Computational
approaches
William
of Arizona,
The results of theoretical recoding
function
E. Skaggs and Bruce 1. McNaughton
University
hippocampal
to hippocampal
formation
events
work may
into patterns
which
Tucson,
have
Opinion
its memory per event,
in Neurobiology
Introduction One of the most striking features of the hippocampus is how rarely most of its cells are active. In an alert moving rat a typical complex-spike cell (these are the output cells of the hippocampus) fires 30-50 spikes per second when it is active, but less than 0.5 spikes per second on long-term average [ 11. Thus at any given time fewer than 1% of the complex spike cells are active. This remarkable ‘spars&y’of firing distinguishes the hippocampus from any other part of the brain. Interestingly, coding sparsity increases as one moves into the hippocampus from its entorhinal cortical inputs, and then decreases again as information is transmitted back to the neocortex via the subiculum [ 1 ] Furthermore, spars&y decreases (and the average activity level correspondingly rises) when an animal is quiescent or sleeping, and increases when the animal is performing the kind of exploratory task most sensitive to hippocampal dysfunction. These considerations suggest that sparse coding is important for some operation intrinsic to the hippocampus. Both human clinical studies and animal experiments involving damage to the hippocampal formation indicate that it plays a crucial role in the initial establishment of long-term associative memory. A variety of evidence favors the hypothesis that the hippocampus acts as a simple interim repository for memories of certain kinds of events, and that other (neocortical) circuitry draws on this repository during a process known as memory consolidation. Twenty years ago Marr [ 2,3**] proposed a theory of the computational mechanisms required for such a function. In essence, it concerned the encoding of events as distributed patterns of activity imposed on a population of hippocampal ‘principal’ cells and stored there by modifying synaptic connections. He performed a series of rough calculations, whose net result was that the capacity of the memory (the number of patterns it could store) increased in proportion to the sparsity of the patterns, up to a maximum level beyond which greater spars@ would cause problems. He predicted that optimal performance would be obtained if each pattern activated about a fraction of 0.003 of the cells in the network. Associative network memories of the type described by Marr store patterns by increasing the strength of con-
USA
to suggest that storage
are as dissimilar
use as few neurons
Current
led researchers
maximize that
Arizona,
capacity
to one another,
the by and
as possible.
1992, 2:209-211
nections between simultaneously active cells. If, later, a subset of the cells in the pattern are activated, the remaining cells will tend to be activated by a .~$Jlateral effect’; that is, they will receive relatively sti’bngiqput from the active cells. In this way subpatterns; of the stored pattern can be completed; less obviously, noisy versions of the stored pattern can also be cleaned up. Storage and recall of a single pattern is easy to arrange, and is most effective when the number of cells participating in the pattern is large, because the strength of the collateral effect at a given cell is then proportional to the number of connections the cell makes with other active cells. Difficulties arise when the attempt is made to store multiple patterns, as they interfere with each other. The magnitude of interference between two patterns is determined by the number of connections they have in common, and hence is proportional to the square of the number of active cells. For this reason, interference is minimized by keeping small the number of cells participating in each pattern. Optimal performance is obtained by balancing the need for a strong collateral effect against the need for low interference. These broad considerations have been appreciated for many years, but the precise constraints they impose on biological memory networks have not been easy to work out. Marr made a number of valuable suggestions, but his arguments are sometimes difficult to follow and sometimes clearly incorrect [4-l. Recent theoretical work has brought the picture into sharper focus. Hebbian
synaptic modification
in the
hippocampus Marr [ 21 predicted the existence of synaptic modification in the hippocampus before any evidence for it was available; his paper includes a note added in press describing the very first finding of long-term potentiation by Lomo [ 51. Twenty years later vastly more is known about this phenomenon, and with the discovery and characterization of the N-methyl-D-aspartic acid (NMDA) receptor, it has become possible to construct preliminary detailed biophysical models of the process. Two such models have recently been published by Zador et al. [6*,7--l and Holmes and Levy [8]. The models differ somewhat in
Abbreviation NMDA-N-methyl-o-aspartic
acid.
@ Current Biology Ltd ISSN 0959-4388
209
210
Cognitive
neuroscience
their assumptions and in their behavior. As the behavior of a memory network can be quite sensitive to the specific form of the learning rule, such differences may turn out to be important. Theoretical
studies of sparse coding
The principal hippocampal circuit involves a unidirectional flow of information from the entorhinal cortex, to the fascia dentata, to the CA3 subregion (which also receives a strong direct projection from the entorhinal cortex), to the CA1 subregion, and finally to the subiculum, the main exit point, which sends output to the entorhinal cortex and several other parts of the brain. In addition to this forward flow, there is also an extensive network of excitatory recurrent collaterals in CM. CA3 was the heart of Marr’s model, and was conceived of as something similar to what later came to be known as a ‘Hopfield model’ [9]. A number of studies of as sociative memory networks, using approaches originally developed by physicists working on statistical mechanics, have now appeared. A recurring theme is the effectiveness of sparse coding in increasing the capacity (defined as the number of patterns storable) of a network (for examples, see [ 10,111). One of the most interesting of such studies, by Baum, Moody, and Wilczek [ 121, found that very large capacities could be obtained for sparse patterns in a five-layered network bearing a remarkable resemblance to the hippocampal circuit. This result is especially interesting because, unlike Marr, the authors did not have the hippocampus in mind when they designed their network. Rolls and Treves [13-J have explored several different possible learning paradigms and shown that there is generally an advantage to storage capacity when sparse coding is employed. They have also reviewed the response properties of neurons in the primate gustatory and temporal visual association cortex, showing that, as just suggested, the sparseness of the representation tends to increase from the periphery inward. Moreover, Rolls and Treves make the interesting point that it is rarely the case that modalities become mixed (i.e. associated) before the representation has been sparsified. Formation
of efficient
representations
Thus, in general, the principle of sparse coding is useful for systems whose main task is associative storage of events. Generating an effective sparse code, which preserves the essential information, is not necessarily easy, however. It is probably fair to say that much of the early processing of sensory events is devoted to this task. It has previously been suggested that the fascia dentata serves this purpose [ I4,15**] by transforming potentially highly correlated patterns in the entorhinal cortex into much sparser and much less correlated patterns. Treves and Rolls [I6**] have given an information-theoretic argument that the fascia dentata could force CA3 to create representations unrelated to previously stored patterns, whereas the direct entorhinalto-CA3 projections could more effectively evoke recall.
At the more biophysically inspired level, Brown et al. [7**] have shown that a modified Hebb rule that incorporates both cooperativity and competition can lead to the formation of local clusters (in an electrotonic sense) of strengthened synapses. Under certain assumptions concerning the distribution of active conductances in the dendrites, it is suggested that this could lead to individual hippocampal pyramidal cells becoming selectively tuned to respond to particular feature sets. Hippocampal
place cells
One of the most striking features of the hippocampus is the existence of ‘place cells’, each of which fires at a greatly increased rate when an animal is in a particular small portion of its environment (the ‘place field’ of the cell). With the right sort of synaptic modification rule (Hebbian learning modified to keep the total input to each cell constant), sparse networks will show competitive learning [ 171, which gradually builds up a representation reflecting the structure of the set of input patterns. Sharp [ 18-] has based a model of place cells upon this principle. It borrows the idea of a winner-take-all’ network from connectionist theory, proposing that the CA3 layer of the hippocampus is such a network. Input comes from high-order sensory cortex, which is assumed to contain a variety of spatial-feature detectors. The learning causes place fields, which start out widely varying in size and shape, to evolve gradually into a more regular configuration. The model, when simulated on a computer, gives rise to place fields very similar to those experimentally observed in a small cylindrical ‘maze’. It also succeeds in reproducing a peculiar experimentally observed difference between cylindrical mazes and radial-arm mazes (hippocampal place-cell activity seems to be much more sensitive to an animal’s head direction in a radial arm maze than in a cylinder). A particularly appealing feature of the model is that the only computation it requires of the hippocampus is the enforcement of spars@. The hippocampus
as a dynamic
system
For several years Traub and colleagues have been developing detailed biophysical models of the CA3 region, with the principal aim of understanding the involvement of this region in epilepsy. This work has recently been collected and organized in book form [19-l. Fytte et al. [20] have published a greatly simplified (cellular-automaton style) version of the model that nevertheless reproduces the main features of the earlier detailed versions This promises to make it possible to do mean ingful large-scale simulations in reasonable amounts of computer time. Conclusions In nature, it is never possible to understand any system in complete detail; not even relatively simple systems such as the solids, liquids, and gases studied by statistical physics. For something as complex as the hippocam pus, a whole series of simplifications and abstractions will surely be necessary to turn it into a system whose
Computational
approaches to hippocampal
behavior can be understood - and each one of the simplifications must be motivated and justified. Twenty years ago, Marr took the first tentative steps in that direction. There remains today a vast distance to travel, but the journey is well under way. At the level of biophysics, and at the level of mathematical theory, the shape of the scene is beginning to clarify. One of the clearest themes to emerge is the importance of sparse encoding.
References
and recommended
the National
Institute
reading
HOPFIEU) JJ: Neural Networks and Physical Systems with Emergent Collective Computational Abilities. Proc Nat1 Acud Sci USA 1982, 79:2554-2558.
10.
AMARl S: Characteristics of Sparsely Encoded Memory. Neural Networks 1989, 2:451-457.
11.
GOLOMB D, RUBIN N, SOMPOLINSKY H: Wiishaw Model: Associative Memory with Sparse Coding and Low Firing Rates. Pbys Rev [A] 1990, 41:1843-1854.
12.
BAUM EB, MOODY J, WILCZEK F: Representations for Associative Memory. Biol Cybern 1988, 59~217~228.
Rous ET, TREXS A: The Relative Advantages of Sparse Versus Distributed Encoding for Associative Neuronal Networks in the Brain. Network 1990, 1:407-421. Discusses the advantages of sparse coding for the memory capacity of networks using a variety of learning rules, and reviews the nature of coding in several sensory systems.
within the annual period of rep
BARNESCA, MCNAUGHTON BL, MIZ~JMORISJY, LEONARDBW, LLN L-H: Comparison of Spatial and Temporal Characteristics of NeuronaI Activity in Sequential Stages of HippocampaI Processing In lindersiunding the Brain 7brough the Hip pocampus. Edited by Storm-Mathisen J, Zimmer J, Ottersen OP. Amsterdam: Elsevier; 1990: 287-300.
2.
MARR D: Simple Memory: a Theory for Archicortex. Trans R Sot Lond [B] 1971, 262:23-81.
Phil
From the Retina to the Neocortex: Selected Mat-r. Boston: Birkhauser; 1991. Marr’s early work, including his papers on the and neocortex, with critical commentary by
Assessment of Marr’s Theory of the Hippocampus as a Temporary Memory Store. Phil Tram R Sot Lond [BJ 1990, 329:205-215. Summarizes Marr’s theory [2], and criticizes some of the reasoning beg hind it. Shows, with computational simulations, that a simpler network may perform as well as Marr’s.
4. ..
5.
WII~SHAW DJ, BIJCKINCHAM JT: An
MM0 T: Potentiation of Monosynaptic EPSPs in the Perforant Path-Dentate Granule Cell Synapse. Eq Brain Res 1’1970, 1234663.
ZA~~R A, KOCH C, B~owiv TH: BiophysicaI Model of a Hebbian Synapse. Proc Nat1 Acad Sci WA 1990, 87:671ti722. &poses a specific experimentally justified model of the dynamics of long-term potentiation in hippocampal synapses.
6.
BROWN TH, ZAD~R AM, MAINENZF, CLA~HORNEBJ: Hebbian Modifications in HippocampaI Neurons. In Long~term Po tent&ion: a Debate of Current Issues. Edited by Baudty M, Davis JL. Cambridge, Massachusetts: MIT Press; 1991:357-389. Summarizes the material presented in [6*], and explores the consequences of long~term potentiation for the representations formed within the hippocampus, using compartmental modeling techniques. 7. ..
8.
HOUZES WR, LEW Term POtentiation Receptor-Mediated cium Concentration 1168.
MCNAUGHTON BL: Neural Computation:
Hip&campus. In Macmillan Encyclopedia of Learning ~lzdh$~~ Edited by Squire L. New York: Macmillan Press; fi92< inspress.
MCNA~JCHTON BL, NADEI. L: Hebb-i&r Networks and the Neurobiological Representation of Action in Space. In Neurcxcience and Connection& Tbeoly. Edited by Gluck MA, Rumelhart DE. Hillsdale, New Jersey: Erlbaum; 19901-64. Extends Marr’s ideas [2] into a theory of how hippocampus and neocortex interact in spatial navigation and spatial memory, and discusses experimental data supporting the theory
15. ..
1.
VAINA LM (ED) 3. .. Papers of Dauid Contains a collection of cerebellum, archicortex, current authorities.
Associative
13. .
14. Papers of particular interest, published view, have been highlighted as: . of special interest .. of outstanding interest
and McNaughton
9.
Acknowledgement Supported by grant number MH 46823 from of Mental Health
function Skaggs
WB: Insights into Associative Longfrom Computational Models of NMDA Calcium Influx and Intracellular CaIChanges. J Neuropbysioll990, 63:114X-
16. ..
TREVESA, Rous ET: Computational
Constraints Suggest the Need for Two Distinct Input Systems to the HippocampaI CA3 Network. Hippocampus 1992, in press. Proposes that the function of the fascia dentata is to create good representations in CA3 during memorization of an input, while the direct connections from the entorhinal cortex to CA3 serve better to re-evoke the stored pattern during recall. Justifies the argument with numerical calculations. 17.
R~JMELHART DE, ZIPSER D: Feature Discovery by CompetiEdited by tive Learning. In Pamllel Distributed Procesing. Rumelhart DE, McClelland JL. Cambridge, Massachusett..: MIT Press/Bradford; 1986, 1:151-193.
SHARpP: Computer Simulations of Place Cells. Psychohioloey 1991, 19:103-116. Eoposes a very simple model of place cells as a winner~take-all network receiving input from spatial feature detectors. Simulates a rat moving in a cyhndricdl maze, and finds place fields closeiy resembling those experimentally observed. Examines the consequences of competitive learning on the behavior of the cells. 18.
TRWB RD, MILESR: Neuronal Networks of the Hippocampus 19. Cambridge: Cambridge University Press; 1991. .. Describes the anatomy and biophysics of the hippocampus, particularly the CA3 region, and lays out the results of a several-year experimental and computational exploration of the mechanisms of epilepsy in CA3. 20.
PYTTE E, GUNSTEIN G, TKAUB RD: Cellular Automaton Models of the CA3 Region of the Hippocampus. Network 1991, 2:149-l%.
WE Skaggs and BL McNaughton, Division of Neural Systems, Memory and Aging, University of Arizona, 384 Life Sciences North Building, Tucson, Arizona 85724, USA.
211
approaches
William
of Arizona,
The results of theoretical recoding
function
E. Skaggs and Bruce 1. McNaughton
University
hippocampal
to hippocampal
formation
events
work may
into patterns
which
Tucson,
have
Opinion
its memory per event,
in Neurobiology
Introduction One of the most striking features of the hippocampus is how rarely most of its cells are active. In an alert moving rat a typical complex-spike cell (these are the output cells of the hippocampus) fires 30-50 spikes per second when it is active, but less than 0.5 spikes per second on long-term average [ 11. Thus at any given time fewer than 1% of the complex spike cells are active. This remarkable ‘spars&y’of firing distinguishes the hippocampus from any other part of the brain. Interestingly, coding sparsity increases as one moves into the hippocampus from its entorhinal cortical inputs, and then decreases again as information is transmitted back to the neocortex via the subiculum [ 1 ] Furthermore, spars&y decreases (and the average activity level correspondingly rises) when an animal is quiescent or sleeping, and increases when the animal is performing the kind of exploratory task most sensitive to hippocampal dysfunction. These considerations suggest that sparse coding is important for some operation intrinsic to the hippocampus. Both human clinical studies and animal experiments involving damage to the hippocampal formation indicate that it plays a crucial role in the initial establishment of long-term associative memory. A variety of evidence favors the hypothesis that the hippocampus acts as a simple interim repository for memories of certain kinds of events, and that other (neocortical) circuitry draws on this repository during a process known as memory consolidation. Twenty years ago Marr [ 2,3**] proposed a theory of the computational mechanisms required for such a function. In essence, it concerned the encoding of events as distributed patterns of activity imposed on a population of hippocampal ‘principal’ cells and stored there by modifying synaptic connections. He performed a series of rough calculations, whose net result was that the capacity of the memory (the number of patterns it could store) increased in proportion to the sparsity of the patterns, up to a maximum level beyond which greater spars@ would cause problems. He predicted that optimal performance would be obtained if each pattern activated about a fraction of 0.003 of the cells in the network. Associative network memories of the type described by Marr store patterns by increasing the strength of con-
USA
to suggest that storage
are as dissimilar
use as few neurons
Current
led researchers
maximize that
Arizona,
capacity
to one another,
the by and
as possible.
1992, 2:209-211
nections between simultaneously active cells. If, later, a subset of the cells in the pattern are activated, the remaining cells will tend to be activated by a .~$Jlateral effect’; that is, they will receive relatively sti’bngiqput from the active cells. In this way subpatterns; of the stored pattern can be completed; less obviously, noisy versions of the stored pattern can also be cleaned up. Storage and recall of a single pattern is easy to arrange, and is most effective when the number of cells participating in the pattern is large, because the strength of the collateral effect at a given cell is then proportional to the number of connections the cell makes with other active cells. Difficulties arise when the attempt is made to store multiple patterns, as they interfere with each other. The magnitude of interference between two patterns is determined by the number of connections they have in common, and hence is proportional to the square of the number of active cells. For this reason, interference is minimized by keeping small the number of cells participating in each pattern. Optimal performance is obtained by balancing the need for a strong collateral effect against the need for low interference. These broad considerations have been appreciated for many years, but the precise constraints they impose on biological memory networks have not been easy to work out. Marr made a number of valuable suggestions, but his arguments are sometimes difficult to follow and sometimes clearly incorrect [4-l. Recent theoretical work has brought the picture into sharper focus. Hebbian
synaptic modification
in the
hippocampus Marr [ 21 predicted the existence of synaptic modification in the hippocampus before any evidence for it was available; his paper includes a note added in press describing the very first finding of long-term potentiation by Lomo [ 51. Twenty years later vastly more is known about this phenomenon, and with the discovery and characterization of the N-methyl-D-aspartic acid (NMDA) receptor, it has become possible to construct preliminary detailed biophysical models of the process. Two such models have recently been published by Zador et al. [6*,7--l and Holmes and Levy [8]. The models differ somewhat in
Abbreviation NMDA-N-methyl-o-aspartic
acid.
@ Current Biology Ltd ISSN 0959-4388
209
210
Cognitive
neuroscience
their assumptions and in their behavior. As the behavior of a memory network can be quite sensitive to the specific form of the learning rule, such differences may turn out to be important. Theoretical
studies of sparse coding
The principal hippocampal circuit involves a unidirectional flow of information from the entorhinal cortex, to the fascia dentata, to the CA3 subregion (which also receives a strong direct projection from the entorhinal cortex), to the CA1 subregion, and finally to the subiculum, the main exit point, which sends output to the entorhinal cortex and several other parts of the brain. In addition to this forward flow, there is also an extensive network of excitatory recurrent collaterals in CM. CA3 was the heart of Marr’s model, and was conceived of as something similar to what later came to be known as a ‘Hopfield model’ [9]. A number of studies of as sociative memory networks, using approaches originally developed by physicists working on statistical mechanics, have now appeared. A recurring theme is the effectiveness of sparse coding in increasing the capacity (defined as the number of patterns storable) of a network (for examples, see [ 10,111). One of the most interesting of such studies, by Baum, Moody, and Wilczek [ 121, found that very large capacities could be obtained for sparse patterns in a five-layered network bearing a remarkable resemblance to the hippocampal circuit. This result is especially interesting because, unlike Marr, the authors did not have the hippocampus in mind when they designed their network. Rolls and Treves [13-J have explored several different possible learning paradigms and shown that there is generally an advantage to storage capacity when sparse coding is employed. They have also reviewed the response properties of neurons in the primate gustatory and temporal visual association cortex, showing that, as just suggested, the sparseness of the representation tends to increase from the periphery inward. Moreover, Rolls and Treves make the interesting point that it is rarely the case that modalities become mixed (i.e. associated) before the representation has been sparsified. Formation
of efficient
representations
Thus, in general, the principle of sparse coding is useful for systems whose main task is associative storage of events. Generating an effective sparse code, which preserves the essential information, is not necessarily easy, however. It is probably fair to say that much of the early processing of sensory events is devoted to this task. It has previously been suggested that the fascia dentata serves this purpose [ I4,15**] by transforming potentially highly correlated patterns in the entorhinal cortex into much sparser and much less correlated patterns. Treves and Rolls [I6**] have given an information-theoretic argument that the fascia dentata could force CA3 to create representations unrelated to previously stored patterns, whereas the direct entorhinalto-CA3 projections could more effectively evoke recall.
At the more biophysically inspired level, Brown et al. [7**] have shown that a modified Hebb rule that incorporates both cooperativity and competition can lead to the formation of local clusters (in an electrotonic sense) of strengthened synapses. Under certain assumptions concerning the distribution of active conductances in the dendrites, it is suggested that this could lead to individual hippocampal pyramidal cells becoming selectively tuned to respond to particular feature sets. Hippocampal
place cells
One of the most striking features of the hippocampus is the existence of ‘place cells’, each of which fires at a greatly increased rate when an animal is in a particular small portion of its environment (the ‘place field’ of the cell). With the right sort of synaptic modification rule (Hebbian learning modified to keep the total input to each cell constant), sparse networks will show competitive learning [ 171, which gradually builds up a representation reflecting the structure of the set of input patterns. Sharp [ 18-] has based a model of place cells upon this principle. It borrows the idea of a winner-take-all’ network from connectionist theory, proposing that the CA3 layer of the hippocampus is such a network. Input comes from high-order sensory cortex, which is assumed to contain a variety of spatial-feature detectors. The learning causes place fields, which start out widely varying in size and shape, to evolve gradually into a more regular configuration. The model, when simulated on a computer, gives rise to place fields very similar to those experimentally observed in a small cylindrical ‘maze’. It also succeeds in reproducing a peculiar experimentally observed difference between cylindrical mazes and radial-arm mazes (hippocampal place-cell activity seems to be much more sensitive to an animal’s head direction in a radial arm maze than in a cylinder). A particularly appealing feature of the model is that the only computation it requires of the hippocampus is the enforcement of spars@. The hippocampus
as a dynamic
system
For several years Traub and colleagues have been developing detailed biophysical models of the CA3 region, with the principal aim of understanding the involvement of this region in epilepsy. This work has recently been collected and organized in book form [19-l. Fytte et al. [20] have published a greatly simplified (cellular-automaton style) version of the model that nevertheless reproduces the main features of the earlier detailed versions This promises to make it possible to do mean ingful large-scale simulations in reasonable amounts of computer time. Conclusions In nature, it is never possible to understand any system in complete detail; not even relatively simple systems such as the solids, liquids, and gases studied by statistical physics. For something as complex as the hippocam pus, a whole series of simplifications and abstractions will surely be necessary to turn it into a system whose
Computational
approaches to hippocampal
behavior can be understood - and each one of the simplifications must be motivated and justified. Twenty years ago, Marr took the first tentative steps in that direction. There remains today a vast distance to travel, but the journey is well under way. At the level of biophysics, and at the level of mathematical theory, the shape of the scene is beginning to clarify. One of the clearest themes to emerge is the importance of sparse encoding.
References
and recommended
the National
Institute
reading
HOPFIEU) JJ: Neural Networks and Physical Systems with Emergent Collective Computational Abilities. Proc Nat1 Acud Sci USA 1982, 79:2554-2558.
10.
AMARl S: Characteristics of Sparsely Encoded Memory. Neural Networks 1989, 2:451-457.
11.
GOLOMB D, RUBIN N, SOMPOLINSKY H: Wiishaw Model: Associative Memory with Sparse Coding and Low Firing Rates. Pbys Rev [A] 1990, 41:1843-1854.
12.
BAUM EB, MOODY J, WILCZEK F: Representations for Associative Memory. Biol Cybern 1988, 59~217~228.
Rous ET, TREXS A: The Relative Advantages of Sparse Versus Distributed Encoding for Associative Neuronal Networks in the Brain. Network 1990, 1:407-421. Discusses the advantages of sparse coding for the memory capacity of networks using a variety of learning rules, and reviews the nature of coding in several sensory systems.
within the annual period of rep
BARNESCA, MCNAUGHTON BL, MIZ~JMORISJY, LEONARDBW, LLN L-H: Comparison of Spatial and Temporal Characteristics of NeuronaI Activity in Sequential Stages of HippocampaI Processing In lindersiunding the Brain 7brough the Hip pocampus. Edited by Storm-Mathisen J, Zimmer J, Ottersen OP. Amsterdam: Elsevier; 1990: 287-300.
2.
MARR D: Simple Memory: a Theory for Archicortex. Trans R Sot Lond [B] 1971, 262:23-81.
Phil
From the Retina to the Neocortex: Selected Mat-r. Boston: Birkhauser; 1991. Marr’s early work, including his papers on the and neocortex, with critical commentary by
Assessment of Marr’s Theory of the Hippocampus as a Temporary Memory Store. Phil Tram R Sot Lond [BJ 1990, 329:205-215. Summarizes Marr’s theory [2], and criticizes some of the reasoning beg hind it. Shows, with computational simulations, that a simpler network may perform as well as Marr’s.
4. ..
5.
WII~SHAW DJ, BIJCKINCHAM JT: An
MM0 T: Potentiation of Monosynaptic EPSPs in the Perforant Path-Dentate Granule Cell Synapse. Eq Brain Res 1’1970, 1234663.
ZA~~R A, KOCH C, B~owiv TH: BiophysicaI Model of a Hebbian Synapse. Proc Nat1 Acad Sci WA 1990, 87:671ti722. &poses a specific experimentally justified model of the dynamics of long-term potentiation in hippocampal synapses.
6.
BROWN TH, ZAD~R AM, MAINENZF, CLA~HORNEBJ: Hebbian Modifications in HippocampaI Neurons. In Long~term Po tent&ion: a Debate of Current Issues. Edited by Baudty M, Davis JL. Cambridge, Massachusetts: MIT Press; 1991:357-389. Summarizes the material presented in [6*], and explores the consequences of long~term potentiation for the representations formed within the hippocampus, using compartmental modeling techniques. 7. ..
8.
HOUZES WR, LEW Term POtentiation Receptor-Mediated cium Concentration 1168.
MCNAUGHTON BL: Neural Computation:
Hip&campus. In Macmillan Encyclopedia of Learning ~lzdh$~~ Edited by Squire L. New York: Macmillan Press; fi92< inspress.
MCNA~JCHTON BL, NADEI. L: Hebb-i&r Networks and the Neurobiological Representation of Action in Space. In Neurcxcience and Connection& Tbeoly. Edited by Gluck MA, Rumelhart DE. Hillsdale, New Jersey: Erlbaum; 19901-64. Extends Marr’s ideas [2] into a theory of how hippocampus and neocortex interact in spatial navigation and spatial memory, and discusses experimental data supporting the theory
15. ..
1.
VAINA LM (ED) 3. .. Papers of Dauid Contains a collection of cerebellum, archicortex, current authorities.
Associative
13. .
14. Papers of particular interest, published view, have been highlighted as: . of special interest .. of outstanding interest
and McNaughton
9.
Acknowledgement Supported by grant number MH 46823 from of Mental Health
function Skaggs
WB: Insights into Associative Longfrom Computational Models of NMDA Calcium Influx and Intracellular CaIChanges. J Neuropbysioll990, 63:114X-
16. ..
TREVESA, Rous ET: Computational
Constraints Suggest the Need for Two Distinct Input Systems to the HippocampaI CA3 Network. Hippocampus 1992, in press. Proposes that the function of the fascia dentata is to create good representations in CA3 during memorization of an input, while the direct connections from the entorhinal cortex to CA3 serve better to re-evoke the stored pattern during recall. Justifies the argument with numerical calculations. 17.
R~JMELHART DE, ZIPSER D: Feature Discovery by CompetiEdited by tive Learning. In Pamllel Distributed Procesing. Rumelhart DE, McClelland JL. Cambridge, Massachusett..: MIT Press/Bradford; 1986, 1:151-193.
SHARpP: Computer Simulations of Place Cells. Psychohioloey 1991, 19:103-116. Eoposes a very simple model of place cells as a winner~take-all network receiving input from spatial feature detectors. Simulates a rat moving in a cyhndricdl maze, and finds place fields closeiy resembling those experimentally observed. Examines the consequences of competitive learning on the behavior of the cells. 18.
TRWB RD, MILESR: Neuronal Networks of the Hippocampus 19. Cambridge: Cambridge University Press; 1991. .. Describes the anatomy and biophysics of the hippocampus, particularly the CA3 region, and lays out the results of a several-year experimental and computational exploration of the mechanisms of epilepsy in CA3. 20.
PYTTE E, GUNSTEIN G, TKAUB RD: Cellular Automaton Models of the CA3 Region of the Hippocampus. Network 1991, 2:149-l%.
WE Skaggs and BL McNaughton, Division of Neural Systems, Memory and Aging, University of Arizona, 384 Life Sciences North Building, Tucson, Arizona 85724, USA.
211
