Contrast adaptation in simple cells by changing 
the transmitter release probability 
Pdter Adorjtin Klaus Obermayer 
Dept. of Computer Science, FR2-1, Technical University Berlin 
Franklinstrasse 28/29 10587 Berlin, Germany 
{adp, oby}@cs.tu-berlin.de http://www. ni.cs.tu-berlin.de 
Abstract 
The contrast response function (CRF) of many neurons in the primary vi- 
sual cortex saturates and shifts towards higher contrast values following 
prolonged presentation of high contrast visual stimuli. Using a recurrent 
neural network of excitatory spiking neurons with adapting synapses we 
show that both effects could be explained by a fast and a slow compo- 
nent in the synaptic adaptation. (i) Fast synaptic depression leads to sat- 
uration of the CRF and phase advance in the cortical response to high 
contrast stimuli. (ii) Slow adaptation of the synaptic transmitter release 
probability is derived such that the mutual information between the input 
and the output of a cortical neuron is maximal. This component--given 
by infomax learning rule--explains contrast adaptation of the averaged 
membrane potential (DC component) as well as the surprising experi- 
mental result, that the stimulus modulated component (F1 component) 
of a cortical cell's membrane potential adapts only weakly. Based on our 
results, we propose a new experiment to estimate the strength of the ef- 
fective excitatory feedback to a cortical neuron, and we also suggest a 
relatively simple experimental test to justify our hypothesized synaptic 
mechanism for contrast adaptation. 
1 Introduction 
Cells in the primary visual cortex have to encode a wide range of contrast levels, and they 
still need to be sensitive to small changes in the input intensities. Because the signaling 
capacity is limited, this paradox can be resolved only by a dynamic adaptation to changes 
in the input intensity distribution: the contrast response function (CRF) of many neurons 
in the primary visual cortex shifts towards higher contrast values following prolonged pre- 
sentation of high contrast visual stimuli (Ahmed et al. 1997, Carandini & Ferster 1997). 
On the one hand, recent experiments, suggest that synaptic plasticity has a major role 
Contrast Adaptation and Infomax 77 
in contrast adaptation. Because local application of GABA does not mediate adaptation 
(Vidyasagar 1990) and the membrane conductance does not increase significantly during 
adaptation (Ahmed et al. 1997, Carandini & Ferster 1997), lateral inhibition is unlikely to 
account for contrast adaptation. In contrast, blocking glutamate (excitatory) autoreceptors 
decreases the degree of adaptation (McLean & Palmer 1996). Furthermore, the adaptation 
is stimulus specific (e.g. Carandini et al. 1998), it is strongest if the adapting and testing 
stimuli are the same. On the other hand, plasticity of synaptic weights (e.g. Chance et 
al. 1998) cannot explain the weak adaptation of the stimulus driven modulations in the 
membrane potential (F1 component) (Carandini & Ferster 1997) and the retardation of the 
response phase after high contrast adaptation (Saul 1995). These experimental findings 
motivated us to explore how presynaptic factors, such as a long term plasticity mediated 
by changes in the transmitter release probability (Finlayson & Cynader 1995) affect con- 
trast adaptation. 
2 The single cell and the cortical circuit model 
The cortical cells are modeled as leaky integrators with a firing threshold of -55 mV. The 
interspike membrane potential dynamics is described by 
C,m 0 ( t ) 
0---[- = --aeak ((t) -- Erest) -- ((t) -- Esyn)  (1) 
The postsynaptic conductance gij (t) is the integral over the previous presynaptic events 
and is described by the alpha-function 
Ispikesl t 
gij(t) = gmax  Pij(t;)'lij(t;)' (t- t;).exp (1 --tj), (2) 
Tpeak s Tpeak 
where tj is the arrival time of spike number s from neuron j. Including short term synaptic 
depression, the effective conductance is weighted by the portion of the synaptic resource 
Pij (t)  lij (t) that targets the postsynaptic side. The model parameters are Cm = 0.5 nF, 
gleak -- 31 nS, Erest -- -65 mV, Esyn --5 mV, _xc = = 
-- - $tma x 7.8 nS, and ;peak 1 ms, 
and the absolute refractory period is 2 ms, and after a spike, the membrane potential is re- 
set 1 mV below the resting potential. Following Tsodyks & Markram (1997) a synapse 
between neurons j and i is characterized by the relative portion of the available synaptic 
transmitter or resource lrij. After a presynaptic event, lrij decreases by Pij lrij, and re- 
covers exponentially, where pij is the transmitter release probability. The time evolution 
of Rij between two presynaptic spikes is then 
ij(t) '- 1 - (1 - (ij(t) - Pij()ij(i)))exp , (3) 
Trec 
where i is the last spike time, and the recovery time constant rr = 200 ms. Assuming 
Poisson distributed presynaptic firing, the steady state of the expected resource is 
1 (4) 
st 
RiJ(fJ'PiJ): 1 + Pijfjrrc 
The stationary mean excitatory postsynaptic current (EPSC) Ii7 (fj, Pij) is proportional to 
the presynaptic firing frequency fj and the activated transmitter pij Rj (fj, Pij) 
I7(fj,Pij) cx f Pij RiT(fj,Pij) . (5) 
The mean current saturates for high input rates fj and it also depends on the transmitter 
release probability Pij: with a high release probability the function is steeper at low presy- 
naptic frequencies but saturates earlier than for a low release probability. 
78 P Adorjdn and K. Obermayer 
80 
-64 
-64.2 
-64.4 
-64.6 
-64.8 
: 60 -- p-=O.24 ;'/ 
 20 ?" o 
010 101 IO- 
Firing rate [Hz] 
-650 50 100 150 200 
(a) (b) Time [ms ] 
Figure 1: Short term synaptic dynamics at high and low transmitter release probability. 
(a) The estimated transfer function O(f, p) for the cortical cells (Eq. 7) (solid and dashed 
lines) in comparison with data obtained by the integrate and fire model (Eq. 1, circles and 
asterisks). (b) EPSP trains for a series of presynaptic spikes at intervals of 31 ms (32 Hz). 
p--0.55 (0.24) corresponds to adaptation to 1% (50%) contrast (see Section 4). 
In order to study contrast adaptation, 30 leaky-integrator neurons are connected fully via 
excitatory fast adapting synapses. Each "cortical" leaky integrator neuron receives its 
"geniculate" input through 30 synapses. The presynaptic geniculate spike-trains are inde- 
pendent Poisson-processes. Modeling visual stimulation with a drifting grating, their rates 
are modulated sinusoidally with a temporal frequency of 2 Hz. The background activity for 
each individual "geniculate" source is drawn from a Gaussian distribution with a mean of 
20 Hz and a standard deviation of 5 Hz. In the model the mean geniculate firing rate (Fig. 
2b) and the amplitude of modulation (Fig. 2a) increases with stimulus log contrast accord- 
ing to the experimental data (Kaplan et al. 1987). In the following simulations CRFs are 
determined according to the protocol of Carandini & Ferster (1997). The CRFs are calcu- 
lated using an initial adaptation period of 5 s and a subsequent series of interleaved test and 
re-adaptation stimuli (1 s each). 
3 The learning rule 
We propose that contrast adaptation in a visual cortical cell is a result of its goal to maxi- 
mize the amount of information the cell's output conveys about the geniculate input  . Fol- 
lowing (Bell & Sejnowski 1995) we derive a learning rule for the transmitter release proba- 
bility p to maximize the mutual information between a cortical cell's input and output. Let 
O(f, p) be the average output firing rate, f the presynaptic firing rate, and p the synaptic 
transmitter release probability. Maximizing the mutual information is then equivalent to 
maximizing the entropy of a neuron's output if we assume only additive noise: 
H [O(f,p)] - -E [ln Prob(O(f,p))] 
Prob(f) 
: -I In 100(f,p)/Ofl] 
: E[lnlOO(f'P) I - E[lnProb(f)] . (6) 
(In the following all equations apply locally to a synapse between neurons j and i.) 
In order to derive an analytic expression for the relation between O and f we use the fact 
that the EPSP amplitude converges to its steady state relatively fast compared to the mod- 
ulation of the geniculate input to the visual cortex, and that the average firing rates of the 
A different approach of maximizing mutual information between input and output of a single 
spiking neuron has been developed by Stemmler & Koch (1999). For non-spiking neurons this strat- 
egy has been demonstrated experimentally by, e.g. Laughlin (1994). 
Contrast Adaptation and Infomax 79 
presynaptic neurons are approximately similar. Thus we approximate the activation func- 
tion by 
O(f,p) oc S(f) pR(f,p), 
(7) 
where S(f) - f+o accounts for the frequency dependent summation of EPSCs. The 
parameters o = 1.8 and  = 15 Hz are determined by fitting O(f,p) to the firing rate 
of our integrate and fire single cell model (see Fig. la). The objective function is then 
maximized by a stochastic gradient ascent learning rule for the release probability p 
Op OH[O(f,p)] 0 
Tadapt 07 = Op : 07 
in c90(f, p) . 
Of 
(8) 
Evaluating the derivatives we obtain a non-Hebbian learning rule for the transmitter release 
probability p, 
op - 
Tadapt tt --2rrecf R + - + , (9) 
p a + recp(fa- 1) 
where a -   and the adaptation time constant Tadapt : 7 S (Ohzawa et al. 1985). 
f 
This is similar in spirit to the anti-Hebbian learning mechanism for the synaptic strength 
proposed by Barlow & F61difik (1989) to explain adaptation phenomena. Here, the first 
term is proportional to the presynaptic firing rate f and to the available synaptic resource 
R, suggesting a presynaptic mechanism for the learning. Because the amplitude of the 
EPSP is proportional to the available synaptic resource, we could interpret/ as an output 
related quantity and -2rrfR as an anti-Hebbian learning rule for the "strength of the 
synapse", i.e. the probability p of the transmitter release. The second term ensures that p is 
always larger than 0. In the current model setup for the operating range of the presynaptic 
geniculate cells p also stays always less than 1. The third term modulates the adaptation 
slightly and increases the release probability p most if the input firing rate is close to 20 Hz, 
i.e. the stimulus contrast is low. 
Image contrast is related to the standard deviation of the luminance levels normalized by 
the mean. Because ganglion cells adapt to the mean luminance, contrast adaptation in the 
primary visual cortex requires only the estimation of the standard deviation. In a free view- 
ing scenario with an eye saccade frequency of 2-3 Hz, the standard deviation can be esti- 
mated based on 10-20 image samples. Thus the adaptation rate can bd fast (Tadap t = 7 $), 
and it should also be fast in order to maintain good a representation whenever visual con- 
trast changes, e.g. by changing light conditions. Higher order moments (than the standard 
deviation) of the statistics of the visual world express image structure and are represented 
by the receptive fields' profiles. The statistics of the visual environment are relatively 
static, thus the receptive field profiles should be determined and constrained by another 
less plastic synaptic parameter, such as the maximal synaptic conductance gmax. 
4 Results 
Figure 2 shows the average geniculate input, the membrane potential, the firing rate and the 
response phase of the modeled cortical cells as a function of stimulus contrast. The CRFs 
were calculated for two adapting contrasts 1% (dashed line) and 50% (solid line). The 
cortical CRF saturates for high contrast stimuli (Fig. 2e). This is due to the saturation of the 
postsynaptic current (cf. Fig. 1 a) and thus induced by the short term synaptic depression. In 
accordance with the experimental data (e.g. Carandini et al. 1997) the delay of the cortical 
response (Fig. 2f) decreases towards high contrast stimuli. This is a consequence of fast 
synaptic depression (c.f. Chance et al. 1998). High modulation in the input firing rate 
leads to a fast transient rise in the EPSC followed by a rapid depression. 
80 P Adorjtin and K. Obermayer 
LGN 
 40 
 20 
 0 o  2 
(a) 10 10 10 
 40 
C2 00  , 
1 10  102 
(b) Contrast [%] 
(c) 
0 0o 
1 10  102 
, 30 
20 
m 10 
m 0 
(e) 
-58 
-6210o 
(d) 
o 
-20 
-40 
-60 
0  10  102 
' -80 0o 
101 102 1 10  102 
Contrast [%] (f) Contrast [%] 
Figure 2: The DC (a) and the F1 (b) component of the geniculate input, and the response of 
the cortical units in the model with strong recurrent lateral connections and slow adaptation 
of the release probability on both the geniculocortical and lateral synapses. The F1 (c) 
and the DC (d) component of the subthreshold membrane potential of a single cortical 
unit, the F1 component of the firing rate (e), and the response phase (f) are plotted as a 
function of stimulus contrast after adaptation to 1% (solid lines) and to 50% (dashed lines) 
contrast stimuli. The CRF for the membrane potential (c, d) is calculated by integrating 
Eq. 1 without spikes and without reset after spikes. The cortical circuitry involves strong 
recurrent lateral connections. 
The model predicts a shift of 3-5 mV in the DC component of the subthreshold membrane 
potential (Fig. 2d)-- a smaller amount than measured by Carandini & Ferster (1997). Nev- 
ertheless, in accordance with the data the shift caused by the adaptation is larger than the 
change in the DC component of the membrane potential from 1% contrast to 100% con- 
trast. The largest shift in the DC membrane potential during adaptation occurs for small 
contrast stimuli because an alteration in the transmitter release probability has the largest 
effect on the postsynaptic current if the presynaptic firing rate is close to the geniculate 
background activity of 20 Hz. The maximal change in the F1 component (Fig. 2c) is 
around 5mV and it is half of the increase in the F1 component of the membrane poten- 
tial from 1% contrast to 100% contrast. The CRF for the cortical firing rate (Fig. 2e) shifts 
to the right and the slope decreases after adaptation to high contrast. The model predicts 
that the probability p for the transmitter release decreases by approximately a factor of two. 
The F1 component of the cortical firing rate decreases after adaptation because after tonic 
decrease in the input modulated membrane potential, the over-threshold area of its F1 com- 
ponent decreases. The adaptation in the F1 firing rate is fed back via the recurrent ex- 
citatory connections resulting in the observable adaptation in the F1 membrane potential. 
Without lateral feedback (Fig. 3) the F1 component of the membrane potential is basically 
independent of the contrast adaptation. At high release probability a steep rise of the EPSC 
to a high amplitude peak is followed by rapid depression if the input is increasing. At low 
release probability the current increases slower to a lower amplitude, but the depression is 
Contrast Adaptation and Infomax 81 
10 
0 0o 
(a) ! 
-62 0o 
1 
W 30 
20 
m 0 
102 (c) 10  10  102 
0 00 02 
101 (a) 1 10  I 
0 
-20 
-40 
-60 
0 
Contrast [%] 
I 
-80 0o 02 -60 0o 
101 102 1 10  1 1 10  102 
(b) Contrast [%] (d) Contrast [%] (b) Contrast [%] 
Figure 3 Figure 4 
Figure 3: The membrane potential (a, b), the phase (d) of the F1 component of the firing 
rate, and the F1 component (c) averaged for the modeled cortical cells after adaptation to 
1% (dashed lines) and 50% (solid lines) contrast. The weight of cortical connections is 
set to zero. The CRF for the membrane potential (a, b) is calculated by integrating Eq. 1 
without spikes and without reset after spikeso 
Figure 4: Hysteresis curve revealed by following the ramp method protocol (Carandini & 
Ferster 1997). After adaption to 1% contrast, test stimuli of 2 s duration were applied with 
a contrast successively increasing from 1% to 100% (asterisks), and then decreasing back 
to 1% (circles). 
less pronounced too. As a consequence, the power at the first harmonic (F1 component) 
of the subthreshold membrane potential does not change if the release probability is modu- 
lated. It is modulated to a large extent by the recurrent excitatory feedback. The adaptation 
of the F1 component of the firing rate could therefore be used to measure the effective 
strength of the recurrent excitatory input to a simple cell in the primary visual cortex. 
Additional simulations (data not shown) revealed that changing the transmitter release 
probability of the geniculocortical synapses is responsible for the adaptation in our model 
network. Fixing the value of p for the geniculocortical synapses abolishes contrast adapta- 
tion, while fixing the release probability p for the lateral synapses has no effect. Simula- 
tions show that increasing the release probability of the recurrent excitatory synapses leads 
to oscillatory activity (e.g. Senn et al. 1996) without altering the mean activity of simple 
cells. These results suggest an efficient functional segregation of feedforward and recur- 
rent excitatory connections. Plasticity of the geniculocortical connections may play a key 
role in contrast adaptation, while--without affecting the CRF--plasticity of the recurrent 
excitatory synapses could could play a key role in dynamic feature binding and segregation 
in the visual cortex (e.g. Engel et al. 1997). 
Figure 4 shows the averaged CRF of the cortical model neurons revealed by the ramp 
method (see figure caption) for strong recurrent feedback and adapting feedforward and 
recurrent synapses. We find hysteresis curves for the F1 component of the firing rate simi- 
82 P. Adorjdn and K. Obermayer 
lar to the results reported by Carandini & Ferster (1997), and for the response phase. 
In summary, by assuming two different dynamics for a single synapse we explain the sat- 
uration of the CRFs, the contrast adaptation, and the increase in the delay of the cortical 
response to low contrast stimuli. For the visual cortex of higher mammals, adaptation of 
release probability p as a substrate for contrast adaptation is so far only a hypothesis. This 
hypothesis, however, is in agreement with the currently available data, and could addition- 
ally be justified experimentally by intracellular measurements of EPSPs evoked by stimu- 
lating the geniculocortical axons. The model predicts that after adaptation to a low contrast 
stimulus the amplitude of the EPSPs decreases steeply from a high value, while it shows 
only small changes after adaptation to a high contrast stimulus (cf. Fig. lb). 
Acknowledgments The authors are grateful to Christian Piepenbrock for fruitful discus- 
sions. Funded by the German Science Foundation (Ob 102/2-1, GK120-2). 
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