Progress in brain research, volume 219

The review describes specific research questions that could be answered using large-scale population recording, including questions about the circuit dynamics under-lying coding of dimen

Vincent WalshInstitute of Cognitive NeuroscienceUniversity College London

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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

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

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

spe-cies A special and important function has been ascribed to it as a result of the

pio-neering 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:

long-term potentiation and amnesia Long-long-term potentiation, the demonstration that

syn-apses 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

ab-lation 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

Some-times, 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

as-suage 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

infor-mation processing, a key point sometimes be overlooked in analyses favoring of

hip-pocampally 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

thalamo-hippocampal 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

in-vestigation, as signal processing in the hippocampal formation does not always

fol-low 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

capable of experience-dependent change over a wide range of timescales We fore hope that we will correct the common misconception that the hippocampus is aclosed system, self-sufficiently responsible for the declarative memory formation.

there-We here would like to thank all the authors of the chapters presented in thisvolume—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 NeuroscienceTrinity College, Dublin

If I had a million neurons:

Potential tests of

Michael E Hasselmo1Department 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: hasselmo@bu.edu

Abstract

Considerable excitement surrounds new initiatives to develop techniques for simultaneous

re-cording of large populations of neurons in cortical structures This chapter focuses on the

po-tential 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

under-lying 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

indi-vidual 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, http://dx.doi.org/10.1016/bs.pbr.2015.03.009

Dombeck, 2014), and further benefits will also arise from recording tens ofthousands of neurons or hundreds of thousands of neurons.

The scientific inspiration for the title comes as a response to a surprising ment that I have heard from other scientists over the years This comment takes dif-ferent forms, but the common gist is that recordings of thousands or millions ofneurons would not be any more useful than data from current technology I find thiscomment surprising because it seems obvious how expanding the numbers of neu-rons would be useful But I have heard the comment multiple times, even from re-searchers who were instrumental in developing techniques for the current state of theart for multiple single-unit recording in behaving animals So I want to take the op-portunity 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

com-of this initiative proposes support for recording com-of activity in large populations com-ofneurons, 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 an-swered if we had large populations of neurons in a well-structured data set obtainedfrom an awake, behaving rat with well-described behavior Answering this questionnot only supports the idea of funding innovative neurotechnology but also provides aframework 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 ofrecorded neurons, I will also assume additional highly desirable features about thedata I will assume that the spiking activity of neurons can be observed at a high tem-poral resolution, such as that obtained with multiple single-unit recording This con-trasts with the slower time course of activation data obtained from current techniquesfor calcium imaging in large populations of neurons I will assume the data arerecorded simultaneously over at least 10 min in an awake, behaving rat actively mov-ing around its environment I will assume the data include tracking the head directionand movement direction of the behaving rat in space and time I will assume that wecan record in multiple different anatomical regions, and, in some cases, that we canidentify the individual molecular identity of the neurons in the population I will notinitially make any assumptions about knowledge of the connectivity of the neurons,though connectome data would be useful when coupled with data on physiology andmolecular 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 gridcells and place cells are generated Fundamental questions about the nature of spatialrepresentations in the cortex would be answered through an understanding of themechanisms of generation of the spatial firing patterns of grid cells Extensive datafrom multiple interacting brain regions should be able to elucidate the mechanism of

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

direc-tion, 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

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

ad-dress 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

attractor models use circularly symmetric inhibitory connectivity within a large

pop-ulation of grid cells to generate competition between grid cells coding nearby

loca-tions 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

ex-plicitly 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;

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-head-direction cells to represent the movement grid-by-head-direction of an animal, as described in

Section 2.1 A similar problem occurs for oscillatory interference models of grid cells

as an input Data show that the movement direction coding required by these modelscannot be provided by cells coding head 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 ofspatial representations in the cortex This paradox concerns the fact that most models

of location coding require movement direction as input, but experimental data showthat neurons in these structures primarily code head direction rather than movementdirection (Raudies et al., 2014)

Many theories of spatial coding by the hippocampus and associated structurespropose that the coding of space depends upon path integration (Etienne andJeffery, 2004; McNaughton and Nadel, 1990; McNaughton et al., 2006;

self-motion signal of velocity to generate a representation of spatial location These ories 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 cellactivity within a population (Burak and Fiete, 2009; Couey et al., 2013; McNaughton

the-et al., 2006) and the oscillatory interference models that use a velocity signal to shiftthe frequency of velocity-controlled oscillators (Blair et al., 2008; Burgess et al.,

2006) For movement direction, these papers commonly cite studies showing rons that respond on the basis of head direction (Jankowski et al., 2014; Taube,

well-documented responses of neurons to head direction in the presubiculum (Taube

et al., 1990), anterior thalamus (Taube, 1995; Tsanov et al., 2011), and medial torhinal cortex (Brandon et al., 2011, 2013; Sargolini et al., 2006) However, there

en-is a fundamental logical flaw to the citation of head direction data for a model ing movement direction as part of a velocity signal Analysis of behavioral trackingdata shows that the behavioral measures of head direction are not equivalent tomovement direction in the same rat (Raudies et al., 2014), even when performing

requir-a running requir-averrequir-age over extended periods of different herequir-ad 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

either the movement direction or the head direction of the rat We previously

ana-lyzed a few hundred entorhinal neurons (from separate data sets presented by

Brandon et al., 2011; Hafting et al., 2005) during behavioral periods with a

discrep-ancy 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

direc-tion 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

of spatial responses (Brown et al., 2010, 2014; Sherrill et al., 2013)

The problem of movement direction neurons could be solved by sampling a

mas-sive population of neurons, searching for the elumas-sive 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

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

idiosyn-cratic, 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

dem-onstrated by early lesion studies showing that lesions of the medial septum cause

impairments in spatial memory tasks (Givens and Olton, 1994; Martin et al.,

abil-ity 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

with-out a loss of head direction selectivity in conjunctive grid-by-head-direction cells

(Brandon et al., 2011)

An important question about these results concerns the role of cholinergicneurons in the medial septum The loss of grid cell periodicity with medial septuminactivation might be due to loss of cholinergic modulation in the entorhinal cortex.This is supported by effects of systemic injections of the muscarinic cholinergic an-tagonist scopolamine on grid cells (Newman et al., 2014) and on spatial memoryfunction (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 Thesequestions could be addressed by effective recording of identified cholinergic versusGABAergic 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 fre-quency of theta rhythm oscillations in the medial septum Different data sets showthat the frequency of theta rhythm oscillations in the rat field potential increases withrunning speed (Hinman et al., 2011, 2013; Maurer et al., 2005; Rivas et al., 1996;

(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 rhythmoscillations (Blair et al., 2008, 2013; Burgess et al., 2007; Bush and Burgess, 2014;

oscilla-tions with velocity would cause a shift in the relative phase of oscillaoscilla-tions that wouldcorrespond to the current location of the animal (because temporal phase is theintegral of temporal frequency) This idea formed the basis for the category ofoscillatory interference models of grid cells that use velocity-controlled oscillators

velocity-controlled oscillators are in the medial septum (Blair et al., 2008, 2013;

This model has already been tested by analysis of individual theta rhythmicneurons in the medial septum, anterior thalamus, and hippocampus (Welday

on the direction and speed of movement Another important part of this model isthe proposal that neurons might be organized in ring attractors in which the spikingactivity 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 travelingwaves with different direction and wave number to generate grid cells (Hasselmo

would allow analysis of the relative phase of spikes in different cells in medial tum to determine whether activity appears to propagate through neurons as a travel-ing wave that codes different movement directions Recordings could also showwhether differences in wave number could code nonuniform spatial dimensionsand could underlie differences in spatial scale of different grid cell modules Record-ings could also show whether these traveling waves shift in relative phase dependent

sep-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)

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

cat-ion 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.,

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)

Large-scale 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

the membrane potential within the firing fields of grid cells that support the

proper-ties of attractor dynamic models (Burak and Fiete, 2009; Couey et al., 2013;

promi-nent subthreshold membrane potential oscillations, but these oscillations do not

systematically change in amplitude within firing fields (Domnisoru et al., 2013;

Schmidt-Hieber and Hausser, 2013), which has been used as an argument againstoscillatory interference models (Domnisoru et al., 2013) However, these effectscan be replicated in a recent hybrid model that combines oscillatory interference withattractor dynamics to generate grid cell firing fields without a change in the magni-tude of subthreshold oscillations within firing fields (Bush and Burgess, 2014) Thishybrid model effectively accounts for the clear precession of intracellular membranepotential oscillations relative to theta rhythm oscillations in the extracellular fieldpotential in both entorhinal cortex (Schmidt-Hieber and Hausser, 2013) and hippo-campus (Harvey et al., 2009) It is important to note that oscillatory interferencemodels 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

If I had data from a million neurons, I would test theories about the coding of sensorycues for self-localization This could demonstrate alternate mechanisms that drivethe 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 pathintegration Path integration also suffers from the problem of accumulation of errorthat could be overcome by recalibration based on sensory cues There are also in-triguing changes in the firing of grid cells and place cells associated with shifts inthe sensory cues associated with boundaries of the environment

Grid cells and place cells show strong dependence on sensory cues Rotation of awhite cue card on the wall of a circular environment causes rotations of the firinglocation 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 firinglocation 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 tical cells predicted to coding the direction and angle of boundaries (Burgess et al.,

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 datashow that changing the open field environment to a zig-zag maze results in a dra-matic change in the grid cell firing pattern to firing at specific intervals from turnswithin the maze (Derdikman et al., 2009)

These data demonstrate that path integration of self-motion cannot account forthe changes in grid cell firing patterns due to sensory coding of boundaries The com-pression or expansion occurs without contact with distant boundaries, indicating thatthe 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 corticalregions in behaving rats could allow analysis of the nature of this input, which hasonly rarely been studied (Ji and Wilson, 2007) Models show that grid cells (Raudies

visual odometry based on optic flow templates similar to responses observed in

mon-key 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

local-ization and mapping used in robotic applications by researchers such as Milford

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

main-tain 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

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

entorhi-nal cortex but also within the hippocampal formation This aentorhi-nalysis 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

mul-tiple mechanisms by which such time cell responses could be generated One explicit

mathematical theory uses the components of an inverse Laplace transform (Howard

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.,

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,

there is a gradual, exponential decrease in the self-similarity of a population asmeasured by the Mahalanobis distance (Manns et al., 2007a) This supports the no-tion that neurons are changing in firing properties in an exponential manner Mech-anisms for this process also exist on a cellular level (Tiganj et al., 2014) Individualneurons recorded in slice preparations often respond to a current injection with per-sistent spiking that continues for a period after the current injection, but may termi-nate at different intervals in different neurons, as shown in the postsubiculum

2008), and the hippocampus (Knauer et al., 2013) Recording from large populationswould allow explicit testing of the full coding capability of a population, to deter-mine if there is a decay of self-similarity across a population and within individualneurons 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 pocampus and adjacent structures This could resolve one of the fundamentalparadoxes about data on the hippocampus Behavioral data gathered after lesions in-dicate that the hippocampus and parahippocampal regions are essential to the recall

hip-of recently encoded episodic memories (Corkin et al., 1997; Scoville and Milner,

events occurring at a specific time and location But most electrophysiological datafrom the hippocampus and parahippocampal regions focus on stable neural represen-tations such as place cells and grid cells that occur across multiple exposures to anenvironment rather than a single episode

Numerous studies have proposed that hippocampal neurons perform replay of theexperience of being in a specific location in the environment (Wilson and

record-ing of populations of neurons that could exceed 100 simultaneously recorded cells.However, it is important to remember that recording over 100 cells does not meanthat one is recording 100 place cells, as the number of neurons estimated to code agiven 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 adjacentpositions along a trajectory that allows them to show sequential activation.Recording from a million neurons would provide an opportunity to show theencoding and retrieval of a specific episodic memory within a behavioral task, whichcould be seen as a central test of the theory of hippocampus as the locus of storage ofepisodic memories Previous experiments analyzed the Bayesian probability of aneuron firing when the rat was in a specific spatial location, and then during rippleactivity tested for a high-resolution replay of the prior sequence of behavior

(Davidson et al., 2009) Using a million neurons will allow two qualitatively

differ-ent compondiffer-ents of this analysis First, it will allow determination of the represdiffer-enta-

representa-tion 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

hippo-campal 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

dif-ferent and a quantitatively difdif-ferent 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

esti-mated to contain one million neurons in the rat, and region CA3 is estiesti-mated to

con-tain 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,

allow-ing the explicit identification and trackallow-ing of subpopulations representallow-ing individual

memories or environments or sensory cues When recording a thousand neurons inhippocampus, one would expect a few hundred active neurons but might not haveextensive place cell coverage of a given portion of the environment In entorhinalcortex, the percentages of individual functional subtypes such as boundary cellsare 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 fewerneurons 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, oftennonfunctional, scale For example, in studies of replay, researchers can conjecturethat a trajectory is being followed based on the sequential activation of a sparse sub-set 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 therepresentation of neurons when recording from a million versus a thousand neurons.However, the qualitative advantage of larger numbers might be present even withrecording of a few thousands of neurons

In the quantitative sense, it is important to realize that most tests of network namics use populations of tens of neurons Even if the full recorded population isover 100 neurons using current techniques, the number of cells that can be param-eterized effectively in terms of behavior is on the order of tens of cells Not only doesthis reduce the statistical power of specific measures, but it has a huge impact on theprogression of research Unit recording research is notoriously slow, as the data fromeach rat involves building a highly complex implant, obtaining a successful surgeryboth in terms of survival of the rat and proper anatomical placement of the drive,effectively isolating a population of neurons and then obtaining effective behaviorduring the period that neurons are isolated A highly successful experiment mightyield over 100 recorded neurons, but usually only a few successful experiments takeplace over a period of 2–3 years during which the researcher usually has other ex-amples that are only partially successful If we consider that a current successfulstudy yields about 300 neurons in 3 human-years of work, then recording from amillion neurons does not just enhance statistical significance, but a single successfulrecording on this scale could constitute many centuries of scientific progress incurrent human-years

dy-ACKNOWLEDGMENTS

This work was supported by National Institute of Mental Health R01 MH061492, R01MH060013, P50 MH094263, NSF grant PHY1444389, and the Office of Naval ResearchMURI grant N00014-10-1-0936

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Diluted connectivity

in pattern association

networks facilitates the recall

of information from the

hippocampus to the

neocortex

2

Edmund T Rolls*,†,1

*Oxford Centre for Computational Neuroscience, Oxford, UK

† Department of Computer Science, University of Warwick, Coventry, UK

1 Corresponding author: e-mail address: edmund.rolls@oxcns.org

Abstract

The recall of information stored in the hippocampus involves a series of corticocortical

back-projections via the entorhinal cortex, parahippocampal gyrus, and one or more neocortical

stages Each stage is considered to be a pattern association network, with the retrieval cue

at each stage the firing of neurons in the previous stage The leading factor that determines

the capacity of this multistage pattern association backprojection pathway is the number of

connections onto any one neuron, which provides a quantitative basis for why there are as

many backprojections between adjacent stages in the hierarchy as forward projections The

issue arises of why this multistage backprojection system uses diluted connectivity One

rea-son is that a multistage backprojection system with expansion of neuron numbers at each stage

enables the hippocampus to address during recall the very large numbers of neocortical

neu-rons, which would otherwise require hippocampal neurons to make very large numbers of

syn-apses if they were directly onto neocortical neurons The second reason is that as shown here,

diluted connectivity in the backprojection pathways reduces the probability of more than one

connection onto a receiving neuron in the backprojecting pathways, which otherwise reduces

the capacity of the system, that is the number of memories that can be recalled from the

hip-pocampus to the neocortex For similar reasons, diluted connectivity is advantageous in pattern

association networks in other brain systems such as the orbitofrontal cortex and amygdala; for

related reasons, in autoassociation networks in, for example, the hippocampal CA3 and the

neocortex; and for the different reason that diluted connectivity facilitates the operation of

competitive networks in forward-connected cortical systems

Progress in Brain Research, Volume 219, ISSN 0079-6123, http://dx.doi.org/10.1016/bs.pbr.2015.03.007

Hippocampus, Memory, Recall, Diluted cortical connectivity, Pattern association, jections, Episodic memory, Autoassociation, Cortical backprojections, CA3, CA1, Dentategranule cells

Backpro-1 INTRODUCTION

The operation of hippocampal circuitry as a memory system, and evidence that ports the theory that has been developed, is considered in detail elsewhere (Kesner

develop-ment of the theory (Rolls, 1987, 1989a,b,c, 1996; Rolls and Stringer, 2005; Rolls

et al., 2002; Treves and Rolls, 1992, 1994), and its relation to other theories and proaches (Marr, 1971; McClelland et al., 1995; McNaughton and Morris, 1987) Thiscomputational theory of hippocampal function remains the only quantitative theory

ap-of hippocampal function in memory and its recall to the neocortex

In this chapter, I focus on how information is recalled from the hippocampus tothe neocortex, and introduce new hypotheses and evidence about the advantages ofdiluted connectivity in this backprojection circuitry, as well as in pattern associationnetworks in the brain in general I also compare this advantage to the advantages ofdiluted connectivity in autoassociation networks in the cortex such as those in theCA3 region of the hippocampus and local areas of the neocortex, and to the advan-tages of diluted connectivity in competitive networks in the brain, including thoseimplemented in the forward connectivity between cortical areas By diluted connec-tivity, I mean that there are fewer synaptic connections onto each neuron that thereare neurons in the population If there areC¼10,000 connections onto every neuron,andN¼100,000 neurons that receive the inputs, then the dilution of the connectivity

is 0.1 Full connectivity refers to the situation in which there is one synaptic tion onto every neuron from all of the inputs

connec-I start with a brief overview of the operation of hippocampal circuitry (which isdescribed in detail elsewhere,Kesner and Rolls, 2015; Rolls, 2008a, 2010), in which

I treat the issue of the advantages of diluted connectivity within CA3 Then,

I consider the recall of information from the hippocampus to the neocortex, includinghere the new hypotheses and evidence about the advantages of diluted connectivity

in pattern association networks in the cortex

2 OVERVIEW OF THE OPERATION OF HIPPOCAMPAL

CIRCUITRY

The hypothesis is that the hippocampus is involved in storing information in an structured way that can be used for episodic memory of single events or sequences of

un-events, and that recall from the hippocampus back to the neocortex is used to help

build semantic including autobiographical memories To implement this, the

hippo-campus is involved in spatial, object–place, reward–place, and object–temporal

se-quence memory (Kesner and Rolls, 2015) The systems-level neurophysiology of the

primate hippocampus shows that it contains representations of space “out there,” that

is, spatial view cells (Georges-Franc¸ois et al., 1999; Robertson et al., 1998; Rolls and

O’Mara, 1993, 1995; Rolls and Xiang, 2005, 2006; Rolls et al., 1989, 1997, 1998,

2005), which are appropriate for a human episodic memory system, for which

asso-ciations between objects or rewards and the places where they are seen are

prototypical.1

Hippocampal circuitry is illustrated inFigs 1 and 2

2.3.1 Dentate Granule Cells

The theory is that the dentate granule cell stage of hippocampal processing which

precedes the CA3 stage acts in a number of ways including competitive learning

and the randomizing effect of the small numbers of mossy fiber connections onto

each CA3 neuron (seeFig 2) to produce during learning the sparse, yet efficient

(i.e., nonredundant) representation in CA3 neurons that is required for the

autoasso-ciation performed in CA3 to perform well (Kesner and Rolls, 2015; Rolls, 1989a,b,d,

memory is that the dentate by acting in this way would perform pattern separation (or

orthogonalization; Rolls, 1989b, 2008a, 2013b,c; Rolls and Kesner, 2006; Rolls

memories of even similar events, and this prediction has been confirmed by

inves-tigations in rodents (Kesner and Rolls, 2015)

2.3.2 CA3 as an Autoassociation Memory

The hypothesis is that the CA3 operates effectively as a single autoassociation

net-work (seeFigs 2 and 3) to allow arbitrary associations between inputs originating

from very different parts of the cerebral cortex to be formed, and later for the whole

1

John O0Keefe was one of the recipients of the Nobel Prize for Physiology or Medicine in 2014, after

this paper was written His work on the discovery of hippocampal place cells in rats (“ O0Keefe and

Dostrovsky, 1971 ”) was cited, and he is congratulated Indeed, the announcement for the award of

the Nobel Prize described this system as a “component of a positioning system, an ‘inner GPS’ in

the brain.” John O0Keefe has continued to emphasize the role of the hippocampus and rodent place

cells in navigation ( Hartley et al., 2014 ; “ O0Keefe, 1990 ”) Rolls’ discoveries and theory are thus

some-what different, in that Rolls has shown that spatial view cells may be especially relevant to the

oper-ation of the hippocampus in primates including humans; and in that the roles of the hippocampal system

in memory are emphasized ( Kesner and Rolls, 2015; Rolls, 2008a; Rolls and Xiang, 2006 ).

memory to be recalled from any part in the process termed completion We have tended previous formal models of autoassociative memory (see Amit, 1989;Hopfield, 1982) by analyzing a network with graded response units, so as to representmore realistically the continuously variable rates at which neurons fire, and with in-complete connectivity and with sparse representations (Treves, 1990; Treves and

patterns that can be (individually) retrieved is proportional to the number CRCof(associatively) modifiable recurrent collateral synapses per cell, by a factor that in-creases roughly with the inverse of the sparsenessa of the neuronal representation

Cortex Entorhinal

cortex Perirhinal

Fo nix r

Parietal Prefrontal Temporal

2 3

DG

Entorhinal pp

mf

Neocortex

F S D

D S

5

Nucleus accumbens, medial septum

CA1 CA3

& Perirhinal PHG

Mammillary bodies ant nuc of the thalamus Subiculum Presubiculum

FIGURE 1

Forward connections (solid lines) from areas of cerebral association neocortex via theparahippocampal gyrus and perirhinal cortex, and entorhinal cortex to the hippocampus; andbackprojections (dashed lines) via the hippocampal CA1 pyramidal cells, subiculum, andparahippocampal gyrus to the neocortex There is a great convergence in the forwardconnections down to the single network implemented in the CA3 pyramidal cells and a greatdivergence again in the backprojections Left: block diagram Right: more detailedrepresentation of some of the principal excitatory neurons in the pathways D, deep pyramidalcells; DG, dentate granule cells; F, forward inputs to areas of the association cortex frompreceding cortical areas in the hierarchy; mf, mossy fibers; PHG, parahippocampal gyrusand perirhinal cortex; pp, perforant path; rc, recurrent collateral of the CA3 hippocampalpyramidal cells; S, superficial pyramidal cells; 2, pyramidal cells in layer 2 of the entorhinalcortex; 3, pyramidal cells in layer 3 of the entorhinal cortex The thick lines above the cellbodies represent the dendrites

(The sparseness for a binary representation is the proportion of neurons firing for any

one pattern.) Approximately,

pmaxffi CRC

a ln 1a

wherek is a factor that depends weakly on the detailed structure of the rate

distribu-tion, on the connectivity pattern, etc., but is roughly in the order of 0.2–0.3 (Treves

and Rolls, 1991)

only 12,000 recurrent collateral synapses per neuron The dilution of the connectivity

is thus 12,000/300,000¼0.04 We have shown how analysis of the capacity of attractor

networks (Hopfield, 1982) can be extended to the case with diluted connectivity, and

also with sparse representations with graded firing rates (Rolls and Treves, 1990; Rolls

However, the question has recently been asked about whether there are any

ad-vantages to autoassociation or attractor networks with diluted connectivity compared

to fully connected attractor networks (Rolls, 2012a) One biological property that

3600 Perforantpath inputs

Recurrent collaterals

Pyramidal cell layer

inputs 46

The numbers of connections from three different sources onto each CA3 cell from three

different sources in the rat

After Rolls and Treves (1998) and Treves and Rolls (1992)

may be a limiting factor is the number of synaptic connections per neuron, which is12,000 in the CA3–CA3 network just for the recurrent collaterals (seeFig 2) Thenumber may be higher in humans, allowing more memories to be stored in the hip-pocampus than order 12,000 I note that the storage of large number of memoriesmay be facilitated in humans because the left and right hippocampus appear to bemuch less connected between the two hemispheres than in the rat, which effectivelyhas a single hippocampus (Rolls, 2008a) In humans, with effectively two separateCA3 networks, one on each side of the brain, the memory storage capacity may bedoubled, as the capacity is set by the number of recurrent collaterals per neuron ineach attractor network (Eq.1) In humans, the right hippocampus may be devoted toepisodic memories with spatial and visual components, whereas the left hippocam-pus may be devoted to memories with verbal/linguistic components, i.e., in whichwords may be part of the episode (e.g., who said what to whom and when;

Barkas et al., 2010; Bonelli et al., 2010; Sidhu et al., 2013)

w ij

= Dendritic

= Output firing activation

h i

y i

Output

i e

External input

x j

FIGURE 3

Autoassociation memory The architecture of an autoassociation memory The external input

eiis applied to each neuroni by unmodifiable synapses This produces firing yiof eachneuron Each output neuroni is connected by a recurrent collateral connection to the otherneurons in the network, via modifiable connection weightswij This architecture effectivelyenables the output firing vectory to be associated during learning with itself Later on,during recall, presentation of part of the external input will force some of the output neurons tofire, but through the recurrent collateral axons and the modified synapses, other neurons

iny can be brought into activity This process can be repeated a number of times, and recall of

a complete pattern may be perfect Effectively, a pattern can be recalled or recognizedbecause of associations formed between its parts This of course requires distributedrepresentations

The answer that has been suggested to why the connectivity of the CA3

autoas-sociation network is diluted (and why neocortical recurrent networks are also

di-luted) is that this may help to reduce the probability of having two or more

synapses between any pair of randomly connected neurons within the network,

which it has been shown greatly impairs the number of memories that can be stored

in an attractor network, because of the distortion that this produces in the energy

landscape (Rolls, 2012a) In more detail, the hypothesis proposed is that the diluted

connectivity allows biological processes that set up synaptic connections between

neurons to arrange for there to be only very rarely more than one synaptic connection

between any pair of neurons, assuming that synapses are made at random between

neurons If the average connectivity between neurons was 1, then some neurons

would receive more than one synaptic input from a given afferent neuron, with

the proportions of multiple synapses set by the Poisson distribution withl¼1 If

probabilistically there were more than one connection between any two neurons,

it was shown by simulation of an autoassociation attractor network that such

connec-tions would dominate the attractor states into which the network could enter and be

stable, and thus strongly reduce the memory capacity of the network (the number of

memories that can be stored and correctly retrieved), below the normal large capacity

for diluted connectivity (Rolls, 2012a) Diluted connectivity between neurons in the

cortex thus has an important role in allowing high capacity of memory networks in

the cortex, and helping to ensure that the critical capacity is not reached at which

overloading occurs leading to an impairment in the ability to retrieve any memories

from the network (Rolls, 2012a) The diluted connectivity is thus seen as an

adap-tation that simplifies the genetic specification of the wiring of the brain, by enabling

just two attributes of the connectivity to be specified (e.g., from a CA3 to another

CA3 neuron chosen at random to specify the CA3–CA3 recurrent collateral

connec-tivity), rather than which particular neuron should connect to which other particular

neuron (Rolls, 2012a; Rolls and Stringer, 2000) Consistent with this hypothesis,

there are NMDA receptors with the genetic specification that they are NMDA

recep-tors on neurons of a particular type, CA3 neurons (as shown by the evidence from

CA3-specific vs CA1-specific NMDA receptor knockouts;Nakazawa et al., 2002,

2003, 2004; Rondi-Reig et al., 2001) A consequence is that the vector of output

neu-ronal firing in the CA3 region, i.e., the number of CA3 neurons, is quite large

(300,000 neurons in the rat) The large number of elements in this vector may have

consequences for the noise in the system (Rolls and Webb, 2012)

Part of the answer to why there is a large number of neurons in CA3 (300,000 in

the rat) compared to the number of synapses onto each neuron (12,000 in the rat, see

min-imize the number of multiple connections between any pair of CA3 neurons, which

would degrade the memory storage capacity of CA3 very considerably (Rolls,

2012a)

The theory is also that the perforant path inputs to CA3 cells with the necessary

associative synaptic modifiability initiate recall in CA3 and contribute to

generali-zation (Treves and Rolls, 1992)

2.3.3 CA1 Cells

The CA3 cells connect to the CA1 cells by the Schaeffer collateral synapses ciativity in these connections increases the number of patterns that can be correctlytransferred to CA1; the information from the parts of a memory such as about objectand place, necessarily separate in CA3 so that they can be associated, can be com-bined in CA1 to make a more efficient retrieval cue for the whole memory; and ex-pansion of cell numbers occurs, in preparation for the massive divergence needed toaddress large areas of the neocortex during recall (Kesner and Rolls, 2015; Rolls,

3 BACKPROJECTIONS TO THE NEOCORTEX, EPISODIC

MEMORY RECALL, AND CONSOLIDATION

HIPPOCAMPUS COULD IMPLEMENT RECALL

The need for information to be retrieved from the hippocampus to affect other brainareas was noted inSection 1 The way in which this could be implemented via back-projections to the neocortex (Rolls, 1995, 1996, 2008a, 2010; Treves and Rolls, 1994)

is considered here in the context of recalling a complete memory representation in thecomplete set of cortical areas that provide inputs to the hippocampus (seeFig 1)

It is suggested that the modifiable connections from the CA3 neurons to the CA1neurons allow the whole episode in CA3 to be produced in CA1 This may be assisted

by the direct perforant path input to CA1 (Treves and Rolls, 1994) This might allowdetails of the input key for the recall process, as well as the possibly less information-rich memory of the whole episode recalled from the CA3 network, to contribute tothe firing of CA1 neurons The CA1 neurons would then activate, via their termina-tion in the deep layers of the entorhinal cortex, at least the pyramidal cells in the deeplayers of the entorhinal cortex (seeFig 1) These entorhinal cortex layer 5 neuronswould then, by virtue of their backprojections (Lavenex and Amaral, 2000; Witter

the hippocampus, terminate in the superficial layers (including layer 1) of those cortical areas, where synapses would be made onto the distal parts of the dendrites ofthe (superficial and deep) cortical pyramidal cells (Markov et al., 2014; Rolls,

could include multimodal cortical areas (e.g., the cortex in the superior temporal cus which receives inputs from temporal, parietal, and occipital cortical areas, andfrom which it is thought that cortical areas such as 39 and 40 related to languagedeveloped; and the orbitofrontal and anterior cingulate cortex to retrieve the re-ward/affective aspects of an episodic memory; Rolls, 2014a,b) and also areas ofunimodal association cortex (e.g., inferior temporal visual cortex; Lavenex and

provide information useful to the neocortex in the building of new representations

in the multimodal and unimodal association cortical areas, which by building new

long-term representations (sometimes called schemas; Preston and Eichenbaum,

2013) can be considered as a form of memory consolidation (Rolls, 1989a,b,d,

1990a,b, 2008a), or in organizing actions

The hypothesis of the architecture with which this would be achieved is shown in

(solid lines inFig 1) show major convergence as information is passed to CA3, with

the CA3 autoassociation network having the smallest number of neurons at any stage

of the processing The backprojections allow for divergence back to neocortical

areas The way in which we suggest that the backprojection synapses are set up to

have the appropriate strengths for recall is as follows (Rolls, 1989a,b,d, 2008a)

Dur-ing the settDur-ing up of a new episodic memory, there would be strong feedforward

ac-tivity progressing toward the hippocampus During the episode, the CA3 synapses

would be modified, and via the CA1 neurons and the subiculum, a pattern of activity

would be produced on the backprojecting synapses to the entorhinal cortex Here, the

backprojecting synapses from active backprojection axons onto pyramidal cells

be-ing activated by the forward inputs to entorhinal cortex would be associatively

mod-ified A similar process would be implemented at preceding stages of neocortex, that

is, in the parahippocampal gyrus/perirhinal cortex stage and in association cortical

areas, as shown inFig 1

The concept is that during the learning of an episodic memory, cortical

pyrami-dal cells in at least one of the stages would be driven by forward inputs but would

simultaneously be receiving backprojected activity (indirectly) from the

hippocam-pus, which would, by pattern association from the backprojecting synapses to the

cortical pyramidal cells, become associated with whichever cortical cells were

be-ing made to fire by the forward inputs Then later on, durbe-ing recall, a recall cue

from perhaps another part of cortex might reach CA3, where the firing during

the original episode would be completed The resulting backprojecting activity

would then, as a result of the pattern association learned previously, bring back

the firing in any cortical area that was present during the original episode Thus,

retrieval involves reinstating the activity that was present in different cortical areas

that was present during the learning of an episode (The pattern association is also

called heteroassociation, to contrast it with autoassociation The pattern association

operates at multiple stages in the backprojection pathway, as made evident in

Fig 1) If the recall cue was an object, this might result in recall of the neocortical

firing that represented the place in which that object had been seen previously As

noted elsewhere in this chapter and byMcClelland et al (1995), that recall might be

useful to the neocortex to help it build new semantic memories, which might

in-herently be a slow process and is not part of the theory of recall It is an interesting

possibility that recall might involve several cycles through the recall process After

the information fed back from the first pass with a recall cue from perhaps only one

cortical area, information might gradually be retrieved to other cortical areas

in-volved in the original memory, and this would then act as a better retrieval cue

for the next pass

The timing of the backprojecting activity would be sufficiently rapid, in that, forexample, inferior temporal cortex neurons become activated by visual stimuli withlatencies of 90–110 ms and may continue firing for several hundred milliseconds

object-and-place and conditional spatial response tasks with latencies of 120–180 ms

backpro-jected activity from the hippocampus might be expected to reach association corticalareas such as the inferior temporal visual cortex within 60100 ms of the onset oftheir firing, and there would be a several hundred milliseconds period in which therewould be conjunctive feedforward activation present with simultaneous backpro-jected signals in the association cortex

During recall, the backprojection connections onto the distal synapses of corticalpyramidal cells would be helped in their efficiency in activating the pyramidal cells

by virtue of two factors The first is that with no forward input to the neocortical ramidal cells, there would be little shunting of the effects received at the distal den-drites by the more proximal effects on the dendrite normally produced by the forwardsynapses Further, without strong forward activation of the pyramidal cells, therewould not be very strong feedback and feedforward inhibition via GABA cells, sothat there would not be a further major loss of signal due to (shunting) inhibition

py-on the cell body and (subtractive) inhibitipy-on py-on the dendrite (The cpy-onverse of this

is that when forward inputs are present, as during normal processing of the ment rather than during recall, the forward inputs would, appropriately, dominate theactivity of the pyramidal cells, which would be only influenced, not determined, bythe backprojecting inputs; seeDeco and Rolls, 2005b; Rolls, 1989b,d, 2008a).The synapses receiving the backprojections would have to be Hebb-modifiable,

environ-as suggested byRolls (1989b,d) This would solve the deaddressing problem, which

is the problem of how the hippocampus is able to bring into activity during recall justthose cortical pyramidal cells that were active when the memory was originally beingstored The solution hypothesized (Rolls, 1989b,d) arises because modification oc-curs during learning of the synapses from active backprojecting neurons from thehippocampal system onto the dendrites of only those neocortical pyramidal cells ac-tive at the time of learning Without this modifiability of cortical backprojectionsduring learning at some cortical stages at least, it is difficult to see how exactlythe correct cortical pyramidal cells active during the original learning experiencewould be activated during recall Consistent with this hypothesis (Rolls, 1989b,d),there are NMDA receptors present especially in superficial layers of the cerebral cor-tex (Monaghan and Cotman, 1985), implying Hebb-like learning just where thebackprojecting axons make synapses with the apical dendrites of cortical pyramidalcells The quantitative argument is that the backprojecting synapses in at least onestage have to be associatively modifiable parallels that applied to the pattern retrievalperformed at the entorhinal to CA3 synapses (Treves and Rolls, 1992) and at theCA3–CA1 synapses (Schultz and Rolls, 1999) and is that the information retrievedwould otherwise be very low The performance of pattern association networks isconsidered in detail by Rolls and Treves (Rolls, 2008a; Rolls and Treves, 1990,

1998) and other authors (Hertz et al., 1991) It is also noted that the somewhat greater

anatomical spread of the backprojection than the forward connections between two

different stages in the hierarchy shown inFig 1would not be a problem, for it would

provide every chance for the backprojecting axons to find co-active neurons in an

earlier cortical stage that are part of the representation that is relevant to the current

memory being formed

If the backprojection synapses are associatively modifiable, we may consider the

duration of the period for which their synaptic modification should persist What

fol-lows from the operation of the system described above is that there would be no

point, indeed it would be disadvantageous, if the synaptic modifications lasted for

longer than the memory remained in the hippocampal buffer store What would

be optimal would be to arrange for the associative modification of the backprojecting

synapses to remain for as long as the memory persists in the hippocampus This

sug-gests that a similar mechanism for the associative modification within the

hippocam-pus and for that of at least one stage of the backprojecting synapses would be

appropriate It is suggested that the presence of high concentrations of NMDA

syn-apses in the distal parts of the dendrites of neocortical pyramidal cells and within the

hippocampus may reflect the similarity of the synaptic modification processes in

these two regions (cf.Kirkwood et al., 1993) It is noted that it would be appropriate

to have this similarity of time course (i.e., rapid learning within 1–2 s, and slow decay

over perhaps weeks) for at least one stage in the series of backprojecting stages from

the CA3 region to the neocortex Such stages might include the CA1 region,

subi-culum, entorhinal cortex, and perhaps the parahippocampal gyrus/perirhinal cortex

However, from multimodal cortex (e.g., the parahippocampal gyrus) back to earlier

cortical stages, it might be desirable for the backprojecting synapses to persist for a

long period, so that some types of recall and top-down processing (Rolls, 1989b,d,

backprojecting synapses could be stable and might not require modification during

the learning of a new episodic memory

An alternative hypothesis to that above is that rapid modifiability of

backprojec-tion synapses would be required only at the beginning of the backprojecting stream

Relatively fixed associations from higher to earlier neocortical stages would serve to

activate the correct neurons at earlier cortical stages during recall For example, there

might be rapid modifiability from CA3 to CA1 neurons, but relatively fixed

connec-tions from there back (McClelland et al., 1995) For such a scheme to work, one

would need to produce a theory not only of the formation of semantic memories

in the neocortex but also of how the operations performed according to that theory

would lead to recall by setting up appropriately the backprojecting synapses

We have noted elsewhere that backprojections, which included corticocortical

backprojections, and backprojections originating from structures such as the

hippo-campus and amygdala, may have a number of different functions (Rolls, 1989a,b,d,

top-down attention by biased competition (Deco and Rolls, 2003, 2004, 2005a; Deco

et al., 2005; Grabenhorst and Rolls, 2010; Rolls, 2008a,b, 2013a; Rolls and Deco,

2002, 2006) The particular function with which we have been concerned here is howmemories stored in the hippocampus might be recalled in regions of the cerebral neo-cortex, and this is not at all incompatible with such theories of top-down attentionalcontrol.

OF CONNECTIONS ONTO EACH NEURON

How many backprojecting fibers does one need to synapse on any given neocorticalpyramidal cell in order to implement the mechanism outlined above? Consider a poly-synaptic sequence of backprojecting stages, from hippocampus to neocortex, as a se-ries of simple (hetero-)associative (i.e., pattern association) memories in which, ateach stage, the input lines are those coming from the previous stage (closer to the hip-pocampus;Rolls, 2008a; Treves and Rolls, 1994;Fig 1) (The interesting concepthere is that one can treat for a capacity analysis the series of backprojection stages

to the cerebral cortex, which each involves a pattern association, as an “unrolled” sion of an autoassociator Each backprojection pattern association stage would cor-respond to one iteration round the autoassociation system.) Implicit in this framework

ver-is the assumption that the synapses at each stage are modifiable and have been indeedmodified at the time of first experiencing each episode, according to some Hebbianassociative plasticity rule A plausible requirement for a successful hippocampo-directed recall operation is that the signal generated from the hippocampally retrievedpattern of activity, and carried backward toward neocortex, remains undegradedwhen compared to the noise due, at each stage, to the interference effects caused

by the concurrent storage of other patterns of activity on the same backprojecting aptic systems That requirement is equivalent to that used in deriving the storage ca-pacity of such a series of heteroassociative memories, and it was shown inTreves and

that can be retrieved is given, essentially, by the same formula as(1)above where,however,a is now the sparseness of the representation at any given stage, and C isthe average number of (back-)projections each cell of that stage receives from cells

of the previous one (Treves and Rolls, 1991) In more detail, the number of memorypatternsp that can be retrieved in a multistage pattern association network is

wherek is a factor that depends weakly on the detailed structure of the rate tion, on the connectivity pattern, etc., but is roughly in the order of 0.2-0.3 (Trevesand Rolls, 1991) (This result for the storage capacity is derived using threshold lin-ear neurons as model M2 in the appendix ofTreves and Rolls (1991) The storagecapacity of a one-stage pattern association network is similar, as derived byRollsand Treves (1990), wherea there refers to the sparseness of the output representation

Ifp is equal to the number of memories held in the hippocampal memory, it is

limited by the retrieval capacity of the CA3 network,pmax Putting together the

for-mula for the latter with that shown here(2), one concludes that, roughly, the

require-ment implies that the number of afferents of (indirect) hippocampal origin to a given

neocortical stage (CHBP), must beCHBP¼CRC

anc/aCA3, whereCRCis the number ofrecurrent collaterals to any given cell in CA3,ancis the average sparseness of a neo-

cortical representation, andaCA3is the sparseness of memory representations in CA3

(Treves and Rolls, 1994)

The above requirement is very strong: even if representations were to remain as

sparse as they are in CA3, which is unlikely, to avoid degrading the signal,CHBP

should be as large asCRC, i.e., 12,000 in the rat Moreover, other sources of noise

not considered in the present calculation would add to the severity of the constraint

and partially compensate for the relaxation in the constraint that would result from

requiring that only a fraction of thep episodes would involve any given cortical area

If thenCHBPhas to be of the same order asCRC, one is led to a very definite

con-clusion: a mechanism of the type envisaged here could not possibly rely on a set

of monosynaptic CA3-to-neocortex backprojections This would imply that, to make

a sufficient number of synapses on each of the vast number of neocortical cells, each

cell in CA3 has to generate a disproportionate number of synapses onto neocortical

neurons (i.e.,CHBPtimes the ratio between the number of neocortical and that of CA3

cells) The required divergence can be kept within reasonable limits only by

assum-ing that the backprojectassum-ing system is polysynaptic, provided that the number of cells

involved grows gradually at each stage, from CA3 back to neocortical association

areas (Treves and Rolls, 1994; cf.Fig 1)

Although backprojections between any two adjacent areas in the cerebral cortex

are approximately as numerous as forward projections, and much of the distal parts

of the dendrites of cortical pyramidal cells are devoted to backprojections, the actual

number of such connections onto each pyramidal cell may be on average only in the

order of thousands Further, not all might reflect backprojection signals originating

from the hippocampus, for there are backprojections which might be considered to

originate in the amygdala (seeAmaral et al., 1992) or in multimodal cortical areas

(allowing, for example, for recall of a visual image by an auditory stimulus with

which it has been regularly associated) In this situation, one may consider whether

the backprojections from any one of these systems would be sufficiently numerous to

produce recall One factor which may help here is that when recall is being produced

by the backprojections, it may be assisted by the local recurrent collaterals between

nearby (1 mm) pyramidal cells, which are a feature of neocortical connectivity

These would tend to complete a partial neocortical representation being recalled

by the backprojections into a complete recalled pattern (Note that this completion

would be only over the local information present within a cortical area about, e.g.,

visual inputor spatial input; it provides a local “clean-up” mechanism and could not

replace the global autoassociation performed effectively over the activity of very

many cortical areas which the CA3 could perform by virtue of its widespread

recur-rent collateral connectivity.) There are two alternative possibilities about how this

would operate First, if the recurrent collaterals showed slow and long-lasting aptic modification, then they would be useful in completing the whole of long-term(e.g., semantic) memories Second, if the neocortical recurrent collaterals showedrapid changes in synaptic modifiability with the same time course as that of hippo-campal synaptic modification, then they would be useful in filling in parts of the in-formation forming episodic memories, which could be made available locally within

syn-an area of the cerebral neocortex

This theory of recall by the backprojections thus provides a quantitative account

of why the cerebral cortex has as many backprojection connections as forward jection connections (Rolls, 2008a)

pro-These concepts show how the backprojection system to neocortex can be tualized in terms of pattern completion, as follows The information that is presentwhen a memory is formed may be present in different areas of the cerebral cortex, forexample, of a face in a temporal cortex face area (Rolls, 2012b), of a spatial location

concep-in a neocortical location area, and of a reward received concep-in the orbitofrontal cortex(Rolls, 2014a) To achieve detailed retrieval of the memory, reinstatement of the ac-tivity during recall of the neuronal activity during the original memory formationmay be needed This is what the backprojection system described could achieveand is a form of completion of the information that was represented in the differentcortical areas when the memory as formed In particular, the concept of completionhere is that if a recall cue from a visual object area is provided, then the emotionalparts of the episodic memory can be recalled in the orbitofrontal cortex, and the spa-tial parts in parietal cortical areas, with the result that a complete memory is re-trieved, with activity recalled into several higher-order cortical areas Becausesuch a wide set of different neocortical areas must be content-addressed, a multistagefeedback system is required to keep the number of synapses per neuron in the back-projection pathways down to reasonable numbers (Having CA1 directly addressneocortical areas would require each CA1 neuron to have tens of millions of synapseswith cortical neurons That is part of the computational problem solved by the mul-tistage backprojection system shown inFig 1.) Thus, the backprojection system withits series of pattern associators can each be thought of as retrieving the complete pat-tern of cortical activity in many different higher-order cortical areas that was presentduring the original formation of the episodic memory

ROLE IN HIPPOCAMPO-NEOCORTICAL RECALL OF MEMORIES STORED

IN THE HIPPOCAMPUS

The new hypotheses described and tested in this chapter are that having multiple nections between the inputs and the output neurons can decrease the capacity of pat-tern association networks; that dilution of connectivity in pattern associationnetworks can minimize this loss of capacity by reducing the probability of multiplesynapses if they are made at random between input and output neurons; and that thisdilution helps in this way to ensure that the recall of information from the

con-hippocampus to the neocortex by several stages of pattern association network is

ef-ficient and has high capacity It is further suggested that the accuracy and capacity of

the recall process is helped by autoassociation implemented by the recurrent

collat-eral connections between nearby neocortical pyramidal cells, which has previously

been shown to be beneficial in autoassociation networks (Rolls, 2012a) The new

analyses described here show that a similar process applies in pattern association

networks

The hypotheses were tested by simulations of a pattern association network, the

architecture of which is shown inFig 4, and the properties of which have been

described elsewhere (Rolls, 2008a; with the relevant Appendices available online

for the inputs to the network (default sparseness 0.05) and for the outputs of the

net-work (default sparseness 0.05) The netnet-work was trained with an associative

FIGURE 4

A pattern association memory An unconditioned stimulus has activity or firing rateeifor the

ith neuron and produces firing yiof theith neuron The conditioned stimuli have activity

or firing ratexjfor thejth axon In the context of a pattern association network in the

hippocampo-cortical backprojection system, the following correspondences apply The

unconditioned stimulus input is the firing of the postsynaptic neuron during learning of the

episodic memory The conditioned stimulus input is the backprojection input originating

in the hippocampus The output neurons, or neurons connected to them within a cortical

area, send back their outputs to act as the recall cue for the preceding cortical area