recording in visual cortical
regions in behaving rats could allow analysis of the nature of this input, which has
only rarely been studied (Ji and Wilson, 2007). Models show that grid cells (Raudies
et al., 2012) and boundary cells (Raudies and Hasselmo, 2012) can be driven by


3 Coding of time

visual odometry based on optic flow templates similar to responses observed in monkey area MT and MST. The location of a rat can also be computed on the basis of
visual features in a manner related to bioinspired mechanisms of simultaneous localization and mapping used in robotic applications by researchers such as Milford
(Erdem et al., 2014; Milford and Schultz, 2014; Milford and Wyeth, 2008;
Milford et al., 2010).
Many scientists have already concluded that oscillatory interference is not a valid
model of grid cells based on data from bats that shows grid cells with only transient
bouts of theta rhythm oscillations rather than continuous oscillations that could maintain a phase code (Yartsev et al., 2011). However, these data may reflect a stronger
influence of sensory features in maintaining location coding in bats, which can better
sample distant sensory reference points using echolocation or vision compared to
rats. In fact, there might be a relationship between the nature of optic flow in different
parts of the visual field and difference in intrinsic properties in the dorsal to ventral
region of medial entorhinal cortex. Data from rats show that intrinsic frequency of
neurons decreases along the dorsal to ventral axis of medial entorhinal cortex
(Giocomo and Hasselmo, 2008; Giocomo et al., 2007), whereas data from the bat
show the opposite gradient (Heys et al., 2013). This could be related to the difference
in speed of optic flow from the ground plane. The proximity of the ground plane in
rats would result in rapid optic flow in the upper visual field, whereas the distance to
the ground plane in bats would result in much slower optic flow. The pattern of optic
flow in different parts of the visual field corresponds to different responses in

different portions of higher-order visual areas that may then propagate to different
anatomical subregions of medial entorhinal cortex.

3 CODING OF TIME
If I had data from a million neurons, I would test theories about the neural coding of
time. In particular, I would look for coding of time in the form of exponential decay
of similarity between neural representations, particularly within the medial entorhinal cortex but also within the hippocampal formation. This analysis would address
specific questions about the mechanism of generation of time cells.
Time cells are neurons that respond at specific time intervals within behavioral
tasks, as shown in the hippocampal formation (Kraus et al., 2013; MacDonald et al.,
2011; Pastalkova et al., 2008) as well as other structures. There are potentially multiple mechanisms by which such time cell responses could be generated. One explicit
mathematical theory uses the components of an inverse Laplace transform (Howard
et al., 2014a,b). In this framework, each event in the environment activates a trace
that decays exponentially. The inverse transform of these traces across a population
of neurons can drive output of spiking at a specific temporal interval (Howard et al.,
2014a) with a time course that widens with temporal delay in a manner similar to the
experimental data.
Currently, there is intriguing evidence that individual neurons show exponential
decrease in neural activity over time. In recordings of small populations of neurons,

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there is a gradual, exponential decrease in the self-similarity of a population as
measured by the Mahalanobis distance (Manns et al., 2007a). This supports the notion that neurons are changing in firing properties in an exponential manner. Mechanisms for this process also exist on a cellular level (Tiganj et al., 2014). Individual
neurons recorded in slice preparations often respond to a current injection with persistent spiking that continues for a period after the current injection, but may terminate at different intervals in different neurons, as shown in the postsubiculum

(Yoshida and Hasselmo, 2009), the medial entorhinal cortex (Yoshida et al.,
2008), and the hippocampus (Knauer et al., 2013). Recording from large populations
would allow explicit testing of the full coding capability of a population, to determine if there is a decay of self-similarity across a population and within individual
neurons that has the temporal resolution necessary to generate time cell responses,
and to mediate the accuracy of behavioral timing estimates.

4 REPLAY OF EPISODES
If I had data from a million neurons, I would look for replay of episodes in the hippocampus and adjacent structures. This could resolve one of the fundamental
paradoxes about data on the hippocampus. Behavioral data gathered after lesions indicate that the hippocampus and parahippocampal regions are essential to the recall
of recently encoded episodic memories (Corkin et al., 1997; Scoville and Milner,
1957; Zola-Morgan et al., 1993). The term episodic memory refers to memory for
events occurring at a specific time and location. But most electrophysiological data
from the hippocampus and parahippocampal regions focus on stable neural representations such as place cells and grid cells that occur across multiple exposures to an
environment rather than a single episode.
Numerous studies have proposed that hippocampal neurons perform replay of the
experience of being in a specific location in the environment (Wilson and
McNaughton, 1994) or of following a trajectory through an environment
(Davidson et al., 2009; Diba and Buzsaki, 2007; Johnson and Redish, 2007; Lee
and Wilson, 2002; Skaggs and McNaughton, 1996). These studies involved recording of populations of neurons that could exceed 100 simultaneously recorded cells.
However, it is important to remember that recording over 100 cells does not mean
that one is recording 100 place cells, as the number of neurons estimated to code a
given environment is about 30% (Thompson and Best, 1989). Even with a population
of over 30 place cells, this does not guarantee that the place cells are in adjacent
positions along a trajectory that allows them to show sequential activation.
Recording from a million neurons would provide an opportunity to show the
encoding and retrieval of a specific episodic memory within a behavioral task, which
could be seen as a central test of the theory of hippocampus as the locus of storage of
episodic memories. Previous experiments analyzed the Bayesian probability of a
neuron firing when the rat was in a specific spatial location, and then during ripple
activity tested for a high-resolution replay of the prior sequence of behavior

5 If I had a thousand neurons

(Davidson et al., 2009). Using a million neurons will allow two qualitatively different components of this analysis. First, it will allow determination of the representation of the memory. Is it replayed in full, or is it really just represented by a discrete
subset of the previously activated neurons? Second, it would finally allow evaluation
of the true episodic nature of a memory. Instead of determining the Bayesian coding
of neurons based on repeated experience of a similar behavioral event (i.e., visiting a
similar location), the Bayesian coding could be determined on the basis of a single
behavioral episode (or differential coding could be computed for an array of different
behavioral episodes). Then individual replay events could be evaluated to determine
if they match all the statistical features of a single episode versus other episodes. The
ultimate test of mechanisms of episodic memory require showing neural activity
coding a specific episode versus other episodes and then demonstrating the selective
retrieval of one episode versus another episode.
The ultimate demonstration of episodic memory could be done in the context of
general behavioral exploration, but could be enhanced if it is performed in a more
limited behavioral task, such as spatial alternation, where the experience of a
sequence of behavioral trials can be analyzed, and the neural activity at the choice
point of the task could be evaluated to determine if it selectively matches only the
immediately previous trial (which must be used to determine the correct choice on
the current trial) in a manner that differentiates it from other more remote trials.
Large-scale recording would also allow testing of differential dynamics during
encoding and retrieval, including the proposal that activity of cholinergic neurons
should set appropriate dynamics for encoding and should suppress retrieval via
presynaptic inhibition of glutamatergic synaptic transmission (Hasselmo, 2006),
and the proposal that encoding should preferentially occur on one phase of hippocampal theta, while retrieval occurs on the opposite phase (Hasselmo et al.,
2002). Existing data support this phase specificity in the firing of neurons during
match or nonmatch trials (Manns et al., 2007b) and specificity in the phase reset
of field potential oscillations to different phases during encoding and retrieval

(Rizzuto et al., 2006).

5 IF I HAD A THOUSAND NEURONS
An interesting question concerns whether a million neurons would be better than a
thousand neurons. Scientific questions could be answered in both a qualitatively different and a quantitatively different way when recording from a million (or even tens
of thousands of cells) versus a thousand neurons.
The total population of neurons in individual hippocampal subregions of the rat
has been estimated on the order of one million or fewer. The dentate gyrus is estimated to contain one million neurons in the rat, and region CA3 is estimated to contain on the order of 250,000 neurons (Amaral et al., 1990). Thus, recording from one
million neurons will give a complete picture of the all neurons within a region, allowing the explicit identification and tracking of subpopulations representing individual

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memories or environments or sensory cues. When recording a thousand neurons in
hippocampus, one would expect a few hundred active neurons but might not have
extensive place cell coverage of a given portion of the environment. In entorhinal
cortex, the percentages of individual functional subtypes such as boundary cells
are even lower, so that a thousand cells might still not yield a sufficient number
of boundary cells to analyze their interactions. Thus, recording from 1000 or fewer
neurons is analogous to looking at a tree house and trying to conjecture the function
of a full house. Everything is represented on a much smaller and incomplete, often
nonfunctional, scale. For example, in studies of replay, researchers can conjecture
that a trajectory is being followed based on the sequential activation of a sparse subset of neurons, but this does not explicitly demonstrate the full coding of a trajectory
by the full population. Thus, there is a qualitative difference in the capacity to test the
representation of neurons when recording from a million versus a thousand neurons.
However, the qualitative advantage of larger numbers might be present even with

recording of a few thousands of neurons.
In the quantitative sense, it is important to realize that most tests of network dynamics use populations of tens of neurons. Even if the full recorded population is
over 100 neurons using current techniques, the number of cells that can be parameterized effectively in terms of behavior is on the order of tens of cells. Not only does
this reduce the statistical power of specific measures, but it has a huge impact on the
progression of research. Unit recording research is notoriously slow, as the data from
each rat involves building a highly complex implant, obtaining a successful surgery
both in terms of survival of the rat and proper anatomical placement of the drive,
effectively isolating a population of neurons and then obtaining effective behavior
during the period that neurons are isolated. A highly successful experiment might
yield over 100 recorded neurons, but usually only a few successful experiments take
place over a period of 2–3 years during which the researcher usually has other examples that are only partially successful. If we consider that a current successful
study yields about 300 neurons in 3 human-years of work, then recording from a
million neurons does not just enhance statistical significance, but a single successful
recording on this scale could constitute many centuries of scientific progress in
current human-years.

ACKNOWLEDGMENTS
This work was supported by National Institute of Mental Health R01 MH061492, R01
MH060013, P50 MH094263, NSF grant PHY1444389, and the Office of Naval Research
MURI grant N00014-10-1-0936.

REFERENCES
Alonso, A., Klink, R., 1993. Differential electroresponsiveness of stellate and pyramidal-like
cells of medial entorhinal cortex layer II. J. Neurophysiol. 70 (1), 128–143.
Alonso, A., Llinas, R.R., 1989. Subthreshold Na-dependent theta-like rhythmicity in stellate
cells of entorhinal cortex layer II. Nature 342, 175–177.


References

Amaral, D.G., Ishizuka, N., Claiborne, B., 1990. Neurons, numbers and the hippocampal network. Prog. Brain Res. 83, 1–11.
Barry, C., Hayman, R., Burgess, N., Jeffery, K.J., 2007. Experience-dependent rescaling of
entorhinal grids. Nat. Neurosci. 10 (6), 682–684.
Barry, C., Ginzberg, L.L., O’Keefe, J., Burgess, N., 2012a. Grid cell firing patterns signal
environmental novelty by expansion. Proc. Natl. Acad. Sci. U.S.A. 109, 17687–17692.
Barry, C., Heys, J.G., Hasselmo, M.E., 2012b. Possible role of acetylcholine in regulating
spatial novelty effects on theta rhythm and grid cells. Front. Neural Circuits 6, 5.
Blair, H.T., Gupta, K., Zhang, K., 2008. Conversion of a phase- to a rate-coded position signal
by a three-stage model of theta cells, grid cells, and place cells. Hippocampus 18 (12),
1239–1255.
Blair, H.T., Wu, A., Cong, J., 2013. Oscillatory neurocomputing with ring attractors: a network
architecture for mapping locations in space onto patterns of neural synchrony. Philos.
Trans. R. Soc. Lond. B Biol. Sci. 369, 20120526.
Blokland, A., Honig, W., Raaijmakers, W.G.M., 1992. Effects of intra-hippocampal scopolamine injections in a repeated spatial acquisition task in the rat. Psychopharmacology
109, 373–376.
Boehlen, A., Heinemann, U., Erchova, I., 2010. The range of intrinsic frequencies represented
by medial entorhinal cortex stellate cells extends with age. J. Neurosci. 30 (13),
4585–4589.
Bonnevie, T., Dunn, B., Fyhn, M., Hafting, T., Derdikman, D., Kubie, J.L., Roudi, Y.,
Moser, E.I., Moser, M.B., 2013. Grid cells require excitatory drive from the hippocampus.
Nat. Neurosci. 16 (3), 309–317.
Brandon, M.P., Bogaard, A.R., Libby, C.P., Connerney, M.A., Gupta, K., Hasselmo, M.E.,
2011. Reduction of theta rhythm dissociates grid cell spatial periodicity from directional
tuning. Science 332, 595–599.
Brandon, M.P., Bogaard, A.R., Schultheiss, N.W., Hasselmo, M.E., 2013. Segregation of
cortical head direction cell assemblies on alternating theta cycles. Nat. Neurosci.
16 (6), 739–748.
Brioni, J.D., Decker, M.W., Gamboa, L.P., Izquierdo, I., McGaugh, J.L., 1990. Muscimol
injections in the medial septum impair spatial learning. Brain Res. 522, 227–234.
Brown, T.I., Ross, R.S., Keller, J.B., Hasselmo, M.E., Stern, C.E., 2010. Which way was I

going? Contextual retrieval supports the disambiguation of well learned overlapping navigational routes. J. Neurosci. 30, 7414–7422.
Brown, T.I., Hasselmo, M.E., Stern, C.E., 2014. A high-resolution study of hippocampal and
medial temporal lobe correlates of spatial context and prospective overlapping route memory. Hippocampus 24, 819–839.
Burak, Y., Fiete, I.R., 2009. Accurate path integration in continuous attractor network models
of grid cells. PLoS Comput. Biol. 5 (2), e1000291.
Burgess, N., 2008. Grid cells and theta as oscillatory interference: theory and predictions.
Hippocampus 18 (12), 1157–1174.
Burgess, N., Jackson, A., Hartley, T., O’Keefe, J., 2000. Predictions derived from modelling
the hippocampal role in navigation. Biol. Cybern. 83 (3), 301–312.
Burgess, N., Barry, C., O’Keefe, J., 2007. An oscillatory interference model of grid cell firing.
Hippocampus 17 (9), 801–812.
Bush, D., Burgess, N., 2014. A hybrid oscillatory interference/continuous attractor network
model of grid cell firing. J. Neurosci. 34 (14), 5065–5079.
Canto, C.B., Witter, M.P., 2012. Cellular properties of principal neurons in the rat entorhinal
cortex. II. The medial entorhinal cortex. Hippocampus 22, 1277–1299.

13


14

CHAPTER 1 A million neurons

Chrobak, J.J., Stackman, R.W., Walsh, T.J., 1989. Intraseptal administration of muscimol
produces dose-dependent memory impairments in the rat. Behav. Neural Biol.
52, 357–369.
Climer, J.R., Newman, E.L., Hasselmo, M.E., 2013. Phase coding by grid cells in unconstrained environments: two-dimensional (2D) phase precession. Eur. J. Neurosci.
38 (4), 2526–2541.
Corkin, S., Amaral, D.G., Gonzalez, R.G., Johnson, K.A., Hyman, B.T., 1997. H. M.’s medial
temporal lobe lesion: findings from magnetic resonance imaging. J. Neurosci.

17, 3964–3979.
Couey, J.J., Witoelar, A., Zhang, S.J., Zheng, K., Ye, J., Dunn, B., Czajkowski, R., Moser, M.B.,
Moser, E.I., Roudi, Y., Witter, M.P., 2013. Recurrent inhibitory circuitry as a mechanism for
grid formation. Nat. Neurosci. 16 (3), 318–324.
Davidson, T.J., Kloosterman, F., Wilson, M.A., 2009. Hippocampal replay of extended experience. Neuron 63, 497–507.
Derdikman, D., Whitlock, J.R., Tsao, A., Fyhn, M., Hafting, T., Moser, M.B., Moser, E.I.,
2009. Fragmentation of grid cell maps in a multicompartment environment. Nat. Neurosci.
12 (10), 1325–1332.
Diba, K., Buzsaki, G., 2007. Forward and reverse hippocampal place-cell sequences during
ripples. Nat. Neurosci. 10, 1241–1242.
Dombeck, D.A., Harvey, C.D., Tian, L., Looger, L.L., Tank, D.W., 2010. Functional imaging
of hippocampal place cells at cellular resolution during virtual navigation. Nat. Neurosci.
13 (11), 1433–1440.
Domnisoru, C., Kinkhabwala, A.A., Tank, D.W., 2013. Membrane potential dynamics of grid
cells. Nature 495, 199–204.
Erchova, I., Kreck, G., Heinemann, U., Herz, A.V., 2004. Dynamics of rat entorhinal cortex
layer II and III cells: characteristics of membrane potential resonance at rest predict oscillation properties near threshold. J. Physiol. 560, 89–110.
Erdem, U.M., Hasselmo, M., 2012. A goal-directed spatial navigation model using forward
trajectory planning based on grid cells. Eur. J. Neurosci. 35 (6), 916–931.
Erdem, U.M., Hasselmo, M.E., 2014. A biologically inspired hierarchical goal directed navigation model. J. Physiol. Paris 108 (1), 28–37.
Erdem, U.M., Milford, M.J., Hasselmo, M.E., 2014. A hierarchical model of goal directed navigation selects trajectories in a visual environment. Neurobiol. Learn. Mem. 117, 109–121.
Etienne, A., Jeffery, K.J., 2004. Path integration in mammals. Hippocampus 14 (2), 180–192.
Fernandez, F.R., White, J.A., 2008. Artificial synaptic conductances reduce subthreshold oscillations and periodic firing in stellate cells of the entorhinal cortex. J. Neurosci.
28, 3790–3803.
Fernandez, F.R., Malerba, P., Bressloff, P.C., White, J.A., 2013. Entorhinal stellate cells show
preferred spike phase-locking to theta inputs that is enhanced by correlations in synaptic
activity. J. Neurosci. 33, 6027–6040.
Fuhs, M.C., Touretzky, D.S., 2006. A spin glass model of path integration in rat medial entorhinal cortex. J. Neurosci. 26 (16), 4266–4276.
Fyhn, M., Molden, S., Witter, M.P., Moser, E.I., Moser, M.B., 2004. Spatial representation in
the entorhinal cortex. Science 305 (5688), 1258–1264.

Gee, J.M., Smith, N.A., Fernandez, F.R., Economo, M.N., Morris, S.C., Brunert, D.,
Rothermal, M., Morris, S.C., Talbot, A., Palumbos, S., Ichida, J., Shepherd, J.D., West, P.J.,
Wachowiak, M., Capecchi, M.R., Wilcox, K.S., White, J.A., Tvrdik, P., 2014. Imaging
activity in neurons and glia with a new GCaMP5G reporter mouse. Neuron 83, 1058–1072.


References

Ghosh, K.K., Burns, L.D., Cocker, E.D., Nimmerjahn, A., Ziv, Y., Gamal, A.E., Schnitzer, M.J.,
2011. Miniaturized integration of a fluorescence microscope. Nat. Methods 8 (10),
871–878.
Giocomo, L.M., Hasselmo, M.E., 2008. Time constants of h current in layer II stellate cells
differ along the dorsal to ventral axis of medial entorhinal cortex. J. Neurosci.
28, 9414–9425.
Giocomo, L.M., Hasselmo, M.E., 2009. Knock-out of HCN1 subunit flattens dorsal-ventral
frequency gradient of medial entorhinal neurons in adult mice. J. Neurosci. 29 (23),
7625–7630.
Giocomo, L.M., Zilli, E.A., Fransen, E., Hasselmo, M.E., 2007. Temporal frequency of subthreshold oscillations scales with entorhinal grid cell field spacing. Science 315 (5819),
1719–1722.
Giocomo, L.M., Hussaini, S.A., Zheng, F., Kandel, E.R., Moser, M.B., Moser, E.I., 2011. Grid
cells use HCN1 channels for spatial scaling. Cell 147, 1159–1170.
Givens, B., Olton, D.S., 1994. Local modulation of basal forebrain: effects on working and
reference memory. J. Neurosci. 14, 3578–3587.
Guanella, A., Kiper, D., Verschure, P., 2007. A model of grid cells based on a twisted torus
topology. Int. J. Neural Syst. 17 (4), 231–240.
Haas, J.S., White, J.A., 2002. Frequency selectivity of layer II stellate cells in the medial
entorhinal cortex. J. Neurophysiol. 88, 2422–2429.
Hafting, T., Fyhn, M., Molden, S., Moser, M.B., Moser, E.I., 2005. Microstructure of a spatial
map in the entorhinal cortex. Nature 436 (7052), 801–806.
Hafting, T., Fyhn, M., Bonnevie, T., Moser, M.B., Moser, E.I., 2008. Hippocampusindependent phase precession in entorhinal grid cells. Nature 453 (7199), 1248–1252.

Hartley, T., Burgess, N., Lever, C., Cacucci, F., O’Keefe, J., 2000. Modeling place fields in
terms of the cortical inputs to the hippocampus. Hippocampus 10 (4), 369–379.
Harvey, C.D., Collman, F., Dombeck, D.A., Tank, D.W., 2009. Intracellular dynamics of
hippocampal place cells during virtual navigation. Nature 461 (7266), 941–946.
Hasselmo, M.E., 2006. The role of acetylcholine in learning and memory. Curr. Opin. Neurobiol. 16 (6), 710–715.
Hasselmo, M.E., 2008. Grid cell mechanisms and function: contributions of entorhinal persistent spiking and phase resetting. Hippocampus 18 (12), 1213–1229.
Hasselmo, M.E., 2013. Neuronal rebound spiking, resonance frequency and theta cycle skipping may contribute to grid cell firing in medial entorhinal cortex. Philos. Trans. R. Soc. B.
369, 20120523.
Hasselmo, M.E., Brandon, M.P., 2012. A model combining oscillations and attractor dynamics
for generation of grid cell firing. Front. Neural Circuits 6, 30.
Hasselmo, M.E., Shay, C.F., 2014. Grid cell firing patterns may arise from feedback interaction between intrinsic rebound spiking and transverse traveling waves with multiple heading angles. Front. Syst. Neurosci. 8, 201.
Hasselmo, M.E., Bodelon, C., Wyble, B.P., 2002. A proposed function for hippocampal
theta rhythm: separate phases of encoding and retrieval enhance reversal of prior learning.
Neural Comput. 14 (4), 793–817.
Heys, J.G., Hasselmo, M.E., 2012. Neuromodulation of I(h) in layer II medial entorhinal
cortex stellate cells: a voltage-clamp study. J. Neurosci. 32, 9066–9072.
Heys, J.G., Giocomo, L.M., Hasselmo, M.E., 2010. Cholinergic modulation of the resonance
properties of stellate cells in layer II of medial entorhinal cortex. J. Neurophysiol. 104 (1),
258–270.

15


16

CHAPTER 1 A million neurons

Heys, J.G., MacLeod, K.M., Moss, C.F., Hasselmo, M.E., 2013. Bat and rat neurons differ in
theta frequency resonance despite similar coding of space. Science 340, 363–367.
Heys, J.G., Rangarajan, K.V., Dombeck, D.A., 2014. The functional micro-organization of

grid cells revealed by cellular-resolution imaging. Neuron 84 (5), 1079–1090.
Hinman, J.R., Penley, S.C., Long, L.L., Escabi, M.A., Chrobak, J.J., 2011. Septotemporal variation in dynamics of theta: speed and habituation. J. Neurophysiol.
105, 2675–2686.
Hinman, J.R., Penley, S.C., Escabi, M.A., Chrobak, J.J., 2013. Ketamine disrupts theta synchrony across the septotemporal axis of the CA1 region of hippocampus.
J. Neurophysiol. 109, 570–579.
Howard, M.W., MacDonald, C.J., Tiganj, Z., Shankar, K.H., Du, Q., Hasselmo, M.E.,
Eichenbaum, H., 2014a. A unified mathematical framework for coding time, space, and
sequences in the hippocampal region. J. Neurosci. 34, 4692–4707.
Howard, M.W., Shankar, K.H., Aue, W.R., Criss, A.H., 2014b. A distributed representation of
internal time. Psychol. Rev. 122, 24–53.
Jankowski, M.M., Islam, M.N., Wright, N.F., Vann, S.D., Erichsen, J.T., Aggleton, J.P.,
O’Mara, S.M., 2014. Nucleus reuniens of the thalamus contains head direction cells.
ELife 3, e03075.
Jeewajee, A., Barry, C., O’Keefe, J., Burgess, N., 2008a. Grid cells and theta as oscillatory
interference: electrophysiological data from freely moving rats. Hippocampus 18 (12),
1175–1185.
Jeewajee, A., Lever, C., Burton, S., O’Keefe, J., Burgess, N., 2008b. Environmental novelty
is signaled by reduction of the hippocampal theta frequency. Hippocampus 18 (4), 340–348.
Jeffery, K.J., Donnett, J.G., O’Keefe, J., 1995. Medial septal control of theta-correlated unit
firing in the entorhinal cortex of awake rats. Neuroreport 6 (16), 2166–2170.
Ji, D., Wilson, M.A., 2007. Coordinated memory replay in the visual cortex and hippocampus
during sleep. Nat. Neurosci. 10, 100–107.
Johnson, A., Redish, A.D., 2007. Neural ensembles in CA3 transiently encode paths forward of
the animal at a decision point. J. Neurosci. 27, 12176–12189.
Knauer, B., Jochems, A., Valero-Aracama, M.J., Yoshida, M., 2013. Long-lasting intrinsic
persistent firing in rat CA1 pyramidal cells: a possible mechanism for active maintenance
of memory. Hippocampus 23, 820–831.
Koenig, J., Linder, A.N., Leutgeb, J.K., Leutgeb, S., 2011. The spatial periodicity of grid cells
is not sustained during reduced theta oscillations. Science 332 (6029), 592–595.
Kraus, B.J., Robinson 2nd., R.J., White, J.A., Eichenbaum, H., Hasselmo, M.E., 2013. Hippocampal “time cells”: time versus path integration. Neuron 78 (6), 1090–1101.

Lee, A.K., Wilson, M.A., 2002. Memory of sequential experience in the hippocampus during
slow wave sleep. Neuron 36 (6), 1183–1194.
Lever, C., Burton, S., Jeewajee, A., O’Keefe, J., Burgess, N., 2009. Boundary vector cells in
the subiculum of the hippocampal formation. J. Neurosci. 29 (31), 9771–9777.
MacDonald, C.J., Lepage, K.Q., Eden, U.T., Eichenbaum, H., 2011. Hippocampal “time cells”
bridge the gap in memory for discontiguous events. Neuron 71, 737–749.
Manns, J.R., Howard, M.W., Eichenbaum, H., 2007a. Gradual changes in hippocampal activity support remembering the order of events. Neuron 56 (3), 530–540.
Manns, J.R., Zilli, E.A., Ong, K.C., Hasselmo, M.E., Eichenbaum, H., 2007b. Hippocampal
CA1 spiking during encoding and retrieval: relation to theta phase. Neurobiol. Learn.
Mem. 87, 9–20.


References

Martin, M.M., Horn, K.L., Kusman, K.J., Wallace, D.G., 2007. Medial septum lesions disrupt
exploratory trip organization: evidence for septohippocampal involvement in dead reckoning. Physiol. Behav. 90, 412–424.
Maurer, A.P., Vanrhoads, S.R., Sutherland, G.R., Lipa, P., McNaughton, B.L., 2005. Selfmotion and the origin of differential spatial scaling along the septo-temporal axis of the
hippocampus. Hippocampus 15, 841–852.
McNaughton, B.L., Nadel, L., 1990. Hebb-Marr networks and the neurobiological representation of action in space. In: Gluck, M.A., Rumelhart, D.E. (Eds.), Neuroscience and Connectionist Theory. Lawrence Erlbaum Assoc, Hillsdale, NJ, pp. 1–64.
McNaughton, B.L., Barnes, C.A., O’Keefe, J., 1983. The contributions of position, direction,
and velocity to single unit-activity in the hippocampus of freely-moving rats. Exp. Brain
Res. 52, 41–49.
McNaughton, B.L., Battaglia, F.P., Jensen, O., Moser, E.I., Moser, M.B., 2006. Path integration and the neural basis of the ‘cognitive map’. Nat. Rev. Neurosci. 7, 663–678.
Milford, M.J., Schultz, R., 2014. Principles of goal-directed spatial robot navigation in biomimetic models. Philos. Trans. R. Soc. B 369, in press.
Milford, M.J., Wyeth, G., 2008. Mapping a suburb with a single camera using a biologically
inspired SLAM system. IEEE Trans. Robot. 24 (5), 1038–1053.
Milford, M.J., Wiles, J., Wyeth, G.F., 2010. Solving navigational uncertainty using grid cells
on robots. PLoS Comput. Biol. 6 (11), e1000995.
Moser, E.I., Moser, M.B., 2008. A metric for space. Hippocampus 18 (12), 1142–1156.
Muller, R.U., Kubie, J.L., 1987. The effects of changes in the environment on the spatial firing

of hippocampal complex-spike cells. J. Neurosci. 7, 1951–1968.
Newman, E.L., Climer, J.R., Hasselmo, M.E., 2014. Grid cell spatial tuning reduced following
systemic muscarinic receptor blockade. Hippocampus 24 (6), 643–655.
O’Keefe, J., 1976. Place units in the hippocampus of the freely moving rat. Exp. Neurol.
51, 78–109.
O’Keefe, J., Burgess, N., 1996. Geometric determinants of the place fields of hippocampal
neurons. Nature 381, 425–428.
O’Keefe, J., Burgess, N., 2005. Dual phase and rate coding in hippocampal place cells: theoretical significance and relationship to entorhinal grid cells. Hippocampus 15 (7),
853–866.
O’Keefe, J., Dostrovsky, J., 1971. The hippocampus as a spatial map. Preliminary evidence
from unit activity in the freely-moving rat. Brain Res. 34, 171–175.
O’Keefe, J., Recce, M.L., 1993. Phase relationship between hippocampal place units and the
EEG theta rhythm. Hippocampus 3, 317–330.
O’Keefe, J., Burgess, N., Donnett, J.G., Jeffery, K.J., Maguire, E.A., 1998. Place cells, navigational accuracy, and the human hippocampus. Philos. Trans. R. Soc. Lond. B Biol. Sci.
353, 1333–1340.
Pastalkova, E., Itskov, V., Amarasingham, A., Buzsaki, G., 2008. Internally generated cell
assembly sequences in the rat hippocampus. Science 321, 1322–1327.
Pastoll, H., Ramsden, H.L., Nolan, M.F., 2012. Intrinsic electrophysiological properties of
entorhinal cortex stellate cells and their contribution to grid cell firing fields. Front. Neural
Circuits 6, 17.
Pastoll, H., Solanka, L., van Rossum, M.C., Nolan, M.F., 2013. Feedback inhibition enables
theta-nested gamma oscillations and grid firing fields. Neuron 77 (1), 141–154.
Raudies, F., Hasselmo, M.E., 2012. Modeling boundary vector cell firing given optic flow as a
cue. PLoS Comput. Biol. 8 (6), e1002553.

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CHAPTER 1 A million neurons

Raudies, F., Mingolla, E., Hasselmo, M.E., 2012. Modeling the influence of optic flow on grid
cell firing in the absence of other cues. J. Comput. Neurosci. 33, 475–493.
Raudies, F., Brandon, M.P., Chapman, G.W., Hasselmo, M.E., 2014. Head direction is coded
more strongly than movement direction in a population of entorhinal neurons. Brain Res,
in press.
Rivas, J., Gaztelu, J.M., Garcia-Austt, E., 1996. Changes in hippocampal cell discharge patterns and theta rhythm spectral properties as a function of walking velocity in the guinea
pig. Exp. Brain Res. 108, 113–118.
Rizzuto, D.S., Madsen, J.R., Bromfield, E.B., Schulze-Bonhage, A., Kahana, M.J., 2006.
Human neocortical oscillations exhibit theta phase differences between encoding and
retrieval. Neuroimage 31, 1352–1358.
Samsonovich, A., McNaughton, B.L., 1997. Path integration and cognitive mapping in a continuous attractor neural network model. J. Neurosci. 17, 5900–5920.
Sargolini, F., Fyhn, M., Hafting, T., McNaughton, B.L., Witter, M.P., Moser, M.B., Moser, E.I.,
2006. Conjunctive representation of position, direction, and velocity in entorhinal cortex.
Science 312, 758–762.
Savelli, F., Yoganarasimha, D., Knierim, J.J., 2008. Influence of boundary removal on the spatial representations of the medial entorhinal cortex. Hippocampus 18, 1270–1282.
Schmidt-Hieber, C., Hausser, M., 2013. Cellular mechanisms of spatial navigation in the medial entorhinal cortex. Nat. Neurosci. 16, 325–331.
Scoville, W.B., Milner, B., 1957. Loss of recent memory after bilateral hippocampal lesions.
J. Neurol. Neurosurg. Psychiatry 20, 11–21.
Shay, C.F., Boardman, I.S., James, N.M., Hasselmo, M.E., 2012. Voltage dependence of subthreshold resonance frequency in layer II of medial entorhinal cortex. Hippocampus
22, 1733–1749.
Sheffield, M.E., Dombeck, D.A., 2014. Calcium transient prevalence across the dendritic
arbour predicts place field properties. Nature 517 (7533), 200–204.
Sherrill, K.R., Erdem, U.M., Ross, R.S., Brown, T.I., Hasselmo, M.E., Stern, C.E., 2013.
Hippocampus and retrosplenial cortex combine path integration signals for successful
navigation. J. Neurosci. 33, 19304–19313.
Skaggs, W.E., McNaughton, B.L., 1996. Replay of neuronal firing sequences in rat hippocampus during sleep following spatial experience. Science 271, 1870–1873.
Skaggs, W.E., McNaughton, B.L., Wilson, M.A., Barnes, C.A., 1996. Theta phase precession
in hippocampal neuronal populations and the compression of temporal sequences.

Hippocampus 6, 149–172.
Solstad, T., Moser, E.I., Einevoll, G.T., 2006. From grid cells to place cells: a mathematical
model. Hippocampus 16, 1026–1031.
Solstad, T., Boccara, C.N., Kropff, E., Moser, M.B., Moser, E.I., 2008. Representation of geometric borders in the entorhinal cortex. Science 322, 1865–1868.
Stensola, H., Stensola, T., Solstad, T., Froland, K., Moser, M.B., Moser, E.I., 2012. The entorhinal grid map is discretized. Nature 492 (7427), 72–78.
Taube, J.S., 1995. Head direction cells recorded in the anterior thalamic nuclei of freely moving rats. J. Neurosci. 15, 70–86.
Taube, J.S., Muller, R.U., Ranck Jr., J.B., 1990. Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. J. Neurosci.
10, 420–435.


References

Thompson, L.T., Best, P.J., 1989. Place cells and silent cells in the hippocampus of freelybehaving rats. J. Neurosci. 9 (7), 2382–2390.
Tiganj, Z., Hasselmo, M.E., Howard, M.W., 2014. A simple biophysically plausible model for
long time constants in single neurons. Hippocampus 25 (1), 27–37.
Tsanov, M., Chah, E., Vann, S.D., Reilly, R.B., Erichsen, J.T., Aggleton, J.P., O’Mara, S.M.,
2011. Theta-modulated head direction cells in the rat anterior thalamus. J. Neurosci.
31, 9489–9502.
Varga, V., Hangya, B., Kranitz, K., Ludanyi, A., Zemankovics, R., Katona, I., Shigemoto, R.,
Freund, T.F., Borhegyi, Z., 2008. The presence of pacemaker HCN channels identifies
theta rhythmic GABAergic neurons in the medial septum. J. Physiol. 586 (16), 3893–3915.
Welday, A.C., Shlifer, I.G., Bloom, M.L., Zhang, K., Blair, H.T., 2011. Cosine directional tuning of theta cell burst frequencies: evidence for spatial coding by oscillatory interference.
J. Neurosci. 31 (45), 16157–16176.
Whishaw, I.Q., 1985. Cholinergic receptor blockade in the rat impairs locale but not taxon
strategies for place navigation in a swimming pool. Behav. Neurosci. 99, 979–1005.
Whishaw, I.Q., Vanderwolf, C.H., 1973. Hippocampal EEG and behavior: changes in amplitude and frequency of RSA (theta rhythm) associated with spontaneous and learned movement patterns in rats and cats. Behav. Biol. 8, 461–484.
Wills, T.J., Barry, C., Cacucci, F., 2012. The abrupt development of adult-like grid cell firing
in the medial entorhinal cortex. Front. Neural Circuits 6, 21.
Wilson, M.A., McNaughton, B.L., 1994. Reactivation of hippocampal ensemble memories
during sleep. Science 265, 676–679.

Winson, J., 1978. Loss of hippocampal theta rhythm results in spatial memory deficit in the rat.
Science 201, 160–163.
Yartsev, M.M., Witter, M.P., Ulanovsky, N., 2011. Grid cells without theta oscillations in the
entorhinal cortex of bats. Nature 479, 103–107.
Yoon, K., Buice, M.A., Barry, C., Hayman, R., Burgess, N., Fiete, I.R., 2013. Specific evidence of low-dimensional continuous attractor dynamics in grid cells. Nat. Neurosci.
16 (8), 1077–1084.
Yoshida, M., Hasselmo, M.E., 2009. Persistent firing supported by an intrinsic cellular mechanism in a component of the head direction system. J. Neurosci. 29 (15), 4945–4952.
Yoshida, M., Fransen, E., Hasselmo, M.E., 2008. mGluR-dependent persistent firing in entorhinal cortex layer III neurons. Eur. J. Neurosci. 28, 1116–1126.
Zilli, E.A., Hasselmo, M.E., 2010. Coupled noisy spiking neurons as velocity-controlled
oscillators in a model of grid cell spatial firing. J. Neurosci. 30 (41), 13850–13860.
Zola-Morgan, S., Squire, L.R., Clower, R.P., Rempel, N.L., 1993. Damage to the perirhinal
cortex exacerbates memory impairment following lesions to the hippocampal formation.
J. Neurosci. 13, 251–265.

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