20814
Smith, Gregory D., Charles L. Cox, S. Murray Sherman, and
John Rinzel.
Fourier analysis of sinusoidally driven thalamocortical
relay neurons and a minimal integrate-and-re-or-burst model. J.
Neurophysiol. 83: 588 610, 2000. We performed intracellular record-
ings of relay neurons from the lateral geniculate nucleus of a cat
thalamic slice preparation. We measured responses during both tonic
and burst ring modes to sinusoidal current injection and performed
Fourier analysis on these responses. For comparison, we constructed
a minimal integrate-and-re-or-burst (IFB) neuron model that re-
produces salient features of the relay cell responses. The IFB model is
constrained to quantitatively t our Fourier analysis of experimental
relay neuron responses, including: the temporal tuning of the response
in both tonic and burst modes, including a nding of low-pass and
sometimes broadband behavior of tonic ring and band-pass charac-
teristics during bursting, and the generally greater linearity of tonic
compared with burst responses at low frequencies. In tonic mode, both
experimental and theoretical responses display a frequency-dependent
transition from massively superharmonic spiking to phase-locked
superharmonic spiking near 3 Hz, followed by phase-locked subhar-
monic spiking at higher frequencies. Subharmonic and superharmonic
burst responses also were observed experimentally. Characterizing the
response properties of the tuned IFB model leads to insights regard-
ing the observed stimulus dependence of burst versus tonic response
mode in relay neurons. Furthermore the simplicity of the IFB model
makes it a candidate for large scale network simulations of thalamic
functioning.
I N T R O D U C T I O N
Considerable attention has been focused in recent years on
the functioning of thalamic relays, because it has become clear
that the thalamus does not serve as a simple, machine-like relay
of information to cortex (for recent reviews, see Sherman and
Guillery 1996, 1998). Instead the thalamus controls the extent
and nature of information being relayed in a dynamic fashion
that appears to be related to behavioral state and perhaps
attentional demands. A good example is the lateral geniculate
nucleus, the thalamic relay of retinal information to visual
cortex. Only 510% of synapses on geniculate relay cells
derive from retina. The rest derive from nonretinal sources,
including local GABAergic cells, feedback afferents from vi-
sual cortex, and various pathways from the brain stem, and
these modulate the nature of retinogeniculate transmission
(Sherman and Guillery 1996, 1998).
In addition to the complexity of thalamic circuitry, the
membrane properties of relay cells contribute to the nature of
the relayed information. In particular, thalamic relay cells
exhibit a voltage- and time-dependent, low-threshold, transient
Ca
2
conductance, that, when activated, allows Ca
2
to enter
the cell via T-type (for transient) Ca
2
channels, producing
a transmembrane current, I
T
, and leading to a large depolar-
ization known as the low-threshold Ca
2
spike. The inactiva-
tion state of I
T
determines whether information is relayed to
cortex in tonic mode or burst mode (Jahnsen and Llinas
1984a,b; Sherman 1996). When the cell starts off relatively
depolarized (above roughly
60 mV for
50 100 ms), I
T
is
inactivated, and the relay cell responds to an excitatory input
[e.g., a retinal excitatory postsynaptic potential (EPSP)] with
sustained ring of unitary action potentials. This is the tonic
ring mode. However, if the cell is hyperpolarized rst (below
roughly
65 mV for
50 100 ms), the inactivation of I
T
is
removed (i.e., I
T
becomes deinactivated), and now a sufcient
depolarization or EPSP will activate I
T
. The result is a low-
threshold Ca
2
spike with a brief burst of 210 action poten-
tials riding its crest.
One of the keys to understanding how thalamic relays work is
to understand in more detail how the input/output properties of
relay cells are affected by the inactivation state of I
T
. We sought
to do this with both an experimental and modeling approach. By
recording from relay cells of the lateral geniculate nucleus of the
cat in vitro, we measured input/output properties by injecting into
the cell sinusoidal currents that varied in amplitude, frequency,
and mean level, and we performed analogous input/output exper-
iments on a minimal relay cell model to test the degree to which
the essential features of I
T
accounted for relay cell responses. In
addition to providing an easily parameterized set of stimuli that
lends itself to Fourier analysis, the use of sinusoidal current
injection allows us to interpret our results in the context of the
spatial and temporal frequency analysis paradigm that has such a
successful history in visual systems neuroscience (for review, see
Shapley and Lennie 1985). Of course, our use of Fourier tech-
niques is not based on an assumption of the linearity of relay
neuron responses but simply reects an historically preferred
method of extracting relevant measures of cellular response (see
METHODS
).
For the theoretical component of this study, we developed a
minimal integrate-and-re-or-burst (IFB) neuron model.
This model is constructed by adding a slow variable represent-
ing the deinactivation level of I
T
to a classical integrate-and-
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.
588
0022-3077/00 $5.00 Copyright © 2000 The American Physiological Society re neuron model (Knight 1972). The IFB model is designed
specically to be as simple as possible while still quantitatively
reproducing much of the empirically observed properties of the
relay cells. One motivation for developing such a minimal
model is to simplify the parameter selection process. Further-
more, because the IFB model is minimal, a detailed character-
ization of its response properties leads to insight regarding the
stimulus dependence of burst versus tonic response modes in
thalamic relay cells. A nal motivation for development of the
IFB model is to have a realistically tuned yet computationally
undemanding relay cell model that can be used in large scale
network simulations of thalamic function.
M E T H O D S
Experimental methods
We performed intracellular recordings with the whole cell cong-
uration on thalamic relay cells of young cats (5 8 wk of age) in
compliance with approved animal protocols. We used a thalamic
brain-slice preparation containing the lateral geniculate nucleus.
Briey, the animals were anesthetized deeply with 25 mg/kg ketamine
and 1 mg/kg xylazine and a block of tissue containing the thalamic
region was removed and placed in cold, oxygenated slicing solution
containing (in mM) 2.5 KCl, 1.25 NaH
2
PO
4
, 10.0 MgCl
2
, 0.5 CaCl
2
,
26.0 NaHCO
3
, 11.0 glucose, and 234.0 sucrose. Thalamic slices
(250 300
m) were cut in a coronal or sagittal plane with a vibrating
tissue slicer and placed in a holding chamber (30°C) for
2 h before
recording. Individual slices were transferred to a submersion-type
recording chamber maintained at 30°C and continuously perfused
with oxygenated physiological solution containing (in mM) 126.0
NaCl, 2.5 KCl, 1.25 NaH
2
PO
4
, 2.0 MgCl
2
, 2.0 CaCl
2
, 26.0 NaHCO
3
,
and 10.0 glucose, all at pH 7.4.
We used an Axoclamp 2A amplier to obtain current-clamp re-
cordings from geniculate relay neurons in the A-laminae, and we
continuously monitored the bridge balance throughout the recordings.
The recording pipette solution contained (in mM) 117.0 K-gluconate,
13.0 KCl, 1.0 MgCl
2
, 0.07 CaCl
2
, 0.1 EGTA, 10.0 HEPES, and 0.5%
biocytin. Data were digitized, stored on-line using Axotape software
(Axon Instruments), and also recorded onto VHS tape for off-line
analysis. Current injection through the recording electrode consisted
of a sinusoidal waveform with an AC component (I
1
) that varied in
both amplitude (50 800 pA) and frequency (0.1100 Hz). The DC
component (I
0
) of the current waveform was altered to manipulate the
ring mode of the neuron (i.e., burst vs. tonic). All experimental
records of membrane potential of relay neuron in whole cell mode
have been adjusted to account for a 10-mV junction potential.
Fourier analysis of experimental and theoretical responses
Customized user M-les were written for MATLAB 5.2.0 (The
MathWorks) to perform data analysis using an SGI Challenge super-
computer that runs the IRIX operating system. For each stimulus
condition, a periodic histogram (q
k
, k an integer, 0
k
N
1, n
64 bins) was constructed that tallied over c cycles of period T the
number of action potentials (q
k
) evoked by the experimental or model
relay neuron at each of N blocks of phase relative to the applied
currents period. Accounting for the number of cycles recorded and
the time represented by one bin of phase (i.e., for 64 bins, 1 bin is
/32 rad), we generated the (periodic) poststimulus response histo-
gram (PSTH) dened by Q
k
q
k
N/cT. A discrete Fourier transform
of this PSTH was performed, leading to a set of N complex valued
numbers, Q n
, given by (Press et al. 1992)
Q n
k
0
N
1
Q
k
exp
2 ikn/N
(1)
each with an associated amplitude, A
n
Q n
, and phase, P
n
arg(Q n
)/2 . With the preceding denitions, F
0
A
0
/N has units of
spikes/second and is the mean ring rate of the neuron; that is, F
0
q
tot
/cT, where q
tot
k
q
k
is the total number of spikes during the
trial. The fundamental or stimulus-driven component of the response,
F
1
, is given by F
1
(A
1
A