1Departamento de Ingeniería Informática, Universidad Autónoma de Madrid, 28049 Madrid; and 2Departamento Investigación, Hospital Ramón y Cajal, 28034 Madrid, Spain
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ABSTRACT |
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Varona, P.,
J. M. Ibarz,
L. López-Aguado, and
O. Herreras.
Macroscopic and Subcellular Factors Shaping Population Spikes.
J. Neurophysiol. 83: 2192-2208, 2000.
Population spikes (PS) are built by the extracellular summation of
action currents during synchronous action potential (AP) firing. In the
hippocampal CA1, active dendritic invasion of APs ensures mixed
contribution of somatic and dendritic currents to any extracellular
location. We investigated the macroscopic and subcellular factors
shaping the antidromic PS by fitting its spatiotemporal map with a
multineuronal CA1 model in a volume conductor. Decreased summation by
temporal scatter of APs reduced less than expected the PS peak in the
stratum pyramidale (st. pyr.) but strongly increased the relative
contribution of far dendritic currents. Increasing the number of firing
cells also augmented the relative dendritic contribution to the somatic
PS, an effect caused by the different waveform of somatic and dendritic
unitary transmembrane currents (Im). Those
from somata are short-lasting and spiky, having smaller temporal
summation than those from dendrites, which are smoother and longer. The
different shape of compartmental Ims is
imposed by the fitting of backpropagating APs, which are large and fast
at the soma and smaller and longer in dendrites. The maximum sodium
conductance (Na) strongly affects the
unitary APs at the soma, but barely the PS at the stratum pyramidale
(st. pyr.). This occurred because somatic Im
saturated at low
Na due to the strong
reduction of driving force during somatic APs, limiting the current
contribution to the extracellular space. On the contrary,
Na effectively defined the PS
amplitude in the st. radiatum. The relative contribution of dendritic
currents to the st. pyr. increases during the time span of the PS, from ~30-40% at the peak up to 100% at its end, a pattern resultant from the timing of active inward currents along the somatodendritic axis, which delay during backpropagation. Extreme changes imposed on
dendritic currents caused only moderate effects on the st. pyr. due to
reciprocal shunting of active soma and dendrites that partially
counterbalance the net amount of instant current. The amplitude of the
PS follows an inverse relation to the internal resistance
(Ri), which turned out to be a most critical
factor. Low Ri facilitated the spread of APs
into dendrites and accelerated their speed, increasing temporal
overlapping of inward currents along the somatodendritic axis and
yielding the best PS reproductions. Model reconstruction of field
potentials is a powerful tool to understand the interactions between
different levels of complexity. The potential use of this approach to
restrain the variability of some experimental measurements is discussed.
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INTRODUCTION |
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During synchronous activation of regularly
arranged neuron ensembles, the coactivated transmembrane currents
(Im) add in the interstitium rising
characteristic field potentials (FPs). Because of their reproducibility
and stability they are widely used to study the global response of
neuron nuclei plus the average behavior of individual neurons and
subcellular electrical events. A precise correlation between field and
subcellular events is hindered because the extracellular part of the
Im spread within the tissue in all directions, so that FPs always are contributed by currents arising from
different cell domains. These so-called volume-propagated currents are
inherent to extracellular recordings. However, the theoretical
knowledge relating extracellular currents and field potentials is well
developed (Lorente de Nó 1947a; Nicholson 1973
) and allows the identification of subcellular membrane
generators during synchronous activation of architectonically complex
neuron ensembles.
Our initial goal in this study was to correlate the averaged electrical
responses of homogeneous populations of neurons with the structural and
biophysical findings obtained with modern techniques at the subcellular
level. These have revealed a variety of voltage-gated channels in
distinct subcellular domains (Hoffman et al. 1997; Magee and Johnston 1995a
,b
) that necessarily will be
coactivated in variable degrees during neuronal operation, their
interplay being essential for neuronal integration. We have
extrapolated the available empiric data using a realistic multineuronal
model of the highly laminated CA1 region to reconstruct the simplest spatiotemporal FP map that is obtained during synchronous antidromic action potential (AP) firing, i.e., the population spike (PS). It can
be anticipated that the small errors on subcellular parameters that
would not affect notably the physiology of a single-cell model,
however, may originate large deviations from the experimental results
when accumulated to reproduce the PS. The process of minimizing these
divergences constitute a powerful tool to study the critical factors
involved in shaping evoked FPs (Klee and Rall 1977
;
Rall and Shepherd 1968
) and to restrict the parametric
space of single-cell models.
The customary hippocampal PS is considered a reliable index for the
number of synchronously firing neurons (Andersen et al. 1971) and so has been used to test changes in average neuron
excitability in countless studies of physiological phenomena, such as
synaptic plasticity. A critical consideration of its extracellular
nature is missing, however. The mentioned interpretation requires that the current contributed by each neuron along its entire morphology remains constant in different physiological situations, an assumption hard to reconcile with some major experimental observations. Thus APs
are fired in the axon and soma membranes, but they can actively spread
to or even be initiated in dendritic regions of many neuronal types
(Chen et al. 1997
; Jefferys 1979
;
Larkum et al. 1996
; Regehr et al. 1992
;
Turner et al. 1991
; Wong et al. 1979
).
This being long known for CA1 pyramidal cells from the inspection of PS
profiles and current-source density (CSD) analysis (Fujita and
Sakata 1962
; Herreras 1990
; Leung
1978
; Sperti et al. 1966
), the relative
contribution of the spatially segregated somatic and dendritic action
currents to the PS has been rarely considered (e.g., Lorente de
Nó 1947b
). For instance, we recently have demonstrated
that backpropagating dendritic APs may contribute as much as 40% to
the antidromic PS amplitude recorded in the stratum pyramidale (st.
pyr.) in vivo (López-Aguado et al. 2000
). Because
somatodendritic action currents can be modulated locally
(Callaway and Ross 1995
; Herreras and Somjen
1993
; Mackenzie and Murphy 1998
; Spruston
et al. 1995
), a further interest of this study is to obtain
some clues as to how the electrical activity of a particular neuronal
domain (soma, dendrites or axon) contribute to shape the FPs recorded
in regions spatially occupied by or shared with others.
Specifically, we sought to determine the effect of the asynchrony of
activation, the cell number (aggregate size), and the relative
contribution of different cellular domains shaping the PS. As a
necessary step, the initiation and propagation of APs and the passive
and active properties of individual cells that give them shape,
including channel distribution and kinetics, also were correlated. Some
of the results have been presented in preliminary form (Herreras
et al. 1997; Varona et al. 1998
).
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METHODS |
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Experimental procedures
GENERAL.
Female Sprague-Dawley rats weighing 200-250 g were anesthetized with
urethan (1.2-1.5 g/kg ip) and fastened to a stereotaxic device. The
animals were breathing spontaneously. Heart rate was monitored
continuously, and body temperature was kept constant at 37 ± 0.1°C with a heating blanket. Surgical and stereotaxic procedures
were as previously described (Herreras 1990;
Herreras et al. 1994
). Two concentric bipolar
stimulating electrodes were positioned in the alvear region and in the
ipsilateral CA3 for anti- and orthodromic activation of the CA1
pyramidal population, respectively (0.07- to 0.1-ms square pulses,
0.1-0.5 mA). A subcutaneous Ag/AgCl wire electrode under the neck skin
was used as reference. The recording electrodes were connected to
DC-coupled field effect transistor (FET) input stages. The
characteristic configuration of evoked potentials guided the placement
of the recording electrodes (Herreras 1990
).
EXTRACELLULAR RECORDING AND CSD ANALYSIS.
Recording electrodes were glass micropipettes backfilled with 150 mM
NaCl (3-6 M). One micropipette remained stationary in the CA1
somatic layer throughout the experiment to test the constancy of the
evoked PS amplitude, and another micropipette was used to explore
dorsoventral trajectories in 25- or 50-µm steps driven by a
piezoelectric micromanipulator. After filtering (1 Hz to 5 kHz
band-pass) and amplification, signals were recorded on VCR, acquired to
a computer (20- to 40-kHz acquisition rate, Digidata 1200, Axon
Instruments, Burlingame, CA) and processed by Axotape software (Axon
Instruments), and then further analyzed by the Axum program (Trimetrix,
Seattle, WA). Depth profiles of evoked FPs were used for CSD analysis,
which provides the magnitude and location of the net
Im generated by unclamped neuronal
elements contained within a very small portion of tissue. A detailed
account of technical and theoretical considerations for the calculation of CSD in vivo has been presented elsewhere (Herreras
1990
). We have assumed that the extracellular space is
homogeneous and isotropic, the derived errors can be ignored (see
following text). Using the method by Demirci et al.
(1997)
, we measured an average
Re of 300
· cm across the
CA1. The customary unidimensional approach for the calculation of
ICSD in the main cell axis
(z) was approximated by the following equation
(Freeman and Nicholson 1975
)
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INTRACELLULAR STUDY.
Micropipettes (1.5 mm OD) were backfilled with 2-4 M potassium acetate
(60-120 M). Signals were amplified using a bridge circuit
amplifier, filtered at 10 kHz, and stored on VCR for later analysis by
using pClamp and Axotape computer programs (20- to 40-kHz acquisition
rate). With the skull fastened to the stereotaxic device, brain
pulsations were greatly reduced by lifting the rear quarters of the
animal and, on occasions, the cisterna magna also was drained out. Care
was taken to keep the overlying cortex from air exposure. No further
requirements were needed to obtain stable lasting impalements (
96
min). Recordings were made from electrophysiologically identified
pyramidal cells located within the st. pyr. of the CA1, identified by
the characteristic field potential. After impalement of a cell,
I-V plots were obtained every 10 min to ensure cell stability. Cells that did not fire a single antidromic AP after alvear
stimulation were rejected. We have considered healthy cells those
having resting membrane potential more negative than
60 mV
(
67.6 ± 2.2 mV; n = 16) and overshooting APs.
The average apparent input resistance calculated from the linear range
of the I-V plots was 31.2 ± 2.7 M
(range, 18-42)
which is within reported values for sharp electrode recordings (e.g.,
Turner et al. 1991
). Once stabilized, most cells fired
spontaneous APs at a very low rate (
1 Hz).
Computer model
ARCHITECTONIC ORGANIZATION OF THE AGGREGATE.
The dorsal CA1 region was modeled with aggregates of different size
preserving an experimentally observed cell density of 64 neurons
oriented in parallel in a 50 × 50 µm anterolateral lattice
(Boss et al. 1987). The anteroposterior and lateromedial dimensions of the aggregates were 0.05 × 0.05, 0.2 × 0.2, 1 × 0.35, 1 × 1, and 3 × 2 mm, corresponding to 64, 1,024, 6,072, 17,424, and 104,544 morphologically identical model
neurons in the total volume, respectively. The dimensions and cell
number of the largest aggregate can be taken as a rough estimation of actual values for the dorsal CA1 region. Dorsoventral extension was set
to 0.8 mm (from the alveus to the distal apical tuft). Three different
spatial distributions of neurons were analyzed with the st. pyr.
(50-µm thick) containing their somata and arranged either in a
monolayer, four layers of even density, or a realistic distribution of
four uneven layers with 66% of somata in the apical side and 22 and
11% in the two layers of the basal side (proportions are rough
estimations made on our own previous histological material; see schemes
in Fig. 3). Each neuron was rotated a random angle around the
somatodendritic axis to ensure that the particular three-dimensional
(3-D) morphology used in our experiments introduced no artifacts in the
(t) calculations. The slight curvatures of the dorsal CA1
region were neglected for this study.
CALCULATION OF THE MODEL FIELD POTENTIAL.
A set of 16 "recording" points 50 µm apart simulating a vertical
track spanning from 250 µm above to 500 µm below the st. pyr. was
placed at the center of the population in parallel to the
somatodendritic axis (we termed as b5-b1, s and ap1-ap10 levels, to
designate the successive positions at the basal tree, st. pyr. and
apical tree, respectively). The value of the FP measured at each point
was calculated as follows
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NEURON MODEL PROTOTYPE.
The single-neuron model reproduced the detailed pyramidal cell
morphology, with an average dendritic branching pattern, total dendritic length, dendritic tapering, and distribution of spine density
obtained from detailed morphometric studies (Bannister and
Larkman 1995a,b
; Trommald et al. 1995
) (see:
http://navier.ucsd.edu/ca1ps for details). The 3-D morphology was
simulated using 265 compartments, distributed in an axon, [consisting
of myelinated portions, Ranvier nodes, initial segment (IS) and axon
hillock (AH)], soma, and apical and basal dendritic trees [a
two-dimensional (2-D) projection of the model neuron is shown in Fig.
2]. Further partitioning of the neuron was unnecessary for the current
purposes. Compartment length was always >0.01 and <0.2
. Spatial
coordinates for each compartment can be found in the preceding http
address. Total effective area of the neuron was 66,800 µm2 (including spine area). The electrotonic
parameters for the majority of the simulations were
Rm = 70,000
· cm2, Ri = 150
· cm (but see Fig. 8), Cm = 0.75 µF/cm2. Values of
Rm and
Cm at the dendritic compartments were
compensated to take into account spine area. The input resistance
measured at the soma was 140 M
, and
was 25 ms, values between
those reported for whole cell recordings (e.g., Spruston and
Johnston 1992
). We checked the effect of a somatic shunt to
reproduce the leak caused by sharp electrode penetration (up to an
input resistance of 45 M
) and found a negligible decrease of the
model PS (~1%).
Comparisons between experimental and model potentials: the relevant parameters
For a fully safe interpretation of the experimental PS based on
model reconstruction, an exact fitting would be required, and the
comparison of the entire spatiotemporal PS map should be performed.
Statistical global comparisons are difficult and may lose physiological
meaning due to the different weight of components. In practice, we
found more useful a direct comparison of the parameters that can be
measured easily by experimentation. At the single-cell level, we used
the amplitude, half-width, and rates of rise and fall of the AP
measured at the soma. Reliable AP parameters at dendritic levels in
vivo are not available, thus an initial approximation was made using
the in vitro AP estimates (Spruston et al. 1995;
Turner et al. 1991
) and later modified as required once
the FP and ICSD maps have been
computed. At the aggregate level we measured the amplitude, width, and
latency of the PS, and the magnitude and duration of the
ICSDs at the st. pyr. and stratum
radiatum (st. rad.) Experimental values are given as the means ± SE.
Although obvious, we want to emphasize that fitting of partial data can
be achieved by many different combinations of the large number of
parameters used in the model. The experimental estimations for
subcellular parameters, which constitute the basic elements for the
computations, are far less reliable than the unitary AP parameters, and
so are these when compared with the highly steady PS. In this study,
fitting the unitary AP parameters constitutes a crucial intermediate
step and an important advantage, as it strongly defines the magnitude
and time course of the compartmental Im necessary for FP computation. This
process yields a strong reduction of the suitable combinations of
subcellular parameters that will be limited further after the ensemble
FP is computed and compared with the experimental one. For the purposes
of the present study, the mentioned reference parameters are
satisfactory. The fitting of realistic AP waveforms to obtain the
Im is analogous to the use of AP
waveforms as the voltage command in voltage-clamp experiments. In a
way, the model is more realistic because the voltage command is
specific for each membrane subregion, which cannot be achieved in
actual experiments. This is an important advantage, for activated
adjacent membranes act as reciprocal shunts, shaping each other's
Im (see López-Aguado et
al. 2000) (see also RESULTS).
Sources of error
The lack of precise experimental values for some parameters is a
potential source of error. Regarding the electrotonic parameters, some
are worth mentioning for their relevance. Our own preliminary measurements of Re in vivo indicate
that the st. pyr. is about twice that in dendrites. It is known that
this anisotropy causes an overestimation of st. pyr. currents that,
however, does not modify their estimated location (Holsheimer
1987; Okada et al. 1994
). In our study, this led
to an underestimation of the FP amplitude at the st. pyr. as compared
with dendritic locations. Uncertainty exists also for the value of
Ri, the used values specified and
justified in RESULTS. The available data on channel
kinetics, maximum conductances, and their spatial distributions are
partial and far from reliable for the accuracy required in this study. However, fitting the realistic AP parameters along the somatodendritic axis as an intermediate step provides values for channel kinetics that
can be examined and compared with those experimentally obtained and
also produces the spatial distribution and the magnitude of the
underlying Im, which are the only
important variables for the calculation of the model FP. Finally, a
deficiency of the model is that the calculation of
Vm does not take in account the ongoing variation of FP. On one side, including this feature in the
model would imply a large computational cost, and on the other side,
only slight quantitative but no qualitative changes should be expected.
A different source of error arises from anatomic and morphological
considerations. The use of a single tridimensional morphology for the
prototype model cells leads to an unrealistic spatial clustering of
identical dendritic portions. It is known that the apical shaft has
variable length and that the branching pattern varies accordingly
(Bannister and Larkman 1995a
). Presumably, using
multiple morphologies will cause some spatial averaging of ensemble
dendritic currents. Also we found that the fanning angle of dendritic
trees has some impact on volume propagated currents (halving and
doubling the used fanning angle caused the antidromic PS to vary
±10%).
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RESULTS |
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General features of real and model pyramidal neurons
Intracellularly recorded pyramidal cells fired a single AP followed by a fast (presumably GABAA) inhibitory postsynaptic potential (IPSP) or an AP riding on an excitatory postsynaptic potential (EPSP) and followed by a fast and a slow (presumably GABAB) IPSP after anti- or orthodromic activation, respectively (Fig. 1, top). They also behaved as expected to current injections, displaying fast and slow intratrain accommodation and slow afterhyperpolarization (Fig. 1, bottom). All prototype model neurons were adjusted so as to reproduce these general features (an example is shown in Fig. 1), although a fine adjustment is unnecessary at this stage for they are barely relevant for the antidromic PS. Of critical relevance, however, are the fine details of the AP and its subcellular peculiarities governed by the fast Na+ and K+ channels. These will be studied in the following text in relation to their impact on the model PSs.
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Experimental antidromic PS: subcellular localization of current generators
Maximal stimulation of the posterior alveus triggered synchronous APs originating a characteristic extracellular sharp monophasic negative spike (i.e., the PS; amplitude: 24.96 ± 0.51 mV; half-width: 0.63 ± 0.01 ms) at the level of the st. pyr. (thick trace in Fig. 2A, FP) that became a positive-negative biphasic spike for ~200-250 µm within the proximal stratum radiatum (st. rad.), and a pure positive spike at more distal positions as the negative component gradually faded. The PS recorded immediately below the st. pyr. was up to 2-3 mV larger. Within the stratum oriens (st. or.), the PS unfolded in a two-spike sequence toward the alveus, the first (asterisk) remaining stationary, whereas the second (dot) increased in latency and declined faster.
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In CSD analysis, extracellular sinks and sources correspond to net cellular inward and outward currents, respectively, terms that will be handled as synonymous throughout the text. The earliest current was a pure sink (net inward currents during AP) at the level of the st. pyr. (Fig. 2A, right), where it reached maximal amplitude (2.09 ± 0.11 A/cm3). The propagation of this sink into the apical and basal dendritic trees (Fig. 2A, arrows) indicated active dendritic invasion of the AP for ~225 and 125 µm, respectively. Except in the st. pyr., the sink always was preceded by a passive source (Fig. 2C) corresponding to the leading outward passive currents (capacitive and leak) closing loop with the active cell domains. The propagating source/sink sequences account for the second negative spike (dot) and its preceding positive interlude in the st. or. (Fig. 2B, double-headed arrow), and the biphasic spike in st. rad. A decreasing source of constant latency was observed distally as expected in the region where the AP propagation became passive. This source corresponds to capacitive outward currents, although active K+ currents also may contribute. Net inward currents in dendrites were always smaller but lasted longer than in the st. pyr. (Fig. 2C). The shorter duration in st. pyr. may be caused by a more spiky local Im of the cell somata, and/or the longer duration in dendrites may be due to spatial averaging of multiple secondary dendritic branches activated with different delays. Measured from its origin at the summit of the preceding source, the peak amplitude at each of the three successive stages below the st. pyr. (in 50-µm steps) was 1.4 ± 0.09, 0.98 ± 0.09, and 1.22 ± 0.1 A/cm3, respectively, decreasing thereafter to extinction. The speed of the dendritic backpropagation was faster in the apical than the basal dendritic tree and slower the farther from cell somata, as noted on the leading outward currents that began progressively more delayed (Fig. 2C). Using the latencies at their summit (Fig. 2C, small vertical bars), we measured an average speed of 0.47 ± 0.02 m/s along the apical shaft (from 50 to 150 µm below the st. pyr.).
For the model, it was important to gain quantitative information on the
contribution of IS/AH currents, as they are possible strong current
generators. Using a 25-µm spatial resolution, the initial sink began
simultaneously and without leading sources in the basal and apical
halves of the st. pyr., but closer to the st. or. border, where ISs
membranes dominate (sp1 in Fig. 2C), the sink was smaller
and began slightly earlier. We did not find a spatially segregated
current sink attributable to IS/AH currents. However, the notch at the
lowering limb of the somatic sink (arrow in sp1, Fig. 2C)
likely results from a slight delay on the sequential activation of two
partially overlapped generators, the IS and the soma/basal stems, the
first of which gave rise to the first stationary negative peak of the
FP in the st. or. This peak also was shaped on its rising limb by the
leading passive sources of the colocalized significant fraction of
basal stems, as they are sequentially invaded by the AP (Fig.
2B, double-headed arrow). We recently reported the unmasking
of the first negative peak during selective blockade of the second one
that marks the AP basal invasion (López-Aguado et al.
2000). In any case, the net contribution of the ISs currents is
small and should be so reproduced in the aggregate model. In contrast,
we were able to discriminate, in some experiments, a small source/sink
sequence (Fig. 2B) located at ~250 µm above the st. pyr.
that clearly initiated earlier than any sink at the st. pyr. (small
arrows in Fig. 2B, ICSD),
most likely caused by synchronous APs at the clustered Ranvier nodes in
the alveus, which admittedly contain a very high density of
Na+ channels. This sink contributes to the
initial part of the first negative peak (arrow in Fig. 2B, FP).
CA1 model antidromic PS
Every combination of the main macroscopic factors, cell number, spatial arrangement, and asynchrony of activation, has been analyzed, and we show only those that accentuate individual effects. In later sections, it will be shown that the effect of some of these factors on the FP may be obscured or potentiated at specific values of the others, but it is not qualitatively modified by the use of other channel distributions in the component model cells. Thus a good fit of model to experimental PS is not essential at this stage.
RELATION TO THE NUMBER OF FIRING CELLS.
We searched for the minimum number of cells required to reproduce a
maximal antidromic PS with CA1 aggregates of increasing size and
constant cell density (see METHODS). When each cell in the
aggregate was activated antidromically without temporal scatter, the
antidromic PS amplitude at the st. pyr. and proximal apical dendrites
(ap1-ap3) was near saturation for a strip 2 mm wide and 3 mm long,
corresponding to a number of cells roughly similar to actual
estimations for the dorsal CA1 region, i.e.,
~105 pyramids (Boss et al.
1987). This is patent from the corresponding curves shown in
Fig. 3A where the PS has been
plotted as a percentage of the maximum amplitude at each recording
level for the largest aggregate. The more distal was the recording
point, the faster was the rate of the PS increase with the cell number.
It became clear from the shape of the distal plots that even with the
largest aggregate the PS is far from saturation. Therefore using
aggregates smaller than real causes a variable underestimation of the
PS amplitude at different strata. The differential saturation occurred because the uneven quantitative distribution of net currents along the
somatodendritic axis (Fig. 2C), allowing volume-propagated currents to reshape FPs. The contribution of far neurons to a distant
electrode, though weighed by distance, is large so that the relative
contribution of nearer generators is decreased. In consequence, the PS
recorded in strata dominated by weakly excitable cell subregions, such
as distal dendrites, has stronger proportional contribution of
volume-propagated currents and is more sensitive to the aggregate size.
By the same token, in aggregates of equal size, the less active are
modeled the distal dendrites the higher is the underestimation for
their calculated FP. To gain computer efficiency, all data presented in
the following text were obtained using an aggregate of 17,000 pyramids
(1 × 1 mm). This constitutes an underestimation <10% for the
regions where we focused our study between the st. pyr. and 150 µm
below cell somata (s to ap3 levels).
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EFFECT OF THE ASYNCHRONY OF ACTIVATION.
A small variability in the latency of antidromic activation of
individual cells is known to occur (Lipsky 1981). The
effect of this small asynchrony or temporal scatter on the PS was
studied by activating each cell with a random delay of variable
dispersion
1 ms (roughly the reported experimental range) (see
Andersen et al. 1971
; Herreras et al.
1987
) obtained from a binomial distribution. In general, the
temporal scatter affects more markedly
ICSDs than FPs (Fig. 3C).
The longer the temporal scatter the smaller and rounded the resultant
FP and ICSD, but the effect was only
meaningful in cell domains where net local currents are short lasting
and spiky, as the soma and axon membranes. A temporal scatter of
0.25-0.5 ms, roughly approaching that experimentally obtained
(Andersen et al. 1971
), caused notable changes in the
initial PS slope at the st. pyr., but it barely affected its amplitude.
The differential effect of asynchrony on somatic
ICSDs and FPs may appear paradoxical. In fact, it is caused by the interaction of asynchrony with some other
subcellular factors that determined different waveforms of
compartmental currents (see following text).
EFFECT OF THE SPATIAL OVERLAP OF DIFFERENT SUBCELLULAR GENERATORS. The spatial overlap of different cell generators is only relevant at the st. pyr., where ISs, and basal and apical dendritic stems are mixed with the dominant somatic generators. We studied the effect of this overlap by using three different distributions of cell somata, monolayer, four-layered of even density, and the realistic uneven distribution (Fig. 3D), while maintaining cell density. Largest FPs and ICSDs were obtained in the monolayer configuration only in the st. pyr. (~20%), as expected in absence of spatial scatter for the strongest generators (somata). Minor differences were noticed between the even and uneven arrangements, the latter showing a slight shift of the maximum PS amplitude toward the apical side, as also found in experiment. This result persisted even with neuron prototypes designed with large differences in soma and IS channel densities. Again, in smaller aggregates the effects were much more marked because the smaller equalizing influence of far located currents.
Sodium channel density differentially affects the single-cell AP and the ensemble field potentials at the somatic region
The PS amplitude depends on the instant amount of extracellular
current during synchronous firing of APs, and these are dominated by
the inward INa. Thus we checked the
effect of somatic Na density at the
soma of a neuron prototype with a moderately excitable apical tree that
enabled active AP backpropagation. The obligatory restriction to the
useful range of
Na is that the APs
of the component model neurons must fit the values of the experimental APs. Because notable differences have been reported in in vitro experiments, we used the values of APs recorded in vivo. Evoked APs
were always smaller (
20 mV) than spontaneous APs, often even after
calculating the actual Vm by
subtraction of the extracellular PS (Fig. 1, top) obtained
on withdrawal of the pipette from the cell. By using the
Vi, we found that the apparent
threshold, rate of rise, and half-width for spontaneous and evoked APs
varied slightly; then we used the parameters of the former to prevent errors in the calculation of Vm. These
always were preceded by a slow depolarizing ramp (threshold: 16.5 ± 1.1 mV), had a rate of rise of 399.1 ± 26.9 V/s (range
232-640, measured as the 10-80% slope from threshold to peak) and a
falling rate of 103 ± 3 V/s. The AP amplitude from rest was
90.7 ± 1.9 mV (range 83-104), and the half-width was 0.82 ± 0.01 ms. An AB-brake was not distinguishable on the rising
limb, usually not even in differentiated records. This can only be
disclosed under conditions of decreased IS/AH-to-soma safety factor for
invasion, e.g., during high-frequency antidromic activation
(López-Aguado et al. 2000
).
Using a model neuron with soma Na
varying from 180 to 1,080 pS/µm2, the somatic
AP grew from 83 to 102 mV and the rising slope from 192 to 688 V/s
(Fig. 4A, Vm). The average
experimental APs were better fitted by a
Na density of ~500
pS/µm2, whereas those in the upper range
required ~900 pS/µm2. In the model, the
lowest value yielded APs with very slow rising slope and disclosed a
distinct AB-brake (arrowhead). The somatic Im (Fig. 4A,
Im) presented a fast peak declining to
a plateau-like current, smaller the higher the
Na. The peak increased from 3.2 to
6.5 nA through the specified
Na
range. It is important to note that because the increment of
INa is limited by
Vm
ENa, the peak of
Im is forced to an asymptotic value so
that much higher
Na would not result
in larger Im (Fig. 4A).
Changes of
Na at the IS did not
modify the somatic Im noticeably.
During aggregate activation, the temporal scatter of activation and the
added volume-propagated currents from other cell generators (mostly
dendrites), made the waveform of the PS at the st. pyr. to differ from
the single-cell somatic Im (Fig.
4B, FP, top). We might expect that increasing
Na will cause a parallel increase of
the antidromic PS amplitude because FPs depend on
Im, but it saturated at low
Na densities. Even more striking was
that the corresponding ICSDs behaved
similarly, as they represent the addition of all unitary somatic
Ims. The explanation lies on the fact
that the somatic Im is short lasting
and spiky, so that even a small activation asynchrony of the firing
cells avoided their temporal summation in the extracellular space. In
fact, when the Im peaks were
time-locked throughout the population (Fig. 4B,
bottom), the aggregate ICSD
peak also increased, and the overall waveform became more akin to that
of the single-cell somatic Im. Also
the initial fast transient of the somatic
Im was revealed on the FP (arrowhead),
and a subsequent hump was uncovered (small arrow). However, the maximum
PS amplitude still saturated at low
Na densities. It can be concluded
that the temporal scatter of activation dissipates the contribution of
the short-lasting somatic Ims so that
the PS peak occurs at an instant when the FP at the st. pyr. is
additionally contributed by slower current components (see following
text). Most relevant is that a much larger
Na was required to fairly reproduce
the antidromic AP of real cells than to achieve the maximum antidromic
PS. At best, this reached about half the experimental value (10-12 vs.
24 mV), thus
Na cannot be considered
a limiting parameter for the PS and other factors must be involved.
Dendritic action currents contribute to the PS peak at the stratum pyramidale
Somata and dendrites of pyramidal cells are segregated spatially,
allowing the study of their relative contribution to the PS shape. We
used a small aggregate (256 units) to minimize the contribution of the
dendrites at the st. pyr., and no scatter of activation to avoid
reduced temporal summation of individual somatic currents (Fig.
5A, left). In this
case, the late hump became residual (compare to Fig. 4B,
bottom left), and the overall PS waveform followed a time
course similar to the individual somatic Im (compare with Fig. 4A,
right). The almost complete dominance of somatic currents also was
revealed by the fact that the PS peak did increase with
Na, matching the single-cell somatic Im behavior and the ensemble
ICSDs in absence of temporal scatter (curved arrows in Figs. 4 and 5). These computations indicate that the
uncovered delayed hump using large aggregates (Fig. 4B) is
caused by volume propagated currents from neuron elements other than
somata, i.e., dendritic currents.
|
If the spatially clustered somata were the only active generators, the size of the aggregate should affect the FP amplitude but not its waveform because all somata generate identical current waveforms and the extracellular space has no capacitive effects. However, this was not the case, and the larger the cell aggregate, the more conspicuous was the late hump in the st. pyr. (Fig. 5B) and the longer was the overall half-width of the PS. This is the expected result when two spatially segregated generators yielding different current waveforms are activated simultaneously. The FP waveform recorded among somata changed with the size of the aggregate because of increased volume-propagated dendritic action currents reaching the st. pyr. The dendritic hump, undetected for the smallest aggregate (asterisk), gradually grew even larger than the somatic initial fast transient, so that the PS peak occurred significantly later. Naturally, with temporal scatter of the activated cells the peak time also will occur at an instant strongly contributed by dendritic currents. Hence measurement of real PSs at the st. pyr. is strongly contaminated by dendrites.
Contribution of volume-propagated currents to the FP in different strata
Along the region where the AP is actively conducted, from the st. or. to the st. rad., the duration of the ensemble current sink was always shorter than the corresponding negativity in the FPs (Fig. 6, left, thick vs. thin tracings). In the st. pyr., the peak of the ICSD always led that of the PS (~0.15 ms), whereas the opposite occurred 150 µm below in the st. rad. (Fig. 6, left, vertical dashed lines). A gradual transition was observed at intermediate locations. The computations matched well the experimental results only when model neurons had excitable dendrites (Fig. 6, compare middle with right). Because CSD excludes volume propagated currents, the longer duration of the FPs as compared with CSDs must be precisely caused by a dominant contribution of these far generated currents at the mismatching times, i.e., when the PS was still negative but the net local current sink had terminated (marked by asterisks in Fig. 6). During antidromic activation, the AP invades first the soma and then the dendrites. Therefore the late part of the PS at the st. pyr. was dominated by the volume-propagated delayed dendritic action currents (sinks), and the initial phase of the PS at the st. rad. was similarly contributed by those action currents of subregions that fired earlier, i.e., the soma and all dendritic locations earlier reached by the AP. Passive dendrites generated only small capacitive currents and did not create extracellular sinks that may spread up to the st. pyr. so that the duration of the FPs and CSDs at the st. pyr. matched well (Fig. 6, top right). In this case, the volume spread can be appreciated in the opposite direction, i.e., from the active somata to the passive dendrites, thus a negative FP is still recorded within this region that did not generate local sinks (Fig. 6, arrow in bottom right panels).
|
This result agrees with the dendritic origin of the late hump at
the st. pyr. in absence of temporal scatter. It is then obvious that at
the time when the PS amplitude is measured at the st. pyr. some
negativity is provided by activated dendrites. Knowing the precise
contribution is difficult. In the example of Fig. 4B (t.s.:
0 ms), the negativity at the hump was 7% larger than at the initial
soma-dominated fast transient. However, because the ensemble somatic
component is reduced by temporal scatter, a larger percentage is
anticipated. Taking the ICSDs as a
reference, in the example of Fig. 4B (maximum
Na), the temporal scatter decreased
the net sink ~22% at the ICSD peak,
whereas the PS maximum peak was unchanged. Thus ~30% of the PS
amplitude at the peak could be actually provided by active dendritic
currents. It can be presumed that any factor increasing the net
Im at dendrites will cause a larger
dendritic contribution to the PS recorded at the st. pyr.
Effect of channel distribution along the somatodendritic axis: optimizing the neuron prototype
The results thus indicate that active currents from both soma and
dendrites contribute to shape the PS at any recording position. Further
optimization of the neuron prototype required that the spatial waveform
of APs and PSs along the somatodendritic axis was considered as a
whole. We have tested a variety of Na+ channel
densities and distributions, summarized in Fig.
7. In a neuron with passive dendrites
(type 1, Fig. 7, 1), the AP presented a fast decay along the
apical shaft and negligible Im in this region. When used in the aggregate model, this prototype unit yielded
an unrealistic antidromic PS as noted by the very fast decline in the
proximal apical shaft and the absence of extracellular source-sink
sequences (see ICSDs). The small
ICSDs (arrowhead) are due
to capacitive currents during the passive spread of the AP (note the
miniature compartmental currents on the
Im plots). A relatively high
Na was needed at the soma and IS/AH
to obtain an AP rising slope within the experimental values and without AB brake.
|
When using excitable dendrites, an important feature to reproduce
is the well-known decremental conduction of APs with increasing duration along the apical shaft (Leung 1978;
Turner et al. 1991
). We first checked homogeneous
Na density throughout soma and dendrites (Magee and Johnston 1995a
,b
; Spruston
et al. 1995
) and proportional
Na. The neuron type 2, shown in Fig.
7, 2, had 200 pS/µm2, which is two
to three times higher than suggested by experimental findings. In this
case, a hot spot in the IS (5 µm long, 50 µm away from the soma in
the example of the figure) was required for somatic AP invasion. This
type of neuron yielded unrealistic results in several ways. First, the
somatic AP always presented a prominent AB-brake (arrowhead in Fig. 7,
2, Vm), indicating a delay
on the IS-to-soma invasion that was never apparent in actual recordings
(Fig. 1). The AB-brake can be concealed acceptably only when the hot
spot is placed near the soma. Second, the AP rate of rise was very slow
(~200 V/s) and the half-width too large (>1 ms), both far from the
measured range of the in vivo APs. Lower
Na densities (<80
pS/µm2) (e.g., Stuart and Sakmann
1994
) yielded even slower APs or failed to invade altogether.
Third, decremental AP conduction was not achieved, and backpropagation
was too slow (see Vm plots, Fig. 7,
2). Fourth, the model FP yielded unrealistic PSs, presenting a pronounced inflection on the negative-going phase, caused by the slow
invasion of IS-currents (arrowhead in Fig. 7, 2,
FP), and half-widths about twofold the experimental values.
Attempts to correct the deviations were made by increasing the somatic
Na (900 pS/µm2) and using a somatofugally decreasing
Na gradient (Fig. 7, 3).
This and many other combinations of distribution and kinetics of this
channel yielded an acceptable attenuation of the AP along the apical
dendrites (arrow on Vm plots) in
parallel to the increase of its half-width, but the speed of invasion
was still too slow (~0.3 vs. 0.47 m/s in vivo, measured on
ICSDs). Also, the half-width of the PS
was too large (>1 vs. 0.7 ms in vivo), and the decay rate of the PS
negativity along the apical dendrites was too slow, showing delayed
positive-going phases (circle-headed arrow in FP plots). Some of these
divergences could be ameliorated by using a somatofugally increasing
gradient of the A-type K+ channels
(Hoffman et al. 1997
) and homogeneous
Na. The neuron type 4 shown in Fig.
7, 4 (500 pS/µm2) yielded a PS with
a faster falling rate of the negativity along the apical tree (arrow in
FP plots) and shorter source-sink sequences. However, the AP speed of
invasion along the apical shaft decreased (~0.2 m/s) and its
half-width increased only slightly. Increasing
Na accelerated the speed of the AP,
but it always felt short of the in vivo values and failed to improve
noticeably other features of the antidromic PS.
In general, the higher the Na
density in dendrites the larger was the PS in the st. rad., in contrast
to the rapid saturation found for the PS at the st. pyr. (compare the
FP plots for neuron types 1-3). This was caused by the longer duration
and smoother waveform of the Im in
dendritic compartments than somata, for it is barely affected by the
scatter of the activation. The precise waveform of the PS at this
region can be strongly modified by the density and distribution of
K+ channels (compare the FP plots for neuron
types 3 and 4).
As described thus far, the main discrepancies between the model and
experimental PSs are the small amplitude, the longer half-width, and
the slower decay rate of apical negativity in the former. Also a slower
speed of AP apical invasion was measured for the model
ICSDs. Larger amplitude could be achieved just by
increasing the Re, but this would
cause a proportional increase of the FP without modifying the waveform.
From the experimental data and the model results obtained so far, we
inferred that a faster AP backpropagation was necessary and should
correct some of the model PS deficiencies. Because increasing
Na densities to accelerate AP speed
was insufficient, we reconsidered the initial set of electrotonic parameters.
Internal resistance is a major determinant of extracellular field potentials
Some single-cell electrotonic parameters had a notable impact on
both AP and PS waveforms. Varying membrane resistivity from 17 to 140 k · cm had negligible effects. As expected, varying membrane capacitance from 1.5 to 0.375 µF/cm2
caused an increasing velocity of APs and PSs, progressively
invading longer distances. Still, the PS at the st. pyr. increased
<10%.
By contrast, internal resistance (Ri)
had a strong impact on the antidromic PS at any location. All preceding
simulations employed a Ri of 150 · cm, which is usual in the literature. Figure
8 shows the comparative results for
Ri of 200, 100, and 50
· cm
(thick, medium, and thin tracings,
respectively). Lowering Ri caused
faster AP propagation and a slight amplitude decrease (Fig.
8A). However, the corresponding model antidromic PS
increased almost linearly to 1/Ri
(~400%, Fig. 8, B and C). A notable decrease of the PS half-width also was observed (1.1 vs. 0.8 ms in the st. pyr.
for 200 and 50
· cm, respectively), getting closer to the in vivo
PS. The plots of the PS amplitude shown in Fig. 8C also show
a much faster decay of the negativity along the apical dendrites. Note
the progressive flattening of the plots and the somatofugal shift of
the maximum negativity with higher Ri.
This result is explained by the different AP speed along the
somatodendritic axis. During fast APs, inward currents along invaded
dendrites are better time-locked, enabling their addition in the
interstitium and increasing the FP. Because this is contributed by far
generators from different strata, this increment of negativity
clustered around a specific stratum, with the maximum shifting toward
the location of stronger generators (see arrows in Fig. 8C).
On the other side, slow APs have inward currents progressing in a
sequential manner, reducing their temporal addition in the
extracellular space.
|
These results at the ensemble level can be accounted at the single-cell level. The slight variations observed in Vm at the soma (Fig. 8A) are associated to moderate changes of capacitive currents (Icap) and to notable increments of ionic currents (Iion) and hence of Im, with the lower Ri (Fig. 8D). The increment of Im also is reflected in the corresponding aggregate ICSDs (Fig. 8E). These computations indicate that a low Ri fit most of the discrepancies of the model and experimental antidromic PS spatiotemporal map that we could not achieve by altering other significant parameters.
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DISCUSSION |
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This study discloses the relevant parameters contributing to the amplitude and shape of the PS. As for any other FP, the PS is built up by the addition of near (local) and far generated (volume propagated) membrane currents. The selective clustering of somata and dendritic elements in different strata, and the different waveform and timing of their respective Ims during APs, constitute the basic factors shaping the PS. The role of any other parameter will depend on the capacity to define or modulate the timing and relative contribution of somatic and dendritic currents to the extracellular space.
Can the aggregate model restrict the variability of experimental measurements?
Except for specific details attributable to species differences or
intact versus in vitro preparations, the overall features of the
antidromic PS spatiotemporal map coincide with previous reports
(Leung 1979; Miyakawa and Kato 1986
;
Sperti et al. 1966
). The extraordinary steadiness of
this evoked potential facilitated the parametric restriction at the
single-cell and subcellular level, the experimental data of which are
more disperse.
The main handicap for model studies is that the experimental
measurement of single-cell and subcellular parameters shows large standard errors. The transcendence of this variability gains practical significance when the experimental values are extrapolated at a large
scale so as to predict their role on the global electrical behavior of
neurons or cell ensembles, as we made in this study. In the aggregate
model, the AP parameters have been used to restrict the useful ranges
of channel density, kinetics and distribution, to obtain the spatial
map of Ims, in a way similar to
voltage clamping of a cell with AP waveform commands along its entire morphology. Once obtained, the spatial map of
Ims, the precise set of subcellular
parameters, becomes irrelevant for the subsequent calculation of FPs as
long as these fitted the experimental PS. In consequence, the combined
reconstruction of real PSs and APs is a powerful tool to restrict the
useful ranges of subcellular parameters that should expectedly match
those experimentally obtained. However, a quick survey of the available
literature is enough to realize that in many cases data obtained from
different labs are only roughly similar but, given their transcendence
for cell function (and modeling), far from reliable. Whether this is
due to low technical resolution or actual variability is not clear. If
we consider the wide experimental ranges as reflecting functional cell
heterogeneity, we are bound to admit striking differences within a
homogenous population of neurons. For instance, the range of AP rising
rates found in our neuron sample would require up to sixfold the
somatic Na calculated in a pyramidal
model cell (Fig. 4), a range too wide to be physiological. On the
contrary, we might consider that data dispersion is caused by a
variable interference of recording devices with ongoing physiology due to mechanical stress (e.g., Somjen et al. 1993
). In this
case we should consider the faster APs the more realistic and
representative of the cell population. Unfortunately, the low
dispersion found for the PS amplitude cannot be used to decide this
issue as it is an averaged population response. As long as this matter
is not clarified, we arbitrarily considered the higher values as the
more representative of an average pyramidal cell. In consequence, we
developed our aggregate model by assuming an admittedly questionable homogeneous electrical behavior for each cell in the population.
Somewhat surprising was the finding that the ISs do not appear to
contribute a significant amount of current. Field compound negative
spikes have been ascribed to IS currents in the CA1 (Sperti et
al. 1966) (see Fig. 1, asterisk) and other structures
(Lorente de Nó 1947b
). Earlier CSD studies also
failed to discriminate a current sink distinct from that attributed to
cell somata (Herreras 1990
; Leung 1979
;
Miyakawa and Kato 1986
), indicating that the mentioned
spike is actually generated in the st. pyr. border and spreads toward
the st. oriens by volume conduction. On the contrary, we are reporting
for the first time a current sink that may be attributed to active axon
generators in the alvear region. The present experimental study shows
no leading passive currents for the initial sink at the st. pyr. nor
does the somatic APs display an AB break, indicating a high safety
factor for AP invasion of the soma and negligible IS-to-soma delay.
When we used neuron prototypes with high
Na density at the IS, the resultant
antidromic AP always showed a prominent AB brake, and this also was
appreciated on the model antidromic PSs. Because this is contrary to
experimental findings, it has to be inferred that the IS
Na density needs to be not much
higher than at the soma. Interestingly, a recent report found low
density of Na+ channels in ISs of subicular
pyramidal cells, comparable with that of soma and dendrite membranes
(Colbert and Johnston 1996
).
Among the more relevant experimental values for this study are those
concerning dendrites. Available data are barely quantitative, and only
gross qualitative features can be reproduced. Although a decremental AP
invasion indicates a decreasing number of activated Na+ channels, the obtained values can be
influenced markedly by geometric and electrotonic factors and does not
necessarily mean a decreasing Na+ channel
density. Certainly, decremental APs run with a decreasing Im, but this may also result from an
homogeneous but low Na density
unable to support fully regenerative APs (see Johnston et al.
1996
). Also the cumulative effect of branching, an increasing density or faster kinetics of repolarizing channels (Hoffman et al. 1997
) or synaptic impingement (Tsubokawa and Ross
1996
) may cause decremental conduction.
Whether Na+ channel density is homogeneous or not
throughout the somatodendritic membrane cannot be decided from the
current model results, but in our opinion, it cannot be rigorously
concluded from the available data obtained from studies on membrane
patches either. The number of estimated channels varied enormously
along the apical shaft (e.g., Magee and Johnston 1995a;
Stuart and Sakmann 1994
), what may be interpreted
similarly as sampling dispersion or as the result of variable
mechanical disruption of functional channels. Somatofugally decreasing
K and increasing
Na are not mutually exclusive, and
some functional aspects, such as AP attenuation, can be achieved in
both ways. Whereas the latter appears well established (Hoffman
et al. 1997
) and the
Na/
K ratio may be the most important parameter shaping dendritic APs, a
moderately decreasing gradient of
Na
may be necessary for a correct increase of its half-width. Further
tuning along the apical shaft requires precise experimental measurement
of AP parameters. Our model can be used then in an iterative manner to
find suitable
Na distributions by
tuning the single-cell channel densities and distributions and
comparing the model to the experimental PS profile.
In any case, it became obvious that low
Na densities (<200
pS/µm2) enable dendritic AP invasion but much
higher densities (500 pS/µm2) are needed to
generate realistic APs at the soma as recorded in vivo. The speed of
APs was too slow even with the higher
Na. Curiously, most single-cell
models for cortical or hippocampal pyramidal neurons use
Na 4-10 times higher than that
calculated in membrane patches to obtain acceptable somatic APs. It is
worth mentioning that the parameters of APs measured in vitro (e.g., Storm 1987
) are much slower than in vivo, and closer to
those reproduced by the neuron type 2, so we can speculate that
Na+ currents are somehow depressed in nonintact
preparations, as it happens in immature cells (Cummins et al.
1994
; Spigelman et al. 1992
) or low-temperature
recordings (Thomson et al. 1985
). A putative decrease of
Na+ channel availability or slower kinetics
should entail remarkable changes in local excitability. This
possibility is supported by the fact that APs are much more easily
initiated in the apical shaft of CA1 pyramids in vivo (Andersen
and Lømo 1966
; Fujita and Sakata 1962
;
Herreras 1990
) than in vitro (Turner et al.
1991
; see Johnston et al. 1996
for a review),
suggesting changes in the local AP threshold, also defined by
Na+ channel availability. No doubt this matter
deserves further attention because computational properties are
strongly dependent on the fine modulation of local dendritic excitability.
The results obtained with varying Ri are the clearest example of the great sensitivity of the aggregate model to unveil the role of some subcellular parameters the effect of which may go unnoticed at the single-cell level. On one side, it is evidenced the advantage of fitting the experimental PS by an aggregate model over the low resolution of single-cell models fitting APs. On the other, two important practical implications can be derived. First, minor changes of Vm measured in single cells actually can be associated to large Im variations (note the negligible difference of the antidromic APs between soma and ap1 compartments in Fig. 7), leaving unnoticed important functional changes during experimental manipulations and causing misinterpretation of the data. Second, an effort to improve the accuracy of the experimental measurement of electrotonic parameters is required: the constancy of experimental PS amplitude is not compatible with the dispersion of available single-cell measurements.
Volume propagation: from evoked field potentials to elementary currents
The factors shaping PSs may be grouped in two classes, those we
called subcellular, which define/modulate the spread and magnitude of
axial and transmembrane currents along the entire morphology of
individual cells, and those defined as macroscopic, which concern the
spread of currents in the extracellular space. Among the latter, tissue
resistivity and spatial and temporal dispersion of activated membrane
generators are the most relevant. For the shake of simplicity, we have
neglected the possible effects of anisotropy, which may cause important
modulations in the spread of extracellular current (Holsheimer
1987; Okada et al. 1994
). It is usually thought
that APs contribute little to evoked FPs due to insufficient synchrony during activation and/or the canceling of action currents in the interstitial space due to irregular spatial arrangement of the activated neuron elements (see Mitzdorf 1985
for a
review). Although the strong stratification of the CA1 region offers
the most favorable conditions and indeed allows distinct PSs to
develop, neither synchrony nor spatial arrangement are ideal. We found
that the experimental variability of these basic parameters did not
cause a notable impact on the model PS amplitude (Fig. 3). Although this may appear paradoxical, it is in fact due to the equalizing influence of volume-propagated currents from different membrane generators. The scheme in Fig. 9 outlines
some relations between different levels of complexity to illustrate the
relative contribution of somata and dendrites to the PS. Even if the
temporal scatter is not a major modulator in itself, it has a critical
role in limiting the role played by other factors. The short duration and spiky waveform of somatic action currents makes the temporal scatter to cause a strong decreasing effect on the ensemble somatic sink (see also Fig. 3, C and D) by reducing the
temporal coincidence required to sum up in the extracellular space.
However, the PS was barely sensitive to temporal scatter at the time of
the peak (Fig. 3C), indicating that other currents from far
generators have a substantial contribution at that time. These are
necessarily of dendritic origin, the extracellular summation of which
is barely modified by the small latency variability due to their longer and smoother waveform. The currents generated by far somata will increase the amplitude but shall not change the waveform. The fast
somatic currents thus define the slope of the initial negative-going limb, whereas dendritic currents have an increasing dominance during
the time span of the PS that is already strong at the PS peak and may
even account for the whole negativity during the rising limb (Figs. 4
and 5) (see also López-Aguado et al. 2000
). Moreover, because of the obligatory delay of dendritic currents during
backpropagation, the increasing contribution is defined also spatially
so that proximal dendrites contribute more at earlier times than distal
dendrites. In turn, the waveform of individual somatic
Im is sharp in correspondence to the
large amplitude and rate of rise of somatic APs (Fig. 9). These are two
key AP parameters governed by inward Na+
currents, limited by the driving force, channel kinetics, and active
repolarizing currents.
|
Among the macroscopic factors fostering the PS amplitude are the number of firing cells, the aggregate size, and the Re. The former two may change also the waveform of the PS, especially at the st. pyr., by altering the relative dominance of somatic and dendritic generators (Figs. 3-5). The bigger the aggregate, the larger the relative contribution of dendrites, which may be relevant to the slice preparation that contains a reduced number of cells. This effect was revealed as the appearance of a delayed hump in the somatic PS in absence of temporal scatter of activation and originated by the different time course of somatic and dendritic currents. If these were similar but slightly delayed, the changes in the somatic PS waveform would be minimal because far somata and far dendrites would contribute with currents of identical time course. It can be inferred easily that the poor temporal summation of somatic currents makes volume-propagated currents from dendrites to gain more relevance at the time of the peak. Thus latency variability among firing cells indirectly favors dendritic contribution the bigger the cell aggregate is because far somata also will contribute less than far dendrites in spite of similar distance to the recording point. It should be mentioned that the peak of the PS in absence of temporal scatter occurs much earlier, whatever the size of the aggregate, as it is almost entirely dominated by the phase-locked spiky somatic currents that peaked at an instant when the AP is just initiating in dendrites. It is the dissipating effect of latency variability on the ensemble somatic currents that makes the peak to be delayed at later times when dendritic contribution is larger. In this sense, even if the natural effect of the latency variability is reducing the ensemble somatic currents, the decrease of the corresponding PS at the st. pyr. occurs at a smaller rate because of the increased weight of dendritic contribution.
Somewhat surprising is the finding that the Na+
channel density is a critical factor for the antidromic PS amplitude at
the st. rad. but not at the st. pyr. The explanation lies on the larger amplitude and rising slope of the somatic than dendritic APs
(Andreasen and Lambert 1995; Turner et al.
1991
), making the Im of the
former short lasting and limited by the Na+
driving force. It can be argued that the dendritic
Na in some computations was smaller
than in somata. However, the used densities are only an optimized
parameter adjusted to reproduce the limiting factors, namely the
experimental somatic APs and the known decrease of backpropagating APs
(Turner et al. 1991
). Further, when the
Na was set homogeneous through the
entire somatodendritic axis and the features of dendritic APs shaped by
somatopetally increasing the K+ channel density
(Fig. 6-8) (see Hoffman et al. 1997
), the behavior of
the dendritic Ims was the same, an
expected result that confirms the limiting effect of the AP amplitude
and duration for local inward currents, whichever the channel assortment.
Different distributions of somatodendritic channel densities strongly
define the antidromic PS at the st. rad. Neither dendritic AP
parameters cause the saturation of inward currents (as it happens in
somata) nor their smooth and longer waveform allows a sensitive reduction of the ensemble extracellular currents by temporal scatter. Yet, the PS amplitude at the st. pyr. changes <20% for extreme cases
of dendritic channel densities (Fig. 6), even when dendritic contribution to this layer has been estimated much larger (~30-40%; see RESULTS) (see also López-Aguado et al.
2000). Comparing ICSDs in the
st. pyr. of aggregates with active and passive dendrite neurons, we
found that the decreased contribution of local somatic currents in the
former was compensated by volume-propagated dendritic currents. This
can be understood in terms of the reciprocal shunt between two near
membrane generators simultaneously activated. The larger and longer
Im contribution to the extracellular
space of somata in passive dendrite neurons is compensated by the
addition of dendritic currents volume-propagated up to the st. pyr. in the model with excitable dendrites. The strong differences in duration
and shape of somatic Ims in the two
neuron types are clear evidence of the interaction between somata and
dendrites. The reciprocal shunt between adjacent active membranes cause
a powerful reshaping of the magnitude and time course of their
respective Ims.
Quantitatively, much more important than the magnitude of subcellular
Ims is their temporal relationship.
The wider the temporal overlap of somatodendritic currents the larger
will be the instantaneous current at the extracellular space and hence
FPs. Temporal overlap of subcellular currents is greater the faster is
the AP backpropagation. Increasing dendritic channel density is far
less effective than lowering Ri (Fig.
8). This parameter controls the electrotonic spread of currents so that
the lower Ri is, the farther and
faster axial currents can spread, activating newer dendritic regions that will add more currents to the extracellular space. Most of the
experimental and model PS discrepancies were eliminated by using a low
Ri, which all were related to the
speed of AP backpropagation. In the experimental CSD analysis, we
measured a much faster speed than could be achieved by using the values
for somatodendritic Na densities,
channel kinetics, and electrotonic constants found in the literature.
The optimum Ri value here used in the
late part of this study is in agreement with that recently reported by
Stuart and Spruston (1998)
of ~75
· cm.
Functional implications of the contribution of dendritic currents to the PS
Because dendritic action currents during AP invasion are barely
susceptible to the latency variability of activation among firing
cells, their contribution to the st. pyr. by volume propagation confers
stability to the PS amplitude on changes of the latency dispersion.
This result argues against the extended idea that desynchronization can
be a powerful decreasing factor of the hippocampal PSs. Indeed, it
seems not to be the case, at least for antidromic activation. In fact,
sizable reduction only could be obtained when the average dispersion in
the population was 1 ms (beyond 2 ms for the latest neurons), which is
too large for antidromic activation of pyramidal cells endowed with
fast conducting axons (Lipsky 1981). It should be
remembered that the half-width of the PS is only 0.6-0.7 ms, and the
duration of the ensemble somatic sink even shorter (~0.4 ms). On the
other side, the PS at the st. pyr. becomes susceptible to the proper
lability of dendritic action currents. It is known that AP dendritic
invasion can be modulated in a variety of experimental paradigms
(Callaway and Ross 1995
; Herreras and Somjen
1993
; López-Aguado et al. 2000
; Mackenzie and Murphy 1998
; Spruston et al.
1995
). In these situations, the soma and dendrites of
individual cells change the timing, magnitude, and spatial distribution
of their current contribution to the extracellular space, making
unreliable the interpretation of the PS (see López-Aguado
et al. 2000
and following text).
In a strict sense, the unavoidable mixed contribution of currents from
somata and dendrites makes the PS to depend on the precise timing of
the currents between two interdependent membrane generators. Because
the AP actively propagates along the somatodendritic axis
(Herreras 1990; Leung 1979
; Turner
et al. 1991
), the magnitude of the
Im at a specific membrane locus will
depend on the speed and direction of the AP and on the electrotonic
status so that variations of the AP speed, the locus of AP initiation,
and the concurrence of synaptic activity will cause strong modulations of the magnitude and timing of Im at
different compartments (Varona et al. 1998
).
In practice, the fact that dendritic currents contribute to the PS at
the st. pyr. may not alter the widespread notion that its amplitude is
proportional to the number of activated cells. However, this only holds
true for a control PS. Once it is altered by any experimental
manipulation or ongoing activity, it cannot be ruled out that the
changes are due to the unbalance of the relative contribution of
somatic and dendritic currents or their timing, regardless of the
number of firing cells (López-Aguado et al. 2000).
Double recordings at the st. pyr. and st. rad. may help to explain PS
variations at the st. pyr. because most modulations will differently
modify the PS in both strata.
Note on aggregate versus single-cell models
Our results modeling the FP and CSD profiles along the entire neuron morphology show that this is a unique method to integrate modeling and experimental techniques to draw reliable conclusions when interpreting physiological data. Several advantages over single neuron models are as follows: 1) the experimental paradigm (PS) is obtained from intact unclamped cells, allowing normal interplay of ion conductances along the entire cell morphology; 2) its aggregational nature makes it extremely sensitive to minor changes of some individual cell parameters obtained from partial single-cell studies, limiting the useful range of, for instance, channel properties and distributions obtained in nonintact preparations; 3) it enables robust predictions of channel density at each loci; and 4) because the paradigm is a well-established macroscopic experimental data, it can be used as a benchmark to any other single neuron model and eventually even to test the accuracy of measured subcellular experimental variables.
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ACKNOWLEDGMENTS |
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We thank P. Somogyi and M. Trommald for help with anatomic data and N. Menéndez with statistics. Also thanks go to P. L. Nunez and J. Lerma for helpful comments.
P. Varona acknowledges support from the Spanish Ministry of Education. This work was supported by Grants PB94/1257 and PB97/1448 of the Spanish Dirección General de Investigación Científica y Técnica and Grant 8.5/15/98 of the Comunidad Autónoma de Madrid.
Present address of P. Varona: Institute for Nonlinear Science, UCSD, La Jolla, CA 92093-0402.
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FOOTNOTES |
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Address for reprint requests: O. Herreras, Dept. Investigación, Hospital Ramón y Cajal, Ctra. Colmenar km 9, Madrid 28034, Spain.
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.
Received 27 September 1999; accepted in final form 2 December 1999.
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REFERENCES |
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