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Neurocomputing 70 (2007) 1695–1701

www.elsevier.com/locate/neucom

Adaptation-induced suppression and facilitation:Effect of intra- and extracellular ionic disturbances

Ketan Bajaj�, Basabi Bhaumik

Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India

Available online 10 November 2006

Abstract

Adaptation to drifting-oriented gratings has been shown to cause orientation plasticity. To study adaptation induced responses we

have developed a V1 population model having isotropic intracortical synaptic connections, incorporating sub-cellular and intrinsic

membrane mechanisms. The model captures the finer details of recently reported experimental results on orientation plasticity and shows

that pinwheel centers are foci of orientation plasticity. The model captures the tilt aftereffect and further explains how orthogonal

adaptation can lead to sharpening of orientation tuning curves. We report here for the first time that adaptation not only causes response

suppression but can simultaneously increase the excitability of the local neural tissue due to accumulated extracellular ionic disturbances.

The increased excitability can lead to response facilitation for cells having the least intracellular ionic disturbances.

r 2006 Published by Elsevier B.V.

Keywords: Adaptation; Orientation plasticity; Calcium; Mitochondria; Extracellular

1. Introduction

Electrophysiological and optical recordings of cat visualcortex have established that orientation selectivity of V1cells in adult visual cortex shows plasticity [10,11].Orientation tuning curves of cells at a pinwheel centershow suppression on the flank which is near the adaptingorientation and facilitation on the opposite flank. It hasbeen discussed earlier that synaptic depression or slow afterhyperpolarizations involved during spike frequency adap-tation might be causing the suppression of responses [6,20].Intracortical recurrent excitation mechanisms might beleading to facilitation of responses on the opposite flank[10]. An intracortical recurrent connectivity based modelrelies on synaptic depression of inhibitory and excitatorysynapses having a Mexican hat profile [22]. Suppression onthe near flank is due to depression of intracorticalexcitatory synapses. Facilitation on the opposite flank isdue to disinhibition caused by depression of the longerrange inhibitory synapses. But instead of maximumsuppression the model shows no suppression for a stimulus

e front matter r 2006 Published by Elsevier B.V.

ucom.2006.10.073

ing author. Tel.: +919899450908; fax: +91 11 26581264.

esses: bajajketan@yahoo.com (K. Bajaj),

td.ac.in (B. Bhaumik).

orientation similar to the adapting orientation (Fig. 6A of[22]). Application of GABAA antagonist bicucullinemethiodide does not prevent adaptation. This indicatesthe limitation of adaptation-induced inhibition basedmodels to explain stimulus specific adaptation effects, see[14] for a review. We show here how orientation adaptationinduced intracellular and extracellular ionic disturbancesalong with isotropic intracortical synaptic connections leadto orientation plasticity.

2. Methods

2.1. V1 population model

A population of regular and fast spiking orientationselective complex cells of cat layer 2/3 primary visual cortexhas been modeled. Each cell is a single compartmenthaving Na+ and K+ conductances for spike generation.The feedforward drive to each cell is due to excitatorypostsynaptic potentials generated through 100 excitatorysynapses (AMPA and NMDA [9]). Each synapse receives aPoisson spike train having a spike frequency given by(exp (�jys�ypj

2/s2)(1�fbase)+fbase)Fmax, where ys is thestimulus orientation, yp the preferred orientation of the

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Table 1

High affinity calcium buffering lowers the peak value of cytosolic calcium

at a cost of slowing down the recovery to basal level.

t (decay) (ms) Recovery time (ms) Kd (mM) [Ca2+]i (peak) (nM)

515 1540 1 55

174 1160 10 75

31 860 100 123

Stimulus duration is 2000ms, with the first 1000ms being the preferred

orientation and the next 1000ms being the blank stimulus. We use

Kd ¼ 1 mM for our simulations (see estimates in [8], 1–10mM for isolated

mitochondria and 0.3mM for intact neurons). This gives a decay time

constant of 515ms, lower than that estimated by [1] using the low-affinity

dye fura-6 f (586ms) and high-affinity dye fura-2 (2076ms).

K. Bajaj, B. Bhaumik / Neurocomputing 70 (2007) 1695–17011696

cell, and jys�ypj ¼ 1801�jys�ypj if jys�ypj4901. Thetuning of the feedforward drive is determined by s andFmax is the maximum pre-synaptic firing rate. To modelbaseline stimulus pre-synaptic firing rate is taken to befbaseFmax where fbase is 0.1 [17]. During the control andpost-adaptation protocols, 8 test f ys (0–157.51) are used for1 s each to determine the pre and post adaptationorientation tuning curves of cells. The adaptation protocolinvolves a continuous presentation of the adaptingstimulus for the adaptation duration (ys ¼ 112.51). Iso-tropic intracortical synapses, within a local region thatcould be at a pinwheel center or within an iso-orientationcolumn, have been modeled. Excitatory cells in the localpopulation are taken to be 160 and inhibitory cells 32,which are approximately the number of cells detected withretrograde tracing within a distance of 150 mm [17]. For apinwheel center cells are grouped into 8 orientation groupshaving an orientation selectivity in the range 0–157.51,whereas for a local region within an iso-orientation column(135.01), 80% of the cells have an orientation preference of135.01 and the remaining have a preference for 112.51 and157.51. Representative cells (0–157.51) at a pinwheel centerand a representative cell within an iso-orientation column(135.01) receive excitatory synaptic input from the rest ofthe cells in the local region. The net maximal synapticconductance from excitatory cells in an orientation groupto a representative cell is determined by gmax exp (�yd

2/s2)Nc, where gmax is the maximal conductance of a singlesynapse, yd the difference in the orientation preferences, sthe tuning bandwidth and Nc the maximum number of cellsper orientation group. Intracortical excitation amplifiesand broadens responses of cells to the feedforward drive,while intracortical inhibition prevents a runway excitationand broadening. Inhibition, modeled as GABAA [9]synaptic input arrives from all orientation tuned inhibitoryinterneurons in the local region. This leads to untunedinhibition at pinwheel centers and tuned inhibition withiniso-orientation columns. For simplicity recurrent intracor-tical excitation is not modeled here, though recurrentconnectivity would magnify the suppression and facilita-tion effects occurring due to ionic disturbances.

2.2. Intrinsic mechanisms and ionic disturbances

Each V1 regular spiking cell contains mechanisms for L-type calcium channels, intracellular calcium buffers,calcium pumps, calcium-activated potassium channels,voltage-activated potassium channels and persistent so-dium channels. Fast spiking cells have a lower value forvoltage-activated potassium conductance. Calcium influx,pumping mechanism and buffering are calibrated to givedecay time constants of cytosolic calcium similar toexperimental data [1]. Mitochondrial calcium dynamicsresults in slow recovery of accumulated cytosolic calciumand mitochondria serves as a memory bank to keep arecord of neuronal stimulation [8,15]. To represent calciumuptake by mitochondria the model includes a high affinity

intracellular buffer. We calibrate calcium decay timeconstant by changing the dissociation time constant ofthe intracellular buffer. A lower dissociation constant, Kd,of the intracellular buffer gives a larger time constant forcytosolic calcium decay. This serves to keep the peak valueof cytosolic calcium to a lower value, but at a cost ofincreased time for recovery to basal level (Table 1).The model includes cytosolic calcium activated (voltage

independent) potassium conductance, SK type, modeled asgKCað½Ca

2þ�iÞ ¼ gbarð½Ca

2þ�4i Þ�ð½Ca2þ�4i þ ½Ca

2þ�41=2Þ, where

[Ca2+]i is the free cytosolic calcium concentration, withan initial value being 50 nM, gbar is the maximalconductance and [Ca2+]1/2 is half-activation Ca2+ con-centration [16,26]. The hyperpolarizing current is given byiKCa ¼ gKCa(v�EK), v is the membrane potential and Ek

the reverse potential. Intracellular calcium accumulationcauses extracellular calcium depletion [5,25]. Intracellularcalcium and sodium accumulation based hyperpolarizationcauses extracellular potassium accumulation [23]. Pro-longed extracellular calcium depletion, extracellular potas-sium accumulation and spreading excitation due to glialcalcium waves can lead to an increased excitability of thelocal cortical tissue [2,13,21,23]. To reflect extracellularionic disturbances based increased excitability of the localtissue we include calcium depletion based facilitation ofpersistent sodium conductances [21]. Calcium depletionwould also slow down the closure of Na channels [2] andtend to reduce spike frequency adaptation due to reducedcalcium influx. Calcium accumulation within each cell inthe local population determines the extracellular calciumconcentration, Cao moles(t+1) ¼ Cao moles(t)�

P(Camoles(t,

influx)�Camoles(t, efflux)). The summation is over allregular spiking cells in the local region. Number of molesduring calcium influx or efflux are given by charge carriedacross channels or pumps divided by 2Faraday’s constant.Tissue volume is taken to be (400 mm)3 and extracellularspace occupies a small fraction, 0.2 [18]. Diffusion inthe extracellular space is not modeled, though calciumwill diffuse towards and potassium will diffuse away fromcells responding to the adapting stimulus. Dependencyof persistent sodium conductance on extracellularcalcium depletion is taken as gNaPð½Ca

2þ�oÞ ¼ gbarð1:2�

ARTICLE IN PRESSK. Bajaj, B. Bhaumik / Neurocomputing 70 (2007) 1695–1701 1697

½Ca2þ�4oÞ�ðð1:2� ½Ca2þ �oÞ

4Þ þ ½Ca2þ�41=2Þ, where [Ca2+]o is

the extracellular Ca2+ concentration having an initial valueof 1.2mM. The free parameters are gbar, the maximalconductance, gbar and the depleted concentration ofextracellular calcium at which gNaP is half-activated,[Ca2+]1/2. The depolarizing current is given by iNaP ¼ g-

NaPm(v�ENa), where m is the channel state and ENa thereverse potential [24]. A typical simulation period of 30 scauses extracellular calcium concentration to deplete to�0.8mM. V1 cells are simulated using Neuron 5.8 anddata analysis is done using Matlab 7.

3. Results

As cells do not get sufficient time for recovery, theintracellular and extracellular ionic disturbances accumu-late over the long adaptation period. Intracellular ionicdisturbances cause a varying degree of response suppres-sion in selective cells. Extracellular ionic disturbancesincrease excitability of the local region causing responsefacilitation in cells having least intracellular ionic dis-turbances. Isotropic intracortical connectivity of thesesuppressed and facilitated cells leads to orientationplasticity.

3.1. Adaptation induced response suppression and

facilitation

Studies show that intracellular calcium levels closelyfollow spiking activity [1]. Recent calcium imaging clearlyestablishes the importance of intracellular somatic calciumaccumulation in determining orientation preferences ofnearby cells in visual cortex [19]. Fig. 1 capturesintracellular calcium accumulation due to a prolonged

Fig. 1. Adaptation causes intrace

presentation of the adapting stimulus (112.51). Largeraccumulation occurs for cells (90.01, 112.51, 135.01) havingan orientation preference near the adapting orientation.Least accumulation occurs for cells (180.01, 22.51, 45.01)having an orientation preference near orthogonal toadapting. Extent of accumulation at the end of stimuluspresentation depends upon orientation preferences andtuning characteristics of individual cells.Calcium activated potassium conductance gradually

increases as cytosolic calcium increases. Activation ofhyperpolarizing potassium channels leads to suppression ofspike responses. Fig. 2 shows orientation tuning curves asmeasured during control and post-adaptation protocols.Cells receive only feedforward activity without anyintracortical synaptic contributions. It can be visually seenthat maximum suppression occurs for cell having anorientation preference of 112.51 (same as adapting),whereas cells 90.01 and 135.01 show lesser suppression.The accumulated extracellular ionic disturbances in-

crease the excitability of the local neural tissue. The forcesof suppression (intracellular disturbances) and facilitation(extracellular disturbances) act against each other. Sup-pression dominates for cells having larger intracellularionic disturbances and facilitation dominates for cellshaving the least intracellular disturbances. This is depictedin Fig. 2 for nearby cells at a pinwheel center. Responsesshow maximum facilitation for cells (01, 22.51, 45.01).These cells have an orientation preference orthogonal tocells showing larger response suppression (90.01, 112.51,135.01). Note that post-adaptation orientation tuningcurves shown in Fig. 2 show no change in orientationpreferences. In the next section we show how intracorticalcontributions lead to adaptation induced orientationplasticity.

llular calcium accumulation.

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Fig. 2. Adaptation induced suppression and facilitation at a pinwheel center. Control is bold lines and post-adaptation is dotted lines.

Fig. 3. Adaptation induced orientation plasticity at a pinwheel center.

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3.2. Adaptation induced orientation plasticity

Control and post-adaptation orientation tuning curves aregenerated after including intracortical synaptic contributionsalong with suppression and facilitation due to ionicdisturbances, see Fig. 3. A cell at a pinwheel center havingan orientation preference of 135.01 when adapted to 112.51shows suppression on the left flank and facilitation on theright flank. The suppression on the left flank is not only dueto its intrinsic mechanisms, but also due to the reducedintracortical amplification drive from the population of cells(90.01, 112.51, 135.01) that show larger intracellular ionic

disturbances. The facilitation on the right flank is due to anincreased intracortical amplification drive from the popula-tion of cells (01, 22.51, 45.01) that show maximum facilitationdue to extracellular ionic disturbances. Thus our modelproposes that suppression on the near flank and facilitationon the opposite flank are respectively due to decreased andincreased intracortical amplification drive arriving at thatflank. The shifts in orientation preferences are away from theadapting orientation. Fig. 3 shows a rightward shift for135.01, 157.51 and 0.01 cells and a leftward shift for 90.01,67.51 and 45.01 cells. Our results show that suppression ofresponses on the near flank decreases as difference between

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the adapting orientation and preferred orientation of a cellincreases (compare suppression on left flank of 0.01 cell to135.01 and 157.51 cells). This happens because contributionsfrom cells showing larger intracellular ionic disturbances arelesser so their suppression has a lesser effect. Suppression onthe near flank also decreases as difference between theadapting and the test orientation increases. This is becausecells having orientation preferences away from the adaptingare lesser suppressed; thus intracortical amplification fromthese cells is lesser effected.

Model results show that magnitude of orientationpreference shift decreases as difference between the adaptingand the preferred orientation of a cell increases (denoted bydecreasing magnitude of arrows). This is because of tworeasons. First, the suppression on the near flank decreases asthe difference between the adapting and the preferredorientation increases. Second, the difference between thepreferred orientation and orthogonal to the adaptingorientation decreases. As cells having orientation preferencesorthogonal to adapting show maximum facilitation, thefacilitation on the opposite flank gets closer to the peak ofthe tuning curve. This reduces the magnitude of the oppositedirection shift. A large shift in post-adaptation orientationpreference also leads to a large change from pre- to post-adaptation response (spikes/s) at the new preferred orienta-tion. For example, a larger percentage change in response isseen for the 135.01 cell. The facilitation on the opposite flankincreases as extracellular ionic disturbances increase. Themodel replicates experimental results on orientation plasticity[10,11], and explains how orientation plasticity is dependenton adapting, preferred, and test orientations.

3.3. Plasticity within iso-orientation columns vs. at pinwheel

centers

In agreement with experimental results [10], our modelshows lesser plasticity within iso-orientation columns ascompared to a pinwheel center. Within an iso-orientationcolumn (135.01) majority of cells that contribute to theamplification of an orientation tuning curve have similar ornearby orientation preferences. When the adapting orientationis 112.51 maximum intracellular disturbances are in 112.51followed by 135.01 and 157.51 cells. Cells that have orientationpreferences that are near orthogonal to the adapting (0.01,22.51 and 45.01) and show maximum facilitation due tominimal intracellular ionic disturbances do not exist in thelocal population. Thus facilitation of the opposite flank of135.01 cells that occurred at pinwheel centers is missing withiniso-orientation columns. This leads to a lesser shift oforientation preference in the opposite direction; thus lesserorientation plasticity within iso-orientation columns.

3.4. Tilt aftereffect

We use test orientations that differ from the adaptingorientation by 01, 22.51, 45.01, 67.51 and 901 and plotpopulation responses; i.e. firing rates of each of the

representative cells at a pinwheel center against theirorientation preferences (0.0–157.51). The peak of apopulation response curve is used to detect the orientationrepresented in the population. Differences in the orienta-tion represented in the population, before and afteradaptation, for each test orientation, are calculated. Thisgives the tilt aftereffect, i.e. the difference between the trueand the perceived stimulus orientations.Our data shows a larger magnitude of tilt aftereffect than

psychophysical measurements possibly because it is basedonly on pinwheel data. Psychophysical data would bebased on an entire orientation map and would includeeffects of higher visual areas and attention. In [4] weexplain mechanisms by which attention to the orientationof the adapting stimulus reduces the magnitude of tiltaftereffect. Maximum tilt aftereffect occurs when differencebetween adapting and test stimulus orientations is 22.51and the aftereffect approaches 01 as the differenceapproaches 901 or 01 (Fig. 4). This reduction is inagreement with experimental data on tilt aftereffect [7].

3.5. Sharpening of orientation selectivity by orthogonal

adaptation

Adaptation to an orientation leads to an improvement indiscrimination of stimuli that are orthogonal to theadapting [7]. Our model suggests an explanation for thisobservation. The representative 22.51 cell has an orienta-tion preference orthogonal to the adapting orientation(112.51). It receives maximum intracortical excitatorycontribution from other 22.51 cells, and these cells getfacilitated due to orthogonal adaptation (Fig. 2). This leadsto maximum facilitation at the peak rather than atorientations further away, causing sharpening of orienta-tion tuning (Fig. 3). Sharpening of orientation tuning couldexplain improvement in orientation discrimination, but themechanism shown here is only for cells at a pinwheelcenter. In [3] we discuss how orthogonal adaptation cancause response facilitation in other regions of an orienta-tion map. We also discuss how concepts presented herecould explain adaptation induced facilitation of directiondiscrimination and even face identification [3].

4. Discussion

In this model we show importance of sub-cellular andmembrane mechanisms in explaining slow adaptationeffects. We also highlight the importance of extracellularspace in explaining adaptation induced cortical plasticity.The model shows how adaptation while inducing a varyingdegree of response suppression in selective cells alsoincreases the excitability of the local neural tissue. Responsesuppression dominates for cells having higher intracellularionic disturbances whereas response facilitation dominatesfor cells having the least intracellular ionic disturbances.Suppressed and facilitated responses in a local populationalong with isotropic intracortical synaptic connectivity

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Fig. 4. Tilt aftereffect from population responses at a pinwheel center.

K. Bajaj, B. Bhaumik / Neurocomputing 70 (2007) 1695–17011700

reshape the orientation tuning curves. This happens in amanner dependent upon adapting, preferred and testorientations. The model includes only calcium accumulationbased hyperpolarization though other mechanisms such assodium accumulation based hyperpolarization [20], synapticdepression and adaptation induced suppression of feedfor-ward drive would contribute to response suppression.Similarly, other than calcium depletion, extracellular potas-sium accumulation and spreading excitation due to glialcalcium waves would contribute to the excitability of thelocal tissue. We do not model calcium dynamics ininhibitory interneurons though we expect slow adaptationof inhibitory interneurons to further oppose orientationplasticity within iso-orientation columns. Model predictionscan be verified by calcium imaging and electrophysiologicalexperiments. As per our model adaptation induced increasedexcitability would facilitate responses of cells to orthogonalto adapting stimulus. This explains recent fMRI experimentsthat show an increase in BOLD signal on presentation oftest stimulus orthogonal to adapting [12].

In this paper we have proposed adaptation inducedcellular competition. Cells least affected by the adaptingstimulus grow stronger while the cells most affected growweaker in their response to stimulus. In [3] we discuss howthis principle is related to homeostasis in a cortical tissue.We further suggest that adaptation induced responsesuppression and facilitation as described here couldpossibly explain other adaptation aftereffects [3].

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Ketan Bajaj received his M.Tech. in Computer

Science and Engineering from Indian Institute of

Technology, Delhi (1997–98) and BE in Instru-

mentation and Control Engineering from Delhi

Institute of Technology, Delhi (1991–95). Since

1995 he has been working in the technology

industry in multiple areas such as VHDL

compilers, internet technologies and enterprise

applications, besides having research experience

in computer vision and satellite data networks.

He is presently a Project Scientist at the Department of Electrical

Engineering, Indian Institute of Technology, Delhi and is pursuing Ph.D.

studies (2004–06) in computational neuroscience.

Basabi Bhaumik received her Ph.D. and M.Tech.

in Electrical Engineering from Indian Institute of

Technology, Kanpur, and B.E. in Electronics and

Telecommunication from Jadavpur University,

Calcutta. She joined the Faculty in Indian

Institute of Technology, Delhi, in 1980. She is

currently a Professor in the Department of

Electrical Engineering. Her research interests

are in the areas of biological neural networks

and analog /mixed signal VLSI design.