1Department of Computer Science and
2Department of Neurobiology,
Volfovsky, N.,
H. Parnas,
M. Segal, and
E. Korkotian.
Geometry of Dendritic Spines Affects Calcium Dynamics in
Hippocampal Neurons: Theory and Experiments.
J. Neurophysiol. 82: 450-462, 1999.
The role of dendritic
spine morphology in the regulation of the spatiotemporal distribution
of free intracellular calcium concentration
([Ca2+]i) was examined in a unique
axial-symmetrical model that focuses on spine-dendrite interactions,
and the simulations of the model were compared with the behavior of
real dendritic spines in cultured hippocampal neurons. A set of
nonlinear differential equations describes the behavior of a spherical
dendritic spine head, linked to a dendrite via a cylindrical spine
neck. Mechanisms for handling of calcium (including internal stores,
buffers, and efflux pathways) are placed in both the dendrites and
spines. In response to a calcium surge, the magnitude and time course
of the response in both the spine and the parent dendrite vary as a
function of the length of the spine neck such that a short neck
increases the magnitude of the response in the dendrite and speeds up
the recovery in the spine head. The generality of the model, originally
constructed for a case of release of calcium from stores, was tested in
simulations of fast calcium influx through membrane channels and
verified the impact of spine neck on calcium dynamics. Spatiotemporal
distributions of [Ca2+]i, measured in
individual dendritic spines of cultured hippocampal neurons injected
with Calcium Green-1, were monitored with a confocal laser scanning
microscope. Line scans of spines and dendrites at a <1-ms time
resolution reveal simultaneous transient rises in
[Ca2+]i in spines and their parent dendrites
after application of caffeine or during spontaneous calcium transients
associated with synaptic or action potential discharges. The magnitude
of responses in the individual compartments, spine-dendrite disparity,
and the temporal distribution of [Ca2+]i were
different for spines with short and long necks, with the latter being
more independent of the dendrite, in agreement with prediction of the model.
The ability of neurons to maintain a low
intracellular calcium concentration is a combined function of calcium
binding proteins, pumps, exchangers, and intracellular calcium stores
(Sharp et al. 1993 The spine head is a closed cellular compartment separated from
its parent dendrite by a thin neck (Harris and Kater
1994 Three-dimensional spine shape
To describe biological spine shapes (Fig.
1, A1-A3) as
faithfully as possible and yet to simplify the complex calculations involved in a three-dimensional (3D) model, we reduced it to an axiosymmetric model where the spine head was described as a sphere, the
neck was described as a cylinder, and the dendrite was treated as a
fragment of a disk set at 90° to the spine. This fragment of the
dendrite bearing a single spine is represented in Fig. 2A and is denoted as "spine
domain."
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
; Simpson et al. 1995
).
Activation of calcium channels causes a large and transient rise in
[Ca2+]i. Calcium influx has been shown to
constitute a necessary step in long-term synaptic plasticity in central
neurons (Bliss and Collingridge 1993
; Lynch et
al. 1983
). Being the primary site of excitatory synaptic
interactions, dendritic spines are likely to play a major role in
neuronal plasticity, and their ability to regulate calcium is of prime
interest for the understanding of mechanisms underlying plasticity.
). The spine shape, length, and neck diameters were
proposed to be critically important for processes of synaptic
transduction (Segev and Rall 1988
). Indeed some
morphological changes were detected in size and density of dendritic
spines in correlation with neuronal activity, learning, and memory
(Lowndes and Stewart 1994
; Moser et al.
1994
; Segal 1995b
). Recent experiments with high
spatial and temporal resolution microscopy suggest that dendritic
spines are unique calcium compartments, regulating local [Ca2
+]i changes independently of parent dendrites
(Denk et al. 1995
; Guthrie et al. 1991
;
Jaffe et al. 1994
; Korkotian and Segal
1998
; Muller and Connor 1991
; Segal
1995a
; Yuste and Denk 1995
). Earlier models
addressed the possibility that the spines are independent calcium
compartments (Gamble and Koch 1987
; Holmes and
Levy 1990
; Koch and Zador 1993
; Schiegg
et al. 1995
; Wickens 1988
). In fact, direct
measurements of coupling between spines and parent dendrites were
conducted with photobleaching of fluorescent compounds in the spine
head (Svoboda et al. 1996
). This coupling may, however, be different for calcium ions than for a fluorescent compound. Immunocytochemical studies revealed the existence of ryanodine receptors in dendrites and in spine heads (Sharp et al.
1993
; Korkotian and Segal 1998
). Release of
calcium from ryanodine-sensitive stores can play an important role
during synaptic activation accompanying calcium influx. We first
investigated the role of calcium stores in the temporal distribution of
Ca2+ in spine and its associated dendritic shaft. To
discern the specific role of the stores we initially conducted
experiments and computer simulations where the sole source of
Ca2+ is that released from the stores. We further examined
theoretically and experimentally the effect of spine neck length on the
distribution of [Ca2+]i in the two
compartments. Finally, we extended the model to present simulation and
experimental results that demonstrate that the morphology of spine
retains its decisive role in regulating Ca2+ dynamics even
when influx of Ca2+ through membrane channels in the spine
head is considered.
METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Fig. 1.
Dendritic spines in cultured hippocampal neurons respond to caffeine.
A: 3 dendritic spines (1-3) taken from cells loaded
with Calcium Green-1 (CG-1) and reconstructed from serial confocal
sections of dendritic segments having long (1), middle (2), and short
(3) spine necks. B: spine-dendrite segment seen in
A1, line scanned at 0.8 ms/line, before and after puff
application (bar) of 10 mM caffeine. The entire frame, top to bottom,
comprises 512 lines. Segments a-c
correspond to the region of interest for the analysis illustrated in
C, with a being the dendrite,
b the spine neck, and c the spine head.
The regions of interest in B were quantified and plotted
as a function of time since the application of caffeine
(C). D and E: 2 spines
with long (D) and short (E) necks, imaged
at a fast frame rate (200 ms/frame), in control condition before
application of caffeine (1), soon after (2), and 1 frame later (3). The
frames 1-3 in both D and E are presented
as DF/F relative to predrug
fluorescence.
View larger version (35K):
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Fig. 2.
Three-dimensional (3D) dendritic spine model. A: 3D
representation of a spine domain. B: schematic
description of all processes that are considered in the model. Numerals
correspond to the equation numbers in the text. C: model
spine-dendrite collapsed into a 2D one. Axial symmetric presentation
of the spine domain.
Mathematical model
The model that relates to the experiments described in BIOLOGICAL EXPERIMENTS includes the following processes: 1) processes associated with calcium stores, 2) diffusion, 3) Ca2+ buffering, and 4) Ca2+ extrusion.
Calcium stores were located in the spine head and in the adjacent
dendrite (Fig. 2B). No stores were included in the neck because line scan recording did not show a significant indication for a
short latency calcium responses in the neck (Fig. 1, B and C). Following Bezprozvanny et al. (1991) and DeYoung and
Keizer (1992)
, we distinguish between two processes, uptake to the
stores from the cytoplasm and efflux from the stores. The uptake is
ATP-dependent and described by
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(1) |
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(2) |
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(3) |
The diffusion process in the spine domain (Fig. 2A) is
described by the classical diffusion equation for cylindrical
coordinates
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(4) |
The mechanism of Ca2+ buffering is given by
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(5) |
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(6) |
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(7) |
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(8) |
Ca2+ extrusion is conducted by pumps located throughout the
entire spine and dendrite membrane and given by
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(9) |
Ca2+ dynamics is given by the sum of Eqs. 4 and 6
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(10) |
To account for the results described in BIOLOGICAL
EXPERIMENTS, influx of Ca2+ through spine head was
added to the previous model. On the basis of previous studies by
Miyakawa et al. (1992) and Jaffe and Brown (1997)
we assumed
tentatively that the main Ca2+ influx is through
voltage-gated channels.
Ca2+ flux through voltage-dependent channels situated in
the membrane of the spine head and dendrite is described by
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(11) |
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Solution of the model equations
The specific geometry of a real spine (e.g., Figs. 1A
and 2A) allows us to present the model as possessing axial
symmetry around the z-axis. There is also no swirling motion in the
considered problem. This permits the use of an axial-symmetrical
approximation that reduces the 3D diffusion equation (Eq. 4)
to a 2D axial-symmetrical one (Eq. 4a and Fig.
2C)
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(4a) |
To solve the problem numerically the spine domain was subdivided into a
number of simply shaped, small regions, finite elements (Fig.
2C). Computations were carried out with FIDAP software
(version 7.6) (Engelman 1996) modified in our laboratory
(for more details see Aharon and Bercovier 1993
;
Aharon et al. 1996
).
As seen in Fig. 2, stores in the dendrite are presented by a single-store compartment situated at the base of the spine and in the boundaries of the dendrite fragment. As in reality, the stores are continuously distributed along the entire dendrite.
As mentioned previously the "spine domain" consists of the spine itself and a fragment of the entire dendrite. The question is what length of dendrite fragment to consider in the simulations such as the solution in the spine domain be minimally dependent on the diameter of the fragment. Toward this end, Eqs. 1-10 were solved in spine domain with a dendrite fragment diameter of 2-µm length. Then the fragment diameter was increased to 4 µm, and the equations were solved again. We found that Ca2+ concentration at the peak was ~2% higher for the 2 µm. The rate of decay, however, was very similar. We therefore used, for the simulations, the 2-µm diameter.
Biological experiments
Three-week-old E19 hippocampal cultures grown on glass coverslip
were prepared as described previously (Papa et al.
1995). A glass coverslip was transferred into the recording
chamber, placed in a confocal laser scanning microscope (Leica;
Heidelberg, Germany), and perfused continuously at room temperature
with medium containing (in mM) 129 NaCl, 4 KCl, 1 MgCl 2, 2 CaCl, 4.2 glucose, 10 HEPES, and 0.5 µM tetrodotoxin (TTX). pH was
adjusted to 7.4 with NaOH, and osmolarity was adjusted to 330 mosmol
with sucrose. Caffeine (Sigma, 5-10 mM) was prepared in the recording
medium. It was loaded in a pressure pipette with a tip diameter of 1-2 µm, which was placed ~20 µm from the spine-dendrite segment
studied, at right angle to the spine dendrite axis, equidistant from
both compartments. A micropipette containing 10 mM Calcium-Green-1 (CG-1) impaled somata of individual cells and the dye was iontophoresed for 1-2 min with negative currents of 1-2 nA. The fluorescence of the
cell was continuously monitored during dye filling. Images of 256 × 256 pixels were taken with a ×63 water immersion objective. The
intensity of the argon-ion laser was reduced to 2-3% of nominal value. Experiments were conducted
1 h after loading of a cell with
the dye and withdrawal of the micropipette to allow its equilibration into thin secondary branches of the dendritic tree and recovery from
the initial penetration injury. Dendrites were 3D reconstructed at the
beginning and end of the experiment with 5-10 successive optical
sections with 0.1-µm steps. To reveal fast changes in fluorescence
after caffeine application, single lines were scanned between the head
of the spine and its parent dendrite at a rate of ~0.9 ms/line. Given
the low-intensity laser light, lines of spine-dendrite segments could
be scanned repeatedly without significant photodynamic damage or
bleaching of the dye (Korkotian and Segal 1998
).
Fluorescence intensity was quantified with Leica analysis software.
Changes in Calcium Green-1 (CG-1) fluorescence were standardized by
dividing the net fluorescence by the pretreatment fluorescence with
background subtracted, separately for the spine and its parent
dendrite. Autofluorescence, measured in
bis-(o-aminophenoxy)-N,N,N',N'-tetraacetic acid-loaded cells under identical conditions, was insignificant. In
some experiments, TTX was omitted from the recording medium, and
spontaneous changes in fluorescence resulting from back-propagating action potentials and excitatory postsynaptic potentials (EPSPs) were
recorded. Further details of the methodology are presented elsewhere
(Korkotian and Segal 1998
).
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RESULTS |
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Model simulations: increase in [Ca2+]i is obtained via Ca2+ release from internal stores
To simulate the spatiotemporal distribution of Ca2+ under the experimental conditions where no influx of Ca2+ occurs but Ca2 + is released from the internal stores, model equations (Eqs. 1-10 and Table 1) were solved. As in the experiments to be described, Ca2+ stores were open in response to caffeine. Accordingly, Eq. 2 was modified such that O(C) is constant and independent of C.
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(2a) |
Three cases were examined: a long spine (1.5-µm length of neck, Fig. 3A), a medium spine (1 µm, Fig. 3B), and a short spine (0.1 µm, Fig. 3C). Spine head diameter was in all cases 0.6 µm, and spine neck diameter was 0.1 µm. In the spine head the average [Ca2+]i is presented (Fig. 3, line 1). To best represent the relevant [Ca2+]i in the dendrite we selected a volume, at the spine base, equal to the volume of the spine head. Line 2 depicts average [Ca2+]i in this volume.
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Figure 3, A-C, demonstrates that the length of the spine affects the interaction between [Ca2+]i in the spine and the dendrite; the difference in peak [Ca2+]i between spine and dendrite is maximal in the longer spines (Fig. 3, A and B). Most importantly, the peak [Ca2+]i in the dendrite is affected by the spine length in that it is highest in the dendrite with the shortest spine. This is interpreted to indicate that the short spine contributes to the calcium surge in the parent dendrite more than the long spine. Not surprisingly, the peak of [Ca2+]i in the spine is not much affected by the length of the neck. The decay of [Ca2+]i in both spines and dendrite is faster in the short spine in comparison with either medium or long spines. Finally, the decay of [Ca2+]i in the spines is faster than in the dendrites in all spine-dendrite configurations.
As the diffusible buffer CG-1 is not present under normal physiological conditions, we repeated the simulations of Fig. 3, A-C, but without inclusion of CG-1. The results of the simulations are seen in Fig. 3, D-F.
Basically, the results with and without a diffusible buffer are rather similar. In particular, the same difference among spines of different length is preserved in both cases. Also, the time to peak of Ca2+ concentration and the ratio between the level of Ca2+ in the spine head and in the dendritic shaft are very similar for various spines. Also, the time constant of Ca2+ decay is ~15% slower in the presence of 10 µM of CG-1. Naturally, for the same spine length the overall concentrations of Ca2+ both in the spine and in the dendrite are lower when the diffusible buffer is added (Fig. 3, A-C) than in its absence (Fig. 3, D-F). The lower Ca2+ concentration should, however, be attributed mainly to the overall higher concentration of buffer in the simulations of Fig. 3, A-C, and less to the fact that one of the buffers is diffusible. (Compare dotted to solid lines in Fig. 3, A-C). The dotted lines correspond to the higher (10 µM more) concentration of buffer but all of it stationary. The solid lines corresponded to the same higher concentration of the buffer, but the 10 µM additional buffer is diffusible. It can be seen that the main reduction in [Ca2+]i was caused by the addition of 10 µM buffer (compare Fig. 3, A-C, with D-F).
We continue our study with the more physiological case where no diffusible buffer is added to the system. To evaluate quantitatively the effects of neck length on each of the compartments we present in Fig. 4 the results of Fig. 3 but where each compartment is shown alone (Fig. 4, spine head, A, C, and E; dendrite, B, D, and F). To demonstrate the similarity in behavior when CG-1 is included or being absent we show in Fig. 4, A and B, simulations with CG-1. The quantitative analysis is carried on, however, only for the case when CG-1 is not included.
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To evaluate the time constant of Ca2+ decay, the semilog plots of lines a-c from Fig. 4, C and D, were drawn from 480 ms to the end of the curve. The initial time point of 480 ms was selected because it occurs after the [Ca2+]i peak and therefore reflects the decay phase better than the peak itself does. Also, calcium in the stores is at steady-state at this time (not shown). The use of semilog plots to evaluate the time constant of decay provides an approximation. It assumes that only one process governs the decay, and this process is of an exponential nature. In fact, several processes govern the decay (see MATHEMATICAL MODEL), and not all of them are of exponential nature. Indeed, the semilog plots in Fig. 4, E and F, do not exhibit an absolute straight line. Nevertheless, because we are not interested in discerning the contribution of each of the processes alone to the net decline in Ca2+ concentration, we use the "lumped time constant" extracted from Fig. 4, E and F, as an indicator to the differences in the rate of decline of [Ca2+]i in the various compartments.
Concerning the spine head, Fig. 4E shows that the shortest time constant of decay, 900 ms, is for the short spine, and it increases as the neck elongates (1,050 ms for medium spine and 2,010 ms for long spine).
The effect of neck length on the dendritic calcium is basically similar to that of the spine head (Fig. 4D). Specifically, shortest time constant of decay is for the dendrite with a short spine (970 ms) and obviously for a dendrite alone (960 ms). For the dendrite with longer spines, the time constants for decay were 1,330 and 2,100 ms for the medium and long spine, respectively (Fig. 4F). Thus the long and medium spines have greater influence on duration of the response of the parent dendrite compared with the short spine whose calcium decay at the later stage is of approximately the same speed as the dendrite alone.
Biological experiments
We now examine whether the model conclusions, that the length of the spine neck affects Ca2+ dynamics in both spine and dendrite, can be validated experimentally.
As seen from F/F processed (Fig. 1, D1 and E1)
and 3D reconstructed images (Fig. 1, A1-A3) the
dye distributed evenly along the dendrites and spines. Sizes and
diameters of spine heads and necks varied significantly in the same
optical fields. Spines and their parent dendrites responded transiently
to brief (100-200 ms) application of caffeine (5 mM), demonstrating
calcium release from ryanodine-sensitive stores (Korkotian and
Segal 1998
). Of 44 spine-dendrite pairs, 35 (80%) responded
to caffeine by a transient increase in fluorescence. In the majority of
cases the fluorescence response was initiated simultaneously in the two
compartments (Fig. 1, B and C) with the same
latency (~40 ms) from the onset of drug application, indicating that
it is unlikely that a calcium wave is generated in one compartment and
travels into the other one, as suggested previously (Jaffe and
Brown 1994
, 1997
). The response peaked within ~300 ms and
recovered to half-maximum within 760 ± 40 (SE) ms.
To test predictions of the model, we analyzed the data separately for short (0.1-0.4 µm) and long (>0.7 µm) spine necks. A subset of spines, where the line was scanned through the neck, was analyzed. Other cases, where necks were not scanned, were included in a larger sample. The rise time and decay of the grouped responses with long (Fig. 5A, 5 spines) and short (Fig. 5B, 8 spines) necks were similar to those predicted by the model (Figs. 3 and 4). Different dynamics of [Ca2+]i surge in individual spines with long (top line) and short (bottom line) length of spine necks are illustrated in Fig. 1, D and E. The entire population of spines was divided into long (>0.7 µm, n = 9, group 1), middle (0.3-0.7 µm, n = 11, group 2), and short (0.1-0.3 µm, n = 15, group 3) spine necks as in Fig. 1, A1-A3. The time between the peak and one-half recovery (Fig. 5C) in response to caffeine was measured for each spine-dendrite pair. In the spine heads, the duration of response, between the peak and one-half recovery, was longer in the longest neck group compared with the shortest spines (t = 3.5, P < 0.01). Likewise, in the dendrites, those with the longest spine necks were slower to recover compared with either the medium group (t = 2.65, P < 0.01) or the short group (t = 4.47, P < 0.01). These results confirm the predictions of the model.
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Robustness of the model
As shown previously, the model predictions agree with experimental results. The question that still arises is how robust is the model and how sensitive are its conclusions to changes in parameters values. Figure 3 already shows that adding a diffusible buffer affects the overall concentration of Ca2+ but does not alter the key conclusions. In Fig. 6 we examined the effect of additional parameters on Ca2+ dynamics. For clarity, Fig. 6A displays the "control" case. In the rest of Fig. 6 the concentration of the stationary buffer (Fig. 6B), the diffusion coefficient for Ca 2+ (Fig. 6C), the dissociation constant of the stationary buffer (Fig. 6D), and the concentration of the diffusible buffer (Fig. 6E) were modified. It can be seen that the overall concentration of Ca2 was naturally affected by changing the values of the various parameters. However, our main conclusion regarding the effect of spine length on Ca2+ dynamics was not altered. This holds also for the case where all the stationary buffer was replaced by a diffusible buffer (not shown). Changing the values of the parameters associated with extrusion has similarly no effect on the basic results.
|
As Ca2+ stores play an important role in this study we
tried to find how changes in size and differential location of the
stores will affect Ca2+ dynamics. Morphological studies
(Spacek and Harris 1997) indicate that spines may have a
smaller volume of endoplasmic reticulum than the parent dendrites.
Also, spines may vary in their size and relative density of their
calcium stores. Experimentally, the averaged response to caffeine in
spines and dendrites do not vary by much, indicating that our initial
choice of equal stores in spines and dendrite is not unrealistic.
Nonetheless, we tested the effect of a differential volume of calcium
stores in spines and dendrites. We used two arbitrary conditions; in
the first (Fig. 7), the volume of the
calcium stores in the spines was reduced to one-half that of the parent
dendrite (thus reducing the surface of the stores to 2/3 of the initial
value). In this case, calcium changes in the spines were smaller than
under "control" conditions, but the differences among them remained
the same (compare Fig. 3, right panel, and Fig. 7). The
effect of changes in the shorter spine on the parent dendrite was
smaller, and the parent dendrites of the longer spines were not
affected.
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The other condition tested involved the lack of calcium stores either in the spines or in the dendrites. In the case of no stores in the spine (Fig. 8A), the calcium change seen in dendrite caused a significant change in the spine with short neck and a marginal effect in the spine with a long neck. The dendrites had the same responses irrespective of the spines. In the opposite case, where stores were not present in the dendrites, there was a sizable change in the dendrite adjacent to the short spine and none in the dendrite next to the long spine (Fig. 8B). It is interesting to note that the magnitude of the calcium response in the spine with the long neck is largest compared with the other two cases.
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Our model demonstrates the significance of Ca2+ stores and spine morphology to Ca2+ dynamics under conditions where Ca2+ is released from internal stores. The question is whether Ca2+ stores and spine morphology play similarly important roles under physiological conditions where Ca2+ enters via voltage-dependent Ca2+ channels. These investigations are discussed in the following section.
Model simulations: Ca2+ influx and CICR release from stores
To simulate fast synaptic activation of voltage-gated calcium
channels and study their interactions with calcium released from the
stores, Eq. 11 was invoked, and the term
O(C) in Eq. 2 was described
as seen in Eq. 15. As in previous studies
(Gamble and Koch 1987; Zador et al.
1990
), g(t) in Eq.
11 is presented by an
-function. Thus
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(12) |
To calculate CICR (Eq. 2), description of
O(C) is needed. We derived
O(C) from the following kinetic scheme
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(13) |
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(14) |
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(15) |
The simulations of influx combined with release of calcium from stores are illustrated in Fig. 9. It can be seen that, even with the faster time course than in the previous simulations, the morphology of the spine still has a marked effect on the magnitude and decay kinetics of calcium in spines and in their parent dendrites. Furthermore, the presence of stores has a pronounced effect on calcium dynamics, although the initial calcium surge is produced by an influx of calcium rather than by release from stores; the long spine has a slower [Ca2+]i decay than the short one after calcium influx into the spine head and its release from stores, when the parent dendrite is not depolarized (Fig. 9A) or partly depolarized (Fig. 9B, only 1/3 of the channels open). Removal of calcium stores from both compartments results in a strong decrease in calcium responses in both compartments. However, an increase in calcium influx compensates partly for the lack of difference between short and long spines in the absence of stores (Fig. 9C). Re-introduction of stores to the case of enhanced influx causes an amplification of the difference in calcium response (Fig. 9E). For the latter case the decay time constants were 138 and 95 ms for the longer and shorter spines, respectively, and 342 and 145 ms for their parent dendrites.
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Biological experiments
The validity of the predictions of the model for the synaptic influx case was tested in spine-dendrite segments during spontaneous calcium surges found in the cultured cells when synaptic and spike activity are not blocked by TTX. In such conditions, cells tend to fire action potentials spontaneously and evoke EPSPs in follower cells. Both small, synaptically originated events and large, spike-associated events were recorded in both short and long spines. There was a clear difference between the two spine types in latency, magnitude, and similarity to the response in the parent dendrite in the case of the small, probably EPSP-associated calcium change, but the spike-associated, large calcium change was similar in the two compartments (Fig. 10). In all 11 spine-dendrite pairs tested the long spines were more independent of the parent dendrites than the short ones, as predicted by the model.
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DISCUSSION |
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This study combines a computational model of a dendritic spine and experimental results obtained by a transient release of calcium from stores in dendritic spines of cultured hippocampal neurons. The model takes into account the presence of calcium stores in both spines and dendrites and simulates the spatiotemporal distribution of [Ca2+]i in the spine and the dendrite in response to a transient calcium rise. This rise was produced in the initial simulations by calcium released from stores and in advanced simulations by activation of voltage-gated calcium channels, which in turn activate the stores. The model predicts that the length of the spine neck affects both spine and dendritic responses to a calcium surge so that short spines are more similar to their parent dendrites than long ones and contribute to an increase in the response magnitude of the parent dendrites. On the other hand, long spines express a larger calcium response than their parent dendrites. Also, the time course of calcium recovery is slower in spines with long necks than those with short necks. In both short and long spines, calcium stores appear to strongly affect calcium distribution during synaptic and CICR activation. The model is supported by experimental results on calcium released from stores and on influx of calcium during synaptic and spike activity in spines and dendrites of cultured hippocampal neurons.
The effects of spine distance on the magnitude and duration of calcium surge in the spine and dendrite are intuitively simple. The close distance between the spine and its parent dendrite in the case of the short spine makes the calcium surge faster, larger, but shorter in duration. This is due to the fast diffusion of calcium from the spine head into and along the dendritic shaft. With the medium-long spines, the larger response in the spine head than the response in the dendrite is due to the fact that, unlike the shaft, the spine head is a closed spherical compartment. The longer distance causes the same amount of free calcium to move slower out of the spine compartment into the dendrite, making the increase higher and the recovery in both compartments slower than the case of the short spines. Clearly, the extrusion through a longer neck also causes less calcium to reach the dendrite. These mechanisms act also when calcium influxes transiently through membrane channels.
Several models of calcium homeostasis in dendritic spines were
proposed recently (Gold and Bear 1994; Holmes and
Levy 1990
; Koch and Zador 1993
; Wickens
1988
; Zador et al. 1990
). They were initiated by
the realization that the spine neck may not constitute a significant
modulatory barrier for the transfer of synaptic charge from the spine
head into the dendrite (Barrionuevo et al. 1986
;
Brown et al. 1988
) and by the experimental observations that suggested that the spine may constitute a unique cellular calcium
compartment (Guthrie et al. 1991
; Muller and
Connor 1991
). Our model is different from previous ones in that
it contains calcium stores as an essential compartment in the spine
(for the possibility of calcium stores in spines see Jaffe and
Brown 1997
; Jaffe et al. 1994
) and that in fact
it links influx of calcium through voltage-gated channels in the
spine-dendrite to release of calcium from stores. In a previous model,
which focuses on influx pathways as the main source of loading the
spine with calcium (Schiegg et al. 1995
), it is
predicted that the stores cause prolongation of the calcium surge,
which is important for the formation of long-term potentiation of
reactivity to afferent stimulation in central neurons (Brown et
al. 1988
). Experimental data also suggest that calcium stores
are important for the formation of long-term potentiation (Bliss
and Collingridge 1993
). With this exception, other models do
not ascribe a significant function to calcium stores in dendritic spines.
A major difference between our model and previous ones concerns
the dynamics of calcium changes in the dendrites. Although it was
obvious that the dendritic calcium should be affected by spine calcium
(e.g., Jaffe and Brown 1994), in previous models [Ca2+]i in the dendrite was not affected much
by changes in morphology of the spine (Gold and Bear
1994
; Holmes and Levy 1990
), and therefore the
dendrite was ignored altogether (Gamble and Koch 1987
).
Experimentally, both examples, where [Ca2+]i
rise spreads from the spine into the dendrite and where the calcium
rise is restricted to the spine, were reported (Guthrie et al.
1991
; Yuste and Denk 1995
). We found that the
temporal distribution of [Ca2+]i in the
dendrite in response to a calcium surge produced within the dendrite
itself is strongly affected by the morphology of its attached spine. In
reality, when the volume of the dendrite and its stores are several
orders of magnitude larger than the spine, the impact of the latter
compartment on dendritic [Ca2+]i might be
negligible. Such can be the case with spines growing on large proximal
dendrites. This however is the exception, as in most cases the spines
are attached to dendrites of similar diameters, containing about the
same concentrations of calcium stores (Spacek and Harris
1997
) (see Fig. 1).
The disparity between the calcium response of the long spine and
its parent dendrite is strikingly different from the similarity seen in
the case of the short spine and its parent dendrite. This result is
seen in both the model and the experimental data. Concerning the
experiments, there could be several biological explanations for this
disparity; it is possible, for example, that dendrites with long spines
accumulate more dye than the other dendrites, and therefore calcium
changes are buffered more in these dendrites, leading to smaller and
slower responses. However, this is not likely because the protocol for
the dye loading allows ample time for an even distribution of the dye.
It is also possible that dendrites with long spines are different in
concentrations of calcium stores than other dendrites. This is also
less likely because most spines are found to contain calcium stores in
about the same density (Spacek and Harris 1997).
Finally, the CICR mechanism (Verhatsky and Shmigol 1996
)
may contribute to the short spines more than to the long ones. Clearly,
some dendrites are endowed with short and some with long spines, such
that a systematic biological difference between them is quite possible.
However, the model indicates that no such added biological mechanism is
needed to explain the observed results, and a mere morphological
consideration is sufficient to explain the effect of spines on
dendritic responses to a calcium surge.
The current results demonstrate the importance of the morphology
of dendritic spines in regulating calcium dynamics in the parent
dendrites in that small variations in spine length may have a
significant effect on the way the dendrite handles calcium. Such small variations have been shown to take place in living dendritic
spines (Segal 1995b) so that an ongoing control by spine of its parent dendrite is to be expected. Assuming that the duration of
[Ca2+]i surge may be critically important for
causing changes in calcium-dependent biochemical processes in the cell,
in connection with long-term plasticity (Bliss and Collingridge
1993
) it becomes extremely important to be able to control the
amplitude and duration of this calcium surge, which is provided by the spines.
Although the cultured neuron is an ideal test system for examining the interaction between the single spine and its parent dendrite, the situation will be more complex when the real dendrite, endowed with higher density of spines, will be examined. One issue of importance for the interpretation of the current results is that dendritic spines are not present in isolation, and several spines are likely to be activated by the same application of caffeine. Therefore what if short spines reside near long ones? How effective will the individual spine be in its ability to regulate dendritic calcium under such conditions? Luckily, the cultured neuron has quite often very few spines, allowing the examination of the effect of individual spines on dendritic calcium. Also, in most cases, in vivo as well as in the cultured neuron, spines of similar lengths and properties are likely to cluster together on dendritic segments (Segal, unpublished observations). Nonetheless, the issue of interactions among spines with different physical properties remains an exciting subject for future modeling and experiments.
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ACKNOWLEDGMENTS |
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We thank V. Greenberger for preparation of the cultures.
This work was supported by grants from the Binational US-Israel Science Foundation and the Israel Academy of Science to M. Segal.
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FOOTNOTES |
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Address reprint requests to E. Korkotian.
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 26 May 1998; accepted in final form 2 February 1999.
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REFERENCES |
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