Abstract

Synaptic depression is essential for controlling the balance between excitation and inhibition in cortical networks. Several studies have shown that the depression of intracortical synapses is asymmetric, that is, inhibitory synapses depress less than excitatory ones. Whether this asymmetry has any impact on cortical function is unknown. Here we show that the differential depression of intracortical synapses provides a mechanism through which the gain and sensitivity of cortical circuits shifts over time to improve stimulus coding. We examined the functional consequences of asymmetric synaptic depression by modeling recurrent interactions between orientation-selective neurons in primary visual cortex (V1) that adapt to feedforward inputs. We demonstrate analytically that despite the fact that excitatory synapses depress more than inhibitory synapses, excitatory responses are reduced less than inhibitory ones to increase the overall response gain. These changes play an active role in generating selective gain control in visual cortical circuits. Specifically, asymmetric synaptic depression regulates network selectivity by amplifying responses and sensitivity of V1 neurons to infrequent stimuli and attenuating responses and sensitivity to frequent stimuli, as is indeed observed experimentally.

Introduction

Cortical computations depend critically on the integration of excitatory and inhibitory inputs by individual neurons. Understanding these computations requires an analysis of how individual neurons interact as part of their cortical network (Somers et al. 1995; Suarez et al. 1995; Dragoi and Sur 2000; Ferster and Miller 2000; Yoshimura et al. 2005). A remarkable feature of cortical circuits is the extensive pattern of recurrent excitatory and inhibitory connections. Excitatory connections are believed to amplify afferent signals (Douglas et al. 1995; Somers et al. 1995) and improve cortical selectivity (Ben-Yishai et al. 1995; Somers et al. 1995; Sompolinsky and Shapley 1997), whereas inhibitory connections preserve network stability by preventing runaway excitation (Tsodyks et al. 1997; Troyer et al. 1998). One factor that regulates the balance between cortical excitation and inhibition is synaptic depression, that is, the decrease in synaptic strength with repeated stimulation (Thomson et al. 1993; Markram and Tsodyks 1996; Abbott et al. 1997; Varela et al. 1997). It is increasingly being realized that the dynamic adjustment in synaptic strength is advantageous for cortical computations. Thus, it has been proposed that synaptic depression makes each excitatory synapse relatively independent of the presynaptic responses, thus increasing neuronal sensitivity to changes in stimulus features (Abbott et al. 1997; Nelson and Turrigiano 1998). This is particularly useful because cortical neurons receive excitatory synaptic inputs from thousands of afferents that fire at rates within a broad range. However, we know that in addition to excitatory inputs cortical neurons receive inhibitory inputs. Whether and how synaptic depression affects the way in which individual neurons and networks integrate excitatory and inhibitory inputs to process information is unclear. A partial insight into this issue was offered by several studies of short-term plasticity of intracortical synapses in visual and somatosensory cortex (Galaretta and Hestrin 1998; Varela et al. 1999) that have reported that synaptic depression is an “asymmetric” process. That is, inhibitory intracortical synapses exhibit less depression than excitatory synapses, even after brief stimulation. This raises the untested possibility that asymmetric synaptic depression may dynamically change the relationship between excitation and inhibition in an unbalanced fashion to influence the function of cortical circuits.

The differential depression of intracortical synapses has been proposed to contribute to network stability. That is, the activity-dependent decrease in excitation due to the strong depression of excitatory synapses could shift the relative strength of excitatory and inhibitory synapses toward inhibition to prevent runaway excitation (Chagnac-Amitai and Connors 1989). However, this view ignores the fact that the overall gain of cortical circuits depends not only on the relative strength of synaptic connections, but also on the rate of presynaptic firing. Because excitatory synapses onto inhibitory neurons depress more strongly than inhibitory synapses, the reduction in the excitatory input to interneurons could actually reduce recurrent inhibition to oppose the net shift from excitation to inhibition. Clearly, predicting the ultimate effects of asymmetric synaptic depression for cortical function would require an analysis of recurrent interactions between excitatory and inhibitory neurons in the context of their local circuit. However, despite the importance of this issue, models of cortical function have not yet investigated concurrently the dynamic properties of short-term plasticity of excitatory and inhibitory synapses.

Here, we examine whether asymmetric synaptic depression impacts the gain and sensitivity of cortical networks by studying the properties of networks consisting of interconnected excitatory and inhibitory neurons. Contrary to expectation, we demonstrate analytically that despite the fact that excitatory synapses depress more strongly than inhibitory synapses, excitatory responses are reduced less than inhibitory responses. We show that this release from inhibition can cause an increase of the overall response gain in local circuits if the gain of inhibitory neurons is significantly higher than that of excitatory neurons. We further examine this emergent property by modeling recurrent interactions between orientation-selective neurons in V1 layers 2–3 adapting to feedforward inputs from layer 4. Brief adaptation to a stimulus of fixed orientation led to depression of feedforward synapses and asymmetric depression of intracortical synapses. We found that these processes lead to an unbalanced excitation and inhibition regime that explains a fundamental property of cortical networks, that is, the capacity to selectively adapt to rapid changes in stimulus features.

Materials and Methods

Electrophysiology

Single neuron recordings were made from one alert macaque monkey with extracellular electrodes lowered transdurally. Details of recordings are given elsewhere (Dragoi et al. 2001, 2002). Eye position was continuously monitored using an infrared eye tracking system (Iscan, Inc., Burlington, MA). The monkey was trained to fixate on a small red spot (0.1°) presented on a video monitor placed at a distance of 57 cm. Once the animal achieved stable fixation for 100 ms, the visual stimulus was presented within the neuron's receptive field (receptive fields were located at least 2.5° away from the center of fixation). The monkey was required to maintain fixation throughout the stimulus presentation to earn a juice reward; the trial was automatically aborted if fixation instability exceeded 0.25° at any time during stimulus presentation. Stimuli were 5 × 5° sine-wave grating of 2.2 cycles/deg spatial frequency and 75% contrast level presented binocularly. Each trial consisted of a 1.1-s cycle. The monkey triggered the trial by holding a bar, and after 100 ms of fixation, an adapting stimulus was flashed in the center of the neuron's receptive field for 500 ms, followed by a 500-ms test stimulus of random orientation (16 equally spaced orientations spanning 0°–180°). The adapting stimulus was either a 5° × 5° uniform gray patch (control condition) or a sine-wave grating of similar spatial characteristics to the test stimulus, but fixed orientation (adaptation condition). Each test orientation was randomly presented 20 times in each of the control and adaptation conditions. We compared orientation-selective responses in the control and adaptation conditions, including changes in preferred orientation and near/far-flank response magnitude. We determined orientation discrimination performance by calculating d′ in the control and adaptation conditions as the difference between the mean spike rates at 2 adjacent orientations divided by the root-mean-square standard deviation.

Analytical Model

We used a Wilson–Cowan model describing 2 interconnected populations of excitatory and inhibitory neurons (Fig. 1A): 

(1)
graphic
where τe and τi are the time constants of excitatory and inhibitory responses, E represents the response of the excitatory population, I represents the response of the inhibitory population, and Fe and Fi represent excitatory feedforward inputs to excitatory and inhibitory neurons. Neuronal interactions are mediated by the synaptic weights Wij, where the first subscript index indicates the postsynaptic neuron, and the second subscript indicates the presynaptic neuron. The “+” subscript symbols in equation (1) indicate that only the positive terms are added to the subpopulation activity. For simplicity, we assume that the 2 inputs Fi and Fe, are proportional, that is, Fi = kFe. The steady-state solutions of equation (1) are 
(2)
graphic
where Ge is the gain of the excitatory subpopulation and Gi is the gain of the inhibitory subpopulation. The steady-state solutions are stable if the synaptic weights W satisfy the following inequality (Tsodyks et al. 1997, 2004): 
(3)
graphic

Figure 1.

(A) Schematic diagram of a simple recurrent model. The excitatory population E is connected to itself through recurrent excitatory connections (Wee) and to the inhibitory population I through inhibitory connections (Wei). The inhibitory population I is connected to itself through recurrent inhibitory connections (Wii) and to the excitatory population through excitatory connections (Wie). Open circles: excitatory connections; filled circles: inhibitory connections. (B) Asymmetric synaptic depression (β > α) causes a larger decrease of the gain of inhibitory responses than excitatory responses. When α > β, there is a smaller decrease of the gain of inhibitory responses than the gain of excitatory responses. Parameter values were Wee = 3.3, Wei = 4.8, Wie = 4.4, Wii = 6; Fi = kFe (k = 0.45). These values were chosen such that to ensure the stability of both the undepressed and depressed model equations. However, the results hold for a wide range of parameters (cf. Materials and Methods). The depression coefficients were α = 0.3 and β = 0.9. The gray area represents the area in which the recurrent model does not have stable and positive solutions. (C) Asymmetric synaptic depression leads to a larger reduction of inhibitory responses relative to excitatory ones, whereas symmetric synaptic depression (α = β) leads to a similar decrease of excitatory and inhibitory responses. Red: excitatory responses; blue: inhibitory responses.

Figure 1.

(A) Schematic diagram of a simple recurrent model. The excitatory population E is connected to itself through recurrent excitatory connections (Wee) and to the inhibitory population I through inhibitory connections (Wei). The inhibitory population I is connected to itself through recurrent inhibitory connections (Wii) and to the excitatory population through excitatory connections (Wie). Open circles: excitatory connections; filled circles: inhibitory connections. (B) Asymmetric synaptic depression (β > α) causes a larger decrease of the gain of inhibitory responses than excitatory responses. When α > β, there is a smaller decrease of the gain of inhibitory responses than the gain of excitatory responses. Parameter values were Wee = 3.3, Wei = 4.8, Wie = 4.4, Wii = 6; Fi = kFe (k = 0.45). These values were chosen such that to ensure the stability of both the undepressed and depressed model equations. However, the results hold for a wide range of parameters (cf. Materials and Methods). The depression coefficients were α = 0.3 and β = 0.9. The gray area represents the area in which the recurrent model does not have stable and positive solutions. (C) Asymmetric synaptic depression leads to a larger reduction of inhibitory responses relative to excitatory ones, whereas symmetric synaptic depression (α = β) leads to a similar decrease of excitatory and inhibitory responses. Red: excitatory responses; blue: inhibitory responses.

This means that if recurrent excitatory connections are strong, recurrent inhibition has to match the strength of recurrent excitation in order to ensure stability. For the particular weights chosen for the simulations (Wee = 3.3, Wei = 4.8, Wie = 4.4, Wii = 6), the steady-state solutions are stable and positive (D > 0, Ge > 0 and Gi > 0). The gain of inhibitory responses is greater than the gain of excitatory responses (Gi > Ge) if the following condition is satisfied: 

(4)
graphic
This inequality holds when: 
(5)
graphic
Assuming that Wei is approximately equal to Wie, this condition is equivalent to the fact that excitatory-to-inhibitory synaptic strengths should be weaker than the mean strength of recurrent excitatory and inhibitory synapses.

The possible values of parameter k (the ratio between Fi and Fe) are constrained by 1) Ge > 0, that is, 1 + WiikWei > 0, which is equivalent to k < (1 + Wii)/Wei; and 2) Gi > 0, that is, Wiek(Wee − 1) > 0, which is equivalent to k < Wie/(Wee − 1). For instance, the condition k = 0.45, used in the simulation below, ensures that Gi ∼ 1.5Ge. If, for instance, k > 1.5, Ge becomes negative. We simulated the steady-state effects of synaptic depression by multiplying the synaptic weights with positive subunitary parameters (α for excitatory synapses and β for inhibitory synapses). We also assumed that the excitatory inputs Fe and Fi undergo depression by the same factor, that is, α. The steady-state depressed responses, Ed and Id, are given by 

(6)
graphic
Ed and Id are stable and positive for all α and β values used in the simulations, 0.3 < α, β < 0.9.

The response E′ of a cortical neuron that receives depressed excitatory (E) and inhibitory (I) inputs (Fig. 2A) is written as the weighted difference E′ = WeEWiI, where E and I represent the responses of the efferent excitatory and inhibitory neurons. After synaptic depression, the response Ed is given by Ed= αWeEd−βWiId, where Ed = δeE, and Id = δiI represent the excitatory and inhibitory efferent responses after depression (δe and δi represent the degree of suppression of excitatory and inhibitory responses), and α, β have been previously defined. Thus, the difference ΔE′ between the depressed and undepressed response of neuron E′ is given by 

(7)
graphic
ΔE′ is positive if the term inside the square brackets is positive, which is equivalent to (1 − βδi)/(1 − αδe) > γ. If we assume that αδe = λβδi the condition ΔE′ > 0 becomes (1 − βδi)/(1 − λβδi) > γ. Because γ > 1 (WeE > WiI for E′ > 0), this is equivalent to λ > 1. Thus, ΔE′ > 0 if δe = λδiβ/α, where λ > 1. Because the ratio β/α is greater than 1 (for asymmetric synaptic depression) or equal to 1 (for symmetric depression) this condition becomes δe = ρδi, ρ = λβ/α, ρ ≥ λ > 1. The subunitary variables δe and δi depend on the relative gain changes of the afferents after depression. They can be written as δe = 1 − ΔGe and δi = 1 − ΔGi where ΔGe = (GeGed)/Ge and ΔGi = (GiGid)/Gi are the relative excitatory and inhibitory gain changes. If δe or δi is close to 1, the relative gain changes are small, whereas if they are close to 0, the relative gain changes are large. Thus, the cell's depressed response (Ed) increases if the ratio between the relative gain change of the inhibitory input and the relative gain change of the excitatory input is larger than a fixed supraunitary threshold. Otherwise, the cell's response will decrease after synaptic depression. In the case of symmetric synaptic depression (α = β), ΔE′ > 0 if δe = λδi (this condition is less restrictive than in the case of asymmetric depression).

Figure 2.

Emergent properties of a simple recurrent model with asymmetric synaptic depression. (A) An extension of the model illustrated in Figure 1A. Cortical neuron E′ receives excitatory (E) and inhibitory (I) local cortical inputs via depressing synapses. The rectangle marks the recurrent circuit represented in Figure 1A. (B) Asymmetric synaptic depression causes an increase in response E′ only when the decrease in the gain of inhibitory inputs exceeds the decrease in the gain of excitatory inputs by a fixed supraunitary threshold (cf. Materials and Methods). The excitatory and inhibitory response gains were varied by increasing parameter α between 0.3 and 0.54 while keeping β fixed at 0.85. The synaptic connections between neurons EE′ and IE′ were We = 3 and Wi = 3.75. (C) Asymmetric synaptic depression causes an increase in the activity of excitatory cortical neurons (E′) that receive asymmetrically reduced excitatory and inhibitory inputs. Black line: neuronal response without depression; gray line: neuronal response after asymmetric synaptic depression; dashed line: neuronal response after symmetric synaptic depression. The changes in responses are examined for a range of input levels (Fe). The synaptic connections between neurons EE′ and IE′ were similar to those in panel B.

Figure 2.

Emergent properties of a simple recurrent model with asymmetric synaptic depression. (A) An extension of the model illustrated in Figure 1A. Cortical neuron E′ receives excitatory (E) and inhibitory (I) local cortical inputs via depressing synapses. The rectangle marks the recurrent circuit represented in Figure 1A. (B) Asymmetric synaptic depression causes an increase in response E′ only when the decrease in the gain of inhibitory inputs exceeds the decrease in the gain of excitatory inputs by a fixed supraunitary threshold (cf. Materials and Methods). The excitatory and inhibitory response gains were varied by increasing parameter α between 0.3 and 0.54 while keeping β fixed at 0.85. The synaptic connections between neurons EE′ and IE′ were We = 3 and Wi = 3.75. (C) Asymmetric synaptic depression causes an increase in the activity of excitatory cortical neurons (E′) that receive asymmetrically reduced excitatory and inhibitory inputs. Black line: neuronal response without depression; gray line: neuronal response after asymmetric synaptic depression; dashed line: neuronal response after symmetric synaptic depression. The changes in responses are examined for a range of input levels (Fe). The synaptic connections between neurons EE′ and IE′ were similar to those in panel B.

Model of Orientation-Selective Neurons in V1

We implemented a firing rate model describing the interactions between excitatory and inhibitory orientation-selective neurons in the superficial layers of V1. The network consisted of Ne = 180 excitatory neurons and Ni = 48 inhibitory neurons that receive feedforward inputs from neurons in layer 4. The layer 4 inputs to cortical excitatory and inhibitory cells in layers 2–3 are modeled as cosine functions centered on stimulus orientation θ: 

(8)
graphic
where JINP = 9.6 mV/spikes/s, and f(c) is a nonlinear contrast function (Supplementary Fig. 2A) chosen such that to ensure realistic contrast response functions for layer 4 (Supplementary Fig. 2B) and layers 2–3 neurons (Supplementary Fig. 2C): 
graphic

Stimulus contrast c can vary between 1% and 100%. In our simulations, the contrast was held fixed at 100%. The parameters in equation (8) were chosen such that to ensure peak firing rates of about 60 Hz and contrast response functions identical to those obtained experimentally (Dragoi V, unpublished data). The input from layer 4 was sharpened by recurrent excitatory and inhibitory networks in the superficial layers of V1. Excitatory (E) and inhibitory (I) cortical responses in layers 2–3 were computed as: 

(9)
graphic
where Re and Ri are excitatory and inhibitory V1 responses, computed by taking only positive numbers multiplied by a scaling constant (negative responses were made zero). To ensure firing rates in the physiological range (20–60 Hz), we used membrane time constants τe = τi = 15 ms and γe = γi = 10 spikes/s/mV. Despite the fact that these parameters are similar for excitatory and inhibitory cells, the values of the synaptic strengths for inhibitory connections (which will be discussed later) ensured that the inhibitory peak and mean firing rates were approx. 20% larger than the corresponding excitatory firing rates (Connors et al. 1982; McCormick et al. 1985). The differential equations were transformed into difference equations by using first-order differences with a time step of 1 ms.

Each layer 2–3 cell synapses onto a group of cortical cells of a narrow range of orientations (half-amplitude bandwidth [BW] 30°) via feedforward excitatory synapses targeting excitatory (Wfe) and inhibitory (Wfi) cells. Excitatory cortical cells are interconnected by recurrent excitatory synapses (Wee), and inhibitory cortical cells are interconnected by recurrent inhibitory synapses (Wii). In addition, excitatory cells excited neighboring inhibitory cells (via synapses Wie), which in turn inhibited neighboring excitatory cells (via synapses Wei). Synaptic strengths were computed as probability functions such as their area computed over the entire orientation domain was unity (Fig. 4). In agreement with experimental data (Nelson and Frost 1981; Toyama et al. 1981; Michalski et al. 1983; Martin and Whitteridge 1984; Fries et al. 1997), recurrent excitatory connections had a maximum strength of 0.015 and decreased nonlinearly to 75% of the peak value at the 45° orientation difference between the pre- and postsynaptic cell. Excitatory connections to inhibitory cells had a maximum strength of 0.014 and decreased nonlinearly to 75% of the peak value at the 48° orientation difference between the pre- and postsynaptic cell. Consistent with cross-correlation, optical, and in vivo laser stimulation studies (Nelson and Frost 1981; Toyama et al. 1981; Michalski et al. 1983; Martin and Whitteridge 1984; Miller, 1992; Weliky et al. 1995; Fries et al. 1997; Tucker and Katz 1998; Roerig and Chen 2002), the model orientation tuning of inhibitory inputs was significantly broader in layer 2/3 pyramidal neurons compared with the tuning of excitatory inputs (but see the study of Marino et al. 2005, suggesting that the extent of this asymmetry may be smaller than previously thought). Therefore, model inhibitory connections to excitatory cells had a maximum strength of 0.049 and decreased to 75% of the peak value at the 55° orientation difference between the pre- and postsynaptic cell. Finally, recurrent inhibitory connections had a maximum strength of 0.044 and decreased nonlinearly to 75% of the peak value at the 60° orientation difference between the pre- and postsynaptic cell. The values of the peak synaptic strengths were chosen in agreement with experimental data reporting an asymmetry between the strength of excitatory and inhibitory synapses in V1 (Komatsu et al. 1988; Thomson and West 1993; Thomson and Deuchars 1994), that is, peak inhibitory connection strengths were chosen stronger than excitatory ones (by a factor of 3). The undepressed feedforward and intracortical synaptic strengths (measured in mV/spikes/s) were given by 

(10)
graphic

We used powers of cosines for computing the intracortical and feedforward synaptic strengths (the values of the cosine exponents were critical for network stability). The exponents used for the excitatory synapses were in the range of 2–2.4, which is equivalent to a half-peak BW of 60°–65°. For inhibitory synapses, we used cosine exponents in the range of 1.1–1.6 (BW 75°–83°). Using these values we obtained larger synaptic strengths and orientation spread for inhibitory synapses (relative to excitatory synapses), which is consistent with experimental data (Komatsu et al. 1988; Thomson and West 1993; Thomson and Deuchars 1994; Weliky et al. 1995; Roerig and Chen 2002) and is critical for network stability. Although the exact level of this asymmetry is not critical for our results, a slightly broader orientation spread of inhibitory synapses compared with excitatory synapses ensures sharp orientation tuning curves for V1 neurons and stronger inhibitory responses than excitatory ones. The layer 4 input pool for each neuron in layers 2–3 was restricted (within the 30° orientation range) by using high exponents for the feedforward cosine functions, Afe = Afi = 3 (we used Gfe = Gfi = 0.14 for the feedforward synaptic strength parameters). For the intracortical synaptic strengths we used the following exponents: Aee = 2.3, Aei = 1.5, Aie = 2.0, and Aii = 1.2. The exponents of the cosine functions and the input scale parameters (Gfe and Gfi) were trimmed such that for an input of contrast 100% the steady-state excitatory response was ∼50 Hz, in agreement with experimental data (Dragoi et al. 2002).

Synaptic Depression

In agreement with experimental data, we assume that both the excitatory and inhibitory intracortical synapses, as well as the feedforward excitatory synapses, undergo depression. Synaptic depression was implemented as a dynamic process in which the decrease in synaptic strength, W, is controlled by a presynaptic factor, S(t), that ensures that only the synapses of active presynaptic neurons should exhibit plasticity, and an attenuation factor, AF, that directly controls the magnitude of synaptic depression (Supplementary Fig. 3). 

(11)
graphic
where W(t) are the depressed synaptic strengths, and W(0) are the undepressed synaptic strengths (as defined by eq. 10). The presynaptic factors are described as follows: 
(12)
graphic

We used the same time constant (τ = 150 ms) for all the synapses. Function f is equal to the difference 1 − Prel, where Prel is the change in transmitter release probability for excitatory/inhibitory synapses as a function of the presynaptic firing rate, R (Dayan and Abbott 2001): 

(13)
graphic

We used τD = 150 ms and fD = 0.9 (cf. Dayan and Abbott 2001) for both excitatory and inhibitory synapses. The activity-dependent decrease in synaptic strength is ensured by the presynaptic factor S(t). An increase in the presynaptic firing rate ensures that S(t) increases (eq. 12) to cause the weakening of synaptic strengths W(t) (cf. eq. 11). In contrast, when the presynaptic firing rates become zero S(t) converges exponentially to zero (because fe(R) = 0, eq. 12), and hence the synaptic weights, W(t), become equal to those before depression, W(0), that is, synapses will exhibit full recovery.

The attenuation functions, AF, have been implemented as fixed synaptic depression probabilities (centered on the cell's preferred orientation) that are dependent on the orientation difference between the post- and presynaptic neurons. In agreement with the depletion model of depression (Betz 1970), the larger the initial probability of release, the more pronounced is the degree of depression of a synapse (this dependence of the magnitude of depression on the baseline release probability has been observed at many synapses, Markram and Tsodyks 1996; see also Zucker and Regehr 2002, for a review). We thus assumed, in agreement with experimental data (Yang and Faber 1991; Markram and Tsodyks 1996), that the relative degree of depression should depend on the initial synaptic weight (eq. 14). That is, for similar presynaptic firing rates, stronger synapses should undergo proportionally stronger depression than weaker synapses. If strong and weak synapses would have similar depression rates, then high presynaptic firing rates would rapidly depress weaker synapses that may become zero (cf. eq. 11). When the pre-/postsynaptic orientation difference is small, the initial synaptic weights (before depression, W(0)), are strong and this corresponds to proportionally large values for the corresponding depression parameters AF (eq. 14). Alternatively, when the pre-/postsynaptic orientation difference is large, the initial synaptic weights are weak, and this corresponds to small values for the depression parameters AF. 

(14)
graphic

Importantly, equation (14) shows that the attenuation factors are proportional to the initial synaptic weights. The degree of depression for the different synapse types (e-e, i-e, e-i, i-i) are controlled by the amplitude, that is, Cee, Cei,, Cie, and Cii, and sharpness of the attenuation functions, that is, the exponents Dee, Dei, Die, and Dii. The fact that excitatory synapses depress to a larger extent than inhibitory synapses is equivalent to the fact that the attenuation functions associated with excitatory synapses, AFee and AFie, are broader and larger in amplitude than the attenuation functions associated with inhibitory synapses, AFii and AFei (Supplementary Fig. 3). We used the following values in the simulations: Cee = 1, Cei = 0.8, Cie = 1, Cii = 0.5, Dee = 1, Dei = 6, Die = 6, Dii = 6, for asymmetric synaptic depression, and Cee = 1, Cei = 0.95, Cie = 1, Cii = 1, Dee = 1, Dei = 1.8, Die = 1.3, Dii = 2.1, for the control, symmetric synaptic depression, case. The values of the amplitude and exponents of the attenuation functions, AF, were chosen such that to ensure that the time course and strength of synaptic depression are similar to those found experimentally (e.g., Varela et al. 1999) and that the network remains stable during the time course of depression. For feedforward synapses, the degree of depression was controlled by Cfe and Cfi (Cfe = Cfi = 0.5). This ensured that, in agreement with experimental results (Yoshimura et al. 2000), feedforward synaptic depression was reduced with respect to intracortical depression by a factor of 2.

Synaptic Facilitation

Synaptic facilitation was implemented using equations similar to those described above (11–14), except that the minus sign in equation (11) (indicating a decrease in synaptic efficacy) was replaced by the plus sign (indicating an increase in synaptic efficacy). For instance, equation (15) describes the facilitation of intracortical synapses between excitatory and inhibitory neurons: 

(15)
graphic

W(t) is the synaptic strength after facilitation and W(0) is the synaptic strength before facilitation (cf. eq. 10). The presynaptic, Sie, and attenuation functions, AFie, were implemented as in equations (12)–(14).

Population Orientation Discrimination Performance

We approximated the mean number of spikes of cell i over the duration Δt with mi(θ) = Ri(θ)Δt, where Ri(θ) was the response of cell i to a stimulus of orientation θ. The standard deviation σ of the spike count was σ = Cvmi(θ), where Cv is a dimensionless constant having values between 0.7 and 1.2 for V1 neurons (Softky and Koch 1993). We computed the network orientation discrimination performance by calculating the population response at 2 slightly different orientations, θ1 and θ2. These responses were used to generate random activities for the 2 orientations by using normal distributed random variables eij) having the mean mij)= Rijt, Δt = 250 ms, and σ = 1.2mij), j =1,2; i = 1,2, …, Ne. The difference between orientations θ1 and θ2 (on the same side of the orientation tuning curve) was 1°–2°, that is, much smaller than the tuning width (∼35°). For cell i, we considered that the discrimination decision is correct if ei1) > ei2) given that Ri1) > Ri2). The discrimination decision of the population of cells was considered correct if the majority of cells produced a correct response; otherwise the response was considered incorrect. The mean percentage of correct responses was computed in 10 000 trials for each pair of orientations (θ1, θ2). We computed the change in orientation discrimination for the entire stimulus orientation range (−90°, 90°) by using pairs (θk, θk + Δθ), where θk were uniformly distributed across (−90°, 90°) and Δθ was either 1°, 1.5°, or 2°.

Results

Simple Recurrent Model with Asymmetric Synaptic Depression

We first studied the functional consequences of asymmetric synaptic depression by using the simple firing rate model illustrated in Figure 1A that describes the ubiquitous interactions between 2 interconnected excitatory and inhibitory populations (Tsodyks et al. 1997, 2004). This recurrent model is simple enough to allow analytical solutions while capturing key aspects of synaptic depression at the circuit level. In a coarse-grained description, the activity of each individual neuron was replaced by the mean activity of the corresponding population (represented by the fraction of neurons active within a certain time window). This level of description is informative in that it allows us to capture the average behavior of cells with similar response properties (e.g., cells with similar preferred orientations in visual cortex).

The purpose of the simple recurrent model is to show that although synaptic depression is generally viewed as a suppressive process, introducing an asymmetry between the depression of excitatory and inhibitory synapses could lead to response facilitation. Specifically, if the gain of inhibitory neurons is higher than that of excitatory neurons, the stronger depression of excitatory synapses relative to inhibitory ones ensures a larger decrease in inhibitory inputs. This release from inhibition, or disinhibition, acts to shift the relative balance between local excitation and inhibition toward excitation, and thus increase the sensitivity of neuronal responses.

The response of the excitatory (E) and the inhibitory (I) neurons depends on the external inputs Fe and Fi, and their synaptic connections, W (see Materials and Methods). Assuming that the neuronal gain functions (response divided by input drive) are linear (threshold) functions, the response dynamics follow the following equations: 

graphic
where τe and τi are the time constants of excitatory and inhibitory responses. The fact that excitatory synapses depress more than inhibitory ones is equivalent to stronger steady-state inhibitory synapses. To simplify the analysis, we assumed that the steady-state depressed excitatory synapses are αWee and αWie, whereas the steady-state depressed inhibitory synapses are βWii and βWei (α < β < 1 are depression factors; α, β = 1 means no depression).

We reasoned that if depression is more prominent at excitatory synapses, this should result in a larger decrease of excitatory responses relative to inhibitory responses. To test this hypothesis, we calculated the steady-state response of excitatory and inhibitory neurons. The surprising finding was that whereas synaptic depression caused a reduction in both excitatory and inhibitory responses, the stronger depression of excitatory synapses may cause, in some circumstances, a significantly greater reduction of inhibitory responses relative to excitatory responses. The main prerequisite for this counterintuitive result is that the ratio between the undepressed inhibitory and excitatory response gains should be greater than (1 − α)/(1 − β)—this fraction is greater than 1 for asymmetric (α < β) synaptic depression (cf. Supplementary Data, eq. 3; see also Materials and Methods). This condition is consistent with physiological findings that inhibitory interneurons typically fire at higher rates than pyramidal cells (McCormick et al. 1985; Nowak et al. 2003). At the same time, if the ratio between the undepressed inhibitory and excitatory response gains is smaller than (1 − α)/(1 − β), excitatory responses were found to decrease more than inhibitory responses.

Figure 1B exemplifies, for a range of synaptic depression parameters (α and β), that the decrease in the gain of inhibitory responses is more prominent than the decrease in the excitatory gain (the recurrent network does not have stable and positive solutions for α > β). For symmetric synaptic depression (α = β), the decrease in excitatory responses is similar to the decrease in inhibitory responses, hence the circuit works in a balanced excitation and inhibition mode. These results are summarized in Figure 1C, which shows that asymmetric synaptic depression leads to a larger reduction of inhibitory responses relative to excitatory ones, provided that the undepressed gain of inhibitory cells is larger than the gain of excitatory cells.

These results are not restricted to the specific synaptic weight values chosen for the simulation shown in Figure 1B,C. The results hold for a broad range of parameter values as long as synaptic depression is asymmetric (β > α, see also Supplementary eqs. 1–3). The choice of the intracortical synaptic weights is restricted by the following 3 conditions: 1) the recurrent model should be stable (eq. 3, see Materials and Methods); 2) the recurrent model should have positive solutions and positive response gains (eq. 2, see Materials and Methods); and 3) the gain of inhibitory responses should be greater than the gain of excitatory responses (eq. 5, see Materials and Methods). Any combination of parameters that will simultaneously satisfy conditions (1) through (3) would yield results qualitatively similar to those shown in Figure 1B,C.

We propose that the asymmetry between the response gains of excitatory and inhibitory neurons (Fig. 1B,C) would alter the responses of neurons receiving depressed excitatory and inhibitory inputs. To examine this issue, we calculated the response of an excitatory neuron, E′, receiving excitatory (E) and inhibitory (I) cortical inputs via depressing synapses (Fig. 2A). For instance, neuron E′ could be a layer 2–3 cortical cell receiving excitatory and inhibitory inputs within its local circuit. We demonstrate in the Materials and Methods section that when the presynaptic inhibitory inputs decrease more than excitatory inputs (due to asymmetric synaptic depression) the response of the efferent neuron, E′, increases above the level before synaptic depression. In the Materials and Methods section (see eq. 7 and the accompanying text), we describe the conditions in which the depressed response (Ed′) becomes stronger than the undepressed response (E′). Intuitively, the fact that the depressed afferent inhibitory inputs (Id) decrease more than the depressed excitatory inputs (Ed) causes a release from inhibition, or disinhibition, of the efferent response, Ed′ (i.e., Ed′>E′). Consistent with the Materials and Methods section, Figure 2B shows that this effect occurs only when the ratio between the relative gain change of the inhibitory input and the relative gain change of the excitatory input is larger than a fixed supraunitary threshold. Figure 2C shows that when this condition is fulfilled, asymmetric synaptic depression leads to a net increase in the response of the neuron receiving depressed excitatory and inhibitory intracortical inputs over a broad range of feedforward input levels (Fe between 0 and 100 Hz). However, if synaptic depression is symmetric, the afferent inhibitory and excitatory inputs decrease roughly by the same extent, and hence the depressed response Ed is weaker than the undepressed response (Ed′<E′)—Figure 2C shows that symmetric synaptic depression fails to cause an increase in the response of the postsynaptic neuron E′.

This analysis reveals the intriguing possibility that, contrary to expectation, neuronal activity could produce asymmetric synaptic depression to shift the relative balance of cortical circuits from inhibition to excitation. That is, the gain, and hence sensitivity, of excitatory neurons receiving depressed intracortical inputs could increase despite the reduction of the firing of their afferents due to synaptic depression (Fig. 2C). We further examine this emergent property of asymmetric synaptic depression from the perspective of orientation selectivity in primary visual cortex (V1). We focus on selective, stimulus-specific, changes in the sensitivity of cortical responses induced by adaptation, particularly orientation-specific adaptation, as a prominent form of short-term plasticity that has been hypothesized to rely on synaptic depression. However, our results are likely to have broader implication for selective adaptation in general (e.g., auditory or somatosensory cortex), not just visual adaptation, as neuronal circuits such as those described in Figure 1 are ubiquitous in the neocortex (Douglas and Martin 2004).

Experimental Evidence for Selective Adaptation in Primary Visual Cortex

Our analysis in Figures 1 and 2 suggests that despite the fact that synaptic depression is typically viewed as a suppressive process through which the total input received by a neuron is reduced, asymmetric depression could in fact increase neuronal responses and sensitivity. This raises the possibility that brief exposure, or adaptation, to a fixed stimulus, which is believed to cause synaptic depression (Chance and Abbott 2001; Chung et al. 2002; Dragoi et al. 2002), could sometimes cause response facilitation, not just suppression. We examined this issue by recording the activity of monkey V1 neurons, before and after adaptation to an oriented stimulus briefly flashed in the neuron's receptive field.

We recorded orientation-selective responses in V1 of fixating monkey during the presentation of test gratings flashed in the receptive field for 500 ms, before and after adaptation to a grating of fixed orientation close to the cell's optimal (flashed for 500 ms at the same location, see Materials and Methods). The example shown in Figure 3A is consistent with previous orientation adaptation experiments in anesthetized cats (Dragoi et al. 2000, 2001) (time scale of seconds to minutes) and behaving monkey (Dragoi et al. 2002) (time scale of hundreds of milliseconds, but using grating movies instead of simple gratings), revealing that adaptation reorganizes the tuning profile of individual V1 cells rather than passively suppressing responses near the adapting stimulus. Thus, brief adaptation reduces responses on the flank of the tuning curve close to the adapting stimulus (near flank) and increases responses on the flank away from the adapting stimulus (far flank). We analyzed a population of 18 cells, where each cell was adapted within 22.5° of its optimal orientation (Fig. 3B), and found that the changes in near/far-flank responses are statistically significant (P < 0.01, Wilcoxon sign test). In addition to changes in firing rate, brief adaptation induces changes in orientation discriminability on different parts of the neurons' tuning curves. Thus, there was a decrease in the mean orientation discrimination performance, d′ (Green and Swets 1966), on the near flank of the tuning curve (within 34° of the peak) and an increase in the mean discrimination performance on the far flank (within 34° of the peak). Given the hypothesized link between adaptation and synaptic depression in visual cortex, these results raise the possibility that the depression of intracortical synapses could lead to an increase of responses and sensitivity to stimuli that are different from the adapting orientation, which could subsequently cause an improvement in the coding of these stimuli.

Figure 3.

Brief adaptation reorganizes the tuning profile of individual V1 cells. (A) Orientation tuning curves of one representative V1 cell that was adapted for 500 ms to the fixed orientation marked by the gray arrow. Adaptation reduced responses on the flank of the tuning curve close to the adapting stimulus (near flank) and increased responses on the flank away from the adapting stimulus (far flank). (B) The population analysis (n = 18 cells) shows that near flank responses are reduced in magnitude and are less sensitive to changes in orientation (measured as d′). In contrast, far-flank responses are increased in magnitude and more sensitive to changes in orientation. Changes in response magnitude were assessed by averaging responses on the near (within 34° of the cell's peak orientation, including the response to the optimal orientation) and far flank (within 34° of the cell's peak orientation, excluding the response to the optimal orientation), before and after adaptation. Changes in the mean orientation discrimination performance were assessed by averaging the d′ values for each pair of gratings differing in orientation by 11.25° on each flank of the tuning curve (within 34° of the cell's peak orientation). Error bars in all panels represent SEM.

Figure 3.

Brief adaptation reorganizes the tuning profile of individual V1 cells. (A) Orientation tuning curves of one representative V1 cell that was adapted for 500 ms to the fixed orientation marked by the gray arrow. Adaptation reduced responses on the flank of the tuning curve close to the adapting stimulus (near flank) and increased responses on the flank away from the adapting stimulus (far flank). (B) The population analysis (n = 18 cells) shows that near flank responses are reduced in magnitude and are less sensitive to changes in orientation (measured as d′). In contrast, far-flank responses are increased in magnitude and more sensitive to changes in orientation. Changes in response magnitude were assessed by averaging responses on the near (within 34° of the cell's peak orientation, including the response to the optimal orientation) and far flank (within 34° of the cell's peak orientation, excluding the response to the optimal orientation), before and after adaptation. Changes in the mean orientation discrimination performance were assessed by averaging the d′ values for each pair of gratings differing in orientation by 11.25° on each flank of the tuning curve (within 34° of the cell's peak orientation). Error bars in all panels represent SEM.

Selective Adaptation in a Model Network with Asymmetric Synaptic Depression

We further examined the function of asymmetric synaptic depression by constructing a model of recurrent interactions between neurons in the superficial layers of V1 adapting to vertical (feedforward) inputs from neurons in layer 4. We focus on neurons in superficial layers (where most cells are complex) rather than those on layer 4 for the following reasons: 1) the stronger depression of excitatory synapses relative to inhibitory synapses has been reported at intracortical synapses in layers 2–3 (Varela et al. 1999) and in the deep layers of V1 (Galaretta and Hestrin 1998), layers dominated by complex pre- and postsynaptic cells; 2) the neurons exhibiting a far-flank response increase after rapid adaptation (illustrated in Fig. 3) have been recorded in the superficial layers of V1; 3) previous reports of postadaptation far-flank response increase (Dragoi et al. 2000, 2001, 2002) involved recordings mainly performed in superficial and deep layers (although simple cells in layer 4 have also been recorded); 4) neurons in layers 2–3 represent the output of V1, hence their responses could carry information about incoming stimuli that is subsequently used by mid- and high-level visual cortical areas to produce behavioral responses.

We constructed a network representing a hypercolumn of layer 2–3 cells, which consists of 180 excitatory neurons and 48 inhibitory neurons with response dynamics modeled by first-order differential equations (cf. Materials and Methods). Cortical neurons in superficial layers receive relatively sharply tuned feedforward inputs from layer 4 (Douglas et al. 1995; Callaway 1998; simulated using cosine functions) and sharply tuned intracortical inputs from nearby cortical cells (Nelson and Frost 1981; Martin and Whitteridge 1984; Miller 1992; Weliky et al. 1995; Fries et al. 1997). Intracortical synaptic strengths (Fig. 4) were implemented as connection probabilities of larger amplitude and slightly wider orientation spread for inhibitory connections, in agreement with cross-correlation (Toyama et al. 1981; Michalski et al. 1983), intracellular (Tucker and Katz 1998), and laser stimulation (Weliky et al. 1995; Roerig and Chen 2002) studies.

Figure 4.

Spatial profile of intracortical excitatory and inhibitory connection strengths. Excitatory synapses (Wee and Wie) are weaker and narrower than inhibitory synapses (Wei and Wii).

Figure 4.

Spatial profile of intracortical excitatory and inhibitory connection strengths. Excitatory synapses (Wee and Wie) are weaker and narrower than inhibitory synapses (Wei and Wii).

Synaptic depression was implemented as a nonlinear decrease in synaptic strength by using a dynamic process simulating the change in the probability of the synaptic transmitter release with the presynaptic firing rate (see Materials and Methods; see also Tsodyks and Markram 1997; Artun et al. 1998; Dayan and Abbott 2001). We depressed both the feedforward excitatory synapses and intracortical excitatory and inhibitory synapses (in the Discussion section we emphasize that only intracortical synaptic depression is critical for our results). We tested the effects of asymmetric depression (intracortical excitatory synapses depress more strongly than inhibitory synapses) and symmetric depression (intracortical excitatory and inhibitory synapses depress by the same extent).

Figure 5A illustrates that asymmetric synaptic depression causes intracortical synapses to decrease in strength with the increase of the presynaptic firing rates. For intracortical synapses, the maximum reduction of excitatory synapses was ∼55% at 80 Hz (the mean depression across all excitatory synapses was 12%), whereas the maximum reduction of inhibitory synapses was ∼25% at 80 Hz (the mean depression across all inhibitory synapses was 8%). In the case of symmetric depression, all intracortical synapses had a depression profile that matched that of excitatory synapses (Supplementary Fig. 4). Consistent with experimental data (Yoshimura et al. 2000), the depression factor of feedforward synapses was smaller than that of intracortical synapses (by a factor of 2; in the Model Parameters section we vary the strength of feedforward depression and reevaluate our results).

Figure 5.

Adaptation effects in model orientation-selective V1 neurons. (A) Synaptic strength decreases as a function of presynaptic firing rate. The depression factor of excitatory synapses was larger than that of inhibitory synapses. The results in (B)–(H) were obtained after 500 ms of continuous adaptation to a stimulus oriented at 9° (presented at maximum contrast). (B) Relative decrease in synaptic strength after adaptation. For each presynaptic neuron, we computed the mean relative reduction of inhibitory and excitatory synaptic strengths. Red points mark synapses targeting excitatory cells, whereas blue points mark synapses targeting inhibitory cells. The fact that all the points lie above the diagonal indicate that excitatory synapses exhibit stronger depression than inhibitory synapses. (C) Adaptation effects in a representative population of neurons. The adapting stimulus is marked by the red arrow. Postadaptation orientation tuning curves (red) showed a repulsive shift away from the adapting stimulus orientation. Response magnitude decreased on the near flank and increased on the far flank. (D) Changes in preferred orientation after adaptation for the population of cells. The postadaptation repulsive shift in preferred orientation is largest when the adapting stimulus is approximately 10° away from the cell's optimal orientation. The preferred orientation was computed from the responses to the full orientation range (0°–180°) using the vector averaging method (cf. Dragoi et al. 2000, 2001, 2002). (E) Postadaptation change in the excitatory and inhibitory inputs to the cell with preferred orientation 0° in the asymmetric synaptic depression model. The cell is stimulated for 200 ms with 60 equally spaced orientations spanning −90° to +90° (represented on the x-axis), and the steady-state response is represented on the y-axis. The excitatory/inhibitory inputs were computed as the sum of all the weighted excitatory/inhibitory responses that contributed to the cell's membrane voltage. There is a decrease in inhibition and a resultant increase in excitation for stimuli between −50° and −22°, which is the orientation range for which the far-flank responses are increased. (F) Postadaptation change in the excitatory and inhibitory inputs to the cell with preferred orientation 0° in the symmetric synaptic depression model. Whereas excitatory inputs decrease after adaptation, inhibitory inputs remained unchanged. (G) The ratio of the inhibitory and excitatory gain change (ΔGiGe) is significantly greater than 1 only for those input stimuli that cause far-flank response facilitation. Red curve represents the results obtained with the asymmetric depression model; blue curve represents the results obtained with the symmetric depression model. (H) The far-flank response increase of one representative neuron (tuned to 0°) occurs only when the gain change of inhibitory inputs is significantly greater than that of excitatory inputs. Each dot represents the % far-flank response increase after adaptation as a function of the gain ratio ΔGiGe shown in panel G. The far-flank response increase was computed (in steps of 3°) for each stimulus orientation that elicited a positive response from the 0° neuron (orientation range −36° to 36°). The vertical dashed line represents the threshold above which the postadaptation far-flank responses are increased.

Figure 5.

Adaptation effects in model orientation-selective V1 neurons. (A) Synaptic strength decreases as a function of presynaptic firing rate. The depression factor of excitatory synapses was larger than that of inhibitory synapses. The results in (B)–(H) were obtained after 500 ms of continuous adaptation to a stimulus oriented at 9° (presented at maximum contrast). (B) Relative decrease in synaptic strength after adaptation. For each presynaptic neuron, we computed the mean relative reduction of inhibitory and excitatory synaptic strengths. Red points mark synapses targeting excitatory cells, whereas blue points mark synapses targeting inhibitory cells. The fact that all the points lie above the diagonal indicate that excitatory synapses exhibit stronger depression than inhibitory synapses. (C) Adaptation effects in a representative population of neurons. The adapting stimulus is marked by the red arrow. Postadaptation orientation tuning curves (red) showed a repulsive shift away from the adapting stimulus orientation. Response magnitude decreased on the near flank and increased on the far flank. (D) Changes in preferred orientation after adaptation for the population of cells. The postadaptation repulsive shift in preferred orientation is largest when the adapting stimulus is approximately 10° away from the cell's optimal orientation. The preferred orientation was computed from the responses to the full orientation range (0°–180°) using the vector averaging method (cf. Dragoi et al. 2000, 2001, 2002). (E) Postadaptation change in the excitatory and inhibitory inputs to the cell with preferred orientation 0° in the asymmetric synaptic depression model. The cell is stimulated for 200 ms with 60 equally spaced orientations spanning −90° to +90° (represented on the x-axis), and the steady-state response is represented on the y-axis. The excitatory/inhibitory inputs were computed as the sum of all the weighted excitatory/inhibitory responses that contributed to the cell's membrane voltage. There is a decrease in inhibition and a resultant increase in excitation for stimuli between −50° and −22°, which is the orientation range for which the far-flank responses are increased. (F) Postadaptation change in the excitatory and inhibitory inputs to the cell with preferred orientation 0° in the symmetric synaptic depression model. Whereas excitatory inputs decrease after adaptation, inhibitory inputs remained unchanged. (G) The ratio of the inhibitory and excitatory gain change (ΔGiGe) is significantly greater than 1 only for those input stimuli that cause far-flank response facilitation. Red curve represents the results obtained with the asymmetric depression model; blue curve represents the results obtained with the symmetric depression model. (H) The far-flank response increase of one representative neuron (tuned to 0°) occurs only when the gain change of inhibitory inputs is significantly greater than that of excitatory inputs. Each dot represents the % far-flank response increase after adaptation as a function of the gain ratio ΔGiGe shown in panel G. The far-flank response increase was computed (in steps of 3°) for each stimulus orientation that elicited a positive response from the 0° neuron (orientation range −36° to 36°). The vertical dashed line represents the threshold above which the postadaptation far-flank responses are increased.

To assess the effects of asymmetric synaptic depression, we investigated the changes on neuronal responses and sensitivity after 500 ms of adaptation to a high contrast (100%) stimulus of fixed orientation, θa = 9°. Figure 5B shows that after brief adaptation, the strength of inhibitory and excitatory synapses decreased asymmetrically, that is, there was more depression for excitatory synapses (for each neuron, the synaptic strength reduction was computed as the mean depression calculated across all excitatory and inhibitory synapses originating from that neuron). That is, for each presynaptic neuron, excitatory synapses depress more strongly than inhibitory synapses, both for the synapses targeting excitatory and inhibitory neurons.

How does asymmetric synaptic depression affect cortical responses? Figure 5C shows population orientation tuning curves, before and after adaptation. The tuning curves were measured by presenting 60 equally spaced test orientations spanning 0°–180° for 500 ms each. In agreement with experimental data (Dragoi et al. 2000, 2001, 2002), adaptation led to pronounced changes in the orientation tuning curves of individual neurons, that is, pronounced changes in response magnitude and shifts in preferred orientation away from the orientation of the adapting stimulus (we illustrate orientation-selective responses for a representative subpopulation of 12 V1 cells spanning the full orientation range). Indeed, Figure 5D shows that the cells tuned away from the 9° adapting stimulus show a repulsive shift in orientation, that is, an increase in preferred orientation for the cells tuned to orientations greater than 9° and a decrease in preferred orientation for the cells tuned to orientations smaller than 9°. Importantly, the cells tuned to orientations close to the adapting stimulus exhibited the largest postadaptation changes in preferred orientation (cf. Dragoi et al. 2000, 2001, 2002). When the adapting stimulus was at the cell's preferred orientation, there was no change in preferred orientation, but a pronounced decrease in orientation selectivity and a small increase in responses on both flanks (Supplementary Fig. 5). This is in agreement with experimental data (Dragoi et al. 2000, 2001, 2002) reporting that adaptation at the cells' preferred orientation does not alter orientation preference, but significantly reduces orientation selectivity (although found in many cells, the small increase in the distant flank responses after adaptation to a stimulus parallel to the cell's optimal orientation is not a systematic feature).

The asymmetric synaptic depression model captures a key property of rapid adaptation, that is, the fact that neuronal responses on the opposite flank relative to the adapting stimulus (far flank) are increased (Dragoi et al. 2000, 2001, 2002). This feature is indicative of the prominent role of adaptation in actively reorganizing, rather than passively suppressing, stimulus-specific responses in visual cortex (this feature of adaptation has been reported in other sensory cortical areas (Ringo 1996; Ulanovsky et al. 2003) and in slice preparations following repeated electrical stimulation (Eytan et al. 2003). However, this property has been difficult to account for by existing models of cortical function.

Consistent with the predictions of the simplified model (Fig. 2; see also Materials and Methods), we show here that the adaptation-induced differential depression of intracortical synapses leads to specific patterns of excitation and inhibition that cause an increase in responses on the flank of tuning curve away from the adapting stimulus. Indeed, Figure 5C,D illustrates the increase of the far-flank responses for a range of cells (tuned to orientations within the ±50° range) and the postadaptation repulsive shift in orientation preference for the entire population of orientation-selective cells. We explain these results by examining the adaptation-induced changes in total excitatory and inhibitory input to a representative cell (tuned to 0°) as a function of stimulus orientation (within the ±50° range). During adaptation, the excitatory and inhibitory synapses originating from the neuron tuned to the adapting stimulus, that is, 9°, are depressed most strongly. This reduction in synaptic efficacy causes an overall reduction in the total excitatory input to the neurons tuned to orientations close to the adapting stimulus (Fig. 5E). Therefore, stimulating the 0° cell (after adaptation) near its optimal orientation (test stimulus at 0°) yields a strong reduction in excitation (compared with the preadaptation condition), and thus a decrease in response magnitude (this reduction of responses affects the entire population of neurons activated by the 0° stimulus, cf. Supplementary Fig. 6).

However, these suppressive effects are diminished when the test stimulus is oriented away from the adapting orientation (e.g., between −50° and −25°). Indeed, Figure 5E shows that presenting stimuli away from the adapting orientation causes a decrease in local inhibition and an increase in local excitation, which altogether contribute to an enhancement in the cell's response due to disinhibition. These effects occur because synapses originating from the neurons tuned away from the adapting stimulus are depressed less during adaptation (because these presynaptic neurons are only weakly activated by the adapting stimulus). Therefore, the moderate level of depression of these synapses leads to only a small reduction, and even facilitation, of the total excitatory input to the neurons tuned to stimuli away from the adapting orientation (cf. Fig. 5E). This adaptation-induced decrease in inhibition and increase in excitation occurs only when test stimuli are oriented between −50° and −25°, which is exactly the orientation range in which we observe the adaptation-induced response increase on the far flank. In addition, Supplementary Figure 7 shows that the cells in the vicinity of the 0° neuron respond more strongly to the “away” stimuli (e.g., the −30° stimulus) than before adaptation to contribute to an increase in the local excitatory input to the 0° cell.

This asymmetric reduction in local excitation and inhibition resembles the effects illustrated in Figure 2B, which provide the intuition for the effects shown in Figure 5E. Thus, one key prediction of the analytical model is that asymmetric synaptic depression causes response facilitation when the gain change of inhibitory inputs exceeds the gain change of excitatory inputs by a fixed supraunitary threshold (Fig. 2B and Materials and Methods). We thus calculated the postadaptation change in the gain of inhibitory and excitatory inputs for a range of stimulus orientations. We found (Fig. 5G) that the ratio of the inhibitory and excitatory gain change is significantly greater than 1 only for the input stimuli that cause far-flank response facilitation. Indeed, Figure 5H confirms that the far-flank response increases occur only when the gain change of inhibitory inputs is significantly greater than that of excitatory inputs. This demonstrates that, in agreement with the analytical model (Fig. 2C), the reduction in total excitation, combined with a correspondingly larger reduction in total inhibition, yields a postadaptation increase in the responses of neurons when stimuli are presented at orientations away from the adapting stimulus. The increase in responses on the “far flank” is not restricted to the 0° cell, but, as Figure 5C shows, is reliably obtained in a range of cells within 50° of the adapting orientation.

These changes in cortical responses shown in Figure 5C–E are due to the asymmetric depression of intracortical synapses. The symmetric depression model or a model that relies heavily on feedforward depression is unable to generate the full orientation adaptation effects shown in Figure 5C, particularly the far-flank response increase and the repulsive shift in preferred orientation (these issues will be discussed later). For instance, Figure 5F illustrates the total excitatory and inhibitory inputs to the 0° cell in the case of the symmetric depression model. In this case, although the excitatory inputs showed an overall decrease for a broad range of stimulus orientations, there was only a weak decrease in inhibition, hence responses on the far flank were unaltered and the cells' preferred orientation changed only modestly. In addition, we found that the requirement for the far-flank response increase after adaptation, that is, the ratio of the inhibitory and excitatory gain change should be significantly greater than 1, is not satisfied in the case of symmetric synaptic depression (Fig. 5G).

The adaptation effects in Figure 5C–E develop gradually in time. The dynamics of adaptation (Fig. 6A) reveals the time course of the reorganization of cortical responses (illustrated for the representative 0° cell). Thus, as intracortical synapses depress during adaptation, there is a gradual increase of responses on the far flank (−42° to −14° range) and a gradual decrease of responses on the near flank (−14° to 42° range). Correspondingly, both the amplitude of the repulsive shift in preferred orientation and the enhancement of responses on the far flank increase during the time course of adaptation (Fig. 6C). During recovery (no stimulus was presented, Fig. 6B), all synapses return to their preadaptation level causing the excitatory and inhibitory responses to gradually reach their control level. This behavior is due to the fact that during recovery the presynaptic firing rates became zero, and thus the presynaptic factors S(t) were gradually reduced to zero (see Materials and Methods, eqs. 11–12) to cause the synaptic weights to become equal to those before depression. This gradual decrease in synaptic depression corresponds to a gradual decrease in the shift amplitude and far-flank response (Fig. 6D). The gradual increase in the magnitude of the effects induced by the adaptive stimulus, and the gradual decline of the effects during recovery is an important feature of adaptation (Dragoi et al. 2000, 2002).

Figure 6.

Temporal dynamics of adaptation and recovery. (A) Time course of adaptation effects in one representative neuron (tuned to 0°). Response differences (adaptation minus control) are represented throughout stimulus presentation (500 ms). Regions of increased (red) and decreased responses (blue) appeared after approximately 75 ms of adaptation. (B) Time course of recovery from adaptation effects in the neuron tuned to 0°. The recovery process was about 3 times slower than the adaptation process. (C and D) The amplitude of the repulsive shift in preferred orientation and the enhancement of responses on the far flank during adaptation (panel C) and recovery (panel D) for the representative neuron tuned to 0°.

Figure 6.

Temporal dynamics of adaptation and recovery. (A) Time course of adaptation effects in one representative neuron (tuned to 0°). Response differences (adaptation minus control) are represented throughout stimulus presentation (500 ms). Regions of increased (red) and decreased responses (blue) appeared after approximately 75 ms of adaptation. (B) Time course of recovery from adaptation effects in the neuron tuned to 0°. The recovery process was about 3 times slower than the adaptation process. (C and D) The amplitude of the repulsive shift in preferred orientation and the enhancement of responses on the far flank during adaptation (panel C) and recovery (panel D) for the representative neuron tuned to 0°.

Network Behavior

Our results demonstrate that asymmetric synaptic depression during brief adaptation modulates the gain of cortical responses in a stimulus-specific manner. This raises the issue of whether asymmetric synaptic depression is able to generate selective gain control in cortical circuits. Thus, we used the asymmetric depression model to generate predictions about how brief adaptation influences the capacity of the entire network of orientation-selective cells to encode incoming stimuli. In principle, the capacity of individual cells to discriminate stimulus orientation is proportional to the absolute value of the response derivative, which is maximal on the flanks of the orientation tuning curve (see Discussion). For instance, the combined effect of the postadaptation repulsive orientation shift and the increase in responses on the far flank could increase the neuron's capacity to discriminate small changes in orientations away from the adapting orientation (because the slope on the far flank increases after adaptation) and decrease the sensitivity to stimulus orientation on the near flank (Figs 3 and 5C). Indeed, by measuring the slope of individual tuning curves, we found (Fig. 7A–C) that the postadaptation slope increases away from the adapting orientation (on the far flank) and decreases in the nearby of the adapting orientation (on the near flank). Assuming that individual neurons use the flanks of their tuning curves to discriminate orientation, this result advances specific predictions that adaptation should increase the neurons' capacity to distinguish orientations that are different from the adapting stimulus (or infrequent orientations) and decrease the neurons’ capacity to distinguish orientations that are similar to the adapting stimulus (or frequent orientations).

Figure 7.

Changes in neuronal orientation discrimination after adaptation. (A) Changes in tuning curve profile after adaptation. The neuron tuned to −15° was adapted to a stimulus presented at 9° and control orientation tuning curves for the cell with preferred orientation. (B) Tuning curve slope (control and adaptation conditions) for the cell in panel A. The slope was increased on the far flank (around −45°) and decreased on the near flank. (C) Maximum slope of neuronal tuning curves in the control and adaptation conditions. The slope increase was only observed for the asymmetric synaptic depression model, whereas the symmetric depression predicted no change with respect to the control condition. (D) Network orientation discriminability in a simulated task of orientation discrimination for orientation differences of 1°, 1.5°, and 2°. Orientation discriminability was larger after adaptation in the orientation domains in which the slope of the tuning curves exhibited an increase. The increase in orientation discriminability balanced the decrease in discriminability for the cells preferring orientations close to the adapting stimulus. The symmetric depression model predicted no significant change in orientation discriminability after adaptation.

Figure 7.

Changes in neuronal orientation discrimination after adaptation. (A) Changes in tuning curve profile after adaptation. The neuron tuned to −15° was adapted to a stimulus presented at 9° and control orientation tuning curves for the cell with preferred orientation. (B) Tuning curve slope (control and adaptation conditions) for the cell in panel A. The slope was increased on the far flank (around −45°) and decreased on the near flank. (C) Maximum slope of neuronal tuning curves in the control and adaptation conditions. The slope increase was only observed for the asymmetric synaptic depression model, whereas the symmetric depression predicted no change with respect to the control condition. (D) Network orientation discriminability in a simulated task of orientation discrimination for orientation differences of 1°, 1.5°, and 2°. Orientation discriminability was larger after adaptation in the orientation domains in which the slope of the tuning curves exhibited an increase. The increase in orientation discriminability balanced the decrease in discriminability for the cells preferring orientations close to the adapting stimulus. The symmetric depression model predicted no significant change in orientation discriminability after adaptation.

These results raise the issue of whether the capacity of the entire population of cells (e.g., one hypercolumn) to discriminate stimulus orientation is altered by adaptation. We thus used signal detection theory (Green and Swets 1966) to relate the population responses to a performance measure in an orientation discrimination task (using orientation differences of 1°, 1.5°, and 2°). Interestingly, we found that for the orientation range for which the decrease in local inhibition was largest (i.e., between −30° and −60°), adaptation enhances the orientation discriminability of the population response (Fig. 7D). This increase in orientation discriminability away from the adapting orientation was balanced by the decrease in orientation discriminability for stimuli close to the adaptation orientation. At the same time, in contrast with experimental results (Fig. 3), the symmetric synaptic depression model predicted only modest changes in the capacity of population responses to discriminate orientation after adaptation.

Model Parameters

To ensure that the effects described here are not due to particular arrangements of parameters but constitute emergent properties of asymmetric intracortical depression, we varied key parameters controlling the strength of adaptation effects. Thus, we varied the degree of feedforward synaptic depression and the degree of asymmetry between the depression of excitatory and inhibitory intracortical synapses. First, we varied the feedforward depression coefficients (see Supplementary Data), thus altering the degree of depression at vertical synapses from layer 4 to layers 2–3 (while maintaining intracortical depression fixed). We found (Table 1) that reducing feedforward synaptic depression led to an increase in the cells' maximal postadaptation repulsive shifts and far-flank responses, whereas increasing feedforward depression (up to 100%) decreased the cells’ maximal postadaptation repulsive shifts and far-flank responses (but the adaptation effects in single cells remained significant). However, excessively increasing the degree of depression of feedforward synapses (by a factor of 3) virtually abolished the adaptation effects observed in individual cells. Second, we varied the amplitude and orientation spread of the intracortical depression factors that control the degree of depression asymmetry at excitatory and inhibitory synapses (see Supplementary Data). We found (Table 2) that whereas the repulsive shift magnitude and far-flank responses were increased by increasing the depression asymmetry, symmetric synaptic depression (3% in Table 2) virtually eliminated the postadaptation orientation shifts and response changes (see Supplementary Figs 8 and 9). Furthermore, reversing the direction of the asymmetry, that is, stronger depression of inhibitory synapses relative to excitatory synapses, made the postadaptation responses indistinguishable from the preadaptation responses. Third, we assumed that only excitatory intracortical and feedforward synapses depress. Although this maximizes the degree of depression asymmetry at intracortical synapses, we found that, in the absence of depression at inhibitory synapses, adaptation actually decreased the magnitude of the repulsive shifts in preferred orientation by 51%, and did not cause any increase in far-flank responses. This can be explained by the fact that, when neurons are stimulated away from the adapting stimulus, there is a reduction of the degree of disinhibition that maintains responses to preadaptation levels. Fourth, we completely eliminated intracortical synaptic depression and assumed that adaptation relies only on feedforward depression. However, in this case we found that the adaptation effects in individual neurons were insignificant, that is, we obtained orientation shifts of less than 1°, only modest response suppression, and no response facilitation (Supplementary Figs 10 and 11). These results strengthen our hypothesis that intracortical synaptic depression, and its degree of asymmetry, is the major factor responsible for the adaptation-induced response reorganization in V1.

Table 1.

Relationship between the degree of feedforward (layer 4 to layers 2–3) synaptic depression and the strength of adaptation effects

Change in feedforward synaptic depression (%) Change in postadaptation orientation shift (%) Change in postadaptation far-flank response (%) 
−95 13 20 
−66 10 
100 −11 −27 
300 −45 −80 
Change in feedforward synaptic depression (%) Change in postadaptation orientation shift (%) Change in postadaptation far-flank response (%) 
−95 13 20 
−66 10 
100 −11 −27 
300 −45 −80 

Note: The numbers in the first column represent the percentage change in feedforward synaptic depression relative to the situation described in Figure 5. Decreasing feedforward synaptic depression led to an increase in the cells‘ maximal postadaptation repulsive shifts and far-flank responses. Increasing feedforward depression led to a decrease in the cells’ maximal postadaptation repulsive shifts and far flank.

Table 2.

Relationship between the degree of depression asymmetry at intracortical synapses and the strength of adaptation effects

Degree of depression asymmetry at intracortical synapses (exc. vs. inh.) % Change in postadaptation orientation shift (%) Change in postadaptation far-flank response (%) 
100 15 35 
85 14 20 
60 14 
25 −1 −3 
15 −32 −27 
−42 −41 
−6 −52 −46 
−20 −70 −53 
Degree of depression asymmetry at intracortical synapses (exc. vs. inh.) % Change in postadaptation orientation shift (%) Change in postadaptation far-flank response (%) 
100 15 35 
85 14 20 
60 14 
25 −1 −3 
15 −32 −27 
−42 −41 
−6 −52 −46 
−20 −70 −53 

Note: The numbers in the first column represent the percentage change in depression asymmetry relative to the situation described in Figure 7. Increasing the depression asymmetry increases the repulsive shift magnitude and far-flank responses. Symmetric synaptic depression (i.e., 3%) eliminates the postadaptation orientation shifts and response changes. A stronger depression of inhibitory synapses relative to excitatory synapses (negative numbers) abolished the postadaptation changes in preferred orientation and response magnitude.

Other Possible Mechanisms

Although synaptic depression is believed to be the major plasticity phenomenon accompanying adaptation in visual cortex, it is possible that other types of synaptic changes could act to produce activity-dependent shifts in the balance between cortical excitation and inhibition. For instance, it has been shown that certain classes of GABAergic interneurons receive excitatory synapses that exhibit facilitation (Thomson 1997; Markram et al. 1998; Reyes et al. 1998) rather than depression. That is, unlike intracortical pyramid–pyramid synapses that typically depress, it has been shown that a fraction of the pyramid–interneuron synapses actually exhibit activity-dependent facilitation. Although it is unclear that pyramid–interneuron synapses in visual cortex could exhibit facilitation, we nonetheless examined whether synaptic facilitation is consistent with orientation-specific adaptation. We thus altered our V1 model such that a fraction of the excitatory synapses to interneurons exhibited activity-dependent facilitation rather than depression. We found (Fig. 8) that when 30% or less of the excitatory synapses to inhibitory neurons were facilitated, V1 neurons could still exhibit postadaptation changes in responses, that is, a repulsive shift in preferred orientation and an increase of far-flank responses. However, we found that if the majority of pyramid–interneuron synapses are facilitated (which is in fact contrary to experimental evidence, Thomson and Deuchars 1993; Thomson et al. 1993; Thomson 1997), the increase in responses away from the adapting stimulus is abolished, but the repulsive shift in preferred orientation remains unchanged.

Figure 8.

Exploring the strength of adaptation effects using a model that incorporates synaptic facilitation. The x-axis represents the percentage of excitatory synapses to inhibitory neurons that exhibit facilitation. The primary y-axis represents the postadaptation shift in preferred orientation (positive numbers indicate repulsive shifts); the secondary y-axis represents the postadaptation change in far-flank response magnitude. The adapting orientation is 9° and the adaptation effects have been measured in the neuron that showed the maximum postadaptation effects (the neuron tuned to −15°).

Figure 8.

Exploring the strength of adaptation effects using a model that incorporates synaptic facilitation. The x-axis represents the percentage of excitatory synapses to inhibitory neurons that exhibit facilitation. The primary y-axis represents the postadaptation shift in preferred orientation (positive numbers indicate repulsive shifts); the secondary y-axis represents the postadaptation change in far-flank response magnitude. The adapting orientation is 9° and the adaptation effects have been measured in the neuron that showed the maximum postadaptation effects (the neuron tuned to −15°).

Another issue is the differences between the dynamics of different classes of synapses. Thus, whereas several recent studies have failed to reveal significant differences in the short-term plasticity of inhibitory synapses (Thomson et al. 1996; Tamas et al. 1997; Reyes et al. 1998), a fraction of the excitatory intracortical synapses were found to exhibit an initial facilitation followed by depression (Markram and Tsodyks 1996; Thomson 1997; for instance in visual cortex, the excitatory synapses that showed strong initial facilitation were strongly depressed after the first 6–10 stimuli—Varela et al. 1997, 1999). However, changing the kinetics of short-term depression of excitatory synapses to incorporate the initial facilitation is unlikely to change the predictions of our model (because the time scale of the transient synaptic facilitation process is much shorter than the time scale of adaptation). Differences in intrinsic firing properties of excitatory and inhibitory cells are also likely to play a role in modulating the effects of brief adaptation in individual neurons. Thus, pyramidal neuronal firing is known to accommodate, whereas most interneurons do not show accommodation (McCormick et al. 1985). This means that over the time course of stimulus presentation the mean excitatory firing rate will be significantly lower than the mean inhibitory firing rate, which is exactly the prerequisite of the increase in far-flank responses after adaptation. Hence, if anything, neuronal accommodation might have led us to underestimate the actual magnitude of the adaptation effects as it would lead to an amplification of the postadaptation response enhancement and orientation shift magnitude.

Other studies have addressed adaptation effects similar to those discussed here without explicitly incorporating synaptic plasticity mechanisms. For instance, Teich and Qian (2003) used a recurrent model of excitatory neurons to explain the postadaptation repulsive shift in orientation preference. The decrease in population response after adaptation was simulated by appropriately reducing (through bell-shaped windows) both the excitation and inhibition around the orientation of the adapting stimulus, without affecting synaptic strengths. More recently, Compte and Wang (2006) discussed specific network architectures that could result in a shift in orientation tuning curves after adaptation. The effect of adaptation was modeled as a reduction of excitability in the neurons tuned at and around adapting orientation by injecting a biasing hyperpolarizing current to the network (Carandini and Ferster 1997; Sanchez-Vives et al. 2000). Importantly, adaptation was found to generate attractive or repulsive shifts in the neurons' preferred orientation depending on whether recurrent connections are predominantly inhibitory or excitatory. Contrary to this conclusion, we found that large repulsive shifts in orientation preference are obtained in networks with strong recurrent inhibitory connections (see also eq. 3). In addition, the asymmetry between excitation and inhibition is enhanced following exposure to the adapting stimulus due to the fact that inhibitory synapses exhibit weaker depression than excitatory synapses. The differences between the results of our model and those described in Compte and Wang (2006) could be attributed to the difference in the architecture (no inhibitory cells in the Compte and Wang study) and type of synaptic plasticity (synapses are fixed in the Compte and Wang study) employed by the 2 models. Finally, Schwabe and Obermayer (2005) found that adjusting recurrent connections leads to an increase in the tuning curve slopes, a repulsive shift in orientation preference, and a response suppression that leads to an improvement in network discrimination performance. Although the Schwabe and Obermayer model was an optimization model, and therefore lacked a specific synaptic plasticity mechanism, its predictions are consistent with the results shown here.

Discussion

Theories of cortical function have hypothesized that synaptic depression increases neuronal sensitivity to small changes in the firing of its afferents (Abbott et al. 1997), and contributes to cortical response properties, such as frequency-dependent shifts in the temporal phase of V1 responses (Dean and Tolhurst 1986; Reid and Alonso 1995), response decrements at high temporal frequencies in V1 (Kayser et al. 2001), and direction selectivity (Adelson and Bergen 1985; Chance et al. 1998). However, these models have either implicitly assumed that excitatory and inhibitory synapses depress to the same extent, or have focused exclusively on the plasticity of excitatory synapses. Whether the differential depression of excitatory and inhibitory synapses plays any role in cortical computations has remained unknown. Our results indicate that asymmetric intracortical depression regulates network selectivity by amplifying neuronal responses and sensitivity to stimuli occurring infrequently and attenuating responses and sensitivity to stimuli occurring more frequently, as is indeed observed experimentally. This adaptive feature of neuronal responses is fundamental for cortical function as it has been reported both in vitro (Eytan et al. 2003) and in vivo (McCarthy et al. 1997; Dragoi et al. 2000, 2001, 2002;,Ulanovsky et al. 2003) in several cortical areas.

Intracortical Synaptic Depression

The importance of the issues examined here stems from the critical role of synaptic depression for neural computations. Indeed, synaptic depression is known to influence the balance between the strength of local excitatory and inhibitory inputs in a way that controls network behavior (Somers et al. 1995; Ben-Yishai et al. 1995; Tsodyks et al. 1997; Dragoi and Sur 2000) and long-term plasticity (Kirkwood and Bear 1994; Hensch et al. 1998). Balanced excitation and inhibition has been hypothesized to control synaptic strengths in developing networks (Liu 2004; Turrigiano and Nelson 2004) during the critical period of visual development (Desai et al. 2002; Fagiolini and Hensch 2003). In the balanced regime, the depression of excitatory synapses reduces recurrent excitation, whereas the depression of inhibitory synapses reduces recurrent inhibition, to increase the net excitation level such as to maintain high firing rates and stimulus selectivity (Marino et al. 2005). Despite the fact that networks of balanced neurons have been shown to exhibit rich dynamics that allow them to react to afferent inputs on rapid time scales (van Vreeswijk and Sompolinsky 1996), we suggest that the balanced regime may not allow high levels of discrimination performance after adaptation. We propose that asymmetric synaptic depression leads to an unbalanced excitation and inhibition regime that is controlled by the afferent input. Thus, if an oriented stimulus is presented repeatedly, the local excitatory inputs to the neurons tuned to orientations away from the adapting orientation are, on average, stronger than the local inhibitory inputs, whereas the excitatory inputs to the neurons tuned to orientations similar to that of the adapting stimulus are weaker than the inhibitory inputs. These emergent properties of asymmetric synaptic depression regulate network sensitivity to produce selective adaptation. We found that whereas this property arises naturally in V1 networks with asymmetric intracortical synaptic depression, symmetric synaptic depression or mechanisms that depend solely on feedforward depression predict only a mild reduction in responses and sensitivity to the frequent stimuli, without the experimentally observed response enhancement to infrequent stimuli.

Our results rest on the critical assumption that intracortical synapses depress asymmetrically. Intracortical synapses have been shown to exhibit asymmetric depression in vitro in somatosensory and visual cortex (Galaretta and Hestrin 1998; Varela et al. 1999), but in vivo studies reporting intracortical synaptic depression did not differentiate between excitatory and inhibitory synapses (e.g., a recent study has reported strong intracortical depression in visual cortex, but the results are not specific to the synapse type, Reig et al. 2006). Synaptic depression at intracortical synapses is also consistent with a recent in vivo study in visual cortex (Boudreau and Ferster 2005), although another study in somatosensory cortex found only weak intracortical synaptic depression (Chung et al. 2002). An important issue is the extent to which the different types of intracortical synapses depress asymmetrically. There are 4 types of intracortical synapses, that is, excitatory synapses to excitatory neurons and to inhibitory interneurons, and inhibitory synapses to excitatory neurons and to inhibitory interneurons, and 2 types of excitatory feedforward synapses that target excitatory and inhibitory cortical cells. Although most studies do not distinguish between the target of excitatory and inhibitory intracortical synapses (e.g., Dong et al. 2002; Boudreau and Ferster 2005; Reig et al. 2006), the studies revealing the asymmetry of synaptic depression have reported a significant difference between the magnitude of synaptic depression at excitatory-to-excitatory (Galarreta and Hestrin 1998; Varela et al. 1999), and excitatory-to-inhibitory (Galarreta and Hestrin 1998) connections, and the magnitude of synaptic depression at inhibitory-to-excitatory connections (Galarreta and Hestrin 1998; Varela et al. 1999). Although these studies did not specifically investigate the degree of synaptic depression at inhibitory-to-inhibitory synapses, depression mechanisms relying on presynaptic processes would ensure that inhibitory-to-inhibitory synapses would also exhibit weak synaptic depression. With respect to the feedforward synapses from V1 layer 4 to layers 2–3, there is no compelling evidence that the magnitude of depression at excitatory-to-excitatory and excitatory-to-inhibitory synapses would differ (Yoshimura et al. 2000; Chung et al. 2002; Reig et al. 2006)—our model does not differentiate between these 2 types of synapses.

A potential problem for our study is that the extent to which excitatory and inhibitory intracortical synapses undergo depression is not a static feature of synapses, but can change both during development and after variations in environmental factors, such as temperature. For instance, it has been shown that development causes a reduction in the degree of synaptic depression (Varela et al. 1997; Kotak and Sanes 2000), and even a switch from depression to facilitation in many adult synapses (this switch was mainly reported in studies focused on paired-pulse effects, e.g., Reyes and Sakmann 1999). Temperature has also been found to regulate the degree of synaptic depression. Thus, higher temperatures have been typically associated with a reduction of short-term depression (Pyott and Rosenmund 2002; Kushmerick et al. 2006), an increase in the reliability of excitatory synapses (Hardingham and Larkman 1998), and even a switch from short-term depression to short-term facilitation (Klyachko and Stevens 2006—result reported in hippocampal slices). Although the influence of all these factors on the degree of synaptic depression has not been aimed at comparisons between excitatory and inhibitory synapses, it is conceivable, for reasons of stability, that the decreased depression at excitatory synapses observed during development or after temperature increased should be balanced by a decreased depression at inhibitory synapses. However, the age- and temperature-dependent reduction in the degree of synaptic depression may not constitute a problem for our study as the depression levels used in our model are quite modest (on average, there was a 12% reduction in the strength of model excitatory synapses and an 8% reduction in the strength of inhibitory synapses). In addition, we have conducted computer simulations to show that even a significant reduction in the degree of asymmetry between excitatory and inhibitory synaptic depression (Table 2) is unable to completely abolish the adaptation effects discussed here.

It could be argued that asymmetric synaptic depression could change the gain and sensitivity of cortical circuits by influencing not only the strength, but also the delay between excitatory and inhibitory inputs. Delayed, but balanced, excitation and inhibition has been proposed to sharpen cortical responses in time and improve their temporal precision (Wehr and Zador 2003; Higley and Contreras 2006). We have performed computer simulations to examine the relationship between the temporal offset between excitation and inhibition and the strength of adaptation effects. However, because the temporal asynchrony between excitation and inhibition is small relative to the time course of synaptic depression, we found only small differences in the time course of adaptation, but not in the steady-state shift in preferred orientation or in the postadaptation far-flank response increase. Nonetheless, our study does not exclude the possibility that by differentially reducing the strength of excitatory and inhibitory synapses, adaptation could reduce the delay between excitatory and inhibitory inputs to limit the window available for temporal summation of spikes, and thereby increase the temporal precision of cortical neurons.

Repulsive Shifts in Orientation Preference

An emergent property of our model is the fact that rapid adaptation shifts the neurons' preferred orientation away from the adapting stimulus (repulsive shift). Whereas repulsive shifts have been reported in V1 not only in relation to orientation adaptation, but also following spatial frequency (Movshon and Lennie 1979; Saul and Cynader 1989a) and temporal frequency (Saul and Cynader 1989b) adaptation, they appear to be underrepresented in extrastriate areas. For instance, it has recently been reported (Kohn and Movshon 2004) that MT neurons exhibit tuning shifts toward the adapted direction (attractive shift). Despite the fact that the key variable in our study, that is, asymmetric synaptic depression, is inconsistent with postadaptation attractive shifts in tuning, we examined whether there are specific combinations of parameters that would generate attractive shifts.

We found that whereas the shift in preferred orientation was relatively insensitive to changes in the balance between local excitation and inhibition, changing the strength of synaptic depression was able to alter the sign and magnitude of the shift. Specifically, reducing the degree of asymmetry of the depression of intracortical excitatory and inhibitory synapses decreased the magnitude of the repulsive shift, while symmetric synaptic depression was associated with small attractive shifts (<3°; Supplementary Figs 8 and 9). Furthermore, if the asymmetry of synaptic depression was reversed such as to favor the depression of inhibitory synapses, V1 neurons exhibited small (<1°), but highly variable, attractive shifts after adaptation. Importantly, we found that abolishing intracortical synaptic depression and increasing the depression of feedforward synapses led also to attractive shifts (<2.5°). Altogether, these results demonstrate that our key assumptions are entirely consistent with postadaptation repulsive shifts in V1. In addition, our results raise the possibility that (small) attractive shifts in extrastriate cortex may be generated in networks with strong feedforward depression or in those for which intracortical synaptic depression is symmetric.

Model Limitations

One of our important results is that asymmetric synaptic depression controls the postadaptation network discrimination performance. This result has been obtained by assuming that the network discrimination performance depends exclusively on the shape of the neurons' orientation tuning curves, and that V1 neurons fire independently (i.e., the noise in the responses of nearby neurons is uncorrelated). In reality, the noise across a population of cortical cells is not independent, but exhibits correlations. The issue of whether noise correlations impact the network discrimination performance can be addressed by computing Fisher information, which is a measure of network efficiency, using the distribution of population responses to a specific stimulus and taking into account the distribution of pairwise correlations (Abbott and Dayan 1999; Sompolinsky et al. 2001). For instance, it has been shown that an increase in neuronal correlations could decrease the network discrimination performance despite an increase in the slope of the neurons’ tuning curves (Sompolinsky et al. 2001; Series et al. 2004). In particular, recurrent mechanisms, such as those used in our study, that lead to tuning curve sharpening have been shown to be detrimental for stimulus coding due to an increase in noise correlations relative to feedforward mechanisms (Series et al. 2004). One limitation of our model is that it does not allow us to extract information about neuronal correlations, and this limits our ability to assess whether adaptation would change the structure of noise correlations to influence the network discrimination performance. However, preliminary evidence in our lab (Gutnisky and Dragoi 2006) indicates that rapid adaptation decreases interneuronal correlations. The decrease in correlations, along with the orientation-specific enhancements in the tuning curve slopes reported here, can be combined to improve the efficiency of population coding.

Conclusions

Our results indicate that a key property of cortical circuits, such as the ability to selectively adapt to changes in incoming stimuli, arises as an emergent property of interactions between excitatory and inhibitory neurons in the context of their local circuit. These results have potentially broad implications for selective adaptation in other sensory systems, such as auditory and somatosensory cortex, as these systems rely on similar types of circuits as those analyzed here. Only one assumption is critical, that is, the more prominent depression of excitatory intracortical synapses relative to inhibitory synapses. Although this asymmetry has been known for a while, its role for cortical function has always been unclear. We found that asymmetric synaptic depression causes cortical circuits to operate in an unbalanced fashion in which the responses and sensitivity of individual neurons to infrequent stimuli are enhanced, whereas neuronal responses and sensitivity to frequent stimuli are suppressed. These postadaptation changes in cortical responses and sensitivity can possibly improve the population code by creating representations of incoming stimuli that can be efficiently decoded by downstream neurons in order to increase the accuracy of behavioral responses. For instance, adaptive representations could play an important role during natural viewing when V1 neurons are rapidly exposed to image sequences during successive visual fixations (Dragoi and Sur 2006). Our results suggest that V1 networks involved in stimulus processing during fixation would reduce their sensitivity to subsequent familiar stimuli and increase their sensitivity to new stimuli. This could constitute an efficient, metabolically inexpensive, mechanism through which downstream neurons could rapidly identify novel stimuli while reducing their sensitivity to familiar, redundant, stimuli.

Supplementary Material

Supplementary material can be found at: http://www.cercor.oxfordjournals.org/.

We thank Harel Shouval for comments on the manuscript. Supported by the Pew Scholars Program and the James S. McDonnell Foundation (V.D.). Conflict of Interest: None declared.

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