Department of Neuroscience, Brown University, Providence, RI 02912, , 1 Department of Neurobiology, University of Pittsburgh, Pittsburgh, PA 15261 and , 2 Department of Psychology, Queens College, Flushing, NY 11367, USA
Address correspondence to David J. Pinto, Box 1953, Department of Neuroscience, Brown University, Providence, RI 02912, USA. Email: dpinto{at}bu.edu.
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Abstract |
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Introduction |
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An extensive network of interconnected excitatory neurons represents a positive feedback system that can confer highly non-linear transforming properties onto the constituent circuits. Accordingly, considerable theoretical attention has been directed toward understanding the role of positive feedback in the processing of afferent signals by layer IV circuitry. A number of computational models have incorporated these and other common elements of cortical circuitry into a canonical microcircuit. Previous models of cat visual cortical circuitry, for example, employ positive feedback provided by recurrent excitatory connections to enhance response selectivity by amplifying responses to thalamic inputs associated with preferred stimuli (Douglas et al., 1989, 1995
; Douglas and Martin, 1991
; Ben-Yishai et al., 1995
; Somers et al., 1995
; Suarez et al., 1995
; Adorjan et al., 1999
) [reviewed by Ferster and Miller (Ferster and Miller, 2000
)].
Here we examine the role of local intracortical connections in another experimentally well-characterized system, the thalamocortical circuit that processes tactile information from facial whiskers in rodents. Layer IV of the primary somatosensory cortex contains whisker-related clusters of synaptically interconnected neurons, called barrels, that receive the vast majority of their inputs from corresponding groups of neurons in the thalamus, called barreloids (Woolsey and Van der Loos, 1970; Chmielowska et al., 1989
). Physiologically, both thalamic and cortical neurons respond robustly, yet somewhat differently, to relatively simple sensory stimuli in the form of individual whisker deflections (Simons and Carvell, 1989
). In this paper, we review differences in thalamic and cortical receptive field properties that define the thalamocortical response transformation. We then describe how essential principles of barrel organization are implemented in two computational models. Simulation results confirm the sufficiency of these principles in explaining barrel neuron responses and, further, provide an avenue for in-depth analysis of the circuits function.
As in visual cortical circuits, responses of layer IV barrel neurons appear to be determined by the temporal interplay between direct thalamocortical excitation and strong, locally generated cortical inhibition (Miller et al., 2001). In particular, we find that strong feedforward and feedback inhibition render the net effect of intracortical connections damping, in contrast to models of the canonical microcircuit. Recurrent excitation contributes prominently to cortical response selectivity, however, by enabling responses evoked by preferred stimuli to withstand momentarily the pervasive effects of intra-barrel inhibition. These dynamics render both simulated and real barrel circuits highly sensitive to the firing synchrony of thalamic barreloid neurons, a property which may distinguish processing by damping versus amplifying circuitry.
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What Do Barrels Do? |
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Layer IV of rodent somatosensory cortex contains anatomically distinct neuronal aggregates, called barrels, that correspond in one-to-one fashion with individual whiskers on the rats face (Woolsey and Van der Loos, 1970; Welker 1971
). Barrels contain at least two principal neuronal populations, excitatory spiny neurons and inhibitory smooth neurons. The two populations are synaptically connected reciprocally to each other and recurrently to themselves. Both receive afferent input from thalamocortical neurons (White, 1989
; Keller, 1995
). Neurons within a barrel are also related functionally in that each responds most robustly to deflection of the same principal whisker (PW) [for review see (Simons, 1997
; Miller et al., 2001
)].
To understand the transformation of receptive fields between thalamus and cortex in the whisker system, Simons and Carvell (Simons and Carvell, 1989) examined the responses of three types of neurons to the same ramp-and-hold whisker deflection stimuli (Fig. 1
). The three populations included thalamic input neurons and both regular and fast spike neurons in the cortical barrel (Simons, 1978
); the latter are believed to correspond to spiny excitatory and smooth inhibitory neurons, respectively. Figure 1a
presents a schematic of the whisker deflections used in their study. Figure 1bd
show peristimulus time histograms (PSTHs) from representative excitatory (b), inhibitory (c) and thalamic (d) neurons generated in response to 40 stimulus repetitions. In each case, the center PSTH shows the neurons response to PW deflection while the surrounding PSTHs show responses to deflections of each of the four immediately adjacent whiskers (AWs) followed 20 ms later by deflection of the PW.
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Based on these findings as well as a number of anatomical and functional results reported by others, Simons and Carvell (Simons and Carvell, 1989) hypothesized that the thalamocortical response transformation (RFT1RFT4) results from processing within a single cortical barrel and emerges from four principles of barrel organization. First, individual excitatory and inhibitory barrel neurons differ in their nonlinear intrinsic response properties. For instance, inhibitory barrel neurons are able to discharge at high frequencies (McCormick et al., 1985
) and are thought to respond more linearly to input as compared to excitatory neurons (Angulo et al., 1999
). Second, thalamic neurons send convergent monosynaptic input onto both excitatory and inhibitory barrel neurons (White, 1978
; Agmon and Connors, 1991
; Swadlow and Gustev, 2000). Third, there is a network of synaptic connections among and between barrel neurons of both types (Gibson et al., 2000; Petersen and Sakmann, 2001
) [for review see (Miller et al., 2001
)]. Fourth, inhibitory neurons are more responsive to input than excitatory neurons (Simons, 1978
; Swadlow, 1995
; McCasland and Hibbard, 1997
). A major goal of the analysis presented below is to explain how the thalamocortical response transformation (RFT1RFT4) emerges from these four principles.
Computational Modeling
To test the hypothesis of Simons and Carvell, Kyriazi and Simons (Kyriazi and Simons, 1993) constructed a computational model of a whisker barrel based on the above four principles of barrel organization (Fig. 2a
). The model consists of 100 barrel neurons, 70 excitatory (Vek) and 30 inhibitory (Vik). Each neuron is represented as a leaky linear integrator that describes membrane voltage. Figure 2c
presents the equation describing the membrane voltage of an excitatory neuron; the equation for inhibitory neurons is similar. The generation of action potentials is governed in stochastic fashion using nonlinear voltage-to-firing rate probability functions Pe(V), Pi(V). Both the firing rate functions and time constants are distinct for each of the two populations; the voltage-to-firing rate function is more linear for inhibitory versus excitatory neurons and the synaptic decay time constant for excitation (
e) is faster than for inhibition (
i) (see Appendix). Membrane voltages are determined by the spatial and temporal summation of synaptic events received from thalamic input neurons and from other excitatory and inhibitory neurons in the network. The ratio of excitatory to inhibitory neurons, the number of synapses received by each neuron (i.e. convergence: ec, ic, tc) and the relative strength of each type of synapse is based on estimates made from previously published light and electron microscopy studies [summarized by White (White, 1989
); see also Keller (Keller, 1995
)]. In the model, the mean strength of thalamic synapses onto inhibitory neurons (wti) is set greater than that onto excitatory neurons (wte), and the mean strength of inhibitory synapses (wie, wii) is set greater than that of excitatory synapses (wee,wei). Both factors contribute to the dominance of inhibition in the barrel circuit and, as described in the analysis below, both play major roles in the decoding of thalamic input signals by barrel circuitry.
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Beginning from the model of Kyriazi and Simons, Pinto et al. (Pinto et al., 1996) derive a reduced computational model of the same system (Fig. 2b
). A major goal of the reduced model is to incorporate the same principles of barrel organization within a minimal computational framework while retaining the capacity for both qualitative and quantitative comparisons with real data. Rather than representing activity of individual neurons, the equations of the reduced model describe the average activity in the excitatory and inhibitory cortical populations, reducing the system from over 100 equations to only two. Figure 2d
presents the equation describing activity in the excitatory population; the equation for the inhibitory population is similar (see Appendix). Parameter values that do not come directly from the derivation are adjusted, as with the full model, so that simulated responses match quantitatively a small subset of responses from the real system, particularly the ON and OFF response magnitudes. Thalamic input to the reduced model takes the form of population responses accumulated from the entire set of pre-recorded thalamic neurons (PSTH). The responses of the reduced model match quantitatively those of both the full model and real barrel populations. Importantly, as detailed below, the simple form of the reduced model allows for an analytic investigation of how the response transformation occurs that is not possible with the full model.
Experimental Predictions and Validation
Both the full and reduced barrel models lead to numerous insights and specific predictions regarding the mechanisms of barrel processing. For instance, both models represent activity within a single cortical barrel yet capture all four aspects of the thalamocortical response transformation, including the emergence of strong surround inhibition. This is consistent with the hypothesis of Simons and Carvell (Simons and Carvell, 1989) that surround inhibition results from strong AW activation of inhibitory but not excitatory neurons within a single barrel and does not require horizontal interactions between neighboring barrels. This hypothesis was tested experimentally in a study by Goldreich et al. (Goldreich et al., 1999
) in which ablation of the barrel corresponding to an AW has no effect on the level of surround inhibition in the barrel corresponding to the PW.
Another prediction arises from examining ON versus OFF responses in both real and simulated systems. Figure 3a presents population PSTHs of responses to whisker deflection onset and offset from both thalamic neurons and excitatory barrel neurons. Differences between the population ON and OFF response in cortex are probably due to some difference between those same responses in thalamus. One possibility is that barrel circuitry is sensitive to the slightly larger magnitude of the thalamic ON versus OFF response and responds by enhancing the difference in total spike count. A second possibility is that barrel circuitry is sensitive to the change in initial firing synchrony, i.e. faster onset rate, of the thalamic ON versus OFF response and responds by transforming this difference in population response timing into a difference in response magnitude.
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To test the prediction experimentally, Pinto et al. (Pinto et al., 2000) examined responses of excitatory barrel neurons and thalamic neurons to whisker deflections having different velocities and amplitudes. These stimuli were used because they were found to evoke thalamic responses that varied in both timing and magnitude. Greater whisker deflection velocities evoke thalamic population responses having markedly faster onset rates, while thalamic population response magnitude increases slightly with either deflection velocity or amplitude. The early phase of thalamic local field potentials (LFPs), which presumably reflect synchronous firing among thalamic neurons, display a similar sensitivity to deflection velocity (Temereanca et al., 2000
). Thalamic population responses reflect those of trigeminal ganglion neurons which also encode deflection velocity in terms of their initial firing rates (Shoykhet et al., 2000
). Importantly, this temporal code for velocity is transformed by cortical circuitry, for the first time in the whisker-barrel pathway, into a code based on response magnitude. That is, increasing deflection velocities evoke abrupt increases in firing synchrony among thalamic neurons and, consistent with the models prediction, increasing response magnitudes from the cortical barrel. Changes in deflection amplitude do not affect thalamic firing synchrony and hence evoke only small changes in the cortical response.
The sensitivity of the cortical response to thalamic input timing is a robust feature of barrel processing. Figure 4 presents experimental response data from both thalamus and cortex obtained using a variety of whisker deflection protocols, including deflection onsets of different velocities and amplitudes, PW and AW deflection onsets, short and long plateau deflection offsets, and the initial response to sinusoidal deflections at different frequencies. The data were collected from experiments performed by five sets of investigators over the past 12 years (Simons and Carvell, 1989
; Kyriazi et al., 1994
; Hartings 2000
; Pinto et al., 2000
; Bruno and Simons, 2001
). Cortical responses are quantified in terms of response magnitude, and thalamic responses are quantified in terms of either response magnitude (Fig. 4a
) or the initial change in firing synchrony (Fig. 4b
). Response magnitude is measured as the average number of spikes occurring within a 25 ms response window, and the change in firing synchrony is measured as the initial onset slope of the population PSTH [i.e. TC40, see Appendix and Pinto et al. (Pinto et al., 2000
) for details]. Experimental methods are summarized in Appendix.
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Importantly, these results suggest a different approach to the study of neural coding than those based on quantifying the information contained in neural spike trains (Rieke et al., 1997). In our data, both thalamic response magnitude and timing carry information about ON versus OFF whisker deflections (Fig. 4
, open symbols). However, it is the processing mechanisms of the circuit receiving the signal (i.e. barrels) that determine which aspects of thalamic activity are most salient (i.e. timing), not consideration of which aspect may contain the most information.
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How Do Barrels Work? |
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Our model of barrel function is intentionally constrained to thalamic and cortical responses that are localized both in time (2025 ms) and space (a single barrel), and is based on experiments involving relatively simple stimuli. Our goal is to establish a foundation upon which to build an understanding of responses to more complex and natural stimuli. Longer-lasting responses are likely also to require consideration of short-term synaptic modification (Abbott et al. 1997; Gil et al., 1997
) and corticothalamic feedback (Yuan et al., 1986
; Deschenes et al., 1998
), in addition to the local circuit dynamics explored here. Responses in laminae other than layer IV are explored below.
Phase Plane Analysis of Barrel Responses
An advantage of the simple form of the reduced model is that the networks dynamics can be understood visually using a state diagram called a phase plane (Fig. 5). On the phase plane, the state of the network at each given moment is defined as the level of activity in the excitatory (E) and inhibitory (I) populations, represented on the x-and y-axes respectively. For each possible state, the values of dE/dt and dI/dt (Fig. 2d
) quantify the combined influence of intracortical connections and thalamic input on activity in the excitatory and inhibitory populations, respectively. Because the barrels output is generally represented by activity in the excitatory population (E), we use the color axis on the phase plane to present values of dE/dt. States in which activity in the excitatory population is increasing (dE/dt > 0, e.g. red region) are separated from states in which it is decreasing (dE/dt < 0, e.g. blue region) by the line of zero change called the excitatory nullcline (red-brown line). The inhibitory nullcline is defined similarly (gray line). The intersection of the two nullclines (dE/dt = dI/dt = 0) corresponds to the steady-state or resting level of activity in the network.
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To understand the models sensitivity to thalamic input timing, we first examine the response to a change in thalamic activity that occurs gradually over several seconds. In the limit, this is equivalent to evaluating the networks steady-state response to different levels of tonic input (cf. Fig. 7c). Figure 5a
presents overlaid excitatory and inhibitory nullclines from the phaseplane with low and high levels of tonic thalamic activity. As the tonic level of thalamic input increases, the inhibitory nullcline shifts upward to a greater extent than the excitatory nullcline so that their intersection moves upward and to the left. This corresponds to a cortical resting state with less excitatory but more inhibitory activity (i.e. inhibitory tone). Intuitively, this occurs because (i) feedforward inhibition (ti) is stronger than feedforward excitation (te), and (ii) inhibitory neurons are more responsive to weak input than excitatory neurons. If the change in thalamic activity is sufficiently slow, the networks state will track the nullclines intersection almost perfectly until both arrive at the new resting level (red arrow). The effect of dominant feedforward inhibition in the barrel system has been verified experimentally in that increased tonic activity in the thalamus is accompanied by increased tonic activity among inhibitory barrel neurons; tonic activity among excitatory barrel neurons, already low, is relatively unchanged (Brumberg et al., 1996
). Conversely, trimming the eight surrounding whiskers in behaving rats decreases activity levels in the thalamus and, as a result of disinhibition, increases activity among excitatory neurons of the cortical barrel corresponding to the spared central whisker (Kelly et al., 1999
).
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Beginning from the initial rest state, thalamic input shifts the nullclines upward. The networks state is then below the nullclines, where thalamic input and network dynamics act to increase activity in both excitatory and inhibitory populations (dE/dt > 0, dI/dt > 0). For the slowly rising input, the networks state remains relatively close to the nullclines so that activity in both populations is subject to little change (dE/dt 0, dI/dt
0) (Fig. 5d
, panel i). However, because feedforward inhibition is strong (hence the inhibitory nullcline shifts upward further), inhibition increases to a greater extent than excitation. As a result, the response trajectory quickly overtakes the excitatory nullcline (Fig. 5d
, panel ii), placing the network in a state where activity in the excitatory population is diminishing. When the peak level of thalamic input finally arrives (Fig. 5d
, panel iii), the network is already dominated by inhibition (dE/dt < 0, I > 0), precluding a strong excitatory response.
For the rapidly rising input, the nullclines rise swiftly, placing the networks state far from the nullclines (Fig. 5e, panel ii). Note that the rate of increase in excitatory activity (dE/dt) grows exponentially with the distance of the networks state from the excitatory nullcline, reflecting the nonlinear effects of recurrent excitation. Thus, in contrast to the slowly rising input, the networks state encounters regions on the phase plane where activity is strongly increasing under the influence of recurrent excitation (dE/dt >> 0). This is because, for the rapidly rising input, the peak level of thalamic input arrives early, when inhibition is still near background levels, and the momentary absence of strong inhibition enables the development of a large excitatory response (Fig. 5e
, panel ii). Activity in the inhibitory population also increases due to thalamic input and now also in response to the effects of recurrent excitation (via ei) (Fig. 5e
, panels i,ii). Thus, the rapidly rising input evokes the strongest response from both the excitatory and inhibitory populations. Eventually, the trajectory overtakes the excitatory nullcline (Fig. 5e
, panel ii), and the response tracks the nullclines intersection back to the original rest state (panels iiiv).
These and other analyses (see Pinto et al., 1996) lead to the following description of how the circuit works. In response to a preferred stimulus, e.g. deflection of the PW, many thalamic neurons discharge at least one spike at short latency. This is represented in the thalamic population PSTH as a rapidly rising increase in activity. Excitatory barrel neurons respond to the synchronous input (Fig. 5e
, panel i), and reinforce each others activity nonlinearly (dE/dt > 0) via positive feedback provided by recurrent excitation (ee). Within a few milliseconds, the non-linear increase in activity is transferred, via ei connections, to the inhibitory population (Fig. 5e
, panel ii), which otherwise responds relatively linearly to thalamic input signals (via ti). Now powerfully engaged by both thalamic and local excitatory populations, intrabarrel inhibition overwhelms the excitatory response (via ie) and forces the network back to its rest state (Fig. 5e
, panels iiiv). Thus, even if individual thalamic neurons fire only a single spike to a stimulus, their population effects on barrel neurons can be powerful and rapid, provided that many thalamic neurons fire synchronously and early. On the other hand, when thalamic spikes are temporally dispersed, e.g. following deflections of an AW, the strongly responsive inhibitory cells are more likely to fire than the less responsive excitatory cells. Early on, inhibition dominates the circuit (Fig. 5d
, panel i), strongly limiting all responses to later arriving thalamic spikes, regardless of their synchrony or number (e.g. Fig. 5d
, panels iiiii).
Thus it is the strength of feedforward inhibition and the greater responsiveness of inhibitory neurons to weak, asynchronous inputs that establishes the circuits sensitivity to input timing. The dominance of inhibition allows only a brief window of opportunity for synchronous thalamic inputs to engage positive feedback mechanisms within the barrel circuit, enabling the development of an excitatory response that can momentarily withstand the effects of strong feedforward and feedback inhibition. The circuits sensitivity to input timing is further illustrated in Figure 5c, which presents overlaid final panels of responses on the phase plane to a series of input triangles, all having the same magnitude but systematically varied in rate of onset.
Thalamocortical Response Transformation
The phase plane effectively illustrates how the thalamocortical response transformation emerges from the four principles of barrel organization described above. First, the intrinsic nonlinearities distinct to each of the two populations define the shape and orientation of the excitatory and inhibitory nullclines and contribute to the rate at which each population responds to thalamic input. Second, monosynaptic thalamic input onto both populations contributes to the motion of the nullclines over the course of the input signal. Third, the network of synaptic connections among and between the populations contributes to the spatial relationship between the two nullclines and to the sign and value of dE/dt and dI/dt throughout phase space. Fourth, the responsiveness of inhibitory neurons contributes to the topology of phase space and establishes the dominance of feedforward and feedback inhibition.
The mechanism that accounts for the models sensitivity to rapidly versus slowly rising inputs is sufficient to explain all aspects of the thalamocortical response transformation as defined previously. For instance, the larger ON versus OFF (RFT2) and the larger PW versus AW (RFT3) responses can both be explained directly in terms of the barrels sensitivity to input timing. ON and PW deflections generate rapidly rising population thalamic inputs, whereas OFF and AW deflections generate slowly rising thalamic inputs. At the extreme, as seen in Figure 5a,d, very slowly changing inputs evoke inhibition but little excitation. This is precisely what is observed experimentally for the AW and other deflections that evoke temporally dispersed thalamic responses, as shown in Figure 4b
(see also Fig. 1
). The same mechanism accounts for the low level of background activity among excitatory barrel neurons as explained above (RFT1). Interestingly, these results imply that (i) the spatial focusing of excitatory receptive fields between thalamus and cortex results from the barrels sensitivity to input timing, and (ii) distinguishing a low-velocity PW deflection from a high-velocity AW deflection (for example) should require integration of information from more than a single barrel-related cortical column, perhaps in the superficial or deep cortical layers (see below).
The emergence of surround inhibition (RFT4) can also be understood in terms of strong feedforward inhibition. Intuitively, as described above for the slowly rising input, AW deflections evoke inhibitory activity in the cortex that effectively suppresses subsequent responses to PW deflections. Moreover, the model also suggests that the strength of surround inhibition should depend on the interval between the AW and PW deflections, which is precisely what is found experimentally (Simons and Carvell, 1989).
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Recurrent Excitation in Damping Networks |
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The distinction between damping and amplification may have important implications for a circuits operational characteristics. For instance, data from both visual (Sclar and Freeman, 1982; Skottun et al., 1987
) and somatosensory (Brumberg et al., 1996
) cortex suggest that real cortical circuits maintain their sensitivities to preferred versus non-preferred stimuli over a wide range of signal-to-background ratios. Responses presented in Figure 6c
demonstrate that the sensitivity of simulated barrel responses to input timing are also relatively unaffected by increased levels of thalamic background activity. This is because strong network inhibition suppresses the excitatory populations response to tonic input (see Fig. 5a
), endowing the circuit with an intrinsic mechanism for contrast-gain control.
The equations of the reduced barrel model represent an excitable system (see Appendix). With different parameter values, an excitable system can be made to function as a damper, like the barrel circuit, or as an amplifier. One way to effect this change is to decrease the strength of feedforward inhibition (ti) relative to feedforward excitation (te). In particular, Figure 7a shows that changing the balance of feedforward inhibition over excitation (ti/te) shifts the network from functioning as a damper, in which removing network connections results in larger responses, to an amplifier, in which removing network connections results in smaller responses. The effect is further illustrated on the phase plane, presented in Figure 7b
, which shows excitatory and inhibitory nullclines resulting from low and high levels of tonic thalamic activity, respectively. In comparison with Figure 5a
, however, feedforward excitation (te) is set to be stronger than feedforward inhibition (ti). This causes the excitatory nullcline to rise farther than the inhibitory nullcline so that their intersection moves upward and to the right, resulting in a cortical resting state with more excitatory background activity. Correspondingly, as shown in Figure 7c
, amplifying circuits respond strongly to increased levels of thalamic background activity. Beyond a certain point, in fact, amplifying circuits can become unstable and behave as intrinsic oscillators. The responsiveness of amplifying circuits to tonic input leads to response saturation and a loss of tuning (i.e. an iceberg effect; data not shown) which has proven a challenge for many models of visual cortex to overcome [reviewed by Ferster and Miller (Ferster and Miller, 2000
)].
Figure 7d presents data suggesting that amplifying circuits may have opposite sensitivities to input timing versus magnitude as damping circuits. In particular, using simulated thalamic input triangles, as in Figure 3c
, the responses of the amplifying circuits we tested were highly sensitive to the magnitude of thalamic input but insensitive to the onset rate. This is also consistent with the inability of amplifiers to suppress tonic input as described above.
Further analysis is required for a complete characterization of the functional differences between dampers and amplifiers (see Appendix). However, the response properties presented in Figure 7 are typical for all of the amplifier circuits we examined. Moreover, these data suggest an experimental means by which to identify circuits operating as either dampers or amplifiers. In particular, damping circuits are sensitive to input timing while amplifiers are sensitive to input magnitude. In barrel cortex, the experimentally verified sensitivity to input timing described above, coupled with strong functional and anatomical evidence for the dominance of feedforward inhibition, suggests that barrels function as cortical damping circuits.
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Transformations in the Barrel-related Column |
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The transformation of thalamic signals by barrel circuitry in layer IV provides a basis for understanding response transformations in other circuits within the barrel-related column. In layer IV, barrels are separated by cell-sparse zones called septa. Septal neurons participate in circuits independent from those of barrels, forming synaptic connections in layer IV largely with other septal neurons (Kim and Ebner, 1999). The response properties of septal neurons are similar to those of thalamic neurons (Brumberg et al., 1999
). Interestingly, septal neuron response properties can be captured qualitatively by the reduced model if intracortical connection strengths are reduced by half (data not shown).
In layers superficial to the barrels (layers II/III), excitatory neurons exhibit prolonged responses to both ON and OFF whisker deflections (Brumberg et al., 1999), possibly reflecting a high density of NMDA synapses (Monoghan and Cotman, 1985
; Rema and Ebner, 1996
). Neurons deep to the barrel layer (layers V/VI) often exhibit more complex and dynamic response properties; some are activated only when particular whiskers are deflected in a unique sequence (Simons, 1985
) and/or exhibit multiwhisker receptive fields that evolve over tens of milli-seconds [reviewed by Ghazanfar and Nicolelis (Ghazanfar and Nicolelis, 2001
)]. Neurons in both the superficial and deep layers exhibit multiwhisker receptive fields (Simons, 1985
; Brumberg et al., 1999
), possibly reflecting the convergence of signals from multiple barrels (Chapin, 1986
).
Evidence suggests that processing within the barrel-related column occurs along both serial and parallel pathways. Signals from the thalamus arrive simultaneously in both barrels and septa, and are processed independently within the two networks. Outputs from layer IV converge onto multiple networks in the superficial and deep layers (see below), although the neurons of layer V also receive some direct thalamic input (Agmon and Connors, 1991; Gil et al., 1999
). This processing model is consistent with response latency measurements in which thalamic activation evokes responses first in layer IV, followed by deep and then superficial cortical layers (Carvell and Simons, 1988
; Moore and Nelson, 1998
; Brumberg et al., 1999
).
Multiple Codes in the Cortical Column?
The damping dynamics of the barrel circuit render it more sensitive to the timing of thalamic input than to thalamic input magnitude. Thus, even though information about whisker deflection parameters (e.g. AW versus PW) is contained in both the timing and magnitude of the thalamic response, it is only the former that is decoded by barrel circuitry. Stated differently, the saliency of an afferent code is determined by the dynamics of the circuitry that receives it. In this regard it may be significant that information about whisker deflection parameters is represented in the output of excitatory barrel neurons by at least three codes: population firing synchrony, population response magnitude and response magnitude of individual neurons (Pinto et al., 2000). The multiplicity of codes generated by barrel circuitry suggests that there may be multiple circuits elsewhere in the cortical column, each sensitive to a different code contained in the barrels output.
Is there evidence for such circuits? The response properties of excitatory barrel neurons are consistently more homogeneous than those of neurons in the thalamus (Simons and Carvell, 1989; Kyriazi et al., 1994
; Brumberg et al., 1996
, 1999
; Pinto et al., 2000
). This homogeneity probably reflects the convergence of common input from the thalamus and the strong influence that barrel neurons have on each others activity by means of their shared circuitry. In contrast, the response properties of neurons in both superficial and deep layers are markedly more heterogeneous than those in the layer IV barrel (Simons, 1978
, 1985
; Kyriazi et al., 1998
; Brumberg et al., 1999
). In part, this reflects the more diverse thalamic, columnar, and long-distance corticocortical inputs to these layers (Harvey, 1980
; Crandall et al., 1986
; Grieve and Sillito, 1995
). It also suggests, however, the existence of multiple, anatomically intermingled circuits, each having distinct inputs, distinct shared circuits and distinct outputs. Determining how these circuits work will require an understanding not only of their inputs, from the barrels and elsewhere, but also of their intrinsic dynamics.
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Appendix |
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Details of the experimental methods have been described previously and were similar for all studies from which data were obtained (Simons and Carvell, 1989; Kyriazi et al., 1994
; Hartings, 2000
; Pinto et al., 2000
; Bruno and Simons, 2001
). Briefly, adult female rats (SpragueDawley strain) were anesthetized for surgical procedures using either Halothane or pentobarbital sodium (Nembutal). Following surgery, anesthesia was discontinued for neuronal recordings, rats were lightly narcotized and sedated by steady infusion of fentanyl (Sublimaze, Janssen Pharmaceuticals; 510 µg/kg/h), immobilized with gallamine and/or pancuronium bromide, and artificially respired using a positive pressure respirator. Extracellular single-unit recordings were obtained from either cortical barrel or thalamic ventroposterior medial nucleus neurons using either glass micropipettes filled with 3 M NaCl (Simons and Land, 1987
) or tungsten microelectrodes. The standard stimulus deflection waveform was a ramp-and-hold trapezoid producing a 1 mm deflection of 200 ms duration with onset and offset velocities of 135 mm/s. This stimulus was used to determine the units preferred direction, i.e. the angle evoking the most spikes, by deflecting the whisker in eight directions spanning 360° in 45° increments.
In Figure 4, the ON and short plateau OFF data (open symbols) are averaged from 64 thalamic neurons and 68 excitatory cortical neurons in response to all eight deflection angles of the PW using the standard stimulus (Kyriazi et al., 1994
). The long plateau OFF response (closed circle) was obtained similarly, but with a deflection plateau of 1400 ms duration (Kyriazi et al., 1994
). The AW data (closed diamond) were averaged from 42 thalamic and 33 excitatory cortical neurons in response to deflection onset of an AW in the units best direction using the standard stimulus (Simons and Carvell, 1989
; Bruno and Simons, 2001
). The velocity and amplitude data were averaged from 63 thalamic neurons and 40 excitatory cortical neurons in response to deflection onset of the PW in both the preferred direction (down triangles) and caudally (up triangles). The standard stimulus was modified to produce whisker deflections that varied over five velocities (210, 170, 145, 130, 70 mm/s) and three amplitudes (7.4°/650 µm, 4.5°/390 µm, 2.6°/225 µm) (Pinto et al., 2000
). The sine wave frequency data (squares) were averaged from 22 excitatory cortical neurons and 27 thalamic neurons in response to deflection of the PW in the preferred direction using sinusoidal waveforms with a peak deflection amplitude of 1 mm and frequencies of 4, 8, 10, 12, 16, 20, 30 and 40 Hz; responses beyond the first quarter-cycle (i.e. the initial rise) were not considered in the present study (Hartings. 2000
).
Analysis of Experimental Data
Spike data were accumulated into PSTHs with a binwidth of 100 µs and summed over each sampled population. Responses were measured from spikes occurring within a 25 ms response window beginning with the initial rise above baseline of the population response. Two response measures were calculated. Response magnitude is measured as the average number of spikes comprising the PSTH over the 25 ms response window. The initial change in firing synchrony is calculated as 40% of the response magnitude divided by the time required to generate the first 40% of the response; this approximates the initial slope of the population PSTH (TC40) [further details are given by Pinto et al. (Pinto et al., 2000)].
Modeling and Analysis
Details of the reduced model and its construction have been previously described (Pinto et al., 1996). Activity in the excitatory (E) and inhibitory (I) population is computed according to the following equations, which are similar in form to those described by Wilson and Cowan (Wilson and Cowan, 1972
):
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Differences in parameter values from those previously published (Pinto et al., 1996) reflect the exclusion of refractory terms from the WilsonCowan formulation and the use of a fourth-order RungeKutta method to solve the equations numerically. In the reduced model, the time constant for the excitatory population is set shorter than for the inhibitory population, which may appear to contradict the fact that inhibitory neurons are known to have faster membrane time constants (McCormick et al., 1985
; Gibson et al., 1999
). However, the formulation of the equations indicates that
e and
i represent synaptic decay rates, not membrane time constants [reviewed by Ermentrout (Ermentrout, 1998
)].
Thalamic population inputs (T) were either simulated or constructed from PSTHs obtained previously from in vivo single-unit recordings of thalamic neurons (Simons and Carvell, 1989; Kyriazi et al., 1994
). Simulated inputs consist of input triangles with a 15 ms base and background firing rates of 0.04 spikes/ms unless otherwise specified. Input triangles varied in times-to-peak from 1 to 10 ms, with heights as specified in the figure legends. The triangles onset rate is calculated as the height divided by the time-to-peak. Experimentally obtained PSTHs were synaptically filtered using the following equation to generate a measure of thalamic synaptic drive compatible with the variables E and I (Pinto et al., 1996
):
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Phase planes and simulated response measures were obtained numerically using the XPP (G. Bard Ermentrout, www.pitt.edu/phase) and Maple VR5 (Waterloo Software, Ontario, Canada) software packages. On the phase plane, activity is represented in units of synaptic drive. Otherwise, response magnitudes are measured in spikes/stimulus, the integral of the firing rate in the excitatory population (Pe) over the duration of the evoked response. Fixed durations were established to allow sufficient time for activity to return to rest (25 ms for the damper, 50 ms for the amplifier). Interestingly, phase plane analysis suggests that the reduced model is a Type II excitable system (Rinzel and Ermentrout, 1998
), and that inputs are either damped or amplified depending on whether they evoke sub- or suprathreshold responses from the circuit. In the context of the barrel system, suprathreshold events, which consist of self-sustained responses often lasting hundreds of milliseconds, may represent epileptiform discharges that occur in diseased or injured states producing hyperexcitable tissue.
The reduced model, input files, parameter sets and phase plane animations are available at the Barrels Web online (http://www.neurobio.pitt.edu/barrels).
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Footnotes |
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Acknowledgments |
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References |
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