Using hippocampal place cells for 
navigation exploiting phase coding 
Nell Burgess, John O'Keefe and Michael Recce 
Department of Anatomy, University College London, 
London WC1E 6BT, England. 
(e-mail: n. burgessul. a. 
Abstract 
A model of the hippocampus as a central element in rat naviga- 
tion is presented. Simulations show both the behaviour of single 
cells and the resultant navigation of the rat. These are compared 
with single unit recordings and behavioural data. The firing of 
CA1 place cells is simulated as the (artificial) rat moves in an en- 
vironment. This is the input for a neuronal network whose output, 
at each theta (0) cycle, is the next direction of travel for the rat. 
Cells are characterised by the number of spikes fired and the time 
of firing with respect to hippocampal 0 rhythm. 'Learning' occurs 
in 'on-off' synapses that are switched on by simultaneous pre- and 
post-synaptic activity. The simulated rat navigates successfully to 
goals encountered one or more times during exploration in open 
fields. One minute of random exploration of a lrn 2 environment 
allows navigation to a newly-presented goal from novel starting po- 
sitions. A limited number of obstacles can be successfully avoided. 
1 Background 
Experiments have shown the hippocampus to be crucial to the spatial memory and 
navigational ability of the rat (O'Keefe & Nadel, 1978). Single unit recordings in 
freely moving rats have revealed 'place cells' in fields CA3 and CA1 of the hip- 
pocampus whose firing is restricted to small portions of the rat's environment (the 
corresponding 'place fields') (O'Keefe & Dostrovsky, 1971), see Fig. la. In addi- 
tion cells have been found in the dorsal pre-subiculum whose primary behavioural 
929 
930 Burgess, O'Keefe, and Recce 
a 
! 
- , I II II IIII II I 
I I I I I I I 
Time [s] 
Figure 1: a) A typical CA1 place field, max. rate (over Is) is 13.6 spikes/s. b) One 
second of the EEG 0 rhythm is shown in C, as the rat runs through a place field. 
A shows the times of firing of the place cell. Vertical ticks immediately above and 
below the EEG mark the positive to negative zero-crossings of the EEG, which we 
define as 0  (or 360 ) of phase. B shows the phase of 0 at which each spike was 
fired (O'Keefe & Recce, 1992). 
correlate is 'head-direction' (Taube et al., 1990). Both are suggestive of navigation. 
Temporal as well as spatial aspects of the electrophysiology of the hippocampal 
region are significant for a model. The hippocampal EEG '0 rhythm' is best char- 
acterised as a sinusoid of frequency 7- 12Hz and occurs whenever the rat is making 
displacement movements. Recently place cell firing has been found to have a sys- 
tematic phase relationship to the local EEG (O'Keefe & Recce, 1992), see 3.1 and 
Fig. lb. Finally, the 0 rhythm has been found to modulate long-term potentiation 
of synapses in the hippocampus (Pavlides et al., 1988). 
2 Introduction 
We are designing a model that is consistent with both the data from single unit 
recording and the behavioural data that are relevant to spatial memory and navi- 
gation in the rat. As a first step this paper examines a simple navigational strategy 
that could be implemented in a physiologically plausible way to enable navigation 
to previously encountered reward sites from novel starting positions. We assume 
the firing properties of CA1 place cells, which form the input for our system. 
The simplest map-based strategies (as opposed to route-following ones) are based 
on defining a surface over the whole environment, on which gradient ascent leads to 
the goal (e.g. delayed reinforcement or temporal difference learning). These tend 
to have the problem that, to build up this surface, the goal must be reached many 
times, from different points in the environment (by which time the rat has died of 
old age). Further, a new surface must be computed if the goal is moved. Specific 
problems are raised by the properties of rats' navigation: (i) the position of CA1 
place fields is independent of goal position (Speakman & O'Keefe, 1990); (ii) high 
firing rates in place cells are restricted to limited portions of the environment; (iii) 
rats are able to navigate after a brief exploration of the environment, and (iv) can 
take novel short-cuts or detours (Tolman, 1948). 
Using hippocampal 'place cells' for navigation, exploiting phase coding 931 
To overcome these problems we propose that a more diffuse representation of posi- 
tion is rapidly built up downstream of CA1, by cells with larger firing fields than in 
CA1. The patterns of activation of this group of cells, at two different locations in 
the environment, have a correlation that decreases with the separation of the two 
locations (but never reaches zero, as is the case with small place fields). Thus the 
overlap between t. hc pattern of activity at any moment and the pattern of activity 
at the goal location would bca measure of nearness to the goal. Wc refer to these 
cells as 'subicular' cells because the subiculum seems a likely site for them, given 
single unit recordings (Barnes ctal., 1990) showing spatially consistent firing over 
large parts of the environment. 
We show that the output of these subicular cells is sufficient to enable navigation 
in our model. In addition the model requires: (i) 'goal' cells (see Fig. 4a) that 
fire when a goal is encountered, allowing synaptic connections from subicular cells 
to be switched on, (ii) phase-coded place cell firing, (iii)'head-direction' cells, and 
(iv) synaptic change that is modulated by the phase of the EEG. The relative 
firing rates of groups of goal cells code for the direction of objects encountered 
during exploration, in the same way that ccl. ls in primate motor cortex code for the 
direction of arm movements (Gcorgopoulos ct al., 1988). 
3 The model 
In our simulation a rat is in constant motion (speed 30cm/s) in a square environment 
of size L x L (L _ 150cm). Food or obstacles can be placed in the environment 
at any time. The rat is aware of any objects within 6cm (whisker length) of its 
position. It bounces off any obstacles (or the edge of the environment) with which 
it collides. The 0 frequency is taken to be 10Hz (period 0.1s) and we model each 
0 cycle as having 5 different phases. Thus the smallest timestep (at which synaptic 
connections and cell firing rates are updated) is 0.02s. The rat is either 'exploring' 
(its current direction is a random variable within 300 of its previous direction), or 
'searching' (its current direction is determined by the goal cells, see below). Synaptic 
and cell update rules are the same during searching or exploring. 
3.1 The phase of CA1 place cell firing 
When a rat on a linear track runs through a place field, the place cell fires at 
successively earlier phases of the EEG 0 rhythm. A cell that fires at phase 3600 
when the rat enters the place field may fire as much as 3550 earlier in the 0 cycle 
when exiting the field (O'Keefe & Recce, 1992), see Fig. lb. 
Simulations below involve 484 CA1 place cells with place field centres spread evenly 
on a grid over the whole environment. The place fields are circular, with diameters 
0.25L, 0.35L or 0.4L (as place fields appear to scale with the size of an environment; 
Muller & Kubie, 1987). The fraction of cells active during any 0.1s interval is thus 
vr(0.1252 q- 0.1752 q- 0.22)/3 ----- 9%. When the rat is in a cell's place field it fires 1 to 
3 spikes depending on its distance from the field centre, see Fig. 2b. 
When the (simulated) rat first enters a place field the cell fires 1 spike at phase 
3600 of the 0 rhythm; as the rat moves through the place field, its phase of firing 
shifts backwards by 720 every time the number of spikes fired by the cell changes 
932 Burgess, O'Keefe, and Recce 
a 
d 
lO 
0.0 0.2 0.4 0.6 0.8 
c 
360' 288' 216' 144' 72' 
Figure 2: a) Firing rate map of a typical place cell in the model (max. rate 11.6 
spikes/s); b) Model of a place field; the numbers indicate the number of spikes fired 
by the place cell when the rat is in each ring. c) The phase at which spikes would 
be fired during all possible straight trajectories of the rat through the place field 
from left to right. d) The total number of spikes fired in the model of CA1 versus 
time, the phase of firing of one place cell (as the rat runs through the centre of the 
field) is indicated be vertical ticks above the graph. 
(i.e. each time it crosses a line in Fig. 2b). Thus each theta cycle is divided into 
5 timesteps. No shift results from passing through the edge of the field, whereas a 
shift of 2880 (0.08s) results from passing through the middle of the field, see Fig. 
2c. The consequences for the model in terms of which place cells fire at different 
phases within one 0 cycle are shown in Fig. 3. The cells that are active at phase 
3600 have place fields centred ahead of the position of the rat (i.e. place fields that 
the rat is entering), those active at phase 0  have place fields centred behind the 
rat. If the rat is simultaneously leaving field A and entering field B then cell A fires 
before cell B, having shifted backwards by up to 0.08s. The total number of spikes 
fired at each phase as the rat moves about implies that the envelope of all the spikes 
fired in CA1 oscillates with the 0 frequency. Fig. 2d shows the shift in the firing of 
one cell compared to the envelope (cf. Fig. lb). 
3.2 Subicular cells 
We simulate 6 groups of 80 cells (480 in total); each subicular cell receives one 
synaptic connection from a random 5% of the CA1 cells. These connections are 
either on or off (1 or 0). At each timestep (0.02s) the 10 cells in each group with 
the greatest excitatory input from CA1 fire between i and 5 spikes (depending on 
their relative excitation). Fig. 3c shows a typical subicular firing rate map. The 
consequences of phase coding in CA1 (Figs. 3a and b) remain in these subicular 
cells as they are driven by CAI: the net firing field of all cells active at phase 3600 
of 0 is peaked ahead of the rat. 
Using hippocampal 'place cells' for navigation, exploiting phase coding 933 
a 
Figure 3: Net firing rate map of all the place cells that were active at the 3600 (a) 
and 720 (b) phases of 0 as the rat ran through the centre of the environment from 
left to right. c) Firing rate map of a typical 'subicular' cell in the model; max. rate 
(over 1.0s) is 46.4 spikes/s. Barnes et al. (1990) found max. firing rates (over 0.1s) 
of 80 spikes/s (mean 7 spikes/s) in the subiculum. 
N SEW 
a 0 0 0 0 Goal b 
I 100 % [ Subicular cells 
00.00 0000 0%706x80(480) 
....., ', 
000000000000 22x22 (484) 
Figure 4: a) Connections and units in the model; interneurons shown between the 
subicular cells indicate competitive dynamics, but are not simulated explicitly. b) 
The trajectory of 90 seconds of 'exploration' in the central 126 x 126cm 2 of the 
environment. The rat is shown in the bottom left hand corner, to scale. 
3.2.1 Learning 
The connections are initialised such that each subicular cell receives on average 
one 'on' connection. Subsequently a synaptic connection can be switched on only 
during phases 1800 to 360 o of 9. A synapse becomes switched on if the pre-synaptic 
cell is active, and the post-synaptic cell is above a threshold activity (4 spikes), in 
the same timestep (0.02s). Hence a subicular firing field is rapidly built up during 
exploration, as a superposition of CA1 place fields, see Fig 3c. 
3.3 Goal cells 
The correlation between the patterns of activity of the subicular cells at two differ- 
ent locations in the environment decreases with the separation of the two locations. 
Thus if synaptic connections to a goal cell were switched on when the rat encoun- 
tered food then a firing rate map of the goal cell would resemble a cone covering 
the entire environment, peaked at the food site, i.e. the firing rate would indicate 
934 Burgess, O'Keefe, and Recce 
a 
b 
Figure 5: Goal cell firing fields, a) West, b) East, of 'food' encountered at the centre 
of the environment. c) Trajectories to a goal from 8 novel starting positions. All 
figures refer to encountering food immediately after the exploration in Fig. 4b. 
Notice that much of the environment was never visited during exploration. 
the closeness of the food during subsequent movement of the rat. The scheme we 
actually use involves groups of goal cells continuously estimating the distance to 4 
points displaced from the goal site in 4 different directions. 
Notice that when a freely moving rat encounters an interesting object a fair amount 
of 'local investigation' takes place (sniffing, rearing, looking around and local explo- 
ration). During the local investigation of a small object the rat crosses the location 
of the object in many different directions. We postulate groups of goal cells that 
become excited strongly enough to induce synaptic change in connections from 
subicular cells whenever the rat encounters a specific piece of food and is heading in 
a particular direction. This supposes the joint action of an object classifier and of 
head-direction cells; head-direction cells corresponding to different directions being 
connected to different goal cells. Since synaptic change occurs only at the 1800 to 
3600 phases of 0, and the net firing rate map of all the subicular cells that are active 
at phase 3600 during any 0 cycle is peaked ahead of the rat, goal cells have firing 
fields that are peaked a little bit away from the goal position. For example, goal 
cells whose subicular connections are changed when the rat is heading east have 
firing rate fields that are peaked to the east of the goal location, see Fig. 5. 
Local investigation of a food site is modelled by the rat moving 12cm to the north, 
south, east and west and occurs whenever food is encountered. Navigation is re- 
stricted to the central 126 x 126cra 2 portion of the 150 x 150cra 2 environment (over 
which firing rate maps are shown) to leave room for this. There are 4 goal cells 
for every piece of food found in the environment, (GC_north, GC_south, GC_east, 
GC_west), see Fig. 4a. Initially the connections from all subicular cells are off; they 
are switched on if the subicular cell is active and the rat is at the particular piece of 
food, travelling in the right direction. When the rat is searching, goal cells simply 
fire a number of spikes (in each 0.02s timestep) that is proportional to their net 
excitatory input from the subicular cells. 
3.4 Maps and navigation 
When the rat is to the north of the food, GC_north fires at a higher rate than 
GC_south. We take the firing rate of GC_north to be a 'vote' that the rat is north 
Using hippocampal 'place cells' for navigation, exploiting phase coding 935 
a 
.,.///.,;;' 
/,4 //2? 
/.'..'" . ..5.' 
Figure 6: a) Trajectory of rat with alternating goals. b) an obstacle is interposed; 
the rat collides with the obstacle on the first run, but learns to avoid the collision site 
in the 2 subsequent runs. c) Successive predictions of goal (box) and obstacle (cross) 
positions generated as the rat ran from one goal site to the other; the predicted 
positions get more accurate as the rat gets closer to the object in question. 
of the goal. Similarly the firing rate of GC_south is a vote that the rat is south 
of the goal: the resultant direction (the vector sum of directions north, south, east 
and west, weighted by the firing rates of the corresponding cells) is an estimate 
of the direction of the rat from the food (cf. Georgopoulos et al., 1988). Since the 
firing rate maps of the 4 goal cells are peaked quite close to the food location, their 
net firing rate increases as the food is approached, i.e. it is an estimation of how 
close the food is. Thus the firing rates of the 4 goal cells associated with a piece of 
food can be used to predict its approximate position relative to the rat (e.g. 70cra 
northeast), as the rat moves about the environment (see Pig. 6c). 
We use groups of goal cells to code for the locations at which the rat encountered 
any objects (obstacles or food), as described above. A new group of goal cells is 
recruited every time the rat encounters a new object, or a new (6cra) part of an 
extended object. The output of the system acts as a map for the rat, telling it 
where everything is relative to itself, as it moves around. The process of navigation 
is to decide which way to go, given the information in the map. When there are 
no obstacles in the environment, navigation corresponds to moving in the direction 
indicated by the group of goal cells corresponding to a particular piece of food. 
When the environment includes many obstacles the task of navigation is much 
harder, and there is not enough clear behavioural data to guide modelling. 
We do not model navigation at a neuronal level, although we wish to examine the 
navigation that would result from a simple reading of the 'map' provided by our 
model. The rules used to direct the simulated rat are as follows: (i) every 0.1a the 
direction and distance to the goal (one of the pieces of food) are estimated; (ii) 
the direction and distance to all locations at which an obstacle was encountered 
are estimated; (iii) obstacle locations are classified as 'in-the-way' if (a) estimated 
to be within 45 o of the goal direction, (b) closer than the goal and (c) less than 
L/2 away; (iv) the current direction of the rat becomes the vector sum of the goal 
direction (weighted by the net firing rate of the corresponding 4 goal cells) minus 
the directions to any in-the-way obstacles (weighted by the net firing rate of the 
'obstacle cells' and by the similarity of the obstacle and goal directions). 
936 Burgess, O'Keefe, and Recce 
4 Performance 
The model achieves latent learning (i.e. the map is constructed independently of 
knowledge of the goal, see e.g. Tolman, 1948). A piece of food encountered only 
once, after exploration, can be returned to, see Fig. 5c. Notice that a large part 
of the environment was never visited during exploration (Fig. 4b). Navigation is 
equally good after exploration in an environment containing food/obstacles from the 
beginning. If the food is encountered only during the earliest stages of exploration 
(before a stable subicular representation is built up) then performance is worse. 
Multiple goals and a small number of obstacles can be accommodated, see Fig. 6. 
Notice that searching also acts as exploration, and that synaptic connections can 
be switched at any time: all learning is incremental, but saturates when all the 
relevant synapses have been switched on. Performance does not depend crucially 
on the parameter values, used although it is worse with fewer cells, and smaller 
environments require less exploration before reliable navigation is possible (e.g. 60s 
for a lrr, 2 box). Quantitative analysis will appear in a longer paper. 
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