Retinogeniculate Development: 
The Role of Competition and Correlated Retinal 
Activity 
Ron Keesing* 
Dept. of Physiology 
U.C. San Francisco 
San Francisco, CA 94143 
keesing@phy.ucsf.edu 
David G. Stork 
*Ricoh California Research Center 
2882 Sand Hill Rd., Suite 115 
Menlo Park, CA 94025 
stork@crc.ricoh.com 
Carla J. Shatz 
Dept. of Neurobiology 
Stanford University 
S tanford, CA 
94305 
Abstract 
During visual development, projections from retinal ganglion cells 
(RGCs) to the lateral geniculate nucleus (LGN) in cat are refined to 
produce ocular dominance layering and precise topographic mapping. 
Normal development depends upon activity in RGCs, suggesting a key 
role for activity-dependent synaptic plasticity. Recent experiments on 
prenatal retina show that during early development, "waves" of activity 
pass across RGCs (Meister, et al., 1991). We provide the first 
simulations to demonstrate that such retinal waves, in conjunction with 
Hebbian synaptic competition and early arrival of contralateral axons, 
can account for observed patterns of retinogeniculate projections in 
normal and experimentally-treated animals. 
1 INTRODUCTION 
During the development of the mammalian visual system, initially diffuse axonal inputs 
are refined to produce the precise and orderly projections seen in the adult. In the lateral 
geniculate nucleus (LGN) of the cat, projections arriving from retinal ganglion cells 
(RGCs) of both eyes are initially intermixed, and they gradually segregate before birth to 
form alternating layers containing axons from only one eye. At the same time, the 
branching patterns of individual axons are refined, with increased growth in 
topographically correct locations. Axonal segregation and refinement depends upon 
91 
92 Keesing, Stork, and Schatz 
presynaptic activity -- blocking such activity disrupts normal development (Sretavan, et 
al., 1988; Shatz & Stryker, 1988). These and findings in other vertebrates (Cline, et al., 
1987) suggest that synaptic plasticity may be an essential factor in segregation and 
modification of RGC axons (Shatz, 1990). 
Previous models of visual development based on synaptic plasticity (Miller, et al., 1989; 
Whitelaw & Cowan, 1981) required an assumption of spatial correlations in RGC activity 
for normal development. This assumption may have been justified for geniculocortical 
development, since much of this occurs postnatally: visual stimulation provides the 
correlations. The. assumption was more difficult to justify for retinogeniculate 
development, since this occurs prenatally  before any optical stimulation. 
The first strong evidence for correlated activity before birth has recently emerged in the 
retinogenculate system: wave-like patterns of synchronized activity pass across the 
prenatal retina, generating correlations between neighboring cells' activity (Meister, et al., 
1991). We believe our model is the first to incorporate these important results. 
We propose that during visual development, projections from both eyes compete to 
innervate LGN neurons. Contralateral projections, which reach the LGN earlier, may 
have a slight advantage in competing to innervate cells of the LGN located farthest from 
the optic tract. Retinal waves of activity could reinforce this segregation and improve the 
precision of topographic mapping by causing weight changes within the same eye -- and 
particularly within the same region of the same eye -- to be highly correlated. Unlike 
similar models of cortical development, our model does not require lateral interactions 
between post-synaptic cells -- available evidence suggests that lateral inhibition is not 
present during early development (Shotwell, et al., 1986). Our model also incorporates 
axon growth  an essential aspect of retinogeniculate development, since the growth and 
branching of axons toward their ultimate targets occurs simultaneously with synaptic 
competition. Moreover, synaptic competition may provide cues for growth (Shatz & 
Stryker, 1988). We consider the possibility that diffusing intracellular signals indicating 
local synaptic strength guide axon growth. 
Below we present simulations which show that this model can account for development 
in normal and experimentally-treated animals. We also predict the outcomes of novel 
experiments currently underway. 
2 SIMULATIONS 
Although the LGN is, of course, three-dimensional, in our model we represent just a 
single two-dimensional LGN slice, ten cells wide and eight cells high. The retina is then 
one-dimensional: 50 cells long in our simulations. (This ratio of widths, 50/10, is 
roughly that found in the developing cat.) In order to eliminate edge effects, we "wrap" 
the retina into a ring; likewise we wrap the LGN into a cylinder. 
Development of projections to the LGN is modelled in the following way: projections 
from all fifty RGCs of the contralateral eye arrive at the base of the LGN before those of 
the ipsilateral eye. A very rough topographic map is imposed, corresponding to coarse 
topography which might be supplied by chemical gradients (Wolpert, 1978). 
Development is then modelled as a series of growth steps, each separated by a period of 
Hebb-style synaptic competition (Wigstrom & Gustafson, 1985). During competition, 
synapses are strengthened when pre- and post-synaptic activity are sufficiently conelated, 
Retinogeniculate Development: The Role of Competition and Correlated Retinal Activity 93 
and they are weakened otherwise. More specifically, for a given RGC cell i with activity 
a i, the strength of synapse wij to LGN cell j is changed according to: 
Aw ij= (a i - 0t) (aj - ) [1] 
where  and I are threshholds and  a learning rate. If a "wave" of retinal activity is 
present, the activity of RGC cells is determined as a probability of firing based on a 
Gaussian function of the distance from the center of the wavefront. LGN cell activity is 
equal to the sum of weighted inputs from RGC cells. 
After each wave, the total synaptic weight supported by each RGC cell i is renormalized 
linearly: 
wij (t) 
wij(t+l)= w 
ik (t) [2] 
k 
The weights supported by each LGN cell are also renormalized, gradually driving them 
toward some target value T: 
wij (t+ 1)=w ij (t)+ [T- Wkj (t)] 
k [3] 
Renormalization reflects the notion that there is a limited amount of synaptic weight 
which can be supported by any neuron. 
During growth steps, connections are modified based on the strength of neighboring 
synapses from the same RGC cell. After normalization, connections grow or retract 
according to: 
wij (t+ 1)= wij (t)+ '  Wik(t) 
neighbors [4] 
where , is a constant term. Equation 4 shows that weights in areas of high synaptic 
strength will increase more than those elsewhere. 
3 RESULTS 
Synaptic competition, in conjunction with waves of pre-synaptic activity and early arrival 
of contralateral axons, can account for pattens of growth seen in normal and 
experimentally-treated animals. In the presence of synaptic competition, modelled axons 
from each eye segregate to occupy discrete layers of the LGN -- precisely what is seen in 
normal development. In the absence of competition, as in treatment with the drug TTX, 
axons arborize throughout the LGN (Figure 1). 
The segregation and refinement of retinal inputs to the LGN is best illustrated by the 
formation of ocular dominance patterns and topographic ordering. In simulations of 
normal development, where retinal waves are combined with early arrival of contalateral 
inputs, strong ocular dominance layers are formed: LGN neurons farthest from the optic 
tract receive synaptic inputs solely from the contralateral eye and those closer receive only 
ipsilateral inputs (Figure2, Competition). The development of these ocular dominance 
patterns is gradual: early in development, a majority of LGN neurons receive inputs from 
both eyes. When synaptic competition is eliminated, there is no segregation into eye- 
specific layers .... LGN neurons receive significant synaptic inputs from both eyes. These 
results are consistent with labelling studies of cat development (Shatz & Stryker, 1988). 
94 Keesing, Stork, and Schatz 
contralateral 
Figure 1: Retinogeniculate projections in vivo (adapted from Sretavan, et al., 1988.) 
(left), and simulation results (right). In the presence of competition (top), arbors are 
narrow and spatially localized, confined to the appropriate ocular dominance layer. In the 
absence of such competition (bottom), contralateral and ipsilateral projections are diffuse; 
there is no discernible ocular dominance pattern. During simulations, projections are 
represented by synapses throughout the LGN slice, shown as squares; the particular 
arborization patterns shown above are inferred from related simulations. 
8 
6 
4 
2 
o 
o 
Competition 
No Competition 
8 
6 
4 
2 
0 
0 
Simultaneous 
8 
6 
4 
2 
0 
0 
2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 
Figure 2: Ocular dominance at the end of development. Dark color indicates strongest 
synapses from the contralateral eye, light indicates strongest synapses from ipsilateral, 
and gray indicates significant synapses from both eyes. In the presence of competition, 
LGN cells segregate into eye-specific layers, with the contralateral eye dominating cells 
which are farthest from the optic tract (base). When competition is eliminated (No 
Competition), as in the addition of the drug TTX, there is no segregation into layers and 
LGN cells receive significant inputs from both eyes. These simulations reproduced 
results from cat development. When inputs from both retinae arrive simultaneously 
(Simultaneous), ocular dominance "patches" are established, similar to those observed in 
normal conical development. 
Retinogeniculate Development: The Role of Competition and Correlated Retinal Activity 95 
Retinal waves cause the activity of neighboring RGCs to be highly correlated. When 
combined with synaptic competition, these waves lead to a refinement of topographic 
ordering of retinogeniculate projections. During development, the coarse topography 
imposed as RGC axons enter the LGN is refined to produce an accurate, precise mapping 
of retinal inputs (Figure 3, Competition). Without competition, there is no refinement 
of topography, and the coarse initial mapping remains. 
Competition 
........................................ ,. ooO.[]..On  
................................... o OIDEI..IZO o  ..... 
.............................. .no , .......... 
........................... a m OO[Ii O - ............. 
...................... ' "oO[212E2 o ,  ................. 
.................  . 0 01-11-1-1-100,  ..................... 
.............. o olDEII" o . .......................... 
........ . . nr-II'T'l"lr'10 . ................................ 
 . . . mO[]]O- ...................................... 
No Competition 
-O- - ' ""0  ' -O ......... " ..... -O' -" " .... OoO-  .-oo- 00 
Om .... .I-I.   . ...... m      m    .  ' O' O'  '  m. mO. O. mm m. m 
O' ..... O' -   ...... O' ' ' '  O' O  ' '  O, O O, O,    O O O    O.  
.... 0 ' ' '1-1 .... 0    o'Oo ' 
.... O' ' ' m .... O' m mO. mO. 
.... m .... m   m re.DO m  . a  
 . me m  e  .19, .I-I, am-,,  .,, 
u. []nO.  []-. u. OaOo.  '.O.    []'  
O.,Oo' '[]- '[]' oOoO .... o ....    
D ee , O-   me . . me . . me. me . . . . . . , , . . . 
 .IDa  on   on. [] .O, ..... o ..... o..[] ........ o .... o.   o. 
 auiD.OO.  -[Do.  u ...... [] ..... On- u, ...... non,  .Ouu .On 
Figure 3: Topographic mapping with and without competition. The vertical axis 
represents ten LGN cells within one section, and the horizontal axis 50 RGC cells. The 
size of each box indicates strength of the synapse connecting corresponding RGC and 
LGN cells. If the system is topographically ordered, this connection matrix should 
contain only connections forming a diagonal from lower left to upper right, as is found in 
normal development in our model (Competition). When competition is eliminated, the 
topographic map is coarse and non-contiguous. 
4 PREDICTIONS 
In addition to replicating current experimental findings, our model makes several 
interesting predictions about the outcome of novel experiments. If inputs from each eye 
arrive simultaneously, so that contralateral projections have no advantage in competing to 
innervate specific regions of the LGN, synaptic competition and retinal waves lead to a 
pattern of ocular dominance "patches" similar to that observed in visual cortex (Figure 2, 
Simultaneous). Topography is refined, but in this case a continuous map is formed 
between the two eyes (Figure 4) -- again similar to patterns observed in visual cortex. 
96 Keesing, Stork, and Schatz 
..............................  nOVOn ......... 
Figure 4: Topographic mapping with synchronous arrival of projections from both eyes. 
Light boxes represent contralateral inputs, dark boxes represent ipsilateral. Synaptic 
competition and retinal waves cause ocular segregation and topo:aphic refinement, but in 
this case the continuous map is formed using both eyes rather than a single eye. 
Our model predicts that the width of retinal waves -- the distribution of activity around 
the moving wavefront -- is an essential factor in determining both the rate of ocular 
segregation and topographic refinement. Wide waves, which cause many RGCs within 
the same eye to be active, will lead to most rapid ocular segregation as a result of 
competition. However, wide waves can lead to poor topography: RGCs in distant 
regions of the retina are just as likely to be simultaneously active as neighboring RGCs 
(Figure 5). 
100 
80 
60 
40 
20 
0 
0.0 
0.2 0.4 0.6 0.8 
Average Activity in 
Neighboring RGCs 
.4 
.3 
.2 
1 
0 
1.0 
Figure 5: The width of retinal "waves" determines ocular dominance and topography in 
normal development in our model. Width of retinal waves is represented by the average 
activity in RGC cells adjacent to the Gaussian wavefront: high activity indicates wide 
waves. Topographic error (scale at righ0 represents the average distance from an RGCs 
target position multiplied by the strength of the synaptic connection. LGN cells are 
considered ocularly segregated when they receive .9 or more of their total synaptic input 
from one eye. Wide waves lead to rapid ocular segregation -- many RGCs within the 
same retina are simulaneously active. An intermediate width, however, leads to lower 
topographic error -- wide waves cause spurious correlations, while narrow waves don't 
provide enough information about neighboring RGCs to significantly refine topography. 
Retinogeniculate Development: The Role of Competition and Correlated Retinal Activity 97 
SUMMARY 
Our biological model differs from more developed models of cortical development in its 
inclusion of 1) differences in the time of arrival of RGC axons from the two eyes, 2) lack 
of intra-target (LGN) inhibitory connections, 3) absence of visual stimulation, and 4) 
inclusion of a growth rule. The model can account for the development of topography 
and ocular dominance layering in studies of normal and experimental-treated cats, and 
makes predictions concerning the role of retinal waves in both segregation and 
topography. These neurobiological experiments are currently underway. 
Acknowledgements 
Thanks to Michael Stryker for helpful suggestions and to Steven Lisberger for his 
generous support of this work. 
References 
Cline, H.T., Debski, E.A., & Constantine-Paton, M.. (1987) "N-methyl-D-aspartate 
receptor antagonist desegregates eye-specific stripes." PNAS 84: 4342-4345. 
Meister, M., Wong, R., Baylor, D., & Shatz, C. (1991) "Synchronous Bursts of Action 
Potentials in Ganglion Cells of the Developing Mammalian Retina." Science. 252: 939- 
943. 
Miller, K.D., Keller, J.B., & Stryker, M.P. (1989) "Ocular Dominance Column 
Development: Analysis and Simulation." Science. 245: 605-615. 
Shatz, C.J. (1990) "Competitive Interactions between Retinal Ganglion Cells during 
Prenatal Development." J. Neurobio. 21(1): 197-211. 
Shatz, C.J., & Stryker, M.P. (1988) "Prenatal Tetrodotoxin Infusion Blocks Segregation 
of Retinogeniculation Afferents." Science. 242: 87-89. 
Shotwell, S.L., Shatz, C.J., & Luskin, M.B. (1986) "Development of Glutamic Acid 
Decarboxylase Immunoreactivity in the cat's lateral geniculate nucleus." J. Neurosci. 6(5) 
1410-1423. 
Sretavan, D.W., Shatz, C.J., & Stryker, M.P. (1988) "Modification of Retinal Ganglion 
Cell Morphology by Prenatal Infusion of Tetrodotoxin." Nature. 336: 468-471. 
Whitelaw, V.A., & Cowan, J.D. (1981) "Specificity and plasticity of retinotectal 
connections: a computational model." J. Neurosci. 1(12) 1369-1387. 
Wigstrom, H., & Gustafsson, B. (1985) "Presynaptic and postsynaptic interactions in the 
control of hippocampal long-term potentiation." in P.W. Landfield & S.A. Deadwyler 
(Eds.) Longer-term potentiation: from biophysics to behavior (pp. 73-107). New York: 
Alan R. Liss. 
Wolpert, L. (1978) "Pattern Formation in Biological Development." Sci. Amer. 239(4): 
154-164. 
PART II 
NEU RO- DYNAM I CS 
