Modeling the role of lateral membrane diffusion in AMPA receptor trafficking along a spiny dendrite

AMPA receptor trafficking in dendritic spines is emerging as a major postsynaptic mechanism for the expression of plasticity at glutamatergic synapses. AMPA receptors within a spine are in a continuous state of flux, being exchanged with local intracellular pools via exo/endocytosis and with the surrounding dendrite via lateral membrane diffusion. This suggests that one cannot treat a single spine in isolation. Here we present a model of AMPA receptor trafficking between multiple dendritic spines distributed along the surface of a dendrite. Receptors undergo lateral diffusion within the dendritic membrane, with each spine acting as a spatially localized trap where receptors can bind to scaffolding proteins or be internalized through endocytosis. Exocytosis of receptors occurs either at the soma or at sites local to dendritic spines via constitutive recycling from intracellular pools. We derive a reaction–diffusion equation for receptor trafficking that takes into account these various processes. Solutions of this equation allow us to calculate the distribution of synaptic receptor numbers across the population of spines, and hence determine how lateral diffusion contributes to the strength of a synapse. A number of specific results follow from our modeling and analysis. (1) Lateral membrane diffusion alone is insufficient as a mechanism for delivering AMPA receptors from the soma to distal dendrites. (2) A source of surface receptors at the soma tends to generate an exponential-like distribution of receptors along the dendrite, which has implications for synaptic democracy. (3) Diffusion mediates a heterosynaptic interaction between spines so that local changes in the constitutive recycling of AMPA receptors induce nonlocal changes in synaptic strength. On the other hand, structural changes in a spine following long term potentiation or depression have a purely local effect on synaptic strength. (4) A global change in the rates of AMPA receptor exo/endocytosis is unlikely to be the sole mechanism for homeostatic synaptic scaling. (5) The dynamics of AMPA receptor trafficking occurs on multiple timescales and varies according to spatial location along the dendrite. Understanding such dynamics is important when interpreting data from inactivation experiments that are used to infer the rate of relaxation to steady-state.     

Dynamin-dependent Membrane Drift Recruits AMPA Receptors to Dendritic Spines

The surface expression and localization of AMPA receptors (AMPARs) at dendritic spines are tightly controlled to regulate synaptic transmission. Here we show that de novo exocytosis of the GluR2 AMPAR subunit occurs at the dendritic shaft and that new AMPARs diffuse into spines by lateral diffusion in the membrane. However, membrane topology restricts this lateral diffusion. We therefore investigated which mechanisms recruit AMPARs to spines from the shaft and demonstrated that inhibition of dynamin GTPase activity reduced lateral diffusion of membrane-anchored green fluorescent protein and super-ecliptic pHluorin (SEP)-GluR2 into spines. In addition, the activation of synaptic N-methyl-d-aspartate (NMDA) receptors enhanced lateral diffusion of SEP-GluR2 and increased the number of endogenous AMPARs in spines. The NMDA-invoked effects were prevented by dynamin inhibition, suggesting that activity-dependent dynamin-mediated endocytosis within spines generates a net inward membrane drift that overrides lateral diffusion barriers to enhance membrane protein delivery into spines. These results provide a novel mechanistic explanation of how AMPARs and other membrane proteins are recruited to spines by synaptic activity.AMPA³ receptors (AMPARs) are of fundamental importance because they mediate the majority of fast excitatory synaptic transmission in the mammalian central nervous system (1). Most excitatory synapses are characterized morphologically by dendritic spines that contain an electron-dense postsynaptic density (PSD) at their head (2, 3). PSD is highly enriched in AMPARs and associated proteins equired for synaptic transmission and signal transduction (4-6). Activity-evoked changes in functional postsynaptic AMPARs mediate the two main forms of synaptic plasticity believed to underlie learning and memory in the hippocampus (7). Long term potentiation involves the activity-dependent recruitment of AMPARs to the postsynaptic membrane and a concurrent increase in AMPA-mediated transmission, whereas long term depression is a decrease in synaptic AMPAR function (8).The number and subunit composition of synaptic AMPARs are stringently regulated, but despite intense investigation, the processes by which AMPARs are delivered to and retained at the PSD remain controversial. Using photoreactive antagonists and electrophysiology, it has been proposed that AMPARs are only inserted in the plasma membrane at the cell body and laterally diffuse long distances to synapses (9). In direct contrast, approaches using real-time imaging have suggested that AMPARs are inserted in the plasma membrane of the dendritic shaft close to, but not at, dendritic spines (10). It has also been suggested that AMPARs could be inserted directly into the plasma membrane of the PSD (11).Independent of the route of delivery for new AMPARs to synapses, it is well established that lateral diffusion in the plasma membrane allows the exchange of receptors in and out of the PSD (12-14). Using palmitoylated membrane-anchored GFP (mGFP), which partitions to the inner leaflet of the plasma membrane, it has also been reported that diffusion is significantly retarded within spines compared with the shaft and that AMPAR activation increases the rates of mGFP diffusion in spines (15). In addition, we have shown previously that membrane protein movement into and out of spines is slow compared with lateral diffusion on non-spiny membrane (16), and modeling studies have predicted that spine length is a major determinant of the time a protein takes to reach the PSD (17). More recently, it has been proposed that endocytosis at specialized endocytic zones close to the PSD within spines is required to maintain the steady state complement of synaptic AMPARs (18).Taken together these findings suggest that endocytosis and exocytosis as well as lateral diffusion and membrane topology may all play important roles in regulating membrane protein mobility in spines. The interrelationships between these processes, however, remain unclear. Here we used FRAP (fluorescence recovery after photobleaching) and multisite FLIP (fluorescence loss in photobleaching) to visualize super-ecliptic pHluorin-tagged GluR2 surface expression and AMPAR movement in real time. We examined how lateral diffusion is regulated in spines both by blocking dynamin GTPase activity and stimulating NMDARs. Combined with Monte Carlo simulations on lattices fitting theoretical spines, our data indicate that the membrane topology of spines alone is sufficient to constrain lateral diffusion. NMDAR activation facilitates AMPAR recruitment to spines by a process that involves the recruitment of plasma membrane, together with the constituent membrane proteins, from adjacent regions of the dendritic shaft being drawn into the spine to replace membrane that is internalized during endocytosis. In other words, our results suggest a mode of lateral diffusion that is neither free nor anomalous. Rather, we show the directional diffusion of membrane-embedded proteins toward the postsynapse driven by the endocytosis within the spine. These results provide a new mechanistic explanation of how synaptic activity can overcome topology-induced diffusion barriers to recruit new membrane proteins to the spine.     

Rapid redistribution of synaptic PSD-95 in the neocortex in vivo

Most excitatory synapses terminate on dendritic spines. Spines vary in size, and their volumes are proportional to the area of the postsynaptic density (PSD) and synaptic strength. PSD-95 is an abundant multi-domain postsynaptic scaffolding protein that clusters glutamate receptors and organizes the associated signaling complexes. PSD-95 is thought to determine the size and strength of synapses. Although spines and their synapses can persist for months in vivo, PSD-95 and other PSD proteins have shorter half-lives in vitro, on the order of hours. To probe the mechanisms underlying synapse stability, we measured the dynamics of synaptic PSD-95 clusters in vivo. Using two-photon microscopy, we imaged PSD-95 tagged with GFP in layer 2/3 dendrites in the developing (postnatal day 10–21) barrel cortex. A subset of PSD-95 clusters was stable for days. Using two-photon photoactivation of PSD-95 tagged with photoactivatable GFP (paGFP), we measured the time over which PSD-95 molecules were retained in individual spines. Synaptic PSD-95 turned over rapidly (median retention times τ_r ~ 22–63 min from P10–P21) and exchanged with PSD-95 in neighboring spines by diffusion. PSDs therefore share a dynamic pool of PSD-95. Large PSDs in large spines captured more diffusing PSD-95 and also retained PSD-95 longer than small PSDs. Changes in the sizes of individual PSDs over days were associated with concomitant changes in PSD-95 retention times. Furthermore, retention times increased with developmental age (τ_r ~ 100 min at postnatal day 70) and decreased dramatically following sensory deprivation. Our data suggest that individual PSDs compete for PSD-95 and that the kinetic interactions between PSD molecules and PSDs are tuned to regulate PSD size.     

Shape-Induced Asymmetric Diffusion in Dendritic Spines Allows Efficient Synaptic AMPA Receptor Trapping

Dendritic spines are the primary postsynaptic sites of excitatory neurotransmission in the brain. They exhibit a remarkable morphological variety, ranging from thin protrusions, to stubby shapes, to bulbous mushroom shapes. The remodeling of spines is thought to regulate the strength of the synaptic connection, which depends vitally on the number and the spatial distribution of AMPA-type glutamate receptors (AMPARs). We present numerical and analytical analyses demonstrating that this shape strongly affects AMPAR diffusion. We report a pronounced suppression of the receptor exit rate out of spines with decreasing neck radius. Thus, mushroomlike spines become highly effective at retaining receptors in the spine head. Moreover, we show that the postsynaptic density further enhances receptor trapping, particularly in mushroomlike spines local exocytosis in the spine head, in contrast to release at the base, provides rapid and specific regulatory control of AMPAR concentration at synapses.     

Shape-Induced Asymmetric Diffusion in Dendritic Spines Allows Efficient Synaptic AMPA Receptor Trapping

Dendritic spines are the primary postsynaptic sites of excitatory neurotransmission in the brain. They exhibit a remarkable morphological variety, ranging from thin protrusions, to stubby shapes, to bulbous mushroom shapes. The remodeling of spines is thought to regulate the strength of the synaptic connection, which depends vitally on the number and the spatial distribution of AMPA-type glutamate receptors (AMPARs). We present numerical and analytical analyses demonstrating that this shape strongly affects AMPAR diffusion. We report a pronounced suppression of the receptor exit rate out of spines with decreasing neck radius. Thus, mushroomlike spines become highly effective at retaining receptors in the spine head. Moreover, we show that the postsynaptic density further enhances receptor trapping, particularly in mushroomlike spines local exocytosis in the spine head, in contrast to release at the base, provides rapid and specific regulatory control of AMPAR concentration at synapses.     

Biphasic Synaptic Ca Influx Arising from Compartmentalized Electrical Signals in Dendritic Spines

Excitatory synapses on mammalian principal neurons are typically formed onto dendritic spines, which consist of a bulbous head separated from the parent dendrite by a thin neck. Although activation of voltage-gated channels in the spine and stimulus-evoked constriction of the spine neck can influence synaptic signals, the contribution of electrical filtering by the spine neck to basal synaptic transmission is largely unknown. Here we use spine and dendrite calcium (Ca) imaging combined with 2-photon laser photolysis of caged glutamate to assess the impact of electrical filtering imposed by the spine morphology on synaptic Ca transients. We find that in apical spines of CA1 hippocampal neurons, the spine neck creates a barrier to the propagation of current, which causes a voltage drop and results in spatially inhomogeneous activation of voltage-gated Ca channels (VGCCs) on a micron length scale. Furthermore, AMPA and NMDA-type glutamate receptors (AMPARs and NMDARs, respectively) that are colocalized on individual spine heads interact to produce two kinetically and mechanistically distinct phases of synaptically evoked Ca influx. Rapid depolarization of the spine triggers a brief and large Ca current whose amplitude is regulated in a graded manner by the number of open AMPARs and whose duration is terminated by the opening of small conductance Ca-activated potassium (SK) channels. A slower phase of Ca influx is independent of AMPAR opening and is determined by the number of open NMDARs and the post-stimulus potential in the spine. Biphasic synaptic Ca influx only occurs when AMPARs and NMDARs are coactive within an individual spine. These results demonstrate that the morphology of dendritic spines endows associated synapses with specialized modes of signaling and permits the graded and independent control of multiple phases of synaptic Ca influx.     

Regulation of dendritic spine morphology and synaptic function by Shank and Homer

The Shank family of proteins interacts with NMDA receptor and metabotropic glutamate receptor complexes in the postsynaptic density (PSD). Targeted to the PSD by a PDZ-dependent mechanism, Shank promotes the maturation of dendritic spines and the enlargement of spine heads via its ability to recruit Homer to postsynaptic sites. Shank and Homer cooperate to induce accumulation of IP3 receptors in dendritic spines and formation of putative multisynapse spines. In addition, postsynaptic expression of Shank enhances presynaptic function, as measured by increased minifrequency and FM4-64 uptake. These data suggest a central role for the Shank scaffold in the structural and functional organization of the dendritic spine and synaptic junction.     

Myosin IIb activity and phosphorylation status determines dendritic spine and post-synaptic density morphology

Dendritic spines in hippocampal neurons mature from a filopodia-like precursor into a mushroom-shape with an enlarged post-synaptic density (PSD) and serve as the primary post-synaptic location of the excitatory neurotransmission that underlies learning and memory. Using myosin II regulatory mutants, inhibitors, and knockdowns, we show that non-muscle myosin IIB (MIIB) activity determines where spines form and whether they persist as filopodia-like spine precursors or mature into a mushroom-shape. MIIB also determines PSD size, morphology, and placement in the spine. Local inactivation of MIIB leads to the formation of filopodia-like spine protrusions from the dendritic shaft. However, di-phosphorylation of the regulatory light chain on residues Thr18 and Ser19 by Rho kinase is required for spine maturation. Inhibition of MIIB activity or a mono-phosphomimetic mutant of RLC similarly prevented maturation even in the presence of NMDA receptor activation. Expression of an actin cross-linking, non-contractile mutant, MIIB R709C, showed that maturation into a mushroom-shape requires contractile activity. Loss of MIIB also leads to an elongated PSD morphology that is no longer restricted to the spine tip; whereas increased MIIB activity, specifically through RLC-T18, S19 di-phosphorylation, increases PSD area. These observations support a model whereby myosin II inactivation forms filopodia-like protrusions that only mature once NMDA receptor activation increases RLC di-phosphorylation to stimulate MIIB contractility, resulting in mushroom-shaped spines with an enlarged PSD.     

Confocal laser scanning microscopy reveals voltage-gated calcium signals within hippocampal dendritic spines

The induction of long-term potentiation (LTP) is generally assumed to be triggered by Ca²⁺ entry into dendritic spines via NMDA receptor-gated channels. A previous computational model proposed that spines serve several functions in this process. First, they compartmentalize and amplify increases in [Ca²⁺]_i. Second, they augment the nonlinear relationship between synaptic strength and the probability or magnitude of LTP induction. Third, they isolate the metabolic machinery responsible for LTP induction from increases in [Ca²⁺]_i produced by voltage-gated Ca²⁺ channels in the dendritic shaft. Here we examine this last prediction of the model using methods that combine confocal microscopy with simultaneous neurophysiological recordings in hippocampal brain slices. Either of two Ca²⁺-sensitive dyes were injected into CA1 pyramidal neurons. Direct depolarization of the neurons via the somatic electrode produced clear increases in Ca²⁺ signals within the dendritic spines, a result that was not predicted by the previous spine model. Our new spine model suggests that some of this signal could theoretically result from Ca²⁺-bound dye diffusing from the dendritic shaft into the spine. Dye diffusion alone cannot, however, explain the numerous cases in which the Ca²⁺ signal in the spine was considerably larger than that in the adjacent dendritic shaft. The latter observations raise the possiblity of voltage-gated Ca²⁺ entry directly into the spine or else perhaps via Ca²⁺-dependent Ca²⁺release. The new spine model accommodates these observations as well as several other recent experimental results. 1994 John Wiley & Sons, Inc.     

A Septin-Dependent Diffusion Barrier at Dendritic Spine Necks

Excitatory glutamatergic synapses at dendritic spines exchange and modulate their receptor content via lateral membrane diffusion. Several studies have shown that the thin spine neck impedes the access of membrane and solute molecules to the spine head. However, it is unclear whether the spine neck geometry alone restricts access to dendritic spines or if a physical barrier to the diffusion of molecules exists. Here, we investigated whether a complex of septin cytoskeletal GTPases localized at the base of the spine neck regulates diffusion across the spine neck. We found that, during development, a marker of the septin complex, Septin7 (Sept7), becomes localized to the spine neck where it forms a stable structure underneath the plasma membrane. We show that diffusion of receptors and bulk membrane, but not cytoplasmic proteins, is slower in spines bearing Sept7 at their neck. Finally, when Sept7 expression was suppressed by RNA interference, membrane molecules explored larger membrane areas. Our findings indicate that Sept7 regulates membrane protein access to spines.     

Intracellular Ca2+ and not the extracellular matrix determines surface dynamics of AMPA-type glutamate receptors on aspiny neurons

The perisynaptic extracellular matrix (ECM) contributes to the control of the lateral mobility of AMPA-type glutamate receptors (AMPARs) at spine synapses of principal hippocampal neurons. Here, we have studied the effect of the ECM on the lateral mobility of AMPARs at shaft synapses of aspiny interneurons. Single particle tracking experiments revealed that the removal of the hyaluronan-based ECM with hyaluronidase does not affect lateral receptor mobility on the timescale of seconds. Similarly, cross-linking with specific antibodies against the extracellular domain of the GluA1 receptor subunit, which affects lateral receptor mobility on spiny neurons, does not influence receptor mobility on aspiny neurons. AMPARs on aspiny interneurons are characterized by strong inward rectification indicating a significant fraction of Ca²⁺-permeable receptors. Therefore, we tested whether Ca²⁺ controls AMPAR mobility in these neurons. Application of the membrane-permeable Ca²⁺ chelator BAPTA-AM significantly increased the lateral mobility of GluA1-containing synaptic and extrasynaptic receptors. These data indicate that the perisynaptic ECM affects the lateral mobility differently on spiny and aspiny neurons. Although ECM structures on interneurons appear much more prominent, their influence on AMPAR mobility seems to be negligible at short timescales.     

Estimating the synaptic current in a multiconductance AMPA receptor model

Synaptic transmission starts after the presynaptic neuron has released diffusing neurotransmitters, leading to postsynaptic receptor activation and a postsynaptic current, mostly mediated by glutamatergic (AMPARs) receptors for excitatory neurons. Despite intense experimental and theoretical research, it is still unclear how factors such as the synaptic cleft geometry, the organization, the number and the multiconductance state of receptors, the geometry of postsynaptic density (PSD), and the neurotransmitter release location, shape the mean and the variance of the postsynaptic current and its plastic changes. To estimate the synaptic current amplitude and to account for the stochastic nature of synaptic transmission, we develop a semianalytical method in which we obtain a general expression for the coefficient of variation. The method uses the experimental data about the multiconductance channels. We find that PSD morphological changes can significantly modulate the synaptic current, which is maximally reliable (the coefficient of variation is minimal) for an optimal size of the PSD, that depends on the vesicular release active zone. We show that this optimal PSD size is due to nonlinear phenomena involving the receptor multibinding cooperativity. We conclude that changes in the PSD geometry can sustain a form of synaptic plasticity, independent of a change in the number of receptors.     

The interaction between Stargazin and PSD-95 regulates AMPA receptor surface trafficking

Accumulation of AMPA receptors at synapses is a fundamental feature of glutamatergic synaptic transmission. Stargazin, a member of the TARP family, is an AMPAR auxiliary subunit allowing interaction of the receptor with scaffold proteins of the postsynaptic density, such as PSD-95. How PSD-95 and Stargazin regulate AMPAR number in synaptic membranes remains elusive. We show, using single quantum dot and FRAP imaging in live hippocampal neurons, that exchange of AMPAR by lateral diffusion between extrasynaptic and synaptic sites mostly depends on the interaction of Stargazin with PSD-95 and not upon the GluR2 AMPAR subunit C terminus. Disruption of interactions between Stargazin and PSD-95 strongly increases AMPAR surface diffusion, preventing AMPAR accumulation at postsynaptic sites. Furthermore, AMPARs and Stargazin diffuse as complexes in and out synapses. These results propose a model in which the Stargazin-PSD-95 interaction plays a key role to trap and transiently stabilize diffusing AMPARs in the postsynaptic density.     

Spine neck geometry determines spino-dendritic cross-talk in the presence of mobile endogenous calcium binding proteins

Dendritic spines are thought to compartmentalize second messengers like Ca²⁺. The notion of isolated spine signaling, however, was challenged by the recent finding that under certain conditions mobile endogenous Ca²⁺-binding proteins may break the spine limit and lead to activation of Ca²⁺-dependent dendritic signaling cascades. Since the size of spines is variable, the spine neck may be an important regulator of this spino-dendritic crosstalk. We tested this hypothesis by using an experimentally defined, kinetic computer model in which spines of Purkinje neurons were coupled to their parent dendrite by necks of variable geometry. We show that Ca²⁺ signaling and calmodulin activation in spines with long necks is essentially isolated from the dendrite, while stubby spines show a strong coupling with their dendrite, mediated particularly by calbindin D28k. We conclude that the spine neck geometry, in close interplay with mobile Ca²⁺-binding proteins, regulates the spino-dendritic crosstalk.     

Local control of AMPA receptor trafficking at the postsynaptic terminal by a small GTPase of the Rab family

The delivery of neurotransmitter receptors into the synaptic membrane is essential for synaptic function and plasticity. However, the molecular mechanisms of these specialized trafficking events and their integration with the intracellular membrane transport machinery are virtually unknown. Here, we have investigated the role of the Rab family of membrane sorting proteins in the late stages of receptor trafficking into the postsynaptic membrane. We have identified Rab8, a vesicular transport protein associated with trans-Golgi network membranes, as a critical component of the cellular machinery that delivers AMPA-type glutamatergic receptors (AMPARs) into synapses. Using electron microscopic techniques, we have found that Rab8 is localized in close proximity to the synaptic membrane, including the postsynaptic density. Electrophysiological studies indicated that Rab8 is necessary for the synaptic delivery of AMPARs during plasticity (long-term potentiation) and during constitutive receptor cycling. In addition, Rab8 is required for AMPAR delivery into the spine surface, but not for receptor transport from the dendritic shaft into the spine compartment or for delivery into the dendritic surface. Therefore, Rab8 specifically drives the local delivery of AMPARs into synapses. These results demonstrate a new role for the cellular secretory machinery in the control of synaptic function and plasticity directly at the postsynaptic membrane.     

Propagation of CaMKII translocation waves in heterogeneous spiny dendrites

CaMKII (Ca²⁺-calmodulin-dependent protein kinase II) is a key regulator of glutamatergic synapses and plays an essential role in many forms of synaptic plasticity. It has recently been observed experimentally that stimulating a local region of dendrite not only induces the local translocation of CaMKII from the dendritic shaft to synaptic targets within spines, but also initiates a wave of CaMKII translocation that spreads distally through the dendrite with an average speed of order 1μm/s. We have previously developed a simple reaction–diffusion model of CaMKII translocation waves that can account for the observed wavespeed and predicts wave propagation failure if the density of spines is too high. A major simplification of our previous model was to treat the distribution of spines as spatially uniform. However, there are at least two sources of heterogeneity in the spine distribution that occur on two different spatial scales. First, spines are discrete entities that are joined to a dendritic branch via a thin spine neck of submicron radius, resulting in spatial variations in spine density at the micron level. The second source of heterogeneity occurs on a much longer length scale and reflects the experimental observation that there is a slow proximal to distal variation in the density of spines. In this paper, we analyze how both sources of heterogeneity modulate the speed of CaMKII translocation waves along a spiny dendrite. We adapt methods from the study of the spread of biological invasions in heterogeneous environments, including homogenization theory of pulsating fronts and Hamilton–Jacobi dynamics of sharp interfaces.     

Regulation of dendritic spine morphology by SPIN90, a novel Shank binding partner

Dendritic spines are highly specialized actin-rich structures on which the majority of excitatory synapses are formed in the mammalian CNS. SPIN90 is an actin-binding protein known to be highly enriched in postsynaptic densities (PSDs), though little is known about its function there. Here, we show that SPIN90 is a novel binding partner for Shank proteins in the PSD. SPIN90 and Shank co-immunoprecipitate from brain lysates and co-localize in postsynaptic dendrites and act synergistically to mediate spine maturation and spine head enlargement. At the same time, SPIN90 causes accumulation of Shank and PSD-95 within dendritic spines. In addition, we found that the protein composition of PSDs in SPIN90 knockout mice is altered as is the actin cytoskeleton of cultured hippocampal SPIN90 knockout neurons. Taken together, these findings demonstrate that SPIN90 is a Shank1b binding partner and a key contributor to the regulation of dendritic spine morphogenesis and brain function.     

The impacts of geometry and binding on CaMKII diffusion and retention in dendritic spines

We used a particle-based Monte Carlo simulation to dissect the regulatory mechanism of molecular translocation of CaMKII, a key regulator of neuronal synaptic function. Geometry was based upon measurements from EM reconstructions of dendrites in CA1 hippocampal pyramidal neurons. Three types of simulations were performed to investigate the effects of geometry and other mechanisms that control CaMKII translocation in and out of dendritic spines. First, the diffusional escape rate of CaMKII from model spines of varied morphologies was examined. Second, a postsynaptic density (PSD) was added to study the impact of binding sites on this escape rate. Third, translocation of CaMKII from dendrites and trapping in spines was investigated using a simulated dendrite. Based on diffusion alone, a spine of average dimensions had the ability to retain CaMKII for duration of ~4 s. However, binding sites mimicking those in the PSD controlled the residence time of CaMKII in a highly nonlinear manner. In addition, we observed that F-actin at the spine head/neck junction had a significant impact on CaMKII trapping in dendritic spines. We discuss these results in the context of possible mechanisms that may explain the experimental results that have shown extended accumulation of CaMKII in dendritic spines during synaptic plasticity and LTP induction.     

Calcium dynamics in dendritic spines and spine motility

A dendritic spine is an intracellular compartment in synapses of central neurons. The role of the fast twitching of spines, brought about by a transient rise of internal calcium concentration above that of the parent dendrite, has been hitherto unclear. We propose an explanation of the cause and effect of the twitching and its role in the functioning of the spine as a fast calcium compartment. Our molecular model postulates that rapid spine motility is due to the concerted contraction of calcium-binding proteins. The contraction induces a stream of cytoplasmic fluid in the direction of the dendritic shaft, thus speeding up the time course of spine calcium dynamics, relative to pure diffusion. Simulations indicate that chemical reaction rate theory at the molecular level can explain spine motility. They reveal two time periods in calcium dynamics, as measured recently by other researchers. It appears that rapid motility in dendritic spines increases the efficiency of calcium conduction to the dendrite and speeds up the emptying of the spine. This could play a major role in the induction of synaptic plasticity. A prediction of the model is that alteration of spine motility will modify the time course of calcium in the dendritic spine and could be tested experimentally.