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J Neurophysiol 95: 331-341, 2006. First published September 28, 2005; doi:10.1152/jn.00063.2005
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Using Potassium Currents to Solve Signal-to-Noise Problems in Inhibitory Feedforward Networks of the Striatum

J. Hellgren Kotaleski1, D. Plenz2 and K. T. Blackwell3

1School of Computer Science and Communication, Royal Institute of Technology, Stockholm, Sweden; 2Unit of Neural Network Physiology, Laboratory of Systems Neuroscience, National Institute of Mental Health, National Institutes of Health, Bethesda, Maryland; and 3School of Computational Sciences and the Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia

Submitted 19 January 2005; accepted in final form 20 September 2005


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Fast-spiking (FS) interneurons provide the main route of feedforward inhibition from cortex to spiny projection neurons in the striatum. A steep current-firing frequency curve and a dense local axonal arbor suggest that even small excitatory inputs could translate into powerful feedforward inhibition, although such an arrangement is also sensitive to amplification of spurious synaptic inputs. We show that a transient potassium (KA) current allows the FS interneuron to strike a balance between sensitivity to correlated input and robustness to noise, thereby increasing its signal-to-noise ratio (SNR). First, a compartmental FS neuron model was created to match experimental data from striatal FS interneurons in cortex–striatum–substantia nigra organotypic cultures. Densities of sodium, delayed rectifier, and KA channels were optimized to replicate responses to somatic current injection. Spontaneous {alpha}-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and {gamma}-aminobutyric acid (GABA) synaptic currents were adjusted to the experimentally measured amplitude, rise time, and interevent interval histograms. Second, two additional adjustments were required to emulate the remaining experimental observations. GABA channels were localized closer to the soma than AMPA channels to match the synaptic population reversal potential. Correlation among inputs was required to produce the observed firing rate during up-states. In this final model, KA channels were essential for suppressing down-state spikes while allowing reliable spike generation during up-states. This mechanism was particularly important under conditions of high dopamine. Our results suggest that KA channels allow FS interneurons to operate without a decrease in SNR during conditions of increased dopamine, as occurs in response to reward or anticipated reward.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
The striatum is vital for the proper execution and selection of behavior, and disturbances in striatal dynamics give rise to both motor and cognitive disorders (Brown and Marsden 1990Go; DeLong 1990Go; Tekin and Cummings 2002Go). Of particular interest for our understanding of striatal dynamics is how striatal neurons integrate cortical inputs and participate in local striatal signal processing. In particular, periods of increased synaptic activity depolarize striatal spiny projection (SP) neurons into an "up-state," which is the only time during which action potentials are generated (Wilson and Kawaguchi 1996Go). Although considerable attention has been given to how intrinsic properties of striatal neurons control up-states (e.g., Gruber et al. 2003Go; Nisenbaum et al. 1996Go; Wilson 1993Go; Wilson and Kawaguchi 1996Go), experimental findings on local synaptic transmission in the striatum (Blackwell et al. 2003Go; Czubako and Plenz 2002Go; Guzman et al. 2003Go; Koos and Tepper 1999Go, 2002Go; Koos et al. 2004Go; Plenz and Kitai 1998Go; Taverna et al. 2004Go; Tunstall et al. 2002Go) suggest that GABAergic circuits also play a fundamental role in modulating the spiking of SP neurons, which are the output neurons of the striatum (Plenz 2003Go; Tepper et al. 2004Go).

A major source of GABAergic synaptic input to SP neurons is from the fast-spiking (FS) interneuron, through its dense, local axonal arbor (Kawaguchi 1993Go; Kawaguchi et al. 1995Go). FS interneurons receive glutamatergic inputs from corticostriatal projection neurons; thus they provide feedforward inhibition to striatal neurons (Koos and Tepper 1999Go; Plenz and Kitai 1998Go). In addition, FS interneurons receive GABAergic inputs from striatal interneurons and globus pallidus (GP) neurons. Despite the relatively small population of FS interneurons (1–5%; Kita 1993Go), they may profoundly influence striatal activity because of their ability to fire at high rates (Berke et al. 2004Go; Koos and Tepper 1999Go; Nisenbaum and Berger 1992Go; Plenz and Aertsen 1996Go), dense axonal arborization and preferential innervation of SP neuron somata (Bennett and Bolam 1994Go; Kubota and Kawaguchi 2000Go).

These properties of FS interneurons suggest that small input signals may be translated into powerful inhibition; however, such an arrangement is also sensitive to "noise" such as spurious synaptic inputs. This feedforward inhibitory circuit may require some filter mechanism that prevents irregular activation by a few random cortical inputs. Otherwise, inadvertent FS interneuron action potentials may suppress SP neuron firing, counteracting the selection mechanism of spiny projection neurons for cortical inputs, or disrupting the precise timing of action potentials that control dendritic calcium dynamics (Carter and Sabatini 2004Go; Kerr and Plenz 2002Go, 2004Go).

Sensitivity to spurious synaptic inputs can be suppressed in several ways. For example, a very negative resting potential, as seen in spiny projection neurons, requires multiple synaptic inputs to coincide in time (spatial integration) to depolarize the neuron to spike threshold. Such a mechanism is unlikely to work in FS interneurons because their resting potential is closer to spike threshold. Alternatively, a KA current necessitates multiple synaptic inputs over a more prolonged time period (temporal integration). FS interneurons exhibit a delay in spike generation in response to depolarization, which is suggestive of a KA current (found in fast-spiking interneurons of the neocortex; Goldberg et al. 2003aGo,bGo). In the present study, we use a computer model of an FS interneuron to assess the effect of KA currents on the selectivity of FS interneurons, by comparing spike generation during the up-state to spike generation during the down-state. The latter is representative of the sensitivity to spurious synaptic inputs because down-states represent periods of low synaptic activity. We assessed the robustness of the effect to changes in intrinsic excitability and inhibitory synaptic inputs, as modulated by dopamine (Bracci et al. 2002Go; Centonze et al. 2003Go; Nicola et al. 2000Go).


    METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Model

The compartmental model of an FS interneuron was created using the GENESIS simulation software (http://www.genesis-sim.org/GENESIS/) running on the Redhat Linux operating system. First, the morphology and passive properties were adjusted. Second, the voltage-dependent channels were included (Table 1). Third, synaptic channels and input spike trains were incorporated (Tables 2 and 3).). Model responses to current injection and statistics of synaptic inputs were highly constrained by experimental measurements of synaptic inputs (Table 4).


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TABLE 1. Equations for intrinsic currents

 

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TABLE 2. Densities of ion channel conductances in the different compartments

 

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TABLE 3. Synaptic currents modeled

 

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TABLE 4. Comparison between model and experimental data

 
MORPHOLOGY. The branching structure of the fast-spiking interneuron is a prototype of the morphology revealed by biocytin reconstructions in the acute slice (Kawaguchi 1993Go) and organotypic cultures (Plenz and Kitai 1998Go). The morphology contains three primary branches, six secondary branches, and 12 tertiary branches (Fig. 1 A), each subdivided into multiple, isopotential compartments (membrane resistivity = 20,000 {Omega}cm2; axial resistivity = 300 {Omega}cm; membrane capacitance = 0.7 µF/cm2). These passive properties were modified from commonly accepted values (Major et al. 1994Go; Spruston et al. 1994Go) to reproduce the input resistance and time constants previously measured (Blackwell et al. 2003Go). This branching structure was sufficient to reproduce the effect of electrotonic properties on distributed synaptic inputs (Fig. 1, B and C).



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FIG. 1. Morphology, passive properties, and voltage-dependent currents of fast-spiking (FS) interneuron model reproduce experimentally measured IV curves. A: morphology of FS interneuron. Soma (20 µm length x 15 µm diameter) has 3 primary dendrites, 90 x 1.0 µm (length x diameter). Each primary branch bifurcates to form secondary branches of 148 x 0.75 µm (length x diameter). Each secondary branch bifurcates to form tertiary branches of 240 x 0.5 µm (length x diameter). Each branch is subdivided into compartments no more than 0.1 x the length constant, resulting in a total of 127 compartments for the cell. B: distribution of spike latencies for FS neurons (open squares) and model neuron (solid circle). C: fI curve for FS neurons and model neuron.

 
VOLTAGE-GATED CHANNELS. Action potentials were generated by the fast sodium current and delayed rectifier (Kv3.1/3.2 and Kv1.3) potassium currents in the soma (Erisir et al. 1999Go). Although transient potassium currents have not yet been identified in striatal FS neurons, a transient potassium current was included in the soma and primary dendrite compartments on the basis of the experimentally observed spike latency (Blackwell et al. 2003Go; Kawaguchi 1993Go; Koos and Tepper 2002Go), which is defined as the time between current injection and the first spike. The voltage dependency was modified from that of transient potassium currents in spiny projection neurons (Akins et al. 1990Go; Nisenbaum et al. 1996Go; Tkatch et al. 2000Go) to produce the spike latency observed in experimental data (Blackwell et al. 2003Go). Maximal conductance of these three voltage-dependent channels was optimized, using the simulated annealing routines in GENESIS, to produce spike latency, spike threshold, and frequency–current (fI) relationship similar to that measured in FS interneurons in vitro (Fig. 1, B and C; Blackwell et al. 2003Go). Note that the lack of an axon hillock and initial segment necessitates a high channel density for action potential initiation.

SYNAPTIC INPUTS. {alpha}-Amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) glutamatergic (Gotz et al. 1997Go; Jahn et al. 1998Go; Stefani et al. 1998Go) and GABAergic (Salin and Prince 1996Go) synaptic channels were placed in the soma and dendrite compartments, resulting in 254 evenly distributed synaptic inputs. Each channel was activated by an independent Poisson-distributed input train. As described in RESULTS, this spatial distribution was corrected to better match characteristics of FS interneurons in triple co-cultures. The interspike interval (ISI) of each of the 254 down-state Poisson trains was adjusted to 9 s (frequency 0.11 Hz) to reproduce the experimentally observed down-state intersynaptic event interval (IEI) distribution for the population. The maximal synaptic conductance and distribution of the channels was adjusted to produce the same amplitude and rise time distribution measured experimentally (Blackwell et al. 2003Go). Table 4 illustrates that the mean amplitude, rise time, and interevent interval in the FS interneuron model are within the range found experimentally for synaptic inputs to FS interneurons in co-culture. In addition, simulated postsynaptic potentials (PSPs) had the same skewed distribution as found experimentally (Fig. 2, A and B).



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FIG. 2. Synaptic characteristics of FS interneuron model were similar to experimentally measured values (Blackwell et al. 2003Go). A: histogram of postsynaptic current (PSC) amplitude from simulated neuron (solid line), and cell FS07102 (dashed line); simulated counts were scaled by 2 for comparison with measurements. B: histogram of interevent interval of postsynaptic potentials (PSPs) from simulated neuron (solid line) and cell FS07051 (dashed line). C: spikes per up-state is correlated with up-state reversal potential (R2 = 0.92).

 
Up-states were generated as transient periods of high synaptic input frequency of all AMPA and {gamma}-aminobutyric acid (GABA) synapses. Each of the 254 up-state Poisson trains had an ISI of 0.5 s (2 Hz), compatible with experimental measurements (Blackwell et al. 2003Go), and activated the same set of synapses as the down-state Poisson trains. The duration of the up-states ranged from 50 to 400 ms (the range observed experimentally); down-state duration was set to 300 ms.

Most simulations were performed in current clamp using a time step of 0.01 ms. Additional voltage-clamp simulations were performed at potentials between –70 and –20 mV using an up-state of 200-ms duration to determine the reversal potential of the up-state charge. These simulations used a time step of 0.001 ms. Results were based on simulations of 200 up-states and down-states, each with a different set of synaptic inputs.

Signal-to-noise analysis

Ideally, signal-to-noise ratio (SNR) is quantified as spike rate in response to signal divided by spike rate in response to noise; however, in the striatum, signal synaptic inputs are not discriminable from noise synaptic inputs. Thus under the assumption that important information is transmitted to the globus pallidus by the striatum during up-states, all up-state spikes are defined as signal spikes. Spikes during down-states (periods of low-frequency synaptic inputs) are used as surrogates for noise spikes. The number of noise spikes often was zero, making signal-to-noise ratio (SNR) undefined; therefore the SNR calculation was modified to be the ratio of up-state spikes to total spikes.

The number of up-state spikes and the number of down-state spikes were measured for each combination of down-state activity, gKA, and up-state duration. The effect of these parameters on spike rates during both up-states and down-states was evaluated using the procedure LOGISTIC (which performs logistic regression on data with a limited number of ordinal response values) and GLM (which evaluates general linear models) in the statistical software SAS (SAS Institute, Gary, NC).


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
This study addresses the issue of synaptic integration and the control of action potential generation. Recent in vivo findings show that neurons receive hundreds to thousands of inputs, producing up-states during which action potentials are generated. The present study uses theoretical techniques to address questions regarding synaptic inputs and action potential generation. In the first section, the development of a model highly constrained by electrophysiological data reveals some properties of synaptic inputs. In the second section, simulations evaluate the effect of the KA current on synaptic integration. In the third section, the interaction of dopamine and KA currents is addressed.

Adjustment of population synaptic inputs and spike generation during up-states

In the absence of precise anatomical data on synaptic inputs to striatal FS interneurons, we used electrophysiological data on spontaneous synaptic inputs during up-states in conjunction with model development to evaluate different distributions of synaptic inputs. Two characteristics were used simultaneously to constrain the distribution of synaptic inputs in the FS interneuron model. One characteristic was the up-state synaptic population reversal potential in FS interneurons, which ranged from –33 to –45 mV in triple cocultures (after correction for junction potential of 14 mV) (Blackwell et al. 2003Go). The second characteristic used to constrain model synaptic input characteristics was mean number of spikes per up-state. Although a bimodal membrane potential distribution is not as prominent in FS neurons as in SP neurons (Plenz and Kitai 1998Go), FS neurons alternate between low synaptic activity states and high synaptic activity states. Furthermore, the high synaptic activity states are simultaneous with SP neuron up-states (n = 4, Plenz and Kitai 1998Go; n = 2, Blackwell et al. 2003Go). Using synaptic activity as the indicator of up- and down-states, we calculate that the number of spikes per down-state was 0, compared with a mean of 0.82 spikes per up-state (range of 0–2.25, n = 6 FS interneurons). In addition, the number of spikes per up-state was highly correlated with the PSC reversal potential (Fig. 2C, R2 = 0.92, n = 4 FS interneurons).

The experimentally measured reversal potential was considerably lower than the –30 mV in the model with AMPA and GABA synapses evenly distributed. To lower the simulated reversal potential, GABA synaptic inputs from tertiary branches were redistributed evenly among the soma and both primary and secondary dendritic branches. This spatial distribution, motivated by the spatial gradient of GABAergic inputs measured in hippocampal fast-spiking interneurons (Pettit and Augustine 2000Go), produced a simulated reversal potential of –43 mV, which is within the range measured experimentally (Fig. 3).



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FIG. 3. Reversal potential depends on distribution of synapses. A: simulated up-states in voltage clamp at potentials between –30 and –60 mV to demonstrate reversal of clamp current from inward to outward at a holding potential near –40 mV. Current is clearly inward at –60 mV, outward at –30 mV, and is a mixture of inward and outward at –40 mV. This pattern is similar to that observed experimentally (Blackwell et al. 2003Go). B: mean up-state current vs. holding potential for equal distribution (solid line), or {gamma}-aminobutyric acid (GABA) redistributed toward soma (dashed line), the latter of which had a reversal potential of –43 mV, within the range of measured up-state reversal potentials (circles). Redistributing the synaptic inputs lowers the reversal potential by about 12 mV.

 
Placing GABA synapses close to the soma rescued the reversal potential, but resulted in spontaneous spiking during up-states less frequently than measured experimentally (Fig. 4, A and C, mean rate = 0.17 per up-state). Several adjustments were possible to produce an increase in up-state spikes. One possibility was to increase the amount of glutamate current, either by an increase in frequency or amplitude of synaptic inputs. However, this type of solution raised the synaptic population reversal potential and thus was not acceptable. An alternative was to increase the correlation among the synaptic inputs as demonstrated by paired intracellular recordings (Plenz and Kitai 1998Go; Stern et al. 1998Go). Correlation was increased among all synaptic inputs, both GABA and AMPA, by activating randomly chosen inputs with the same Poisson spike trains (Rudolph and Destexhe 2001Go). The correlation parameter c is given by the equation Ns = N + {surd}c(1 N), where Ns is the number of independent Poisson spike trains and N is the total number of synapses. This results in each spike train being assigned to approximately N/Ns synapses. As observed in Fig. 4, A and B, the increase in membrane potential fluctuations that accompanied the increase in correlation produced an increase in spike rate (mean rate = 0.35 spikes per up-state at correlation = 0.49, Ns/N = 0.3). The resulting spike rate is closer to the values observed experimentally (Fig. 4C); moreover, the correlation is similar to values used for synaptic inputs to cortical neurons (Rudolph and Destexhe 2001Go).



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FIG. 4. Simulating the experimentally observed rate of up-state spiking required correlation among spike trains. A: change in up-state spike rate vs. correlation. B: sample of up-state spike rate for uncorrelated (c = 0.0) and correlated (c = 0.5) Poisson input spike trains. Correlation parameter, c = f(N) [Ns = N + {surd}c(1 – N)], where Ns is number of independent Poisson spike trains and N is the number of synapses (Rudolph and Destexhe 2001Go). C: sample of up-state spiking from data collected in Blackwell et al. (2003)Go, cell FS07102, which had a mean spikes-per-up-state of 0.62. D: expanded view of a simulated (left) and experimental (right) up-state. Selected up-states are indicated with * in B and C.

 
These simulations imply that, given the experimental constraints of reversal potential and spontaneous firing rate during the up-state, GABA synaptic inputs are preferentially located close to the soma and a modest correlation among all synaptic inputs is required during up-states.

Transient potassium currents increase signal-to-noise ratio

This optimized model, which replicates properties of up- and down-states of FS interneurons in triple cultures, was used to investigate the role of the KA current and background noise on signal processing. Specifically, we addressed how the delay to spike initiation, as produced by typical KA currents, influenced the SNR under different amounts of background activity. The role of the KA current was assessed quantitatively by performing simulations with the KA conductance (gKA) adjusted 20% higher and 20 or 40% lower than the control value. SNR is calculated as the ratio of up-state spikes to the sum of down-state and up-state spikes. To evaluate the effect of down-state activity, simulations were performed with a down-state Poisson train having frequencies of 0.012, 0.037, 0.11 (default), 0.33, and 1 Hz. Although spikes during the down-state do not influence firing of spiny projection neurons, down-state spikes are representative of the sensitivity to spurious synaptic inputs.

As noise was increased from 0.1 to 1 Hz, both up-state and down-state spike rates increased significantly, at all values of gKA (Tables 5 and 6; Figs. 5 and 6, B and C). The number of up-state spikes doubled, but the number of down-state spikes increased severalfold. The relative sensitivity of up-states and down-states to noise was captured in the SNR curves (Fig. 6A), which demonstrate that SNR decreases at high noise. Figure 6A also demonstrates that high gKA is particularly important at high noise levels. The average up-state spike rate (the number of spikes divided by the up-state duration) increased as gKA decreased at all noise levels (Figs. 5 and 6B). In contrast during the down-state, the change in spike rate with gKA was seen only for higher noise levels (Figs. 5 and 6C). Therefore the increase in down-state spike rate with noise was particularly prominent at lower gKA. The sensitivity to noise and gKA was the same for up-state durations from 50 to 400 ms, which covers the range of experimentally observed values in vitro (Blackwell et al. 2003Go; Table 4) and in vivo (Stern et al. 1998Go). These results demonstrate that KA is important because it increases SNR at high noise levels.


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TABLE 5. Results of statistical analysis evaluating the effect of noise and gKA on spike production for both down-states and several different up-state durations

 

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TABLE 6. Effect of duration on up-state spike rate (number of spikes divided by duration) was assessed using general linear models

 


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FIG. 5. Effect of noise and gKA on spiking during up-states. Simulated traces of membrane potential for (A) gKA = 100% and (B) gKA = 80% of control values. Black traces show responses with noise frequency = 0.11 Hz (ISI = 9 s), the default value. Red traces show responses to high noise, frequency = 1 Hz (ISI = 1 s). Same random pattern of up-state synaptic inputs are repeated for each condition. C: up-states are created with an increase in synaptic inputs. With down-state activity in the middle of the experimentally measured frequencies (noise frequency = 0.11 Hz), approximately half of the 200-ms duration up-states produce action potentials, and no down-state spikes are observed. When the down-state activity is increased (noise frequency = 1 Hz), the number of up-state spikes increases. When gKA is reduced to 80% of its control value, there is also a small increase in the number of down-state spikes (indicated by *).

 


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FIG. 6. Effect of noise and gKA on (A) signal-to-noise ratio (SNR), defined as up-state spike rate/(up-state spike rate + down-state spike rate); (B) up-state spike rate; and (C) down-state spike rate.

 
To demonstrate that properties attributed to the KA current do not arise from a general decrease in potassium currents, simulations were repeated in models with 80% gKA and a compensatory increase in the Kv3.1/3.2 conductance. The compensatory value was determined by using the simulated annealing parameter optimization routine, which adjusted the Kv3.1/3.2 conductance to produce the best match to the experimentally measured fI curves. This increase in the Kv3.1/3.2 current did not compensate for the decrease in the gKA value in terms of effect on SNR. Thus the ability to suppress down-state and up-state spikes is specific to the KA current.

The ability of the KA current to suppress down-state spikes was robust to variation in unconstrained parameters. High values of gKA prevented an increase in down-state spikes in FS model neurons in which 1) synaptic inputs were uncorrelated, 2) GABA and AMPA synapses were evenly distributed, and 3) PSCs had slower rise times and decay times. Thus the result is not contingent on particular characteristics of synaptic inputs.

N-Methyl-D-aspartate (NMDA) currents were not included in the original model because the NMDA contribution is very small in FS interneurons in the cortex and because the linear relationship between up-state charge and holding potential (Blackwell et al. 2003Go) also suggests that the NMDA contribution is small in striatal FS interneurons. Nonetheless, robustness of our results was further explored with additional simulations performed in two additional models with NMDA channels. In one model, the addition of NMDA currents with a distribution similar to the AMPA channels decreased, but did not eliminate, the correlation needed to produce spiking during up-state periods. In a second model, with both NMDA channels and KA channels in all dendritic compartments, inclusion of KA channels on distal dendrites counteracted the effect of NMDA channels on excitability. In both of these models, the presence of NMDA channels did not change the role of KA currents in improving SNR: both models exhibit higher SNR with higher values of gKA.

KA currents increase SNR during high levels of dopamine

Neuromodulation, especially that produced by dopamine, is an important aspect of striatal function (Gruber et al. 2003Go; Nicola et al. 2000Go). Dopamine release is increased in response to reward (Schultz 2002Go), and dopamine modifies the characteristics of FS interneurons (Bracci et al. 2002Go), producing a small depolarization and decreasing the amplitude of GABA synaptic inputs. The effect of dopamine on the model was simulated as a 2-mV depolarization (produced by increasing the leak reversal potential) and a 20% reduction in amplitude of all GABA synaptic conductances (Centonze et al. 2003Go). This effect of dopamine caused a decrease in the SNR (Fig. 7 A) for higher noise values. The reduced SNR is attributed to an increase in down-state spike frequency seen at higher noise levels. Dopamine also produced a 1-Hz increase in up-state spike frequency at the control value of gKA and a 2-Hz increase in up-state spike frequency with gKA = 80%, although this had little effect on SNR. The decrease in SNR was smaller for gKA = 100%, showing that gKA minimizes the reduction in SNR during times of elevated dopamine. These results demonstrate that multiple factors influence a neuron's function. Under low noise or low dopamine conditions, a reduced gKA may be optimal, but under high dopamine conditions, a larger value of gKA may be needed for suppressing spikes in response to spurious synaptic inputs.



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FIG. 7. Sensitivity to noise (A) and change in input frequency (B) during simulated dopamine modulation of FS interneuron model (+2 mV depolarization, GABA reduced to 80%). A: SNR as a function of noise frequency. B: sensitivity of output spike rate to change in up-state frequency. Down-state frequency is held constant at the control value; up-state frequency is the ratio indicated on the abscissa times the down-state frequency of 0.11 Hz. Slope of this curve, calculated using linear regression, is greatest for gKA = 80% of control and under conditions of increased dopamine.

 
The SNR analysis evaluates sensitivity of the FS interneuron model to noise at a single up-state (signal) input frequency. A different aspect of information processing is sensitivity to changes in input frequency for a given noise level; in other words, how well can FS interneurons detect a change in cortical activity level. A large change in output spike rate in response to a change in input frequency indicates high sensitivity. Thus the effect of gKA and dopamine was evaluated for up-state input frequencies ranging from 1 to 8 Hz, while keeping the down-state frequency constant at the control value of around 0.1 Hz. This set of up-state input frequencies yielded ratios of up-state to down-state synaptic frequency from 10 to 80, which encompassed the experimentally observed range of 11 to 72 (Blackwell et al. 2003Go). Figure 7B illustrates the FS interneuron output spike rate as a function of up-state input frequencies. Either a reduction in gKA or the presence of dopamine increased the sensitivity of the FS interneuron to changes in synaptic input frequency during the up-state.

In summary, in the FS interneuron the control level of gKA conveys robustness to down-state synaptic inputs (noise), whereas the increase in dopamine increases sensitivity to changes in up-state synaptic inputs (signal).


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
We developed a compartmental model of a striatal fast-spiking interneuron to investigate whether synaptic inputs during the down-state adversely affect signal detection during up-states. Furthermore, we examined how up-state firing is controlled by transient potassium currents that produce delays in action potential generation in response to depolarization. Key features of the model, such as morphology, intrinsic currents, and synaptic currents, were matched to experimentally obtained data from cortex–striatum–substantia nigra cultures. Overall, results showed that the KA current serves an important role to enhance signal detection by suppressing action potentials in response to synaptic noise. Thus this study quantitatively tested and confirmed previously proposed ideas on the role of the KA current (Nisenbaum and Wilson 1995Go; Wilson 1995Go).

Reproducing the experimentally observed spike latency and high firing frequency required inclusion of three different potassium channels in the model. Equations for the two delayed rectifier currents were those describing Kv3.1/3.2 and Kv1.3 currents in fast-spiking interneurons of the cortex (Erisir et al. 1999Go). The Kv1.3 and Kv3.1/3.2 have slightly different effects on the spiking behavior and are not interchangeable; both were needed to obtain the best fit to experimental data. The Kv3.1/3.2 potassium current is a faster activating current than Kv1.3, but requires larger depolarizations than the former. It also deactivates quickly, which, given its prominent expression in cortical FS interneurons, may explain the high firing frequency of these neurons (Erisir et al. 1999Go). The high conductance assigned to the Kv3.1/3.2 channel may be a consequence of using parameters obtained from homomeric channels. Specifically, neurons in globus pallidus and hippocampus have Kv3.4 subunits, which coassemble with Kv3.1 subunits (Baranauskas et al. 2003Go). The heterotrimeric channels have a lower activation voltage, but similar kinetics. It is possible that if activation potential were made smaller, consistent with heterotrimeric channels, the optimized conductance in the model would be lower. The parameter modifications made to the KA currents are consistent with the change in kinetics expected if these currents had been recorded at body temperature. A reduction in the voltage dependence of activation is expected from theoretical considerations and has been demonstrated for delayed rectifier potassium currents (Tiwari and Sikdar 1999Go). The twofold reduction in the time constant of activation represents a conservative Q10 of 2.0 (Huguenard et al. 1991Go). Nonetheless, experimental verification of the model requires experimental measurements of potassium currents in striatal FS interneurons.

Although model parameters were adjusted to those of FS interneurons in co-cultures, many of the properties are similar to those measured in slice preparations. The down-state membrane is similar to that of Koos and Tepper (2002)Go, but higher than that of Kawaguchi (1993)Go; spike width is slightly wider than that reported previously, but afterhyperpolarization amplitude is comparable to that reported in Kawaguchi. Latency is not listed in either reference, but traces reveal latencies of 25–50 ms, within the range of those measured in co-cultures. It is not possible to compare synaptic inputs because these have not been quantified for FS interneurons in slice.

Validating the model supported a number of anatomical findings with respect to the spatial distribution of synapses on striatal FS interneurons (Bevan et al. 1998Go). GABAergic inputs to FS neurons are from NADPH interneurons, other striatal FS interneurons, and GP projection neuron collaterals. FS interneurons preferentially target the soma (Kubota and Kawaguchi 2000Go). Similarly, GABAergic synapses from the globus pallidus predominantly target soma and proximal dendrites. A biased localization of GABAergic synapses also is found in fast-spiking interneurons of neocortex and hippocampus (Gulyas et al.1999Go; Pettit and Augustine 2000Go). Consistent with these findings, simulations show that matching both the population reversal potential and the up-state spike rate measured experimentally required placement of GABA synapses close to the soma as compared with glutamatergic synapses in the model neuron. Various spatial distributions have been suggested to serve different functions. For example, GABAergic inputs to the soma might be involved in suppression and timing of action potentials, whereas GABAergic inputs on distal dendrites might be important for integration of synaptic inputs (Reyes et al. 1998Go).

After adjusting for amplitude, time course, and IEI of synaptic inputs during down-states, the correlation among synaptic inputs had to be increased to match experimentally measured spike rates during up-states. Such correlation among synaptic inputs has been demonstrated experimentally. For example, membrane potential fluctuations during up-states reveal correlated synaptic inputs in both in vivo and in vitro conditions in striatum (Plenz and Kitai 1998Go; Stern et al. 1998Go). This requirement of correlated inputs was not eliminated by the addition of NMDA currents to the model. Our correlation used is in the same range as that used in a neocortical pyramidal cell model (Ho and Destexhe 2000Go; Rudolph and Destexhe 2001Go) to reproduce spontaneous in vivo–like subthreshold membrane potential activity and spike rate during up-states. Rather than depolarizing the cell, correlated synaptic inputs produce an increase in membrane potential fluctuations that boosts the rate of action potential generation (Salinas and Sejnowski 2000Go).

The ability of FS interneurons to profoundly influence striatal activity implies that FS interneurons need to be highly selective in their responses to synaptic inputs. Thus in the fully adjusted model, we explored the KA current as a possible mechanism for creating input specificity in FS interneurons. We demonstrated that the ability of KA currents to suppress responses to random synaptic inputs, while allowing responses to correlated synaptic inputs, created such input specificity. In other words, a strong KA current results in a better SNR in high noise conditions by preferentially suppressing down-state spikes.

These findings are robust with respect to changes in synaptic input characteristics and channel distribution. The same effect of the KA current is observed when synaptic currents have slower rise times and when GABA synapses are evenly distributed over all dendritic branches (results not shown). Similarly, the presence of NMDA channels does not change the role of KA currents in improving SNR, although it makes the FS interneuron more excitable. Inclusion of KA channels on distal dendrites counteracts the effect of NMDA channels on excitability, in accordance with previous simulations (Wilson 1995Go), but does not eliminate the ability of KA channels to improve SNR. This robustness includes conditions of elevated dopamine because FS interneurons exhibit input specificity when GABA amplitude is reduced, as observed with dopamine receptor activation (Bracci et al. 2002Go; Centonze et al. 2003Go). More important, this effect is specific to the KA current and cannot be achieved with the Kv3.1/3.2 current, probably as a result of its lower activation voltage. Kv3.1/3.2 is activated after a spike, whereas KA is activated before spike generation because of its lower activation threshold. Our results suggest that KA channels allow FS interneurons to operate without a decrease in SNR during conditions of increased dopamine, as occurs in response to reward or anticipated reward.

Another mechanism to increase input specificity is to increase background synaptic activity (Bernander et al. 1991Go), which lowers the gain of neurons (Chance et al. 2002Go; Ho and Destexhe 2000Go). Gain is the change in output firing frequency with a change in input synaptic frequency. If the gain is too high, a small increase in input frequency may saturate the neuron's output, preventing the neuron from accurately signaling larger changes in input frequency. Background activity improves input specificity by lowering the overall conductance of the neuron, which necessitates large input signals to reliably depolarize the neuron to spike threshold (Bernander et al. 1991Go). In addition, background noise makes the neuron responsive to lower values of signal input, allowing the neuron to spike when a small signal is coincident with background excitatory input (Chance et al. 2002Go; Ho and Destexhe 2000Go).

In contrast to the synchronous excitatory synaptic input used as the signal by other studies, striatal up-states are relatively long periods of increased, relatively asynchronous, excitatory and inhibitory synaptic inputs. As such, the up-state itself is similar to a large increase in background synaptic activity; thus the gain during the up-state is already low (Fig. 7B). Consequently, a small increase in down-state activity does not improve input specificity (Fig. 6) and a large increase in down-state activity may make the gain too low, hindering the ability of the neuron to reliability signal changes in the input signal, or the presence of an up-state.

We performed additional model simulations under conditions of increased dopamine to assist interpretation of a recent experimental finding on the effect of dopamine on FS interneurons. That study showed that dopamine depolarizes the FS interneuron and decreases the amplitude of GABA inhibitory postsynaptic currents onto the FS interneuron. Our simulations show that dopamine increases the gain of the FS interneuron, allowing more reliable up-state spike generation, while maintaining a high SNR (Fig. 7). This increase in gain improves input sensitivity because the FS interneuron's firing rate (<10 Hz) is still significantly below its peak firing rate (200 Hz). This mechanism may make the FS interneuron more responsive to input stimuli when they are associated with reward or anticipated reward, which causes an increase in dopamine release.

These simulation results can be rephrased in terms of a set of experimentally testable predictions: 1) FS interneurons have KA currents: although they exhibit a delay to spike generation during depolarization, which is reminiscent of a KA current, KA currents have not been identified in these neurons; 2) partial pharmacological blockade of the KA current will increase firing rate both in the down-state and in the up-state without a significant decrease in SNR, unless high noise conditions prevail; and 3) under high synaptic input noise conditions, an increased level of dopamine will increase the firing rate in the up-state and even more in the down-state, thereby decreasing the SNR level.

What are the implications of these observations in terms of FS interneuron function in local striatal circuits? The effect of FS interneurons on SP neuron up- and down-states is difficult to analyze with the present FS neuron model without an SP neuron model to receive FS neuron inputs. Experimentally, FS interneurons in the striatum have been shown to fire in two different modes. They fire bursts of action potentials during slow-wave sleep (Berke et al. 2004Go), epilepsy (Slaght et al. 2004Go), and in response to suprathreshold current injections (Kawaguchi 1993Go; Koos and Tepper 1999Go; Plenz and Kitai 1998Go). On the other hand, FS interneurons have been found to fire predominantly single spikes during wakefulness (Berke et al. 2004Go) and in organotypic cortex–striatum–substantia nigra co-cultures (Plenz and Kitai 1998Go). Although burst firing of FS interneurons provides powerful inhibition for prolonged periods of time to the striatal microcircuit, the functional importance of single-spike firing is poorly understood. It has been shown in the acute slice that single spikes from FS interneurons can significantly delay action potentials in SP neurons (Koos and Tepper 1999Go). This is important because the timing of action potentials during the up-state controls intracellular calcium influx through NMDA receptors in SP neurons (Kerr and Plenz 2002Go, 2004Go). Our result from the present study—that correlated, high-frequency synaptic input is required to produce a spike in FS interneurons—implies that single spikes carry information on the underlying synaptic inputs. The single spike provides a temporally precise, short-lasting inhibition in the feedforward circuit formed by the FS interneuron in the striatum. Although these spikes occur irregularly, they are not induced by noise; thus the single FS interneuron spikes that strongly influence SP neuron activity are predominantly produced by correlated, high-frequency synaptic input. Further elucidating how FS interneurons modulate SP neuron dynamics requires simulations using networks of striatal neurons.


    GRANTS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
J. H. Kotaleski was supported by Knut and Alice Wallenbergs Foundation and the Swedish Science Council (project number K2004-33XD-15059-01A). K. T. Blackwell was supported by National Science Foundation Grant IBN-0077509. D. Plenz was supported by the intramural research program of the National Institute of Mental Health, National Institutes of Health.


    ACKNOWLEDGMENTS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
We are grateful to R. Kirchner who helped to develop the initial model.


    FOOTNOTES
 
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Address for reprint requests and other correspondence: K. T. Blackwell, School of Computational Sciences and the Krasnow Institute for Advanced Study, George Mason University, MS 2A1, Fairfax, VA 22030 (E-mail: avrama{at}gmu.edu)


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