Computer simulation of hippocampal place cells

Transcription

1 Psyhobiology 1991,19 (2), Computer simulation of hippoampal plae ells PATRICIA E. SHARP Yale Uniuersity, New Hauen, Connetiut Hippoampal pyramidal ells show loation-speifi firing as animals navigate through an environment. It has been suggested that this firing ould result from the "loal view" available in a ell's field. Hippoampal damage results in learning defiits on a wide variety oftasks. This, along with the fat that an assoiative form ofplastiity has been disovered in the hippoampus has led to the idea that this strueture might serve as a distributed, assoiative-matrix memory devie. Here, these ideas are ombined in a model in whih pyramidal ells are the output layer of a ompetitive-learning, pattern-lassifiation devie. The inputs are patterns of environmental stimuli as viewed by a omputerized "rat" from various loations within a simulated environment. These patterns are "lassified" on the basis oftheir similarity. Sine views available from ontiguous regions of spae are similar, single ells ome to fire in a irumsribed region (plae field). Firing-rate maps for these theoretial units show plae fields remarkably similar to those of aetual plae ells. Also, they show remarkably similar behavior to that of real ells when tested under some of the probe onditions similar to those whih have been used for atual ells. Hippoampal pyramidal eus show loation-speifi firing as animals navigate through an environment (O'Keefe, 1976; O'Keefe & Dostrovsky, 1971). These plaejields are thought to be important in the role played by the hippoampus in spatiallearning. It has been suggested that plae fields may result from the "loal view" available to an animal in the loation ofthe eu's field (MNaughton, 1989; Zipser, 1985). Thus, it may be that sensory-driven ativity of ehs in the areas of assoiation ortex known to projet to the hippoampal formation auses partiular hippoampal pyramidal ehs to fire when partiular onjuntions of stimuli are present. Simple neural-net models demonstrating the plausibility of this suggestion have been presented (Sharp, 1989; Skaggs & MNaughton, 1989). In addition to its dearly established role in spatiallearning (Jarrard, 1983; Morris, arrud, Rawlins, & O'Keefe, 1982; O'Keefe & Nadel, 1978; O'Keefe, Nadel, Keightly, & Kill, 1975; Olton, Walker, & age, 1978; Sutherland, Whishaw, & Kolb, 1983), it is dear that the hippoampus plays a role in learning in many other tasks as weh. Indeed, hippoampal darnage in humans auses global defiits in memory for events and plaes (Corkin, 1984; Milner, Corkin, & Teuber, 1968; Soville & Milner, 1957). Insight into how the hippoampus may aomplish information storage in spatial and other tasks has ome from physiologial studies. Speifially, a long-lasting form of eletrially indued synapti plastiity, known as longterm potentiation or long-term enhanement, has been disovered here (Bliss & ardner-medwin, 1973; Bliss & Lomo, 1973), and has been shown to have the formal This work was partially supported by NINCDS rant NS to the author. Correspondene should be addressed to Patriia E. Sharp, Department of Psyhology, P.O. Box HA, Yale University, New Haven, CT properties outlined by Hebb (1949) in his theoretial mehanism of assoiative information storage in the nervous system (Barrionuevo & Brown, 1983; Kelso & Brown, 1986; Levy & Steward, 1979; MNaughton, 1983; MNaughton & Barnes, 1977; MNaughton, Douglas, & oddard, 1978). Apparently similar types of plastiity have also been indued by environmental, rather than eletrial stimulation, suggesting that this plastiity may our under natural learning onditions as weh (reen, MNaughton, & Barnes, 1990; Ruthrih, Matthies, & Ott, 1982; Sharp, Barnes, & MNaughton, 1987; Sharp, MNaughton, & Barnes, 1985, 1989; Skelton, Sarth, Wilkie, Miller, & Philips, 1987; Weisz, 1982). These fats, along with ertain salient anatomial features of the hippoampus suh as its high divergene and onvergene ratios (see RoUs, 1989; for review), have ontributed to the general theoretial view that the hippoampus serves as a distributed, assoiative-rnatrix memory devie for a wide variety of information (Marr, 1971; MNaughton, 1989; MNaughton & Morris, 1987; RoHs, 1989). The present model ombines the idea that plae fields result from "loal views" with the idea that the hippoampus ontains Hebb-like synapti mehanisms that store patterns of sensory input, in order to model the ativity ofhippoampal plae eus. For this, a simple neural network model, inorporating Hebb-like synapti mehanisms, is used, with the hippoampal pyramidal ehs being viewed as elements in the final, output layer of the devie. The input layer onsists of "neoortial ehs" that have sensory responses to the elements of the patterns of stimuli available to the animal's sensory reeptors from eah of the various loations within an environment. Simulated rats run "sessions" in whih they navigate through an environment, thus exposing themselves to various loal views within it. 103 Copyright 1991 Psyhonorni Soiety, In.

2 104 SHARP Neoortial Cells Entorhinal ells Hippoampal Cells Type 1 Type 2 The partiular type of neural-network devie used here is a ompetitive-learning, pattern-lassifiation devie (rossberg, 1976a, 1976b; Rumelhart & Zipser, 1986; Von der Malsburg, 1973). Suh a devie onsists oftwo or more layers of neuron-like elements, with eah element of a given layer being onneted to eah element of the next lower layer through a Hebb-like synapse (see Figure 1). Suh devies ome to lassify and store input patterns on the basis of their similarity to one another, so that patterns that are similar (i.e., that share many elements in ommon) are likely to be represented by (to ativate) the same output layer units. This type of devie was thought to be appropriate for the simulation of plae ells, sine plaes onsist of patterns of simultaneously available stimuli. The onfigurations available from ontiguous loations are similar, and so might be plaed into the same lass by suh a devie, thus resulting in a firing pattern in whih a given ell fires over a irumsribed region of spae (13, plae field). Also, these devies show pattern ompletion, as do hippoampal plae ells (O'Keefe & Conway, 1978), and their output patterns are dependent on plasti properties of the system, as are those ofplae ells (Bostok, Muller, & Kubie, 1991; Sharp, Kubie, & Muller, 1990). In addition, the model is ompatible with a generalized view of plae ells as responding to a wide variety of relations between stimuli, other than just those whih define a partiular plae (Eihenbaum & Cohen, 1988). Finally, the model is ompatible with the idea, based on defiits resulting from hippoampal formation damage, that the hippoampus is involved in storing onfigural representations (Sutherland & Rudy, 1989). Thus, in this model, plae-ell firing itself is seen as a stored onfigural representation of environmental stimuli. Plae fields, then, are viewed as one example of the type of stored representation postulated to exist in the hippoampus. These representations an be reinstated even in the fae of modest environmental hanges. They presumably provide the rest of the brain with onfigural representations that an be used in other sorts of informationproessing and -storage tasks. THE MODEL Figure 1. Shemati representation of the ompetitive-iearning pattern-1assifiation devie, adapted from Rumelhart and Zipser (1986), used to simulate hippoampai ells. Eah ell in a given layer makes a Hebb-Iike synapti ontat with every ell in the next lower layer. The strengths of these synapti onnetions are initially randomized. Cells in the lower two layers are grouped into winner-takeall lusters, so that only the ell that reeives the most synapti input on any one oasion will fire. Cells in the first (neoortial) layer are sensory ells, whih fire when a stimulus to whih they are ''responsive" is within range. See text for details. The ompetitive-learning pattern-lassifiation devie used here was taken, almost without modifiation, from that ofrumelhart and Zipser (1986), to whom the reader is referred for a theoretial disussion of the devie itself. Units in the first layer (see Figure 1) are oneived of as sensory ells, eah ofwhih is ativated by partiular "environmental stimuli" to whih it happens to be "responsive. " One modifiation to the Rumelhart and Zipser model is that here, this input layer is divided into two types of units with somewhat different response properties, as desribed below. Subsequent layers are divided into winner-take-all lusters, whih means that only the one ell within eah luster that reeives the largest input on

3 COMPUTER SIMULATION OF PLACE CELLS 105 any one oasion will fire. Every ell in a given layer reeives inputs from every ell in the layer above, with the strength of the onnetion between any two ells being randomized initially. All weights are positive, and the sum of these onnetive strengths is normalized over eah postsynapti ell. Determination of whih ell within a luster reeives the largest input is aomplished through first multiplying, for eah ell, the ativity level on eah of the input lines (whih is either 1, if the line is ative, or 0, if it is inative) by the strength of its onnetion with that line (i.e., the synapti strength), and then summing over these produts. Thus, the inner produt of the input (or presynapti) ativity vetor and the synapti weight vetor is alulated. The ell, within eah luster, that has the largest inner produt fires, while the others remain silent. This winner-take-all lustering of units is a simple way of simulating both feedforward and feedbak inhibition provided in the brain by inhibitory interneurons. Suh inhibitory influenes are thought to at to keep the global ativity level in a region onstant, even though the number of ative ells in the input layer may vary dramatially, as a funtion of external stimulus input (Marr, 1 %9). Interneurons thought to be apable of providing both feedforward and feedbak inhibition are found throughout the hippoampus (Andersen, Eles, & Loyning, 1964; Lorente de No, 1934; Ramon y Cajal, 1911; see MNaughton & Morris, 1987, for review). Cells "leam" only on oasions on whih they fire. When this happens, eah synapti onnetion first loses a portion of its strength, and then the sum of this derease in strength is redistributed among the onnetions that have ative input lines. In this way, all onnetions that were ative when the ell fired beome strengthened. (lt should be noted that beause of the way that synapti strength is redistributed on eah oasion, the total amount of synapti strength for any one postsynapti ell remains fixed, and idential to that of allother ells; see rossberg, 1976a, 1976b, for a disussion.) This means that on subsequent oasions, that unit is more likely to fire to that pattern, or to any pattern similar to (having a large proportion of elements in ommon with) that one. In this way, eah layer omes to lassify the patterns from the layer just above it in terms of their similarity. The system an also lassify novel patterns, or impoverished versions of already learned ones. APPLICATION OF THE PATTERN-CLASSIFICATION DEVICE TO THE IDPPOCAMPAL FORMATION In order to apply this devie to plae-field generation, it was first neessary to deide how to set up ativity patterns in the initial, sensory elllayer. Several onsiderations went into this deision. First, it was important that the sensory ells have "response properties" that resembled, as losely as possible, those of ells in areas of the neoortex that projet to the hippoampal formation. It is known that the entorhinal ortex, either diretly or indiretly, reeives inputs from broad areas of polysensory assoiation ortex (Insausti, Amaral, & Cowan, 1987; Van Hoesen & Pandya, 1975; Van Hoesen, Pandya, & Butters, 1975). Although little is known about the physiology of most of these areas, available data suggest that these ells have optimal stimuli that are omplex patterns or objets, that they have broad reeptive fields, and, in ases in whih it has been tested, that they have objet onstany (Baylis, Rolls, & Leonard, 1987; Miyashita & Chang, 1988). Seond, it was thought important to use a simulation of an envirorunent that has atua1ly been used to study hippoampal plae ells, so that the modeled results ould be ompared diretly to real plae-ell data. Finally, it is known that the output of pattern-lassifiation devies is affeted by the order and frequeny with whih eah ofthe patterns is presented (see Rumelhart & Zipser, 1986, for a theoretial disussion). Beause ofthis, it was thought that the series of "loal views" of the environment should be presented to the system in the most realisti way possible. To aommodate eah of these onsiderations, the simulated envirorunent shown in Figure 2 was onstruted. The envirorunent itself onsists of a irular array of eight point stimuli. These are meant to simulate the ylindrial apparatus whih has been used in numerous studies of plae ells (e.g., Muller & Kubie, 1987; Muller, Kubie, & Rank, 1987). In this reording paradigm, rats are plaed into a uniformly painted, gray, ylindrial apparatus (76 m in diameter), whih has one white ard that oupies 100 of ar and extends from the floor to the eiling of the apparatus. The animals are food-deprived, E rat o I I,, \, I I Figure 2. Shemati representation ofthe simulated environment and rat. The irular array of eight point stimuli provides a simulation of the ylindrial reording apparatus used to reord from real hippoampal ells (e.g., Muller & Kubie, 1987; Muller, Kubie, & Rank, 1987). The simulated rat runs "sessions" in this environment, onsisting of onstant loomotion in patterns made to repliate those of atual rats as 10sely as possible. At eah small quantum "step" that the animal takes, alulations are made of the distane and angle of eah of the point stimuli in relation to the rat's urrent head position. The results of these alulations are used to set up firing patterns in the first (neoortial) layer of ells in the pattern-lassifiation devie shown in Figure 1. B A

4 106 SHARP and small food pellets are thrown into the apparatus at pseudorandom l<lcations throughout reording sessions. Rats in this situation ome to generate nearly ontinuous patterns of loomotion, in whih they zigzag through the apparatus in a wide variety of apparently unpreditable, but harateristi, patterns. The use here of the eight point stimuli (Figure 2) to simulate this environment was based on the assumption that eah setion of the ylinder presents a different stimulus for ells in assoiation ortex. Thus, Stimulus A ould be thought of as representing a setion of the ylinder that is overed by the uniform, white ard, while Stimulus B would ontain the edge of the ard against the gray wall, and so forth. The omputerized "rat" that ran "sessions" in this simulated environment is also shown in Figure 2. During suh sessions, the "rat" takes small, quantumjumps (eah overing a distane orresponding to 7% ofthe diameter of the ylindrial enlosure). The overall pattern of these steps was made to simulate, as losely as possible, the atual patterns of trajetories taken by real rats in this situation. The size of eah quantum leap was made to approximate the average distane (in relation to the size of the environment) traveled by an atual rat in IAI of a seond, and the reason for hoosing this distane is explained below. At eah step that the "animal" takes, alulations are made of the angle and distane of eah of the eight stimuli with respet to the "animal's" urrent head position. These alulations are used to set up ativity in the input layer of neoortial ells. Eah ell in this layer has a 0.17 probability ofbeing "responsive', to eah ofthe environmental stimuli. Random determination of whih stimuli eah of the ells is responsive to is made at the beginning of the simulations for any one "rat. " There are two types of these ells. Type 1 ells fire whenever the "rat" is within a ertain range of astimulus to whih it is responsive. Eah suh ell has a harateristi range that varies, aross ells, between 15 and 40 "m," in relation to the simulated 76-m-diam ylinder. Type 2 ells are similar to Type 1 ells in that they fire only when the "rat" is within a given, harateristi distane of a stimulus to whih they are responsive. They have the additional requirement, however, that the stimulus be within a ertain range of angle to the "animal's" head. Thus, these ells have a reeptive field that overs a given portion ofthe angular distane around the "animal's" head. The size of this reeptive field varies between 80 0 and aross ells. This has the effet that, for Type 2 ells, responses are dependent not only on the "animal's" urrent loation, but also on the diretion in whih it is faing. There are 60 Layer 1 ells, with 30 in the Type 1 and 30 in the Type 2 ategories. It should be noted that there is no limit on the number of Layer 1 ells that may fire on any one oasion, whih is not the ase with the ells in subsequent layers. One firing is established in the input layer, the pattern projets through the middle layer, whih has been designated here as the entorhinal ortex. This is in keeping with anatomial studies in whih it has been shown that assoiation areas of neoortex projet to the entorhinal ortex-whih in turn provides the hippoampus with its main soure of ortial afferent input. There are 60 entorhinal ells, divided into 3 lusters. As desribed above, 1 ell in eah of these lusters is seleted to fire on the basis of the strength of its onnetions with urrently ative ells. The ell that fires on any one oasion has its synapti weights hanged in aordane with the Hebb-like rules desribed above. Finally, the pattern of ativity from the entorhinal ortex (onsisting of 3 ative ells at any one time) projets onto the hippoampallayer. Here, there is only one luster of 20 ells. The rules for hoosing whih ell is ative and for synapti plastiity are idential to those already desribed. One slight modifiation in this layer, however, is that an ative ell (i.e., a ell that has won the ompetition) may be in one of two states. If it has an inner produt (ofthe presynapti ativity vetor and the synapti weight vetor) of 0.25 or less, it fires a single spike. If, however, its inner produt is above this level, it fires a omplex spike (Rank, 1973), whih onsists of either 3 or 5 ation potentials, depending on how muh above the 0.25 level it iso Thus, the momentary rate for these ells is dependent on the degree of similarity between the inoming ativity pattern and the synapti weight vetor. "Animals" run 16-min "sessions" of onstant navigation, with the input patterns generated at eah step proessed through the three layers in the manner desribed. Note that sine the "rats" take steps at a simulated rate of 8 Hz, this means that there are a total of 7,680 inputs presented to the model for eah suh session. Over the ourse of the sessions, areord is kept of whih ells fire during eah step the "animal" takes. Afterwards, a firing rate map an be onstruted in whih the rate of firing as a funtion of loation is alulated for an array of pixels overing the apparatus floor. This manner of reording and displaying firing rate as a funtion of loation is diretly analogous to that used for real hippoampal ells, in whih ell ativity and the "animal's" momentary loation are reorded for the purpose of firing-rate map onstrution (Muller & Kubie, 1987; Muller et al., 1987). Finally, it is neessary to onunent on why, as desribed above, the simulated "steps" taken by the "rat" were made to orrespond in size to the relative distane traveled by a real rat in about IAI of a seond. (Note that this means that the input patterns presented to the pattern-lassifiation devie are delivered at a simulated rate of about 8 Hz.) The reason for hoosing this rate is that it orresponds to the approximate frequeny of the theta EE pattern in the hippoampus, whih is present whenever rats engage in loomotor behavior (Vanderwolf, 1969). It has

5 COMPUTER SIMULATION OF PLACE CELLS 107 been shown that hippoampal pyramidal ells fire at theta frequeny when theta is present (Fox, Wolfson, & Rank, 1986). Thus, it seemed reasonable to guess that, in real rats, loal views of the environment are proessed in the hippoampus at a rate of about 8 Hz. RESULTS Typial firing-rate maps for a set of hippoampal ells from one simulated hippoampus, from one 16-min session that was onduted after a total of 64 min of simulated session time, are shown in Figure 3A. Note that only the maps for the ells that were ative in this environment are shown; most of the 20 hippoampal ells were silent. For omparison, a set of firing-rate maps from atual hippoampal ells is also displayed in Figure 3B. It an be seen that the simulated ells display a loationspeifi pattern remarkably sirnilar to that of the real hippoampal ells. Both ell types display patterns that tend to oupy from 20 % to 50 % of the area of the y linder, tend to have a shape that onforms to the ontours of the ylinder, and are shaped like a bullseye, with the highest firing in the middle of the field. These basi harateristis were noted by Muller et al. (1987). Thus, the basi phenomenon of plae-ell firing is generated here. It should be noted that the properties of plae ells observed here are dependent on the plasti properties of the synapses in the system. When simulations are onduted in whih the hanges in synapti weight are turned off, the firing patterns are pathy, and tend to be sattered throughout the ylinder, with no lear field. FURTHER COMPARISONS OF ACTUAL AND SIMULA TED illppocampal CELLS Fields Are Stable Over Time One interesting aspet of plae-ell firing is that, although it has long been suspeted that the firing properties are dependent on experiene (plastiity), existing evidene has suggested that fields are present from the first instant that an animal is plaed into an environment (Hill, 1978), and that, in any one environment, these fields remain stable over long periods oftime (Best & Thompson, 1989; Muller et al., 1987). This is also true for the ells modeled here. Firing-rate maps from one ell are shown in Figure 4, for the 1st, 5th, and 10th onseutive 16- min sessions. The field is similar in size, shape, and 10- ation aross the sessions. To obtain a quantitative measure of the similarity between these firing-rate maps, a pixel by pixel orrelation (Muller & Kubie, 1987) was A SIMULATED PLACE CELLS B ACTUAL PLACE CELLS... ' fi._ t~ '. '.. ~..... e4!... o- e".-. -'.. i~ - : ;:: Co Figure 3. (A) Firing-rate maps for a typial set of simulated "hippoampal ells" from one "rat." For eah map, the total number of times that the given ell fired in eah loation during the simulated 16-min session was divided by the total amount of time that the "rat" spent in that loation. For the purpose of display, the area of the ylinder floor was then divided into a set of pixels, with the average rate in eah pixel being indiated by the darkness of the shading within it. Darker olors orrespond to higher rates, and the olor sale is determined in a relative fashion. (B) Firing-rate maps for typial examples of atual hippoampal pyramidal ells, reorded from rats performing a pellet-hasing task during a 16-min session in a ylindrial apparatus. Reordings of the ellular ativity, as weil as the animal's momentary loation, were made throughout the session, and firing-rate maps were onstruted in a manner analogous to that desribed for Figure 3A. It an be seen that these rate maps for the simulated and atual ells are remarkably similar.

6 .. &~_ A _ 108 SHARP SESSION 1 SESSION 5 SESSION 10 _. _ ~~ _ ;I'/,.~~~- ~.. _... _. -~~~- -- Figure 4. Firing-rate maps (as in Figure 3A) for a simulated ell from a different "rat" during the Ist, 5th, and 10th 16-min sessions. The fleld was similar in size and shape aross these sessions, iiiustrating the stabiiity of these flelds over time. onduted. Tbe R for the orrelation of the map from Session 1 with that from Session 5 was 0.72, whereas that for Sessions 5 and 10 was The differene in these two sores suggests that the field was not exatly in its final form during Session 1, suggesting that there is at least some experiene-dependent hange over the first minutes in an environment. Tbe value for Sessions 5 and 10 is somewhat higher than that obtained using a similar measure for atual hippoampal ells over repeated sessions (Muller & Kubie, 1987; Muller et al., 1987), suggesting that there are fewer soures of variane influening the firing of modeled ells than there are in atual ells, as would be expeted. Fields Persist Even When Some of the Controlling Cues are Removed Early work with a set of four experimenter-ontrolled ues known to jointly ontrol the }(x:ation of fields showed that removal of any subset of the ues left the fields of many ells intat (O'Keefe & Conway, 1978). Firing-rate maps for examples of modeled ells in whih subsets of two stimuli were removed are shown in Figure 5. It an be seen that the fields were quite similar in size and shape even after removal of one quarter ofthe ontrolling ues. Fields Have Diretional Correlates Under Some Conditions When plae ells have been studied under onditions in whih rats are performing on an eight-arm maze, their firing rate has been shown to be dependent on the diretion in whih the animal is faing (MNaughton, Barnes, & O'Keefe, 1983). Results obtained from animals performing in the ylindrial apparatus being simulated here, however, usually show no detetable variation as a funtion of diretion (Bostok, Taube, & Muller, 1988). 1t was reasoned here that these results might be due to the differenes in trajetories taken by animals in the two irurnstanes. In the eight-arm maze, trajetories are tightly restrited to either inward or outward paths on the maze arrns, whereas in the ylinder, animals move through any one loation in a variety of patterns, and thus they view the same loation from many different diretions. In terms of a pattern-lassifiation devie, a system in whih the same ell fires to the "loal view" available from different diretions within the same loation has plaed those views into the same lass. Tbe likelihood that any two patterns will be plaed into the same lass depends on a number of fators. One obvious major fator is the similarity of the two views-that is, the number of elements that they have in ommon. For the present model, any two views from the same loation an be expeted to have all of their Type 1 neoortial ell inputs in ommon, sine these ells respond only as a funtion of distane from environmental stimuli. They would not, however, be expeted to have many Type 2 units in ommon. Another fator influening the likelihood that any two patterns will be plaed in the same lass has to do with the struture of the entire set of patterns that are presented. In partiular, this likelihood also depends on how many patterns intermediate between the two are experiened (where intermediate means that the pattern has more stimulus elements in ommon with both the patterns in question than they have with eah other). Thus, if the two views available when the animal is faing two opposite diretions in a given loation are experiened in addition to other views available from intermediate diretions within that loation, the likelihood that those two opposite views will be plaed into the same ategory is inreased. This is beause, in this ase, the two opposite views are part of a "luster" (a set of stimulus patterns that have relatively large subsets of their elements in ommon) of similar patterns in the input spae (see RumeIhart & Zipser, 1986). Altematively, ifno views of intermediate diretions are available, the views from the loal

7 o (j 3: "'tl C ~ rrj :; CIl ~ C t'"" ~ o z o '"r:1 "'tl t'"" > (j rrj (j rrj t'"" ~ -~ Field s in Standard Stimulus Configu ration Same Fields with Stimuli 0 and Removed Same Fields with Stimuli A and F removed Cell3 B B B E F' H E "'~~~t~~~: ~ ~: ~ ~ ~ ~ ~ ~ ~ A :~::::: :::::::::::::: F.. ::::::::::::. H E'..: :::::::::::. H Cell9 o C '-. e '::::::::: :::' B A E'.: :: ::::::.. ::~I: ::"::. B A o C B.. ~ : : : : : :. : : :.... : : : : : : : : : ::.;. ; ~~-_:. E": :: :::::::: F H F Cell13 0 B E"; : A B E'.:::::: ::,,:: ::::::::::: A,#"70'. _ o B :::::::::::::.... E"; :: : "... F. H F H H Figure 5. Firing-rate maps (as in Figure 3A) for three simulated ells reorded during simulated l6-min sessions in whih either the standard set of eight stimuli (Jen olumn) or a redued set of stimuli (middle and right olumns) was used. Cells reorded under the latter onditions retain fields similar in size and shape to those reorded under standard onditions.

8 Unrestrited Trajetories Restrited Trajetories '" :, :.:.: :.. '. ::!' :. -- :.:~:::i~l ~:l:w:.. /" ::~~:.~.: :. t... :::.: ::. '.::::: ~~TT~; ::::y~::. ~::::. :. ~"i :".: ".::. ~... r. ", : -".y:~y:::.'. rii :... ::::...: ".. ~ '" [1..",,:;~~.::.:. t ::;~~~~=l_ (::::'-'lj':::\:. ",'. -..~ t, """ ".::=:'.::...:.:...: i '\,-. I l. " I. t /... J:.""', '''1 ~~H~ ~,(!~" '" 11..."J' ~~i.i l J' ::~ (~../...» ( n;?,,;~u~ - '~::: I. ill: t.... ~ :.j.1' '.... (, l -/.-!;:ll ~ JI' (:: I ) "'.... ij 1. 1.;l. >r j'-:-"" J 'V 1:1 > I."J t "1.. " '::~I:~ Figure 6. Firing-rate maps as in Figure 3A, ellept tbat bere tbe irular arrays of maps sbow firing rates as a funtion of plae for only tbe sampies taken wben tbe anima\ was faing tbe diretion indiated by the arrow. In the enter of eah array is a standard map in whih all diretions are ombined. The set of maps on the left shows ativity for a eu from a simulated rat performing the "pellet-hasing task," in whih trajetories are relatively unrestrited. The set of maps on the right shows ativity of a eu from an idential "rat" performing in the idential stimulus situation, but for whih trajetories were restrited to those of inward and outward paths along the arms of an eight-arm maze. Firing for tbe eu ShOWD on the left does not show notieable variation as a funetion of diretion. Firing from tbe eu reorded under onditions of restrited trajetories, bowever, is stritly related to head diretion. -o CIl ::t ~ '.

9 COMPUTER SIMULATION OF PLACE CELLS 111 region for eah of the two diretions may eah form their own "luster" in the input spae, and so they would be less likely to be plaed in the same ategory. The firing patterns of the two ells in Figure 6 are taken from two idential "rats," one of whih had been trained in the simulated ylindrial apparatus already desribed (top), and the other ofwhih had been trained in a simulated eight-arrn maze (bottom). All onditions ofthe model and environmental stimuli were idential for the two "rats," exept that for the "rat" that ran on the eightarm maze, trajetories were restrited to inward and outward paths on the arrns. The irular arrays of firing-rate maps show firing rate as a funtion of plae for only the sampies taken when the "animal" was faing in the diretion indiated by the arrow. In the enter is a standard map in whih all diretions are ombined. It an be seen that, in the ylindrial apparatus, the firing pattern is not notieably affeted by the diretion in whih the "animal" is faing. In the maze, however, the ell fires only when the...,..,.,.,... "' ~...,.,..,....,,...,,., "...,.,. I.,,. " I. '. I. "" I, I." I,. I '., I " " I., " I I. I I I "animal" is faing one of the possible diretions. Of the total set of ells tested, only 3 out of 19 were diretional (as assessed visually) in the simulated ylindrial apparatus, whereas 14 out of 20 were diretional in the maze. Inreases in the Size of the Testing Environment Lead to Inreases in the Size of the Fields Original studies of plae ells in the ylindrial apparatus showed that when a given ell was tested in aversion of the environment that was idential to the standard in all ways, exept that it had been inreased in size by a fator of two, fields often showed a similar inrease in size, while maintaining the same relative position and shape (Muller & Kubie, 1987). To test the output of the present model against these results, sessions were onduted in whih the same "rat" was exposed to both the standard stimulus array and one in wh ih the diameter of the irular array had been doubled. Allother parametrie settings ofthe model were left..... ".... I.... ' I I.,., I.,..,.,.,.,.,...,.,., I,,,,, I.." ,...,, '" "'... ",.,...,..,.. "...,..... ',.,,. I I. I,.,..,...,... " ,.,...,...,,. :::: : ~.. ::: ::: ::: ::::: =:=~::= '~. :. :U:::::::::::::::....,... :~~~~,,,,, I ~~~~ I ' I ',.,, 'I I ',, I...,...,....,, I,,, I.,...,...,., "'",...,.,...,.... I I I. " I I I I "" I I ", I",.,,, I ". " ' I '" I' I I I. "... ' "'... ".,...,..,...,.. ",.,,., " I, I ' " ".,. " 0,. ",, 0 I......,...,...,..... '.',,..,., ,',... I.'...., I.. '. I '. '., """ , ,, I,,,,.,.,,,, I ' 0 ' ,..,...,"""" I.... ~,.,... " I. ' ~$:~'" I ' " I ",,.. *...,..,.,..,...,..., ",. 0"' I '.,., " 0"""""'" : : : : : : : : : : : : : I : : : : : ' : : : : : : : : : : ~ : : :,. I. '., ',,,., ' " I,., I " ', I '.,. ", I" ", I,,.,. I"""...,...,...,......,.",.,...,.,.,.,.,, I,., ",. I ',, ",,..,.,,. I,,, ".,...,.,."....,..,...,."...,...,., I '.',, I...,.....,...,. "'..... ".,.....,.,.,..... '"... "."... "..,...,.,.,, I.'.",,.".. I". ".,, "...",..,., "... ""'",, I,., I ",,,. ""","",,,,,,., " I..,,,,, I,,,,.', ". I.. "...,...,...,...,...,...,...,......,...,.,., ,,, ,....., "...,... "..., ,....., I.,., "."..., I ;,, = '~ " '''' ''"'-.....,..., I...,..,...,...,..., I,., I' I'., " l~~~i!;!ie~~~i~~'.., S:'*~~$$',, I ',.... ~~ ~*~ ~,,.... I",.$'*,...,.....,....,., Figure 7. Firing-rate maps (as in Figure 3A) for two different ells in the standard array of stimuli (top) as weil as an expanded version of the same array (bottom). Fields in the two stimulus onfigurations are similar in size and loation, in relation to their respetive stimulus arrays. Thus, the fields are "saled up" in the large ylinder.

10 112 SHARP the same. Of the total of 24 ells tested, 13 had fields in both the small and the large ylinder. Of these, 10 had fields that were related in the two ylinders, in that the field in the large ylinder was sirnilar in shape and loation to that in the small y linder. In most of these ases, the field in the large ylinder was a larger version of the small ylinder field. Two examples of ells of this type are shown in Figure 7. The remaining 11 of the total 24 ells had a field in only one environment. These results are remarkably sirnilar to those of Muller and Kubie (1987) for atual hippoampal ells studied in this paradigm. Of the 22 ells that they tested, 13 had fields in both ylinders, and these were sirnilar to eah other in 9 of these ases. Nine ells had fields in only one of the environments. LIMITATIONS OF THE MODEL One set of phenomena not addressed by the urrent model onsists of those in whih all environmental ues that are ontrolling fators for a plae field are removed. Speifially, experiments have been onduted in whih plae fields are studied in the presene of a set of experimenter-defined ues, whih an be demonstrated to jointly have omplete ontrol over the loation of a ell's field. It has been shown that, under these onditions, when all the ues are made to disappear, either through removal or through extinguishing the room lights, fields remain intat, provided that the animal has been introdued into the enviromnent prior to ue removal (Jones Leonard, MNaughton, & Barnes, 1985; O'Keefe, 1976; O'Keefe & Speakman, 1987; Quirk, Muller, Kubie, & Rank, 1987). If, however, the animal is brought into the environment in the dark or after ue removal, the ell shows some unpreditable firing pattern. It has been suggested that this ability to maintain the same firing field in the absene of all ontrolling ues must be dependent on some sort of information about ongoing motor ativity, along with stored information about the environment and the sensory onsequenes of partiu1ar movements within it (MNaughton, 1989; MNaughton & Morris, 1987). The present model provides no inputs related to the simulated motor patterns, and so it is inapable of generating suh results. Further developments ould, in priniple, however, suessfully inorporate suh information. CONCLUSIONS In the simulation presented here, many of the basi properties of hippoampal plae ells have been repliated through the use of a very simple model in whih simulated sensory responses to the various loal views available in an environment serve as inputs to a ompetitiveleaming, pattern-lassifiation devie. The various patterns of sensory responses to environmental stimuli are lassified aording to their sirnilarity to one another. Sine ontiguous regions of spae offer sirnilar views, ells ome to respond within irumsribed regions, or plae fields. Interpreted in the most general sense, the urrent model simply provides ademonstration that a neural-net devie, when implemented with some reasonable set of assumptions about the hippoampal formation, an repliate ertain plae-ell-like phenomena. Thus, it is sirnilar to any number of neural-net simulations that have appeared over the past several years, and whih have proven able to simulate a wide variety ofbrain-like ativity patterns. The apparent ease with whih suh devies an be onstruted has fueled understandable enthusiasm about them, and wou1d seem to lend support to the idea that the general priniples utilized by these devies (i.e., parallel distributed proessing and Hebb-like synapti plastiity) are likely to be sirnilar to proesses atua11y found in the brain. If any partiular model of a given brain region is to be sientifially useful beyond this general level of demonstration, however, it must make lear its own speifi, testable laims about how the region performs a given information-proessing task. Indeed, the very ease with whih these devies an simulate neural behavior patterns makes it lear that any partiular behavior ould likely be generated by any number of suh devies, eah of whih ould possibly utilize very different assumptions about the struture of the modeled system and the nature of its inputs. One diffiulty involved in eluidating the speifi laims of a model is to make lear whih aspets of the model are meant to be fundamental (meaning that their violation would invalidate the model) and whih are assumed to be trivial. Thus, in the present model, many deisions were made about details suh as the number of ells in eah layer, the number of ells within eah.. luster, " the exat nature of neoortial sensory responses, the number of environmental stimuli, and so forth. Obviously, many of these aspets of the model are either inorret (e.g., the entorhinal ortex does not onsist of just 60 ells) or, at best, oversimplifiations. Deisions were made about them, and inorporated into a working model, in order to demonstrate that the assertions of the model ould, at least in one ase, atually lead to the repliation of plae-ell-like ativity. Other aspets ofthe model, however, are assumed to be entral to the theoretial laim being made. The fundamental assertions of the present model are the following: 1. The hippoampal formation reeives input from ells that individually respond to seletive aspets or omponents of the overall environmental stimulus array. In any environment in whih the plae-ell phenomenon is atually exhibited, the pattern of ativity in this input layer hanges as a funtion ofthe animal's loation, and it does so in suh a way that, in general, the patterns in two ontiguous regions are more sirnilar than the patterns in two regions that are far apart. Although other types of input may also be present (suh as motor information), the input desribed above must playa large role, at least during the initial exposures to

11 COMPUTER SIMULATION OF PLACE CELLS 113 an environment, in determining whieh hippoampal ells fire. 2. The onnetivity within the system shows high levels of both divergene and onvergene. 3. The system shows Hebb-like properties, so that onjuntive ativity of a pre- and postsynapti element auses an inrease in the strength of the onnetion between them. 4. There is some kind of regulatory influene, suh as that provided by inhibitory interneurons, on the overall ativity level of the system, so that only the ells that reeive the most total synapti input, relative to other eus in the area, will fire. Here, this inhibitory influene is modeled by the winner-take-all luster organization within eah layer. Eah of these four assumptions is ompatible with what is known about hippoampal anatomy and physiology, and the justifiation for eah has been disussed individually above. A set of preditions an be generated from this basi set of properties: 1. The likelihood that any two loations will be represented by the same ell is influened by the sirnilarity (in terms of sensory qualities) ofthe two loations. Thus, for example, if animals were trained in an environment that inluded sets of idential "loal views" at different 10- ations, it would be expeted that the probability of the same plae-ell's firing in any two suh loations would be greater than that for two loations that differed in their sensory qualities. Sharp et al. (1990) have presented data ompatible with this predition, although they also emphasize that the model, in its urrent form, is inomplete. In this study, animals were trained to hase food pellets in the ylindrial apparatus desribed above. Lengthy initial training was onduted with a single white ard on the wall. One a ell with a plae field was reorded in this apparatus, additional sessions were onduted in whih a seond, idential ard was added away from the first. In this onfiguration, there are pairs of visually identieal loations, apart. Most ells reorded under these onditions ontinued to show a single, asymmetrial firing pattern, so that the field appeared in only one of two identialloations within any one session, but varied between the two loations aross sessions. This pattern indieates that immediately present visual stimuli are not the only inputs to the system, and it suggests that mnemoni influenes (related to the initial, single-ard training), in onjuntion with motor information, may also be involved. (This point was raised above in the setion on limitations ofthe model.) Further development ofthe model, inorporating movement-related information, will be tested against these results. In ontradistintion to the asymmetrie pattern shown by most eus, however, a small subset of the ells reorded in the two-ard onfiguration showed paired, symmetrial firing fields, so that they showed sirnilar firing in the two visually identialloations. Thus, sensory sirnilarity inreased the likelihood of two areas' being represented by the same ello It is postulated here that if the initial training were also onduted in the two-ue environment, this likelihood would be further inreased, sine mnemonially based representations of the singleard environment would not be present. 2. The likelihood that two loations (or views within loations) with some sensory overlap would be represented by the same ell should be influened by the amount of exposure that the anima! has to the area between the two loations (assuming that this area is more similar sensorially to eah of the two loations than they are to eah other). The reasoning for this predition is the same as that presented above, along with supportive data, in the setion on diretional orrelates. Speifially, the likelihood that any two input patterns will be represented by the same ell is influened by the extent to whih they are part of the same "luster" of patterns in the total set of input patterns. This, in turn, is related to the presene of views intermediate to the two. Studies are urrently being designed to test the likelihood that the same plae ell will fire in two different loations as a funtion of whether the anima1 is allowed to travel through a diret trajetory between them. 3. Plae fields should be resistant to the removal of smau subsets of stimuli, and the partiular stimuli hosen should not make a differene. Data have already demonstrated this property (see, e.g., MuHer & Kubie, 1987; O'Keefe & Conway, 1978). Substantial verifiation of eah of these three preditions should provide evidene that muh of the determination of plae-ell firing patterns takes plae through a proess in whih the hippoampal formation ats as a patternlassifiation devie for sensory inputs. 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