 |
||||
|
||||
|
||||
|
||||
Previous Article | Next Article
The Journal of Neuroscience, December 1, 2002, 22(23):10242-10250
Detectability of Excitatory versus Inhibitory Drive in an Integrate-and-Fire-or-Burst Thalamocortical Relay Neuron Model
Gregory D. Smith1 and S. Murray Sherman2 1 Department of Applied Science, College of William and Mary, Williamsburg, Virginia 23187, and 2 Department of Neurobiology, State University of New York, Stony Brook, New York 11794-5230
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
Although inhibitory inputs are often viewed as equal but opposite to excitatory inputs, excitatory inputs may alter the firing of postsynaptic cells more effectively than inhibitory inputs. This is because spike cancellation produced by an inhibitory input requires coincidence in time, whereas an excitatory input can add spikes with less temporal constraint. To test for such potential differences, especially in the context of the function of thalamocortical (TC) relay nuclei, we used a stochastic "integrate-and-fire-or-burst" TC neuron model to quantify the detectability of excitatory and inhibitory drive in the presence and absence of the low-threshold Ca2+ current, IT, and the hyperpolarization-activated cation conductance, Isag. We find that excitatory inputs are generally superior drivers compared with inhibitory inputs in part because spontaneous activity of a postsynaptic neuron is not required in the case of excitatory drive. Interestingly, the presence of the low-threshold Ca2+ current, IT in a postsynaptic neuron allows the robust detection of inhibitory drive over a certain range of spontaneous and driven activity, a range that can be extended by the presence of the hyperpolarization-activated cation conductance, Isag. These simulations suggest a possible reinterpretation of the role of inhibitory inputs, such as those to the thalamus.
Key words: thalamus; inhibition; excitation; basal ganglia; neuron model; driver; modulator
INTRODUCTION
Inhibitory inputs are often viewed as equal but opposite to excitatory inputs. That is, a reduction of postsynaptic firing resulting from an inhibitory input is often implied to convey information as effectively as an increase of postsynaptic firing caused by an excitatory input. For instance, the inhibitory GABAergic input from the basal ganglia to the ventral lateral and ventral anterior nuclei of the thalamus is often viewed as providing information to be relayed to the cortex (Purves et al., 1997
; Kandel et al., 2000
However, inhibitory inputs are not equal to but in fact are opposite to excitatory ones. EPSPs affect the firing of the postsynaptic cell by adding action potentials, whereas IPSPs remove them. As long as the postsynaptic background firing rate is not near its upper limit, excitatory inputs can always add action potentials. However, because an inhibitory input can only cancel action potentials that are temporally coincident, it follows that IPSPs are ineffective at low postsynaptic firing rates.
Here we use a computational approach to test the hypothesis that excitatory and inhibitory inputs are not equally detectable with regard to postsynaptic effectiveness. Because the thalamus is seen as a site for the relay of information and has both excitatory and inhibitory inputs believed to be the source of information (i.e., drivers as opposed to modulators) of thalamic relay nuclei (Sherman and Guillery, 1998
Some of these results have been published previously in abstract form (Smith and Sherman, 2001
MATERIALS AND METHODS
The integrate-and-fire-or-burst model. For a complete description of the development of the integrate-and-fire-or-burst (IFB) model and parameter selection, see Smith et al. (2000)
(1)
The current balance equation, Equation 1, includes a constant conductance leakage current (IL) of the form, IL = gL(V
(2) VL); the low-threshold Ca2+ current, IT; and two synaptic currents, IS and ID. An action potential occurs whenever the membrane potential reaches the firing threshold (V
). After each action potential, an absolute refractory period of tR = 4 msec is enforced during which the current balance equation, Equation 1, is not integrated and V = Vreset.
The low-threshold Ca2+ current takes the form IT = gT m
h(V
TC-like and thalamic reticular-like simulations. Because of similarities between neurons of the thalamic reticular nucleus (TRN) and TC neurons, a subtle change in Vh, the threshold for IT, or VL, the resting membrane potential, converts an IFB TC neuron model into a model that responds like TRN neurons. In TC cells at rest, IT is inactivated (i.e., VL > Vh), whereas TRN cells at rest are primed to burst in response to depolarizing input (VL < Vh). The phrases "TC-like" and "TRN-like" below refer to this tuning of parameters. In both cases, VL =
View this table: [in this window]
[in a new window]
Table 1. Parameters for the integrate-and-fire-or-burst model Synaptic input. The last two terms in Equation 1, IS and ID, are synaptic currents attributable to excitatory spontaneous input (IS) and excitatory or inhibitory drive (ID). Each synaptic potential received by the IFB model neuron is modeled as an
function (Rall, 1967
). For example, in the case of spontaneous input, an individual EPSP occurring at t = 0 would be given by:
where
(3) S, and the resulting synaptic input was generated using the method put forth by Destexhe et al. (1994)
We integrated the equations for the IFB model using a 1 GHz LINUX workstation running XPP, an ordinary differential equation solver written by Bard Ermentrout at the University of Pittsburgh (Pittsburgh, PA) (http://www.pitt.edu/~phase/). All calculations were performed using the fourth-order Runge-Kutta integration method and a time step of 10-50 µsec.
Receiver operator characteristic analysis of simulated responses. Receiver operator characteristic (ROC) analysis (Green and Swets, 1966
See http://www.as.wm.edu/Faculty/Smith.html for an extended description of the above methods.
RESULTS
ROC calculations without the low-threshold calcium current
To quantify the detectability of excitatory versus inhibitory drive for a model of a thalamic neuron responding purely in tonic mode, we used the IFB model with the conductance underlying IT (i.e., gT) set to zero. Thus, Equation 2 is irrelevant, and the IFB model behaves as a classical integrate-and-fire model that receives EPSPs or IPSPs from two sources (Fig. 1A). The first source provides EPSPs at rate
View larger version (23K):[in this window]
[in a new window]
Figure 1. A, Diagram of the configuration of the model neuron that is postsynaptic to two sources (input). The first input [Spontaneous (noise)] is excitatory, and if sufficiently intense, it causes a certain level of background activity in the postsynaptic neuron. The second input [Driver (signal)] represents either excitatory or inhibitory drive, the presence or absence of which must be detected based on spike count (Output). B, Filled circles, output rate of the IFB model (mean ± SD) as a function of the rate of spontaneous EPSPs. Open circles, Mean output rate of the Hodgkin-Huxley style thalamocortical relay neuron model. Parameters are as described in Table 1 and Materials and Methods.
The focus of this work is the extent to which the presence or absence of the driver input is detectable in the output of the postsynaptic neuron (Fig. 1A). Because this may depend on spontaneous activity, Figure 1B shows the output rate (mean ± SD) of the IFB model as a function of the spontaneous EPSP rate. The input-output relationship increases monotonically and saturates at 250 spikes/sec, because the absolute refractory period of the model, tR, is 4 msec. Saturation becomes appreciable only when the spontaneous input rate is greater than approximately
Figure 2A shows three representative 200 msec plots of the IFB model membrane potential for a spontaneous input rate of
View larger version (27K):[in this window]
[in a new window]
Figure 2. A, Representative membrane potential time courses (200 msec in duration) for an integrate-and-fire model receiving spontaneous EPSPs at 400 EPSPs/sec. B, Time courses when 400 EPSPs/sec of spontaneous input is augmented by 50 EPSPs/sec excitatory drive. C, Time courses when 400 EPSPs/sec of spontaneous input is attenuated by 50 IPSPs/sec inhibitory drive. D, Histogram of spike counts for 1000 trials (from A and B) and a diagram representing the corresponding ROC area calculation (see Materials and Methods), where the probability (Pr) of a hit is plotted against the probability of a false alarm. E, Histogram of spike counts for 1000 trials (from A and C).
Thus, for a neuron receiving 400 EPSPs/sec, the detectability of 50 additional EPSPs/sec and 50 IPSPs/sec is comparable. However, this is not true in general and is, in fact, a consequence of the background activity of the postsynaptic neuron (98 spikes/sec). To clarify the dependence of this result on the rate of spontaneous and driven input, Figure 3 presents a summary of ROC area calculations performed for 28 × 28 (i.e., 784) values of
View larger version (46K):[in this window]
[in a new window]
Figure 3. Summary of ROC area calculations performed for various combinations of spontaneous EPSP rate (spontaneous input rate; y-axis) and rate of excitatory or inhibitory drive (driven input rate; x-axis). ROC area plots summarize ~800 combinations of spontaneous input rate and driven input rate, each leading to a number between 0.5 (chance level) and 1 (perfectly detectable). A, ROC area when the low-threshold Ca2+ current, IT, is not included in the simulations (gT = 0.2 mS/cm2). B, IT is included in the model in a TC-like manner (gT = 0.2 mS/cm2; Vh =
Figure 3A shows that for spontaneous input rates below ~100 EPSPs/sec, a relatively constant amount of excitatory drive leads to detectable signal (for a ROC area of 0.8, ~15 EPSPs/sec drive is required). However, when the spontaneous input rate increases to >100 EPSPs/sec, the amount of excitatory drive necessary to maintain detectability increases. This leads to a sloped (nonvertical) interface between low and high ROC area for a
Figure 3, A and D, shows that excitatory and inhibitory drivers are not equivalent with respect to postsynaptic detectability. In the inhibitory case, spontaneous activity in the postsynaptic neuron is required so that inhibitory drive may be detected as a suppressed spike count (i.e., detectability is near zero for a
View larger version (54K):[in this window]
[in a new window]
Figure 4. ROC analysis from Figure 3, A, B, D, and E replotted as a function of mean output rate of the postsynaptic neuron in the absence of drive (y-axis) and rate of excitatory or inhibitory drive (x-axis). This transformation is possible because in the absence of drive, the mean firing rate of the postsynaptic neuron is a monotonic increasing function of the spontaneous EPSP rate.
ROC calculations with a TC-like, low-threshold calcium current
To quantify the detectability of excitatory versus inhibitory drive in a TC neuron model that includes the low-threshold Ca2+ current, IT, the parameter gT in the IFB model was changed to the standard value of 0.2 mS/cm2 (Table 1). Here Vh, the threshold for activation/inactivation of IT, is
Figure 3, B and E, summarizes ROC analysis for the TC-like IFB model under the influence of spontaneous EPSPs and either excitatory (Fig. 3B) or inhibitory (Fig. 3E) drive. Figure 3B is nearly identical to Figure 3A, so the presence of IT has little effect on the detectability of excitatory drive, because all inputs to the IFB model are depolarizing and, consequently, IT remains inactivated. However, Figure 3, D and E, shows that IT has a significant effect on the detectability of inhibitory drive. In this case, clusters of IPSPs from the inhibitory drive occasionally deinactivate IT. If additional inhibition does not occur, then the membrane potential relaxes toward VL until the burst threshold Vh is crossed, thereby activating IT. Often an appropriately timed spontaneous EPSP accelerates this process. The elevated ROC area observed in Figure 3E (
To clarify this, Figure 5 shows three representative plots of the IFB model membrane potential for a spontaneous (excitatory) input rate of
View larger version (22K):[in this window]
[in a new window]
Figure 5. A, Representative membrane potential time courses (200 msec in duration) for the IFB model with TC-like, low-threshold Ca2+ current receiving spontaneous EPSPs at 30 EPSPs/sec (no response). B, Time courses when 30 EPSPs/sec of spontaneous input is augmented by 30 IPSPs/sec of excitatory drive. C, Cell response increases when 30 EPSPs/sec of spontaneous input is combined with 30 IPSPs/sec of inhibitory drive. D, E, Histograms of spike counts for 1000 trials and the corresponding ROC area calculations. Pr, Probability.
In Figure 5C, inhibitory drive is included at a rate of
When the IFB model neuron was augmented to include the hyperpolarization-activated cation current, Isag, ROC area calculations were qualitatively similar to those performed in the absence of this low-threshold current for both excitatory and inhibitory drive (data not shown; results are similar to Fig. 3B,E). Interestingly, Isag does enlarge the region over which the presence of IT allows the detection of inhibitory drive (Fig. 6).
View larger version (23K):[in this window]
[in a new window]
Figure 6. ROC analysis for the IFB model in the presence ( ) and absence (
) of the hyperpolarization-activated cation current, Isag, as a function of the rate of inhibitory drive (x-axis) for a spontaneous excitatory input rate of 10 EPSPs/sec. In the absence of Isag, this corresponds to a cross section of Figure 3E.
ROC calculations with a TRN-like, low-threshold calcium current
In TC cells at rest, IT is inactivated, i.e., the resting membrane potential is greater than the threshold for activation/inactivation of the low-threshold Ca2+ current (VL > Vh). However, in TRN neurons, the threshold for activation of IT is more depolarized than that in TC cells (Huguenard and Prince, 1992
Figure 3, C and F, summarizes ROC analysis for the TRN-like IFB model when the drive is either excitatory (Fig. 3C) or inhibitory (Fig. 3F). Although the overall comparison of C and F with B and E in Figure 3 gives the impression that the effects of TRN-like IT are subtle, there are some differences. For example, the distinction between Figure 3, C and A, is certainly greater than that between Figure 3, B and A, demonstrating that the presence of IT influences the detectability of excitatory drive in the TRN-like IFB model (as opposed to the TC-like case, in which it had no effect). Interestingly, the presence of TRN-like IT has an overall effect of decreasing the region of elevated ROC area. In particular, the threshold for detectability of excitatory inputs increased when the spontaneous input rate was 10-100 EPSPs/sec (see notch in Fig. 3, C compared with A).
The ROC areas in the presence of TRN-like IT and inhibitory drive (Fig. 3F) are distinct from both the TC-like case (Fig. 3E) and the result in the absence of IT (Fig. 3D). There is an island of detectability for spontaneous input rates between 30 and 300 EPSPs/sec. At
View larger version (23K):[in this window]
[in a new window]
Figure 7. A, Representative membrane potential time courses for the IFB model with TRN-like, low-threshold Ca2+ current receiving spontaneous EPSPs at 100 EPSPs/sec. B, Time courses when 30 EPSPs/sec of excitatory drive is included. C, Cell response increases when 30 IPSPs/sec of inhibitory drive is included. D, E, Histograms of spike counts for 1000 trials and the corresponding ROC area calculations. Pr, Probability.
Figure 3F shows moderate ROC area (0.7-0.8) extending to lower levels of spontaneous EPSP rates than in the absence of IT (compare Fig. 3D), although the effect is not as strong as when IT is TC-like (compare Fig. 3E) and occurs over a different range of rates of inhibitory drive (Fig. 3F,
Voltage dependence of ROC calculations
In the above simulations, ROC area analysis has been performed using the IFB model both with and without IT. In the presence of IT, we have found that the detectability of inhibitory inputs was dependent on the relationship between the IFB model resting membrane potential, VL, and the threshold (Vh) for activation/inactivation of IT. In particular, a region of elevated detectability of inhibitory inputs that is prominent when the IFB model is TC-like and IT is inactivated at rest (VL > Vh) (Fig. 3E) is reduced or absent when the IFB model is TRN-like and IT is deinactivated at rest (VL < Vh) (Fig. 3F). However, because modulatory inputs can change the resting membrane potential of both TC and TRN neurons, it is important to clarify how the detectability of inhibitory input may depend on the resting membrane potential.
To address this question for inhibitory inputs, Figure 8A-E presents ROC area calculations in which VL was varied from
View larger version (40K):[in this window]
[in a new window]
Figure 8. ROC area calculations resulting from inhibitory drive, where VL is varied from
Calculations similar to those presented in Figure 8 indicate that the resting membrane potential affects the detectability of excitatory input as well (data not shown). However, the similarity of TC-like and TRN-like responses to excitatory inputs (Fig. 3, compare B with C) means that the variation in the ROC analysis is modest compared with that observed in Figure 8.
ROC area analysis using a Hodgkin-Huxley-like, conductance-based model
To determine the degree to which the above results generalize, we performed ROC analysis using a truncation of the McCormick-Huguenard TC neuron model (Huguenard and McCormick, 1992
ROC calculations with balanced excitatory and inhibitory spontaneous input
In the simulations presented thus far, the detectability of excitatory or inhibitory drive has been quantified assuming that the background activity of the IFB model is caused solely by excitatory spontaneous input. However, it is more realistic to presume that the background activity of the output neuron in Figure 1A is caused by a mixture of excitatory and inhibitory spontaneous input. To represent this possibility, the current balance equation for the IFB model was extended to include two spontaneous synaptic current terms, one excitatory and the other inhibitory. When the spontaneous excitatory and inhibitory inputs are balanced (both arriving at identical
Despite this difference, the ROC analysis for balanced excitatory and inhibitory spontaneous input is qualitatively similar to the results for pure excitatory spontaneous input (data not shown, similar to Fig. 3). However, in both the absence and the presence of IT, the combination of excitatory and inhibitory spontaneous input does slightly improve detectability of excitatory input when the spontaneous input rate is high (
DISCUSSION
Using an integrate-and-fire-or-burst TC neuron model and a more detailed Hodgkin-Huxley-style model (data not shown), we have quantified the detectability of stochastic excitatory and inhibitory drive in the presence and absence of the low-threshold Ca2+ current, IT. By calculating ROC area, we quantified detectability when the model neuron received postsynaptic potentials from an excitatory source that evokes spontaneous activity (i.e., noise) and a second (excitatory or inhibitory) source that represents an afferent signal (Fig. 1A). Similar results were obtained when the model neuron received spontaneous postsynaptic potentials from a combination of excitatory and inhibitory sources (data not shown).
We find that in the absence of IT detectability is typically poorer for inhibitory than for excitatory drive. This is particularly true for low to moderate levels of spontaneous activity in the postsynaptic neuron, because spontaneous activity is required for inhibitory drive to be detected as a suppressed spike count. In the presence of IT, results depend strongly on whether the threshold for IT activation lies above the resting membrane potential (TRN-like) or below it (TC-like). In the latter case, IT enables the detection of inhibitory drivers even when the postsynaptic neuron is not spontaneously active.
The qualitative aspects of the ROC area analysis presented here are not sensitive to the size of the spontaneous and driven postsynaptic potentials (AS and AD), although a threefold change does shift areas of elevated detectability toward higher or lower EPSP/IPSP rates (data not shown). Interestingly, we found that changes in resting membrane potential can significantly change the overall dependence of the detectability of inhibitory input on spontaneous and driven input rates (Fig. 8). This suggests that the detection of inhibitory inputs enabled by IT may be sensitive to neuromodulation that affects the resting membrane potential of TC neurons.
Limitations of single-compartment modeling
Because both of the models used (IFB and Hodgkin-Huxley) are single-compartmental models, a limitation of this work is that some results may not generalize to situations involving temporally or spatially patterned synaptic input distributed over dendritic arbors. Although excitatory and inhibitory inputs are demonstrably not equivalent in isopotential compartmental models, one might devise a multicompartmental model with various assumptions about dendritic architecture, the distribution of ionic currents, and the spatial organization of synaptic inputs, for which excitatory and inhibitory inputs are less distinguishable on the basis of detectability. Nevertheless, the use of single-compartmental models is appropriate on several grounds. As a practical matter, the choice is motivated by a desire to perform adequate statistics of the stochastic responses that we quantify. Furthermore, previous cable modeling of current flow within dendritic arbors of thalamic relay cells has concluded that they are electronically compact. Thus, a postsynaptic potential generated anywhere in the dendritic arbor of a relay cell spreads with relatively little attenuation throughout the arbor and to its soma (Bloomfield and Sherman, 1989
Can inhibitory inputs be drivers to thalamus?
It has been stressed previously (Sherman and Guillery, 1998
A number of criteria to distinguish drivers from modulators for thalamic relays have been suggested; for example, cross-correlograms from driver inputs are likely to be sharply peaked compared with those from modulatory inputs. Certainly an important functional criteria for a driver input is an ability to transfer information efficiently across the synapse to the relay cell, and thus, the presence or absence of driving input must be detectable on the basis of the postsynaptic neuron response. In the absence of knowledge about presynaptic firing rates, our simulations show that overall detectability is poorer for inhibitory drive than excitatory drive. Thus, we suggest adding to the list of criteria to distinguish drivers from modulators the proposition that, other things being equal, inhibitory inputs are less likely to be drivers than excitatory inputs.
However, an important caveat to this conclusion is that over a certain range of spontaneous and driven activity, the low-threshold Ca2+ current, IT, may allow the detection of inhibitory drive. Indeed, the calculations of elevated detectability mediated by IT presented above suggest three criteria for the identification of an inhibitory driver that uses IT: (1) a candidate inhibitory driver must provide IPSPs at a rate that results in postinhibitory rebound bursting and elevated spike count in the postsynaptic neuron (in Fig. 3E, this range is 10-100 IPSPs/sec), (2) the spontaneous activity of the postsynaptic neuron must be modest (<30 spikes/sec in Fig. 4D), and (3) for robust detectability, the postsynaptic neuron must express the low-threshold Ca2+ current in a TC-like manner, so that inhibitory drive can deinactivate IT. In light of these results, we suggest that inhibitory projections to thalamic relay nuclei should not be presumed to be drivers unless the spontaneous activity of the postsynaptic neuron is relatively high or there is reason to believe that these three conditions for IT-mediated detectability hold. Because relay cells responding in burst mode have nonlinear input-output relationships, we also suggest that IT-mediated detection of inhibitory drive is unlikely to be a mechanism associated with faithful relay of information to the cortex (Sherman, 2001
The implications of these criteria for inhibitory drivers are potentially far reaching. For example, textbook accounts (Purves et al., 1997
To give another example, the identification of inhibitory Purkinje cells of the cerebellar cortex as drivers of the deep cerebellar nuclei may or may not be consistent with the criteria for inhibitory drivers discussed above. If not, another candidate driver input to the deep cerebellar nuclei is excitation from mossy or climbing fiber axon branches, in which case Purkinje cell activity would be an inhibitory modulator rather than an inhibitory driver, providing the basic information for the deep cerebellar nuclei to transmit to other brain centers. Rethinking of the functional organization of this and other neural pathways may be required if responses of presumed inhibitory drivers and their postsynaptic targets are not consistent with the criteria for inhibitory drivers proposed above.
FOOTNOTES Received Aug. 1, 2002; revised Sept. 6, 2002; accepted Sept. 10, 2002.
This work was supported in part by National Science Foundation (NSF) Integrative Biology and Neuroscience Grant IBN 0228273 (G.D.S.) and National Eye Institute Grant EY03038 (S.M.S.). The work was performed in part using computational facilities at the College of William and Mary enabled by grants from the NSF and Sun Microsystems. We thank Hans E. Plesser for a careful reading of this manuscript.
Correspondence should be addressed to S. M. Sherman, Department of Neurobiology, State University of New York, Stony Brook, NY 11794-5230. E-mail: s.sherman{at}sunysb.edu.
REFERENCES
- Bloomfield SA, Sherman SM (1989) Dendritic current flow in relay cells and interneurons of the cat's lateral geniculate nucleus. Proc Natl Acad Sci USA 86:3911-3914
[Abstract/Free Full Text] .- Destexhe A, Mainen Z, Sejnowski T (1994) Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J Comput Neurosci 1:195-230[Medline].
- Dossi RC, Nunez A, Steriade M (1992) Electrophysiology of a slow (0.5-4 Hz) intrinsic oscillation of cat thalamocortical neurones in vivo. J Physiol (Lond) 447:215-234
[Abstract/Free Full Text] .- Gabbiani F, Koch C (1998) Signal processing techniques for spike train analysis using MatLab. In: Methods in neuronal modeling: from ions to networks, Ed 2 (Koch C, Segev I, eds). Cambridge, MA: MIT.
- Green D, Swets J (1966) In: Signal detection theory and psychophysics. New York: Wiley.
- Guido W, Lu S-M, Vaughan J, Godwin D, Sherman SM (1995) Receiver operating characteristic (ROC) analysis of neurons in the cat's lateral geniculate nucleus during tonic and burst response mode. Vis Neurosci 12:723-741[ISI][Medline].
- Guillery RW, Sherman SM (2002) Thalamic relay functions and their role in corticocortical communication: generalizations from the visual system. Neuron 33:1-20[ISI][Medline].
- Huguenard JR, McCormick D (1992) Simulation of the currents involved in rhythmic oscillations in thalamic relay neurons. J Neurophysiol 68:1373-1383
[Abstract/Free Full Text] .- Huguenard J, McCormick D (1994) In: Electrophysiology of the neuron. New York: Oxford UP.
- Huguenard JR, Prince DA (1992) A novel T-type current underlies prolonged Ca2+-dependent burst firing in GABAergic neurons of rat thalamic reticular nucleus. J Neurosci 12:3804-3817[Abstract].
- Jahnsen H, Llinas R (1984a) Electrophysiological properties of guinea-pig thalamic neurones: an in vitro study. J Physiol (Lond) 349:205-226
[Abstract/Free Full Text] .- Jahnsen H, Llinas R (1984b) Ionic basis for the electroresponsiveness and oscillatory properties of guinea-pig thalamic neurones in vitro. J Physiol (Lond) 349:227-247
[Abstract/Free Full Text] .- Kandel ER, Schwartz JH, Jessell TM (2000) In: Principles of neural science. New York: McGraw Hill.
- Keener J, Hoppensteadt F, Rinzel J (1981) Integrate-and-fire models of nerve membrane response to oscillatory input. SIAM J Appl Math 41:503-517.
- MacMillan N, Creelman C (1991) In: Detection theory: a user's guide. Cambridge, MA: Cambridge UP.
- Magnin M, Morel A, Jeanmonod D (2000) Single-unit analysis of the pallidum, thalamus and subthalamic nucleus in Parkinsonian patients. Neuroscience 96:549-564[ISI][Medline].
- Mason A, Ilinsky IA, Maldonado S, Kultas-Ilinsky K (2000) Thalamic terminal fields of individual axons from the ventral part of the dentate nucleus of the cerebellum in Macaca mulatta. J Comp Neurol 421:412-428[Medline].
- McCormick D, Huguenard J (1992) A model of the electrophysiological properties of thalamocortical relay neurons. J Neurophysiol 68:1384-1400
[Abstract/Free Full Text] .- Mukherjee P, Kaplan E (1995) Dynamics of neurons in the cat lateral geniculate nucleus: in vivo electrophysiology and computational modeling. J Neurophysiol 74:1222-1243
[Abstract/Free Full Text] .- Purves D, Augustine GJ, Fitzpatrick D, Katz LC, Lamantia A-S, McNamara JO (1997) In: Neuroscience. Sunderland, MA: Sinauer.
- Radhakrishnan V, Tsoukatos J, Davis KD, Tasker RR, Lozano AM, Dostrovsky JO (1999) A comparison of the burst activity of lateral thalamic neurons in chronic pain and non-pain patients. Pain 80:567-575[ISI][Medline].
- Rall W (1967) Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic inputs. J Neurophysiol 30:1138-1168
[Free Full Text] .- Rinzel J (1980) Models in neurobiology. In: Nonlinear phenomena in physics and biology, Vol 75 (Enns RH, Jones BL, Miura RM, Rangnekar SS, eds), pp 347-367. Alberta, Canada: North Atlantic Treaty Association Advanced Study Institute.
- Sakai ST, Stepniewska I, Qi HX, Kaas JH (2000) Pallidal and cerebellar afferents to pre-supplementary motor area thalamocortical neurons in the owl monkey: a multiple labeling study. J Comp Neurol 417:164-180[ISI][Medline].
- Sherman SM (2001) Tonic and burst firing: dual modes of thalamocortical relay. Trends Neurosci 24:122-126[ISI][Medline].
- Sherman SM, Guillery RW (1996) The functional organization of thalamocortical relays. J Neurophysiol 76:1367-1395
[Abstract/Free Full Text] .- Sherman SM, Guillery RW (1998) On the actions that one nerve cell can have on another: distinguishing "drivers" from "modulators". Proc Natl Acad Sci USA 95:7121-7126
[Abstract/Free Full Text] .- Sherman SM, Guillery RW (2001) In: Exploring the thalamus. San Diego: Academic.
- Sherman SM, Koch C (1998) Thalamus. In: Synaptic organization of the brain, Ed 4 (Shepherd G, ed), pp 246-278. New York: Oxford UP.
- Smith G, Sherman SM (2001) Detectability of excitatory versus inhibitory drive in a stochastic thalamocortical relay neuron model. Soc Neurosci Abstr 27:723.21.
- Smith G, Cox C, Sherman SM, Rinzel J (2000) Fourier analysis of sinusoidally-driven thalamocortical relay neurons and a minimal intergrate-and-fire-or-burst model. J Neurophysiol 83:588-610
[Abstract/Free Full Text] .- Smith G, Cox C, Sherman SM, Rinzel J (2001) Spike-frequency adaptation in sinusoidally-driven thalamocortical relay neurons. Thalamus and Related Systems 1:135-156.
- Tuckwell H (1988) In: Introduction to theoretical neurobiology: nonlinear and stochastic theories, Vol 2. Cambridge, UK: Cambridge UP.
- Tuckwell H (1989) In: Stochastic processes in the neurosciences. Philadelphia: Society for Industrial and Applied Mathematics.
- Wang XJ (1994) Multiple dynamical modes of thalamic relay neurons: rhythmic bursting and intermittent phase-locking. Neuroscience 59:21-31[ISI][Medline].
- Wilson JR, Friedlander MJ, Sherman SM (1984) Fine structural morphology of identified X- and Y-cells in the cat's lateral geniculate nucleus. Proc R Soc Lond B Biol Sci 221:411-436[Medline].
- Zirh TA, Lenz FA, Reich SG, Dougherty PM (1998) Patterns of bursting occurring in thalamic cells during parkinsonian tremor. Neuroscience 83:107-121[ISI][Medline].
Copyright © 2002 Society for Neuroscience 0270-6474/02/222310242-09$05.00/0
This article has been cited by other articles:
Y. Guo, J. E. Rubin, C. C. McIntyre, J. L. Vitek, and D. Terman
Thalamocortical Relay Fidelity Varies Across Subthalamic Nucleus Deep Brain Stimulation Protocols in a Data-Driven Computational Model
J Neurophysiol, March 1, 2008; 99(3): 1477 - 1492.
[Abstract] [Full Text] [PDF]
J. Rubin and K. Josic
The Firing of an Excitable Neuron in the Presence of Stochastic Trains of Strong Synaptic Inputs
Neural Comput., May 1, 2007; 19(5): 1251 - 1294.
[Abstract] [Full Text] [PDF]
This Article Abstract 
Full Text (PDF) Submit an eLetter Alert me when this article is cited Alert me when eLetters are posted Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in ISI Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager
