Quantitative Receptor Properties
March 10th, 2007
Cliff Kerr
Cortex
The purpose of this literature review is to quantify the four most important properties of
neurotransmitter receptors: their time constants, their synaptic currents, their open
probabilities, and their distributions throughout the brain. Once known, these data can
be implemented into the Robinson et al. model (Fig. 1) via the dendritic filter functions,
as shown in Section 3. All data are obtained from physiological experiments.
t0/2
Thalamus
i
e
t0/2
t0/2
t0/2
r
s
tos
n
Fig. 1 The Robinson et al. corticothalamic model, comprised of the
cortex (e and i), thalamic reticular nucleus (r), thalamic sensory nuclei
(s), and sensory afferents (n). The excitatory and inhibitory neuron
populations (white and black boxes, respectively) are interlinked by
bundles of axons (arrowheads for excitatory connections; circles for
inhibitory). Significant time delays are shown in grey.
Outline
1. Physiological background
1.1 Electrical properties
1.2 Ion channel kinetics
1.3 Cell response dynamics
2. Receptor properties
2.1 Time constants
2.2 Current size and opening probability
2.3 Densities
3. Model implementation
3.1 Variable time constant parameter
3.2 Fixed multiple time constants
3.3 Transfer functions
Appendix 1: Full sources
References
1
2
2
3
3
4
4
5
5
6
6
6
7
8
10
1. Physiological background
One property of neurons which survives averaging over ~108 cells is the signal filtering
that occurs as a result of synaptic transmission. This filtering is a product of two factors:
(i) the passive electrical properties of the neuron, and (ii) the ion channel and
neurotransmitter kinetics.
1.1 Electrical properties
The cell membrane acts like an RC circuit, with the resistance determined by the number
and type of open ion channels, and the capacitance determined primarily by the cell size
(Kandel et al. 2000, p. 142). The membrane time constant may then be determined by
applying a step voltage to the cell, as shown in Fig. 2.
ΔV
m
t (ms)
τ
Fig. 2 A standard method for measuring membrane time
constants. The stimulus is a voltage step (dotted line), and the
membrane potential changes like an RC circuit, with a time
constant given by τ = RC.
Typical membrane time constants, measured in this way or in similar ways, are about 15
ms for neocortical pyramidal cells and 20-50 ms for other CNS neurons (Koch et al. 1996,
p. 96), which in our notation gives α = 70 s-1 for pyramidal cells and α = 20-50 s-1 for
other neurons. The value for pyramidal cells agrees fairly well with Rowe et al. (2004,
p. 423), who reported α = 75 s-1 for eyes-closed and α = 93 s-1 for eyes-open.
The membrane time “constant” is actually not constant, as it is dependent upon
spontaneous background activity, since this affects the membrane resistance (and recall
τ = RC). For a typical spontaneous firing rate of about 5-10 Hz (Koch 1999, p. 412), the
membrane time constant may be a small as 1-3 ms (Koch 1999, p. 413), while for zero
background activity, it may exceed 100 ms (Koch 1999, p. 77).
Another problem is that membrane time constants are usually calculated by injecting
current into the soma and measuring its decay (also at the soma). This is a reasonable
method of measuring the response to inhibitory inputs, which are typically located at or
near the soma, but not for excitatory inputs, which are usually located on dendrites
(Kandel et al. 2000, p. 210).
The dendritic properties are described by two decay constants: spatial and temporal. The
spatial decay constant (also called the length constant) is the distance a signal must
propagate along a dendrite to decay to 1/e of its original value. For a pyramidal cell, a
dendritic signal will typically decay to approximately 0.25-0.5 of its original magnitude
after it travels the distance to the cell soma (Magee et al. 1998, p. 338).
The temporal spreading in dendrites is more complicated. Jaslove’s cable model of
dendrites (1992, p. 504) has shown time constants due to dendritic propagation of about
1 ms for a typical dendritic length, with a maximum (for a dendrite of length l =750 m)
of about 6 ms. A similar (though preliminary) result of 1 ms was found physiologically
by Ito and Oshima (1965).
Tsukahara and Kosaka (1968, p. 105) reported a total decay time constant of 7 ms,
including dendritic, receptor, and membrane time constants; they were however using
2
nonpyramidal neurons (red nucleus cells), which have smaller dendritic trees. Svirskis et
al. (1997, p. 3011), using electrophysiology on turtle motor neurons, found an upper limit
of 19 ms for the dendritic time constant plus the membrane time constant. Similar
results are found by Agmon-Snir and Segev (1993, p. 2079), who report total time
constants of about 20 ms, with about 2-4 ms of that being contributed by the basal
dendrites. (The apical dendrite has a larger time constant, but is thought to be less
important [LaBerge 2006, p. 238].)
1.2 Ion channel kinetics
Here, “ion channel kinetics” is used to refer to all the processes involved in synaptic
transmission, which include (i) the duration the neurotransmitter remains in the synaptic
cleft; (ii) how long it takes the receptor to desensitize to the transmitter; (iii) and how
long the channel remains open after the transmitter binds. Other delays are insignificant
compared to these three (implied by, e.g., Tsukahara and Kosaka 1968, p. 108).
Due to reuptake, the duration of (i) is likely to be unimportant (Jones and Westbrook
1996, p. 98). (ii) has been measured at about 5 ms for glutamate receptors (Hausser and
Roth 1997b, p. 82), but is probably not relevant since there is unlikely to be transmitter
present for that long in the synaptic cleft. Hence the most important consideration is (iii),
and it is this which shall be referred to as the receptor time constant. Note that for most
receptors, the rise time constant is so short compared to the decay time constant that it
can be neglected (Hausser and Roth 1997a, p. 7610), at least in the context of our model.
The time constant is thus determined by the type of receptors the downstream (receiving)
population of neurons have, not the transmitter used by the upstream population. (For
example, a GABAergic neuron may produce either a fast or slow response in a
downstream cell, depending on whether that cell uses GABAA or GABAB receptors.)
1.3 Cell response dynamics
To determine how a cell actually responds to stimuli, we must combine the somatic,
dendritic, and receptor time constants. The question we are trying to answer is: how
temporally separated do two synaptic inputs have to be for the cell to respond to them
independently? This difficult problem—directly related to the low-pass filtering which
occurs in neurons—has not yet been solved, but we can make an estimate.
The consensus seems to be that dendritic response times are essentially independent of
the dendritic properties, and depend only on the ion channel kinetics (Koch 1999, p. 80;
Softky 1994, p. 15). However, this is only relevant at the soma if the dendrite responds
to stimuli nonlinearly—which, thanks to voltage-gated ion channels, it does (Softky 1994,
p. 18). Hence, in terms of low-pass filtering, we can assume that the dendrite is limited
only by its receptor time constants, since in any situation where it is receiving input at a
rate greater than ~100 Hz, it is almost certainly going to be in the nonlinear regime.
The somatic membrane time constant, by contrast, cannot be circumvented. The
neuron’s temporal integration period is directly proportional to it (Koch et al. 1996, p. 97;
Douglas and Martin 1991, p. 289), and hence it imposes a lower limit on the overall time
constant (and hence an upper limit on the cell’s frequency response). For a neuron
receiving typical background activity, we will use an effective membrane time constant of
~5-10 ms, with the lower bound taken in the present work.
One final consideration needs to be mentioned. Our effective membrane time constant
implies that the maximal frequency to which a cell can respond is about 100 Hz, which
is reasonable (Koch et al. 1996, p. 100). However, this is a lower limit of the time
constant, and it is likely that larger time constants will also contribute to the EEG signal.
3
This complication can be conveniently ignored, since the model does not use time
constants to derive the scalp potential from neural activity fields , but instead assumes
direct proportionality between the EEG signal and e. Hence, the lower limit of the time
constant is indeed the quantity of interest.
2. Receptor properties
This section discusses the receptor properties relevant to the implementation of time
constants in the model. A summary of the information presented in Secs. 2.1-2.3 and
Appendix 1 is given in Table 1. Note that the reliability of the data varies widely, with
some authors reporting highly contradictory values.
Receptor
type
Non-NMDA
NMDA
GABAA
GABAB
Decay time
Open
constant (ms) probability
5
100
20
100
0.7
0.3
0.5
0.15
Current
size (pA)
Cortical
density
(nmol/kg)
30
10
60
10
1.0
1.2
0.8
0.8
Thalamic sensory Thalamic reticular
nuclei density
nucleus density
(nmol/kg)
(nmol/kg)
1.0
0.3
0.7
0.1
0.6
0.2
0.0
0.0
Table 1 Biophysical data for the most important excitatory and inhibitory
receptors in the brain. Errors are not shown; however, they should be
assumed to be large (see Appendix 1).
2.1 Receptor time constants
Next we need to consider five types of receptor commonly found in the central nervous
system: three glutamate receptors and two GABA receptors. The receptors for other
neurotransmitters have vastly longer time constants—for example, the effects of a single
pulse of serotonin can last up to 10 minutes (McCormick and Wang 1991); noradrenaline
lasts 100-200 s (McCormick and Prince 1988, p. 980); and acetylcholine acting on
nicotinic receptors has latency 150 ms and duration 1.2 s, while on muscarinic receptors
it has latency 1.2 s and duration 21 s (Curro Dossi et al. 1991).
The four common types of glutamate receptor are one metabotropic and three types of
ionotropic (NMDA, AMPA and kainate). Glutamatergic metabotropic receptors, being
mediated by G proteins, have by far the longest durations—up to 30 s (McCormick and
von Krosigk 1992, p. 2774). Hence, they are not likely to be involved in evoked potential
generation, except in terms of potentiation.
NMDA receptors require both the binding of glutamate and a degree of membrane
depolarization (Kandel et al. 2000, p. 1260). From the data on p. 215 in Kandel et al., the
time constant appears to be ~100 ms, and other experiments put the time constant at
about 80 ms, with activity still continuing past 500 ms (Forsythe and Westbrook 1988,
p. 515). Non-NMDA receptors (kainate or AMPA) have much shorter time constants,
typically reported as being 1-5 ms (Hausser and Roth 1997b, p. 7622; Partin et al. 1996, p.
6636; etc.). Rise time constants are typically a fraction of a millisecond and hence are
negligible (e.g., Hausser and Roth 1997a, p. 81).
GABAergic neurotransmission can also occur via metabotropic and ionotropic receptors.
GABAB receptors are metabotropic and hence have long time constants of about 100 ms
(Steriade et al. 1997, p. 702)—which, unlike for glutamatergic metabotropic receptors, are
brief enough to be important for evoked potentials, particularly for later features. Most
sources indicate that GABAA receptors are somewhat slower than non-NMDA receptors;
time constants of 5-20 ms have been reported (Otis and Mody 1992, p. 13; Steriade et al.
1997, p. 702; Thomson et al. 1996, p. 99).
4
2.2 Synaptic current size and opening probabilities
Synaptic currents resulting from receptor bindings are typically determined by patchclamp experiments on single cells or (more rarely) single channels. Fairly reliable
quantitative data are available, with the caveat that the in vitro conditions might vary from
in vivo ones.
The current from a non-NMDA receptor binding event is 10-30 pA (Destexhe and
Sejnowski 2001, p. 135), and approximately three to five times less for NMDA receptors
(Burgard and Hablitz 1993, p. 1847; Spruston et al. 1995, p. 332). The currents for
GABAA receptors are larger, at around 60 pA (De Koninck and Mody 1994, p. 1323),
with the currents for GABAB around 10 pA (Otis et al. 1993, p. 404).
Receptors do not always open when agonist is applied; this is due to binding affinity and
transmitter concentrations, as well as various other factors. Opening probabilities can
similarly be studied easily using in vitro experiments. The opening probability for nonNMDA receptors is 0.7 (Hausser and Roth 1997a, p. 87; Hestrin 1992, p. 996), and about
0.3 for NMDA receptors (Destexhe and Sejnowski 2001, p. 137). For GABAA,
experiments have found opening probabilities of about 0.5 (Birnir et al. 1994, p. 100;
Wagner et al. 1995, p. 10465), while GABAB is approximately 0.15 (Chu et al. 1990, p.
343).
2.3 Receptor distribution and density
The final step is to determine which types of neurons have which types of receptors, and
in what relative proportions. It turns out that each population of neurons has multiple
types of receptor; in other words, most neurons have both NMDA and non-NMDA
glutamate receptors, as well as GABAA and GABAB receptors. Quantitative estimates of
receptor distribution are usually studied through the binding of radioligands, and since
this requires injecting radioactive dye into the brain and then slicing it thinly, few studies
have been done on healthy adult humans. Hence most data quoted below are either
from rats or from human fetuses, though one author (Zilles et al. 2004) did manage to get
adult humans.
Cortical pyramidal neurons use both NMDA and non-NMDA receptors, with the sum
of the densities of all non-NMDA receptors approximately equal to the density of
NMDA receptors (Zilles et al. 2004, p. 423; Lee and Choi 1992, p. 286). Cortical
inhibitory neurons seem to have approximately equal amounts of GABAA and GABAB
(Zilles et al. 2004, p. 421; Bowery et al. 1987, p. 366), though some authors report almost
twice as much GABAA (Chu et al. 1990, p. 346).
In both the reticular and relay nuclei of the thalamus, it appears there are approximately
twice as many non-NMDA receptors as NMDA receptors (Lee and Choi 1992, p. 286),
and at least twice as many GABAA as GABAB (Chu et al. 1987, p. 346), although some
authors report roughly equal amounts (Bowery et al. 1987, p. 366).
There is a slight complication in that upstream populations of neurons might not
innervate downstream ones evenly—in other words, it is possible that cortical excitatory
neurons only synapse onto thalamic neurons with non-NMDA receptors, while thalamic
self-connections use predominantly NMDA. Although there is some evidence for this
(Steriade et al. 1997, p. 708), in the absence of further evidence this possibility will be
ignored.
5
3. Model implementation
Although possible, it is unwieldy to introduce free variables to describe not only all the
different time constants, but also their different predominances across neuronal
populations; hence, one of two simplifications is made.
3.1 Fitted time constant
In this case, which is the default for the Rennie et al. (2002) implementation of the model,
a single dendritic filter function L is used, and is given by
 i 
L  1  


1
1
 i 
1   ,


(Eq. 1)
where is the frequency,  is the decay time constant and  is the rise time constant. In
this model, the parameters  and  are considered to be average time constants for all
populations of neurons, and they are allowed to vary in order to improve the goodness
of fit.
3.2 Fixed multiple time constants
Because of the linearity of the Fourier transform, we can (fortunately) derive very simple
expressions for each of the different time constants. Instead of a single L, we have one
L for each connection. Mathematically,

i
Lab   DR (a, b) I R p R 1 
R
 R



1
1

i 
1 
 ,
 R 
(Eq. 2)
where D is the receptor density of population a innervated by population b, I is the
current, p is the open probability, and the sum is over all types of receptor R. Since we
have eleven connections in the model, we also have eleven Lab. However, these are not
all distinct. In fact, it can be shown between Fig. 1 and Table 1 that
Lee  Lie  Les  Lis
Lse  Lsn
(Eq. 3)
Lre  Lrs
Lii  Lei ,
leaving just L e e , L s e , L r e , L i i , and L s r . Thus, we have the following equations:
Lee  DnN (e, e) I nN p nN nN  D NM (e, e) I NM p NM  NM
Lii  DGA (i, i ) I GA pGA GA  DGB (i, i ) I GB pGB GB
Lse  DnN ( s, e) I nN p nN nN  D NM ( s, e) I NM p NM  NM
(Eq. 4)
Lre  DnN (r , e) I nN p nN nN  D NM (r , e) I NM p NM  NM
Lsr  DGA ( s, r ) I GA pGA GA  DGB ( s, r ) I GB pGB GB ,
where the subscripts refer to the type of receptor (nN=non-NMDA, NM=NMDA,
GA=GABAA, GB=GABAB), and
6

i
 R  1 
 R



1

i
1 
 R
1


 .
(Eq. 5)
Substituting in values from Table 1, we find
Lee  21 nN  3.6 NM
Lii  24 GA  1.2 GB
Lse  21 nN  0.9 NM
(Eq. 6)
Lre  13 nN  0.5 NM
Lsr  21 GA  0.2 GB .
Although fits from these two approaches produce different results, one is not obviously
a better choice. Instead, they reflect different approaches, depending on whether more
emphasis is placed on simplicity (in which case the fitted time constants approach should
be used) or physiological accuracy (in which case the fixed time constants approach
should be used).
3.3 Transfer functions
Here we present briefly and without derivation the transfer functions applicable to
Eqs. (1) and (6). The transfer function for (1) is identical to that given in Rennie et al.
(2002), and is in its simplest form
e
e it / 2 L2 Gesn
,

 n (1  L2 Gsrs )( De (1  LGii )  LGee )  e it ( L2 Gese  L3Gesre )
0
0
(Eq. 7)
where all the symbols have their usual meaning (Kerr et al.). Note that everything makes
perfect sense; the numerator is the plain impulse traveling to the cortex, delayed by a
time t0/2, and the denominator incorporates the effects of cortical (left hand side) and
thalamic (right hand side) loops.
For (6), since each gain now has its own dendritic filter function L, let us define a
quantity H=LG. These behave as we expect, e.g., Habc = HabHbc = LabLbcGabGbc . The
transfer function is now much more complicated, since we can no longer make the
random connectivity assumption (since the condition Hac=Hbc does not necessarily hold
for all a and b). It is:
 H

e it0 / 2  eisn  H esn 
e
 1  H ii

. (Eq. 8)

n


H eie  it0  H eise  H sreis
  e 
(1  H srs ) De  H ee 
 H ese  H esre 
1  H ii 

 1  H ii

Since this version of the transfer function has ten fittable variables (the gains which
appear) and since there are eleven unknown single gains, if we fix any single gain (for
example, Gsn=1, which is sensible) we can determine the others. Although powerful and
physiologically more accurate, this formulation has the major downside that it has many
more free parameters (11 gains instead of 5 gains and two time constants). Still, the extra
parameters might be worthwhile if they allow us to find the single gains—then the
overall picture might indeed turn out to be simpler, with changes in just one or two
single gains producing the observed effects.
7
Appendix 1: Full sources
This section lists the exact values and ranges given in the original papers for the
parameters listed in Table 1 and discussed in Secs. 2.1-2.3.
Non-NMDA
Time constant
 Estimate: 5 ms
 1.12-1.23 ms (Hausser and Roth 1997a, p. 81)
 1-8 ms (Colquhoun et al. 1992, p. 262)
 3-6 ms (Partin et al. 1996, p. 6636)
 5.2 ± 1 ms (Burgard and Hablitz 1993, p. 1845)
 3.9 ms (Forsythe and Westbrook 1988, p. 524)
 3.38 ± 0.24 ms (Hausser and Roth 1997b, p. 7622)
Probability
 Estimate: 0.7
 0.7 ± 0.03 (Hausser and Roth 1997a, p. 87)
 0.64 ± 0.2 (Hestrin 1992, p. 996)
 0.38-0.51 (Silver et al. 1996, p. 231)
 0.6-0.9 for kainate (Li et al. 2003, p. 12372)
Current
 Estimate: 30 pA
 10-30 pA (for “non-NMDA receptors”, Destexhe and Sejnowski 2001, p. 135)
 18 ± 2 pA (for “non-NMDA receptors”, McBain and Dingledine 1992, p. 18)
 30-40 pA or 3 times the NMDA current (Burgard and Hablitz 1993, pp. 1843
and 1847)
 100 pA (Spruston et al. 1995, p. 332)
 0.6 ± 1 pA for a single channel (Hestrin 1992, p. 996)
Cortical density
 Estimate: 1 nmol/kg
 ~0.8 nmol/kg (600 fmol/mg for AMPA and ~200 fmol/mg for kainate, from
the graph in Zilles et al. 2004, p. 423)
 ~2.7 nmol/kg (in fetuses; from Lee and Choi 1992, p. 286)
 ~0.4 nmol/kg (just for AMPA; from Eickhoff et al. 2007, p. 1328)
 ~2.1 nmol/kg (1 nmol/kg for AMPA and 1.1 nmol/kg for kainate; from the
graphs in Zilles et al. 1999, p. 1056)
Thalamic relay density
 Estimate: 1 nmol/kg (calculated by comparing to cortical values)
 ~2.6 nmol/kg (in fetuses; Lee and Choi 1992, p. 286)
Thalamic reticular density
 Estimate: 0.6 nmol/kg (calculated by comparing to cortical values)
 ~1.7 nmol/kg (in fetuses; Lee and Choi 1992, p. 286)
NMDA
Time constant
 Estimate: 100 ms
 ~100 ms (from the graph in Kandel et al. 2000, p. 215)
 85 ms (Forsythe and Westbrook 1998, p. 524)
 180 ± 20 ms (Spruston et al. 1995, p. 334)
Probability
8
 Estimate: 0.3
 0.3 (Jahr 1992, p. 470)
Current
 Estimate: 10 pA
 14 ± 1 pA (Burgard and Hablitz 1993, p. 1847)
 20 pA or 0.2 of the non-NMDA current (Spruston et al. 1995, p. 332)
Cortical density
 Estimate: 1.2 nmol/kg
 ~1.2 nmol/kg (from the graph in Zilles et al. 2004, p. 423)
 ~1.8 nmol/kg (in fetuses; from Lee and Choi 1992, p. 286)
 ~1.2 nmol/kg (Eickhoff et al. 2007, p. 1328)
 0.7-1.0 nmol/kg (in rats; from Monaghan and Cotman 1985, p. 2912)
 3 nmol/kg (Zilles et al. 1999, p. 1056)
Thalamic relay density
 Estimate: 0.3 nmol/kg (calculated by comparing to cortical values)
 ~0.9 nmol/kg (in fetuses; from Lee and Choi 1992, p. 286)
 0.4-0.5 nmol/kg (in rats; from Monaghan and Cotman 1985, p. 2912)
Thalamic reticular density
 Estimate: 0.2 nmol/kg (calculated by comparing to cortical values)
 ~0.6 nmol/kg (in fetuses; from Lee and Choi 1992, p. 286)
 0.2 nmol/kg (in rats; from Monaghan and Cotman 1985, p. 2912)
GABAA
Time constant
 Estimate: 20 ms
 4.2-7.2 ms (Otis and Mody 1992, p. 13)
 ~20 ms (from the graph in Steriade et al. 1997, p. 702)
 21 ± 4 ms (given as FWHM=15 ms; Thomson et al. 1996, p. 99)
Probability
 Estimate: 0.5
 0.98 (Li et al. 2003, p. 12372)
 0.62 (Wagner et al. 1995, p. 10465)
 0.5 (Birnir et al. 1994, p. 100)
 0.4-0.97 (Newland et al. 1991, p. 217)
 0.12—although they seem to have used a different method (Dillon et al. 1995, p.
596)
Current
 Estimate: 60 pA
 57.1 pA (De Koninck and Mody 1994, p. 1323)
Cortical density
 Estimate: 0.8 nmol/kg
 ~0.8 nmol/kg (from the graph in Zilles et al. 2004, p. 421)
 13-64 nmol/kg (in rats1; from Bowery et al. 1987, p. 366)
 2.4-3.2 nmol/kg (Chu et al. 1987, p. 1456)
 4.0-4.7 nmol/kg (in rats; from Chu et al. 1990, p. 343)
 2.5 nmol/kg (Zilles et al. 1999, p. 1056)
1
“The number of GABAA subunits is is higher in the monkey than in the rat”
(Ambardekar et al. 2003, p. 1041)—an observation clearly not present in these results.
9
Thalamic relay density
 Estimate: 0.7 nmol/kg
 ~0.7 nmol/kg (in monkeys; from Ambardekar et al. 2003, p. 1037)
 15-30 nmol/kg (in rats; from Bowery et al. 1987, p. 366)
Thalamic reticular density
 The reticular thalamic nucleus receives almost exclusively glutamatergic input and
hence has very few GABAA receptors.
GABAB
Time constant
 Estimate: 100 ms
 Note: the rise time constant may be significant, of at least 12-20 ms (Otis et al.
1993, p. 395) and possibly as much as 45 ms (Otis et al. 1993, p. 398)
 ~100 ms (from the graph in Steriade et al. 1997, p. 702)
 110 ± 7 ms (Otis et al. 1993, p. 398)
Probability
 Estimate: 0.15
 Three to four times less than GABAA receptors (Chu et al. 1990, p. 343)
Current
 Estimate: 10 pA
 The conductance is approximately 0.2 that of GABAA, and the total charge
transferred is comparable to GABAA (Otis et al. 1993, p. 404)
Cortical density
 Estimate: 0.8 nmol/kg
 ~0.8 fmol/mg (from the graph in Zilles et al. 2004, p. 423)
 12-30 nmol/kg (in rats; from Bowery et al. 1987, p. 366)
 1.1-1.3 nmol/kg (Chu et al. 1987, p. 1456)
 1.9-3.5 nmol/kg (in rats; from Chu et al. 1990, p. 343)
Thalamic relay density
 Estimate: 0.1 nmol/kg
 15-20 nmol/kg (in rats; from Bowery et al. 1987, p. 366)
 70-120 fmol/mg (in monkeys; from Bowery et al. 1999, p. 1679)
Thalamic reticular density
 We make the approximation that there are no GABA receptors in the reticular
nucleus, and this is almost true—the observed density a tiny 0.014 nmol/kg (in
monkeys; from Bowery et al. 1999, p. 1679)
References
Agmon-Snir H, Segev I. Signal delay and input synchronization in passive dendritic
structures. J Neurophysiol. 1993 Nov;70(5):2066-85.
Ambardekar AV, Surin A, Parts K, Ilinsky IA, Kultas-Ilinsky K. Distribution and
binding parameters of GABAA receptors in the thalamic nuclei of Macaca mulatta and
changes caused by lesioning in the globus pallidus and reticular thalamic nucleus.
Neuroscience. 2003;118(4):1033-43.
Birnir B, Everitt AB, Gage PW. Characteristics of GABAA channels in rat dentate gyrus.
J Membr Biol. 1994 Oct;142(1):93-102.
Bowery NG, Hudson AL, Price GW. GABAA and GABAB receptor site distribution in
the rat central nervous system. Neuroscience. 1987 Feb;20(2):365-83.
10
Bowery NG, Parry K, Goodrich G, Ilinsky I, Kultas-Ilinsky K. Distribution of GABA(B)
binding sites in the thalamus and basal ganglia of the rhesus monkey (Macaca mulatta).
Neuropharmacology. 1999 Nov;38(11):1675-82.
Burgard EC, Hablitz JJ. NMDA receptor-mediated components of miniature excitatory
synaptic currents in developing rat neocortex. J Neurophysiol. 1993 Nov;70(5):1841-52.
Chu DC, Albin RL, Young AB, Penney JB. Distribution and kinetics of GABAB
binding sites in rat central nervous system: a quantitative autoradiographic study.
Neuroscience. 1990;34(2):341-57.
Chu DC, Penney JB Jr, Young AB. Quantitative autoradiography of hippocampal
GABAB and GABAA receptor changes in Alzheimer's disease. Neurosci Lett. 1987 Dec
4;82(3):246-52.
Colquhoun D, Jonas P, Sakmann B. Action of brief pulses of glutamate on
AMPA/kainate receptors in patches from different neurones of rat hippocampal slices.
J Physiol. 1992 Dec;458:261-87.
Curro Dossi R, Pare D, Steriade M. Short-lasting nicotinic and long-lasting muscarinic
depolarizing responses of thalamocortical neurons to stimulation of mesopontine
cholinergic nuclei. J Neurophysiol. 1991 Mar;65(3):393-406.
De Koninck Y, Mody I. Noise analysis of miniature IPSCs in adult rat brain slices:
properties and modulation of synaptic GABAA receptor channels. J Neurophysiol. 1994
Apr;71(4):1318-35.
Destexhe A, Sejnowsky TJ. 2001. Thalamocoritcal Assemblies. Oxford University Press.
Dillon GH, Im WB, Pregenzer JF, Carter DB, Hamilton BJ. [4-Dimethyl-3-tbutylcarboxyl-4,5-dihydro (1,5-a) quinoxaline] is a novel ligand to the picrotoxin site on
GABAA receptors, and decreases single-channel open probability. J Pharmacol Exp
Ther. 1995 Feb;272(2):597-603.
Douglas RJ, Martin KA. Opening the grey box. Trends Neurosci. 1991 Jul;14(7):286-93.
Eickhoff SB, Schleicher A, Scheperjans F, Palomero-Gallagher N, Zilles K. Analysis of
neurotransmitter receptor distribution patterns in the cerebral cortex. Neuroimage. 2007
Feb 15;34(4):1317-30.
Forsythe ID, Westbrook GL. Slow excitatory postsynaptic currents mediated by Nmethyl-D-aspartate receptors on cultured mouse central neurones. J Physiol. 1988
Feb;396:515-33.
Hausser M, Roth A. Dendritic and somatic glutamate receptor channels in rat cerebellar
Purkinje cells. J Physiol. 1997a May 15;501 ( Pt 1):77-95.
Hausser M, Roth A. Estimating the time course of the excitatory synaptic conductance
in neocortical pyramidal cells using a novel voltage jump method. J Neurosci. 1997b Oct
15;17(20):7606-25.
Hestrin S. Activation and desensitization of glutamate-activated channels mediating fast
excitatory synaptic currents in the visual cortex. Neuron. 1992 Nov;9(5):991-9.
11
Ito M, Oshima T. Electrical behaviour of the motoneurone membrane during
intracellularly applied current steps. J Physiol. 1965 Oct;180(3):607-35. 1
Jahr CE. High probability opening of NMDA receptor channels by L-glutamate.
Science. 1992 Jan 24;255(5043):470-2.
Jaslove SW. The integrative properties of spiny distal dendrites.
1992;47(3):495-519.
Neuroscience.
Jones MV, Westbrook GL. The impact of receptor desensitization on fast synaptic
transmission. Trends Neurosci. 1996 Mar;19(3):96-101.
Kandel ER, Schwartz JH, Jessell TM. 2000. Principles of Neural Science, Fourth
Edition. New York: McGraw-Hill.
Kerr CC, Rennie CJ, Robinson PA. Physiology-based modeling of auditory evoked
response potentials. Sitting on desk (to be submitted soon).
Koch C. 1999. Biophysics of Computation. New York: Oxford University Press.
Koch C, Rapp M, Segev I. A brief history of time (constants). Cereb Cortex. 1996 MarApr;6(2):93-101.
LaBerge D. Apical dendrite activity in cognition and consciousness. Conscious Cogn.
2006 Jun;15(2):235-57.
Lee H, Choi BH. Density and distribution of excitatory amino acid receptors in the
developing human fetal brain: a quantitative autoradiographic study. Exp Neurol. 1992
Dec;118(3):284-90.
Li G, Oswald RE, Niu L. Channel-opening kinetics of GluR6 kainate receptor.
Biochemistry. 2003 Oct 28;42(42):12367-75.
Magee J, Hoffman D, Colbert C, Johnston D. Electrical and calcium signaling in
dendrites of hippocampal pyramidal neurons. Annu Rev Physiol. 1998;60:327-46.
McBain C, Dingledine R. Dual-component miniature excitatory synaptic currents in rat
hippocampal CA3 pyramidal neurons. J Neurophysiol. 1992 Jul;68(1):16-27.
McCormick DA, Prince DA. Noradrenergic modulation of firing pattern in guinea pig
and cat thalamic neurons, in vitro. J Neurophysiol. 1988 Mar;59(3):978-96.
McCormick DA, von Krosigk M. Corticothalamic activation modulates thalamic firing
through glutamate "metabotropic" receptors. Proc Natl Acad Sci U S A. 1992 Apr
1;89(7):2774-8.
McCormick DA, Wang Z. Serotonin and noradrenaline excite GABAergic neurones of
the guinea-pig and cat nucleus reticularis thalami. J Physiol. 1991 Oct;442:235-55.
Monaghan DT, Cotman CW. Distribution of N-methyl-D-aspartate-sensitive
[3H]glutamate-binding sites in rat brain. J Neurosci. 1985 Nov;5(11):2909-19.
L-
Newland CF, Colquhoun D, Cull-Candy SG. Single channels activated by high
concentrations of GABA in superior cervical ganglion neurones of the rat. J Physiol.
1991 Jan;432:203-33.
12
Otis TS, De Koninck Y, Mody I. Characterization of synaptically elicited GABAB
responses using patch-clamp recordings in rat hippocampal slices. J Physiol. 1993
Apr;463:391-407.
Otis TS, Mody I. Modulation of decay kinetics and frequency of GABAA receptormediated spontaneous inhibitory postsynaptic currents in hippocampal neurons.
Neuroscience. 1992 Jul;49(1):13-32.
Partin KM, Fleck MW, Mayer ML. AMPA receptor flip/flop mutants affecting
deactivation, desensitization, and modulation by cyclothiazide, aniracetam, and
thiocyanate. J Neurosci. 1996 Nov 1;16(21):6634-47.
Rennie CJ, Robinson PA, Wright JJ. Unified neurophysical model of EEG spectra and
evoked potentials. Biol Cybern. 2002 Jun;86(6):457-71.
Rowe DL, Robinson PA, Rennie CJ. Estimation of neurophysiological parameters from
the waking EEG using a biophysical model of brain dynamics. J Theor Biol. 2004 Dec
7;231(3):413-33.
Silver RA, Cull-Candy SG, Takahashi T. Non-NMDA glutamate receptor occupancy
and open probability at a rat cerebellar synapse with single and multiple release sites.
J Physiol. 1996 Jul 1;494 ( Pt 1):231-50.
Softky W. Sub-millisecond coincidence detection in active dendritic trees. Neuroscience.
1994 Jan;58(1):13-41.
Spruston N, Jonas P, Sakmann B. Dendritic glutamate receptor channels in rat
hippocampal CA3 and CA1 pyramidal neurons. J Physiol. 1995 Jan 15;482 ( Pt 2):325-52.
Steriade M, Jones EG, McCormick DA (1997) Thalamus. Oxford: Elsevier.
Svirskis G, Baginskas A, Hounsgaard J, Gutman A. Electrotonic measurements by
electric field-induced polarization in neurons: theory and experimental estimation.
Biophys J. 1997 Dec;73(6):3004-15.
Thomson AM, West DC, Hahn J, Deuchars J. Single axon IPSPs elicited in pyramidal
cells by three classes of interneurones in slices of rat neocortex. J Physiol. 1996 Oct
1;496 ( Pt 1):81-102.
Tsukahara N, Kosaka K. The mode of cerebral excitation of red nucleus neurons. Exp
Brain Res. 1968;5(2):102-17.
Wagner DA, Goldschen-Ohm MP, Hales TG, Jones MV. Kinetics and spontaneous
open probability conferred by the epsilon subunit of the GABAA receptor. J Neurosci.
2005 Nov 9;25(45):10462-8.
Zilles K, Palomero-Gallagher N, Schleicher A. Transmitter receptors and functional
anatomy of the cerebral cortex. J Anat 2004 205:417-432.
Zilles K, Qu MS, Kohling R, Speckmann EJ. Ionotropic glutamate and GABA receptors
in human epileptic neocortical tissue: quantitative in vitro receptor autoradiography.
Neuroscience. 1999;94(4):1051-61.
13