Adaptive Coding in Retinal Ganglion Cells

Xin Jin, Hai-Qing Gong & Pei-Ji LiangDepartmnent of Biomedical Engineering

Shanghai Jiao Tong UniversityShanghai, 200030, China

E-mail: pjliang(sjtu.edu.cn

Abstract-Sensory systems show many aspects of adaptation.The chicken retinal ganglion cells examined in our studyshowed typical light adaptation and contrast adaptation. Theprolonged presence of contrast or luminance stimuli reducedthe firing rate of retinal ganglion celis during the adaptationphase. However, further experimental results suggest that theinformation about stimulation might be stored in the retinalneural network in spite of the reduction in firing rate duringthe adaptation process. We found that the application ofbackground light may result in some modification for retinasensitivity, in an illumination level dependent manner. Thismay indicate a novel adaptive mechanism underlying thephenomena of that contrast discrimination improved when thebackground iliumination was increased. Inspired by thephysiological mechanisms, a simple and biophysically realisticmodel was then employed, where the spiking neuron couldchange their membrane properties, especially the ion channelactivity, during the process of adaptation or synapticmodification. Our analyses reveal that activity-dependentregulation of membrane properties contributes to sensitivityadaptation, which may be potentially useful for neural signaldetection and information processing.

I. INTRODUCTION

In the early stages of the visual pathway, two distincttypes of adaptation were observed, which were termed lightadaptation and contrast adaptation [1, 12]. The biologicalsignificance for retinal neurons to have adaptation is thatindividual neurons have limited signaling ranges but mustencode stimulus intensities that vary over much widerranges. The property of adaptation allows the visual systemto adjust its sensitivity and activity in facing the varyingenvironment and thus to deal with it better [7]. Without suchadaptive adjustment, small signals will be drown in neuronalnoise, and large signals will saturate the system.

Adaptation to the mean illumination intensity, which istermed 'light adaptation', regulates the gain and dynamicsof retinal responses to environmental illumination [7]. Afteran abrupt change in environmental illuminance level, thereis evidence of a fast response mechanism (acting over thefirst tens of milliseconds) with the increased firing of retinalganglion cells, and a slower adaptation mechanism (takingseveral seconds to complete) with decreased firing activitiesof the retinal ganglion cells [10]. A second type ofadaptation which is called contrast adaptation; responds notto the mean level of the visual stimulus but to its 'contrast',

Ai-Hua ChenShanghai Institutes for Biological Sciences

Chinese Academy of SciencesShanghai, 200031, China

E-mail: aihuachen@sibs.ac.cn

which is the relative fluctuation around the meanillumination [1]. Similarly, following a switching from alow-contrast environment to one of high contrast, the firingrates of retinal ganglion cells increase abruptly (< 0. Is), andthen decrease exponentially to a much lower level (- lOs)[1]. By matching their sensitivity to the fluctuations in theinputs, visual neurons can efficiently encode signals withwidely varying temporal and spatial structure [10]. Bothlight adaptation and contrast adaptation revealed phenomenaanalogous to each other: an increase of activity at thetransient switching from weak stimulus to intense stimulus,and a slow reduction in fiing rate during adaptation tosustained stimulation.

In the present study, the retinal ganglion cells that wereexamined revealed typical phenomena of light adaptationand contrast adaptation, similar to the observation made inother species [1]. Moreover, it was found that given a flashwith defined contrast, more spikes could be elicited whenthe sustained illumination was brighter. These resultssuggest that neuronal sensitivities could be modified by thebackground illumination level, although neuronal firing ratewas reduced in exposure to sustained illumination. Abiophysically realistic model was then employed toinvestigate the functional role of dynamic adjustnent ofneuron's sensitivity in neural information processing and itspossible application.

A. Electrophysiological ExperimentsThe detailed experimental procedure and methods for cell

data analysis can be found elsewhere [2]. Simply, chickeneyes were obtained from newly hatched chickens (about 2-4days old). A multi-electrode system (MEA60, MultiChannel Systems MCS GmbH, Reutlingen, Germany) wasused for electrophysiological recording. Spiking sorting andanalysis were conducted off-line. Light stimulus wasgenerated using a computer monitor, and was focused toform spot on the isolated retina via a lens system. The lightintensity of the monitor's output during each stimulus wasmeasured using a light detection system (1L1400,Newburyport Inc, MA, USA) at the retina level when thelight was delivered through the optical system. The contrastof stimuli is defined as (Lmax - Lmin)/(Lmax + Lmin),where Lmax and Lmin are the maximum and minimumluminance in each flash, respectively. For contrastadaptation experiment with flickering stimuli, the intensity

0-7803-9422-4/05/$20.00 ©2005 IEEE1937

of full-field stimulation was renewed every 50 ms followinga pseudorandom m-sequence with a given mean level anddefined contrast of light illumination.

B. Model Structure and Simulation

In the classic H-H equations [6], the cell's membranepotential is considered as predominantly governed bysodium, potassium and leakage channels, and can beequated as:

Ci * dv/dt = -gNa (V -Va) -g (V-vK)gL (V VL) + I(t) + (t) (1)

where Ci is the membrane capacitance, v represents themembrane potential; I(t) is the input signal; { (t) is a noiseterm; vNa, VK, and VL are equilibrium potentials for relevantion currents, which are constant values; m, h, and n arevariables representing processes such as sodium channelactivation, sodium channel inactivation, and potassiumchannel activation, respectively; g and g denote thechannel conductance and maximal conductancerespectively:

gNa = gNa m h_n4gK = gK * n

dm/dt = m(v) (1- m) - P^(v) *mdh/dt = ah(v) ( - h) - lh(v)*hdnldt a,a(V) * (- n) - f(V) * n (2)

where a and fP are rate variables describing eachdynamic process, which are voltage dependent and take thefollowing forms:

am= 0.1.(v+40)a 1= e ( fl = 4 . exp[- (v + 65)/18]

ah= 0.07 - exp[- (v + 65)/20], Phah = 1~~~~~+exp[-(v+35)/10]

=I0.0l.-(v+55)a.n = [-(v+ 55)110]' P = 0.125- exp[-(v+ 65)/80](3)

The units for membrane potential and rate constants aremV and ms ' respectively.

Following these equations, the neuron's output can becalculated and the power spectral density (PSD) of theoutput spike train can be computed. In the present study, thesignal-to-noise ratio (SNR) of the system's output wasmeasured as the ratio of PSD) value at the input frequency (to PSD background level near that frequency [5].We first used equation (1) for calculation, with all model

parameters following that introduced in the classicHodgkin-Huxley equation: Ci= 1.0 pF /cm2, -N = 120

mS/cm2, VNa = 50 mV, g= 36 mS/cm2, VK= -77 mV, gL=0.3 mS/cm2, VL= -54.4 mV. Since the nervous system is fullof noises caused by transmitter release, ion channel activitychanges etc., which can be equivalently modeled as aGaussian white noise with zero mean:

(4(t)) = 0,({i(tl j(t2)) = a2SS,(tl -t2)

where (..) represents the ensemble average over the noisedistributions and a 2 indicates the noise intensity asdeviation [18]. The stimulus current applied in this studytherefore included two components: a periodic input signalI(t)=Ajsin(2 rft) with Ai and fi being its amplitude andfrequency respectively, together with a zero-mean Gaussianwhite noise f (t). The parameters for the sub-thresholdperiodic stimulus I(t) were chosen arbitrarily such that Ai=1.1 ±A/cm2 andfi = 40 Hz. The standard deviation (STD)a of the applied noise sequence was chosen at reasonablelevels (ranging from a minimum value of 1.8 to a maximumof 17.6).

1 II. MAIN RESULTS

Figure 1 is an example of the activity changes of anON-OFF retinal ganglion cell in response to light-ON andlight-OFF transients. Following a step increase in lightintensity, the firing rate of the cell increased abruptly, with apeak level reaching 150 Hz, and then decreased to a muchlower level of less than 5 Hz. Similarly, firing activity had aswift increase after the incident of light offset, whichdecreased to a very low level afterwards.

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t.~~~~~a :: to- ze 3. ' so 0

Fig. 1. Firing activities of an ON-OFF cell in response to spatially uniformlight stimulation. Firing rate was computed for one ON-OFF cell in 50-mstime bins averaged over four trials. The lower trace illustrates the timecourse of the light stimulation between dark (0 mW/m2) and light (10mW/mi).

The retinal ganglion cells also adapt to the range offluctuations around the mean intensity, which is termed'contrast adaptation' [1, 10]. In our experiment, those cells

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with increased activities at the light-ON transient also hadobvious contrast adaptation as shown in Fig. 2.

To test the relationship between the intensity of sustainedambient illumination and the neurons' sensitivity to contrastdiscrimination, light stimuli consisting of a 30-s sustainedillumination followed by six test flashes with definedcontrast were applied in this study. One example of theexperimental results is plotted in Fig. 3, where a sustainedfull-field white light (3.9 mW/m2) was applied for 30 s priorto the application of test flashes. It is shown that theganglion cell's firing activity increased to a peak level of280 Hz at the light-ON transient; this was followed by agradual decrease to a lower level of around 20 Hz during thesustained application of unitary illumination. However,when superimposed white test flashes (with contrast being0.167) were applied, increased spikes were detected again.Neuron activities were then measured following the timeschedule illustrated in Fig. 3a, with test flashes given atvarious contrast levels (ranging from 0.1 to 0.45), in thepresence of sustained (30 s) background illumination (3.9mW/m2). Generally, the firing rate of retinal ganglion cellsincreased when the contrast of the testing was fixed and thebackground illumination level was increased. The statisticalresult given in Fig. 3b.

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of the ion channels are not constant, but rather changeabledepending on both the membrane potential and neuron'sfiring behavior [14]:

9Na - p(r) 9N gK =- q() gK (5)

where p(r) and q(r) are both function of firing frequency,indicating that the conductances of the ion channels areactivity-dependent, and can be defined as 100% in generalconditions and have variation within a certain range whenrelevant regulatory processes occur [14].

(b) :

I IAl

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Fig. 2. Ganglion cell activity changes in adaptation to temporal contrast.Responses of a ganglion cell to full-field pseudorandom flashes (temporalcontrast). The lower trace indicates the contrast (0.5) of the flashing stimuli.The mean level of luminance intensity is 5.9 mW/m2. The firing responsewas calculated using 50-ms time bins.

We then investigated the possible functional role of theadaptive mechanisms of retina using a simple butbiophysically realistic model. The model structure and theapplication of noise are described as equation (1). Fig.4illustrates the relationship between the output SNR and theintensity (v) of noise added (ten different levels of noiseintensity were applied, and twenty noise sequences wereapplied for each intensity level to provide averaged SNRvalues (mean± SD)).

Biological systems are highly adjustable, and neuronalresponses to stimulation- generally show significantadaptation, being characterized by membrane activitychanges [14]. A key issue in this study is that conductances

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Fig. 3. Response activities of retinal ganglion cells to test flashessuperimposed on the leading sustained illumination. (a) The firing activityof an ON-ganglion cell in response to stimuli (lower trace) consisting of a30-s sustained illumination (3.9 mW/m2) followed by six test flashes(marked 0, 1, 2, 3, 4 and 5 in the figure) with defined contrast (0.167 in thisexample). Each test flash was designed so that the mean intensity levelequals to the leading sustained illumination. (b) Relative firing activities toflashes with fixed difference versus various levels of backgroundillumination. The firing activities were shown as closed symbols, inresponse to light flashes with fixed intensity (1.96 mW/m2) in the presenceof the background illumination. Data were collected from 11 ganglion cellsofone retina.

In order to investigate the effect of membraneconductance changes on neuron's sensitivity in signaldetection, we chose to modify the conductance of sodiumand potassium channels within the physiological range.Because increasing sodium conductance generally lowersthe neuron's threshold for discharge and increasing

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potassium conductance should have exactly the oppositeeffect, so we chose to modify these channel conductances inopposite directions for simplicity. The maximum changes ofconductance regulation was defined asp(r) = 120% and q(r)= 80% and vice versa. Corresponding threshold changes in

the H-H neuron are plotted in Fig. 5.

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Fig. 4. The relationship between the noise intensity and the model neuron'sSNR in response to a sub-threshold periodic signal (I(t) = Aisin(27rfit) withAi = 1.1 jIA/cm2 andfi = 40 Hz). The dotted line was fitted from ten datapoints to guide eyes. SNR was computed from the PSDs as the ratio ofpeakamplitude of PSD at the input frequency (f) to the level of backgroundnoise at that frequency (SNR = l0*log(SNRo)). The error bars indicate thestandard deviations ofSNR estimation.

The neuron's ability to detect weak signal was thenre-tested. The same sub-threshold periodic current(I(t)=Ajsin(2 rft) with Ai= 1.1 IAcm2 andf = 40 Hz) was

applied in equation (1), with the channel conductanceregulated following equation (5). Fig. 6 illustrates therelationship between the output SNR and the noise intensity(a) under each condition.

lower noise level side when sodium channel activity isup-regulated with potassium channel activity beingdown-regulated (traces d e, Fig. 6). This suggests thatincreasing sodium conductance and simultaneouslydecreasing potassium conductance improve the neuron'sability to detect the weak signal, especially under low noiselevel, and modification of conductance in the oppositedirection reduces the neuron's ability to detect this weaksignal.

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Fig. 6. Modification of ion channel conductances induced behavior changesin H-H neuron. It gives the relationship between the neuron's SNR and thenoise intensities with various regulations of gNa and gK. The maximal valueof SNR increases and shifts towards lower noise level side when sodiunchannel activity is up-regulated with potassium channel activity beingdown-regulated and vice versa.

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Fig. 5. The H-H neuron's threshold changes vs. different pairs of p(r) andq(r). Increasing sodium conductance by 20% and simultaneouslydecreasing potassium conductance by 20% generally lowers the neuron'sthreshold for nearly 1.7 mV; on the other hand, an opposite operation willbring an increase of threshold for nearly 4.8 mV.

It is clearly shown in Fig. 6 that the maximal value ofSNR decreases with its peak shifting towards higher noiselevel side when sodium channel activity is suppressed andpotassium channel activity enhanced (traces a - b, Fig. 6).On the other hand, SNR increases and shifts towards

III. DISCUSSIONS

The chicken retinal ganglion cells examined in this studyshowed typical light adaptation (Fig. 1) and contrastadaptation (Fig. 2), which is similar to that observed fromretinal ganglion cells in other species [1]. The additionalfinding in this study was that after the completion ofluminance adaptation, a significant increase in neuron firingrate could be observed when the retina was exposed to lightflashes superimposed on the continuously appliedbackground illumination. Moreover, sensitivities to thecontrast stimuli were dependent on the level of backgroundillumination (Fig. 3). More spikes were elicited by theflashes when the sustained illumination became stronger.The results suggest that neuron sensitivities can be modifiedby the presence of background illumination, although theneuron firing rate was reduced during sustainedillumination.

It has been previously reported that the increase inambient illumination could result in a rapid increase in theganglion cell's firing rate, and in the meantime reduce thecell's sensitivity to the superimposed light stimulus [17].

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Similarly, a recent study demonstrated that fast contrastadaptation was marked by increased firings and decreasedsensitivity [1]. During the sustained illumination applied inthis study, the neuron firing rate was reduced; however, thesensitivity was increased. Furthermore, when the intensityof background illumination was increased, the ability forcontrast discrimination was increased accordingly. Theseresults suggest that information about ambient illuminationmight be stored in the retinal neural network, which resultsin some increase in the ganglion cells' sensitivity of contrastdiscrimination. A broadband adaptive mechanism couldpossibly, therefore, help explain why the contrastdiscrimination increased when the background illuminationwas increased.On the other hand, activity-dependent adaptive

noise-aided weak signal detection has rarely been reportedin despite of many theoretical and experimental studiesconcentrating on either stochastic resonance or adaptationphenomena in biological systems. Wenning and Obermayer[16] have proposed one kind of adaptive stochasticresonance in which they constructed a firing-rate-dependentfeedback mechanism to regulate the input synaptic noise.Optimal information transfer is achieved by changing thestrength of noise such that the neuron's average firing rateremains constant [16].

In the neural system, neuron's intrinsic properties are notconstant during neural activities. Activity-dependentdynamical changes of channel conductance and firingthreshold, which contribute to adjustment of neuron'ssensitivity and response behavior, have been widely studiedin various neuronal preparations [3, 9, 13]. When adaptationoccurs, the enhancement of some channel current byCa2+-dependent dynamical modification has been suggestedto play a crucial role in increasing spiking threshold andmaintaining firing rate [4, 11, 15]. In addition, suppressingall spiking activity for two days in cultured neocorticalpyramidal cell resulted in an increment of sodium currentfor nearly 30% and at the mean time decreased thepotassium current by around 50%. These changes wereaccompanied by a reduction in spiking threshold and ahighly significant increase in the cell's sensitivity [3]. Suchfiring-rate- dependent activity regulation was also frequentlyobserved in visual neurons, such as the retinal ganglion cellsexamined in present study. A bi-directional regulation couldbe obviously observed from the processing of 'contrastadaptation'. The phenomenon was such that the retinalganglion cell's response to light stimuli with large variationswas more active than to light stimuli with small variations,the change of firing-rate had a quick dynamic, which hasbeen termed as "fast-adaptation" of the neuron's response tovarying contrast. On the other hand, this fast-adaptation wasusually followed by a "slow-adaptation" (see Fig. 7), duringwhich period a gradual recovery occurred in the neuron'sfiring rate. It has been firther suggested that such"contrast-adaptation" process involved ion channel activitychanges [8]. So, we proposed here that the

activity-dependent regulation of neuronal sensitivity such asthe various kinds of adaptation in retina might sometimescontribute to neuron's ability of detecting sub-thresholdsignals in the presence of background activities. Theimprovement could possibly be achieved by regulating theconductance of ion channels on the membrane, dependenton the neuron's firing activity. However, the more detailedmechanisms of adaptive coding in neural system and itspotential applications in engineering aspects would needadditional exploration in the future.

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Fig. 7. Firing rate of a retinal ganglion cell under flicker stimulation,alternating every 50 seconds between contrast values of 0.09 and 0.35.Averaged firing rate was illustrated in the upper trace and continuous linesare exponential fits with decay time constant T. Middle trace shows the timecourse of contrast C, and bottom trace demonstrates the time course offlickering intensity I. This sensitivity regulation in retinal ganglion cell hasbeen suggested to be dependent on ion channel activity changes (cited fromref [12]).

ACKNOWLEDGMENT

This work is supported by grants from National BasicResearch Program of China (2005CB724301), the NationalFoundation of Natural Science of China (No. 60375039) andMinistry of Education (No. 20040248062).

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