Calcium dynamics in dendritic spines and spine motility

Genetically encoded fluorescent sensors for imaging neuronal dynamics in vivo

The brain relies on many forms of dynamic activities in individual neurons, from synaptic transmission to electrical activity and intracellular signaling events. Monitoring these neuronal activities with high spatiotemporal resolution in the context of animal behavior is a necessary step to achieve a mechanistic understanding of brain function. With the rapid development and dissemination of highly optimized genetically encoded fluorescent sensors, a growing number of brain activities can now be visualized in vivo. To date, cellular calcium imaging, which has been largely used as a proxy for electrical activity, has become a mainstay in systems neuroscience. While challenges remain, voltage imaging of neural populations is now possible. In addition, it is becoming increasingly practical to image over half a dozen neurotransmitters, as well as certain intracellular signaling and metabolic activities. These new capabilities enable neuroscientists to test previously unattainable hypotheses and questions. This review summarizes recent progress in the development and delivery of genetically encoded fluorescent sensors, and highlights example applications in the context of in vivo imaging.

Dendritic spine morphology regulates calcium-dependent synaptic weight change

Dendritic spines act as biochemical computational units and must adapt their responses according to their activation history. Calcium influx acts as the first signaling step during postsynaptic activation and is a determinant of synaptic weight change. Dendritic spines also come in a variety of sizes and shapes. To probe the relationship between calcium dynamics and spine morphology, we used a stochastic reaction-diffusion model of calcium dynamics in idealized and realistic geometries. We show that despite the stochastic nature of the various calcium channels, receptors, and pumps, spine size and shape can modulate calcium dynamics and subsequently synaptic weight updates in a deterministic manner. Through a series of exhaustive simulations and analyses, we found that the calcium dynamics and synaptic weight change depend on the volume-to-surface area of the spine. The relationships between calcium dynamics and spine morphology identified in idealized geometries also hold in realistic geometries, suggesting that there are geometrically determined deterministic relationships that may modulate synaptic weight change.

Nanoscale molecular architecture controls calcium diffusion and ER replenishment in dendritic spines

Dendritic spines are critical components of neuronal synapses as they receive and transform synaptic inputs into a succession of calcium-regulated biochemical events. The spine apparatus (SA), an extension of smooth endoplasmic reticulum, regulates slow and fast calcium dynamics in spines. Calcium release events deplete SA calcium ion reservoir rapidly, yet the next cycle of signaling requires its replenishment. How spines achieve this replenishment without triggering calcium release remains unclear. Using computational modeling, calcium and STED superresolution imaging, we show that the SA replenishment involves the store-operated calcium entry pathway during spontaneous calcium transients. We identified two main conditions for SA replenishment without depletion: a small amplitude and a slow timescale for calcium influx, and a close proximity between SA and plasma membranes. Thereby, spine’s nanoscale organization separates SA replenishment from depletion. We further conclude that spine’s receptor organization also determines the calcium dynamics during the induction of long-term synaptic changes.

A stage-structured population model for activity-dependent dendritic spines

Here we present a novel application of stage-structured population modelling to explore the properties of neuronal dendrites with spines. Dendritic spines are small protrusions that emanate from the dendritic shaft of several functionally important neurons in the cerebral cortex. They are the postsynaptic sites of over 90% of excitatory synapses in the mammalian brain. Here, we formulate a stage-structured population model of a passive dendrite with activity-dependent spines using a continuum approach. This computational study models three dynamic populations of activity-dependent spine types, corresponding to the anatomical categories of stubby, mushroom, and thin spines. In this stage-structured population model, transitions between spine type populations are driven by calcium levels that depend on local electrical activity. We explore the influence of the changing spine populations and spine types on the development of electrical propagation pathways in response to repetitive synaptic input, and which input frequencies are best for facilitating these pathways.

Geometric principles of second messenger dynamics in dendritic spines

Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14-19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity.

Dendritic spine geometry and spine apparatus organization govern the spatiotemporal dynamics of calcium

Dendritic spines are small subcompartments that protrude from the dendrites of neurons and are important for signaling activity and synaptic communication. These subcompartments have been characterized to have different shapes. While it is known that these shapes are associated with spine function, the specific nature of these shape-function relationships is not well understood. In this work, we systematically investigated the relationship between the shape and size of both the spine head and spine apparatus, a specialized endoplasmic reticulum compartment within the spine head, in modulating rapid calcium dynamics using mathematical modeling. We developed a spatial multicompartment reaction-diffusion model of calcium dynamics in three dimensions with various flux sources, including N-methyl-D-aspartate receptors (NMDARs), voltage-sensitive calcium channels (VSCCs), and different ion pumps on the plasma membrane. Using this model, we make several important predictions. First, the volume to surface area ratio of the spine regulates calcium dynamics. Second, membrane fluxes impact calcium dynamics temporally and spatially in a nonlinear fashion. Finally, the spine apparatus can act as a physical buffer for calcium by acting as a sink and rescaling the calcium concentration. These predictions set the stage for future experimental investigations of calcium dynamics in dendritic spines.

Fast calcium transients in dendritic spines driven by extreme statistics

Fast calcium transients (<10 ms) remain difficult to analyse in cellular microdomains, yet they can modulate key cellular events such as trafficking, local ATP production by endoplasmic reticulum-mitochondria complex (ER-mitochondria complex), or spontaneous activity in astrocytes. In dendritic spines receiving synaptic inputs, we show here that in the presence of a spine apparatus (SA), which is an extension of the smooth ER, a calcium-induced calcium release (CICR) is triggered at the base of the spine by the fastest calcium ions arriving at a Ryanodyne receptor (RyR). The mechanism relies on the asymmetric distributions of RyRs and sarco/ER calcium-ATPase (SERCA) pumps that we predict using a computational model and further confirm experimentally in culture and slice hippocampal neurons. The present mechanism for which the statistics of the fastest particles arriving at a small target, followed by an amplification, is likely to be generic in molecular transduction across cellular microcompartments, such as thin neuronal processes, astrocytes, endfeets, or protrusions.

Redundancy principle and the role of extreme statistics in molecular and cellular biology

The paradigm of chemical activation rates in cellular biology has been shifted from the mean arrival time of a single particle to the mean of the first among many particles to arrive at a small activation site. The activation rate is set by extremely rare events, which have drastically different time scales from the mean times between activations, and depends on different structural parameters. This shift calls for reconsideration of physical processes used in deterministic and stochastic modeling of chemical reactions that are based on the traditional forward rate, especially for fast activation processes in living cells. Consequently, the biological activation time is not necessarily exponentially distributed. We review here the physical models, the mathematical analysis and the new paradigm of setting the scale to be the shortest time for activation that clarifies the role of population redundancy in selecting and accelerating transient cellular search processes. We provide examples in cellular transduction, gene activation, cell senescence activation or spermatozoa selection during fertilization, where the rate depends on numbers. We conclude that the statistics of the minimal time to activation set kinetic laws in biology, which can be very different from the ones associated to average times.

Calcium Release Mediated by Redox-Sensitive RyR2 Channels Has a Central Role in Hippocampal Structural Plasticity and Spatial Memory

AIMS

Previous studies indicate that hippocampal synaptic plasticity and spatial memory processes entail calcium release from intracellular stores mediated by ryanodine receptor (RyR) channels. In particular, RyR-mediated Ca²⁺ release is central for the dendritic spine remodeling induced by brain-derived neurotrophic factor (BDNF), a neurotrophin that stimulates complex signaling pathways leading to memory-associated protein synthesis and structural plasticity. To examine if upregulation of ryanodine receptor type-2 (RyR2) channels and the spine remodeling induced by BDNF entail reactive oxygen species (ROS) generation, and to test if RyR2 downregulation affects BDNF-induced spine remodeling and spatial memory.

RESULTS

Downregulation of RyR2 expression (short hairpin RNA [shRNA]) in primary hippocampal neurons, or inhibition of nitric oxide synthase (NOS) or NADPH oxidase, prevented agonist-mediated RyR-mediated Ca²⁺ release, whereas BDNF promoted cytoplasmic ROS generation. RyR2 downregulation or inhibitors of N-methyl-d-aspartate (NMDA) receptors, or NOS or of NADPH oxidase type-2 (NOX2) prevented RyR2 upregulation and the spine remodeling induced by BDNF, as did incubation with the antioxidant agent N-acetyl l-cysteine. In addition, intrahippocampal injection of RyR2-directed antisense oligodeoxynucleotides, which caused significant RyR2 downregulation, caused conspicuous defects in a memorized spatial memory task.

INNOVATION

The present novel results emphasize the key role of redox-sensitive Ca²⁺ release mediated by RyR2 channels for hippocampal structural plasticity and spatial memory.

CONCLUSION

Based on these combined results, we propose (i) that BDNF-induced RyR2-mediated Ca²⁺ release and ROS generation via NOS/NOX2 are strictly required for the dendritic spine remodeling and the RyR2 upregulation induced by BDNF, and (ii) that RyR2 channel expression is crucial for spatial memory processes. Antioxid. Redox Signal. 29, 1125-1146.

Narrow Escape of Interacting Diffusing Particles

The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domain's boundary. Here we develop a formalism which allows us to evaluate the nonescape probability of a gas of diffusing particles that may interact with each other. In some cases the nonescape probability allows us to evaluate the MET of the first particle. The formalism is based on the fluctuating hydrodynamics and the recently developed macroscopic fluctuation theory. We also uncover an unexpected connection between the narrow escape of interacting particles and thermal runaway in chemical reactors.

Hybrid Markov-mass action law model for cell activation by rare binding events: Application to calcium induced vesicular release at neuronal synapses

Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. We present here a hybrid discrete-continuum model that takes into account a stochastic regime governed by rare events and a continuous regime in the bulk. The rare discrete binding events are modeled by a Markov chain for the encounter of small targets by few Brownian particles, for which the arrival time is Poissonian. The large ensemble of particles is described by mass action laws. We use this novel model to predict the time distribution of vesicular release at neuronal synapses. Vesicular release is triggered by the binding of few calcium ions that can originate either from the synaptic bulk or from the entry through calcium channels. We report here that the distribution of release time is bimodal although it is triggered by a single fast action potential. While the first peak follows a stimulation, the second corresponds to the random arrival over much longer time of ions located in the synaptic terminal to small binding vesicular targets. To conclude, the present multiscale stochastic modeling approach allows studying cellular events based on integrating discrete molecular events over several time scales.

The new nanophysiology: regulation of ionic flow in neuronal subcompartments

Cable theory and the Goldman-Hodgkin-Huxley-Katz models for the propagation of ions and voltage within a neuron have provided a theoretical foundation for electrophysiology and been responsible for many cornerstone advances in neuroscience. However, these theories break down when they are applied to small neuronal compartments, such as dendritic spines, synaptic terminals or small neuronal processes, because they assume spatial and ionic homogeneity. Here we discuss a broader theory that uses the Poisson-Nernst-Planck (PNP) approximation and electrodiffusion to more accurately model the constraints that neuronal nanostructures place on electrical current flow. This extension of traditional cable theory could advance our understanding of the physiology of neuronal nanocompartments.

Ca2+ dysregulation in the endoplasmic reticulum related to Alzheimer's disease: A review on experimental progress and computational modeling

Alzheimer's disease (AD) is a devastating, incurable neurodegenerative disease affecting millions of people worldwide. Dysregulation of intracellular Ca(2+) signaling has been observed as an early event prior to the presence of clinical symptoms of AD and is believed to be a crucial factor contributing to its pathogenesis. The progressive and sustaining increase in the resting level of cytosolic Ca(2+) will affect downstream activities and neural functions. This review focuses on the issues relating to the increasing Ca(2+) release from the endoplasmic reticulum (ER) observed in AD neurons. Numerous research papers have suggested that the dysregulation of ER Ca(2+) homeostasis is associated with mutations in the presenilin genes and amyloid-β oligomers. These disturbances could happen at many different points in the signaling process, directly affecting ER Ca(2+) channels or interfering with related pathways, which makes it harder to reveal the underlying mechanisms. This review paper also shows that computational modeling is a powerful tool in Ca(2+) signaling studies and discusses the progress in modeling related to Ca(2+) dysregulation in AD research.

Contribution of Ca2+ release channels to hippocampal synaptic plasticity and spatial memory: potential redox modulation

SIGNIFICANCE

Memory is an essential human cognitive function. Consequently, to unravel the cellular and molecular mechanisms responsible for the synaptic plasticity events underlying memory formation, storage and loss represents a major challenge of present-day neuroscience.

RECENT ADVANCES

This review article first describes the wide-ranging functions played by intracellular Ca2+ signals in the activity-dependent synaptic plasticity processes underlying hippocampal spatial memory, and next, it focuses on how the endoplasmic reticulum Ca2+ release channels, the ryanodine receptors, and the inositol 1,4,5-trisphosphate receptors contribute to these processes. We present a detailed examination of recent evidence supporting the key role played by Ca2+ release channels in synaptic plasticity, including structural plasticity, and the formation/consolidation of spatial memory in the hippocampus.

CRITICAL ISSUES

Changes in cellular oxidative state particularly affect the function of Ca2+ release channels and alter hippocampal synaptic plasticity and the associated memory processes. Emphasis is placed in this review on how defective Ca2+ release, presumably due to increased levels of reactive oxygen species, may cause the hippocampal functional defects that are associated to aging and Alzheimer's disease (AD).

FUTURE DIRECTIONS

Additional studies should examine the precise molecular mechanisms by which Ca2+ release channels contribute to hippocampal synaptic plasticity and spatial memory formation/consolidation. Future studies should test whether redox-modified Ca2+ release channels contribute toward generating the intracellular Ca2+ signals required for sustained synaptic plasticity and hippocampal spatial memory, and whether loss of redox balance and oxidative stress, by altering Ca2+ release channel function, presumably contribute to the abnormal memory processes that occur during aging and AD.

Multiscale modeling and synaptic plasticity

Synaptic plasticity is a major convergence point for theory and computation, and the process of plasticity engages physiology, cell, and molecular biology. In its many manifestations, plasticity is at the hub of basic neuroscience questions about memory and development, as well as more medically themed questions of neural damage and recovery. As an important cellular locus of memory, synaptic plasticity has received a huge amount of experimental and theoretical attention. If computational models have tended to pick specific aspects of plasticity, such as STDP, and reduce them to an equation, some experimental studies are equally guilty of oversimplification each time they identify a new molecule and declare it to be the last word in plasticity and learning. Multiscale modeling begins with the acknowledgment that synaptic function spans many levels of signaling, and these are so tightly coupled that we risk losing essential features of plasticity if we focus exclusively on any one level. Despite the technical challenges and gaps in data for model specification, an increasing number of multiscale modeling studies have taken on key questions in plasticity. These have provided new insights, but importantly, they have opened new avenues for questioning. This review discusses a wide range of multiscale models in plasticity, including their technical landscape and their implications.

Combined computational and experimental approaches to understanding the Ca(2+) regulatory network in neurons

Ca(2+) is a ubiquitous signaling ion that regulates a variety of neuronal functions by binding to and altering the state of effector proteins. Spatial relationships and temporal dynamics of Ca(2+) elevations determine many cellular responses of neurons to chemical and electrical stimulation. There is a wealth of information regarding the properties and distribution of Ca(2+) channels, pumps, exchangers, and buffers that participate in Ca(2+) regulation. At the same time, new imaging techniques permit characterization of evoked Ca(2+) signals with increasing spatial and temporal resolution. However, understanding the mechanistic link between functional properties of Ca(2+) handling proteins and the stimulus-evoked Ca(2+) signals they orchestrate requires consideration of the way Ca(2+) handling mechanisms operate together as a system in native cells. A wide array of biophysical modeling approaches is available for studying this problem and can be used in a variety of ways. Models can be useful to explain the behavior of complex systems, to evaluate the role of individual Ca(2+) handling mechanisms, to extract valuable parameters, and to generate predictions that can be validated experimentally. In this review, we discuss recent advances in understanding the underlying mechanisms of Ca(2+) signaling in neurons via mathematical modeling. We emphasize the value of developing realistic models based on experimentally validated descriptions of Ca(2+) transport and buffering that can be tested and refined through new experiments to develop increasingly accurate biophysical descriptions of Ca(2+) signaling in neurons.

Diffusion laws in dendritic spines

Dendritic spines are small protrusions on a neuronal dendrite that are the main locus of excitatory synaptic connections. Although their geometry is variable over time and along the dendrite, they typically consist of a relatively large head connected to the dendritic shaft by a narrow cylindrical neck. The surface of the head is connected smoothly by a funnel or non-smoothly to the narrow neck, whose end absorbs the particles at the dendrite. We demonstrate here how the geometry of the neuronal spine can control diffusion and ultimately synaptic processes. We show that the mean residence time of a Brownian particle, such as an ion or molecule inside the spine, and of a receptor on its membrane, prior to absorption at the dendritic shaft depends strongly on the curvature of the connection of the spine head to the neck and on the neck's length. The analytical results solve the narrow escape problem for domains with long narrow necks.

The diffusional properties of dendrites depend on the density of dendritic spines

We combined computational modeling and experimental measurements to determine the influence of dendritic structure on the diffusion of intracellular chemical signals in mouse cerebellar Purkinje cells and hippocamal CA1 pyramidal cells. Modeling predicts that molecular trapping by dendritic spines causes diffusion along spiny dendrites to be anomalous and that the value of the anomalous exponent (d(w) ) is proportional to spine density in both cell types. To test these predictions we combined the local photorelease of an inert dye, rhodamine dextran, with two-photon fluorescence imaging to track diffusion along dendrites. Our results show that anomalous diffusion is present in spiny dendrites of both cell types. Further, the anomalous exponent is linearly related to the density of spines in pyramidal cells and d(w) in Purkinje cells is consistent with such a relationship. We conclude that anomalous diffusion occurs in the dendrites of multiple types of neurons. Because spine density is dynamic and depends on neuronal activity, the degree of anomalous diffusion induced by spines can dynamically regulate the movement of molecules along dendrites.

Calcium dynamics in dendritic spines: a link to structural plasticity

Calcium signals evoked either by action potential or by synaptic activity play a crucial role for the synaptic plasticity within an individual spine. Because of the small size of spine and the indicators commonly used to measure spine calcium activity, calcium function can be severely disrupted. Therefore, it is very difficult to explain the exact relationship between spine geometry and spine calcium dynamics. Recently, it has been suggested that the medium range of calcium which induces long term potentiation leads to the structural stability stage of spines, while very low or very high amount of calcium leads to the long term depression stage which results in shortening and eventually pruning of spines. Here we propose a physiologically realistic computational model to examine the role of calcium and the mechanisms that govern its regulation in the spine morphology. Calcium enters into spine head through NMDA and AMPA channels and is regulated by internal stores. Contribution of this calcium in the induction of long term potentiation and long term depression is also discussed. Further it has also been predicted that the presence of internal stores depletes the total calcium accumulation in cytosol which is in agreement with the recent experimental and theoretical studies.

Postsynaptic signal transduction models for long-term potentiation and depression

More than a hundred biochemical species, activated by neurotransmitters binding to transmembrane receptors, are important in long-term potentiation (LTP) and long-term depression (LTD). To investigate which species and interactions are critical for synaptic plasticity, many computational postsynaptic signal transduction models have been developed. The models range from simple models with a single reversible reaction to detailed models with several hundred kinetic reactions. In this study, more than a hundred models are reviewed, and their features are compared and contrasted so that similarities and differences are more readily apparent. The models are classified according to the type of synaptic plasticity that is modeled (LTP or LTD) and whether they include diffusion or electrophysiological phenomena. Other characteristics that discriminate the models include the phase of synaptic plasticity modeled (induction, expression, or maintenance) and the simulation method used (deterministic or stochastic). We find that models are becoming increasingly sophisticated, by including stochastic properties, integrating with electrophysiological properties of entire neurons, or incorporating diffusion of signaling molecules. Simpler models continue to be developed because they are computationally efficient and allow theoretical analysis. The more complex models permit investigation of mechanisms underlying specific properties and experimental verification of model predictions. Nonetheless, it is difficult to fully comprehend the evolution of these models because (1) several models are not described in detail in the publications, (2) only a few models are provided in existing model databases, and (3) comparison to previous models is lacking. We conclude that the value of these models for understanding molecular mechanisms of synaptic plasticity is increasing and will be enhanced further with more complete descriptions and sharing of the published models.

The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement

We describe an immersed boundary method for problems of fluid-solute-structure interaction. The numerical scheme employs linearly implicit timestepping, allowing for the stable use of timesteps that are substantially larger than those permitted by an explicit method, and local mesh refinement, making it feasible to resolve the steep gradients associated with the space charge layers as well as the chemical potential, which is used in our formulation to control the permeability of the membrane to the (possibly charged) solute. Low Reynolds number fluid dynamics are described by the time-dependent incompressible Stokes equations, which are solved by a cell-centered approximate projection method. The dynamics of the chemical species are governed by the advection-electrodiffusion equations, and our semi-implicit treatment of these equations results in a linear system which we solve by GMRES preconditioned via a fast adaptive composite-grid (FAC) solver. Numerical examples demonstrate the capabilities of this methodology, as well as its convergence properties.

Cell surface topology creates high Ca2+ signalling microdomains

It has long been speculated that cellular microdomains are important for many cellular processes, especially those involving Ca²⁺ signalling. Measurements of cytosolic Ca²⁺ report maximum concentrations of less than few micromolar, yet several cytosolic enzymes require concentrations of more than 20 μM Ca²⁺ to be activated. In this paper, we have resolved this apparent paradox by showing that the surface topology of cells represents an important and hitherto unrecognized feature for generating microdomains of high Ca²⁺ in cells. We show that whereas the standard modeling assumption of a smooth cell surface predicts only moderate localized effects, the more realistic “wrinkled” surface topology predicts that Ca²⁺ concentrations up to 80 μM can persist within the folds of membranes for significant times. This intra-wrinkle location may account for 5% of the total cell volume. Using different geometries of wrinkles, our simulations show that high Ca²⁺ microdomains will be generated most effectively by long narrow membrane wrinkles of similar dimensions to those found experimentally. This is a new concept which has not previously been considered, but which has ramifications as the intra-wrinkle location is also a strategic location at which Ca²⁺ acts as a regulator of the cortical cytoskeleton and plasma membrane expansion.

Structural plasticity can produce metaplasticity

BACKGROUND

Synaptic plasticity underlies many aspect of learning memory and development. The properties of synaptic plasticity can change as a function of previous plasticity and previous activation of synapses, a phenomenon called metaplasticity. Synaptic plasticity not only changes the functional connectivity between neurons but in some cases produces a structural change in synaptic spines; a change thought to form a basis for this observed plasticity. Here we examine to what extent structural plasticity of spines can be a cause for metaplasticity. This study is motivated by the observation that structural changes in spines are likely to affect the calcium dynamics in spines. Since calcium dynamics determine the sign and magnitude of synaptic plasticity, it is likely that structural plasticity will alter the properties of synaptic plasticity.

METHODOLOGY/PRINCIPAL FINDINGS

In this study we address the question how spine geometry and alterations of N-methyl-D-aspartic acid (NMDA) receptors conductance may affect plasticity. Based on a simplified model of the spine in combination with a calcium-dependent plasticity rule, we demonstrated that after the induction phase of plasticity a shift of the long term potentiation (LTP) or long term depression (LTD) threshold takes place. This induces a refractory period for further LTP induction and promotes depotentiation as observed experimentally. That resembles the BCM metaplasticity rule but specific for the individual synapse. In the second phase, alteration of the NMDA response may bring the synapse to a state such that further synaptic weight alterations are feasible. We show that if the enhancement of the NMDA response is proportional to the area of the post synaptic density (PSD) the plasticity curves most likely return to the initial state.

CONCLUSIONS/SIGNIFICANCE

Using simulations of calcium dynamics in synaptic spines, coupled with a biophysically motivated calcium-dependent plasticity rule, we find under what conditions structural plasticity can form the basis of synapse specific metaplasticity.

Excitatory amino acid involvement in dendritic spine formation, maintenance and remodelling

In the central nervous system, most excitatory synapses occur on dendritic spines, which are small protrusions from the dendritic tree. In the mature cortex and hippocampus, dendritic spines are heterogeneous in shape. It has been shown that the shapes of the spine can affect synapse stability and synaptic function. Dendritic spines are highly motile structures that can undergo actin-dependent shape changes, which occur over a time scale ranging from seconds to tens of minutes or even days. The formation, remodelling and elimination of excitatory synapses on dendritic spines represent ways of refining the microcircuitry in the brain. Here I review the current knowledge on the effects of modulation of AMPA and NMDA ionotropic glutamate receptors on dendritic spine formation, motility and remodelling.

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 Ca(2+)-binding proteins may break the spine limit and lead to activation of Ca(2+)-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 Ca(2+)-binding proteins, regulates the spino-dendritic crosstalk.

Calmodulin activation by calcium transients in the postsynaptic density of dendritic spines

The entry of calcium into dendritic spines can trigger a sequence of biochemical reactions that begins with the activation of calmodulin (CaM) and ends with long-term changes to synaptic strengths. The degree of activation of CaM can depend on highly local elevations in the concentration of calcium and the duration of transient increases in calcium concentration. Accurate measurement of these local changes in calcium is difficult because the spaces are so small and the numbers of molecules are so low. We have therefore developed a Monte Carlo model of intracellular calcium dynamics within the spine that included calcium binding proteins, calcium transporters and ion channels activated by voltage and glutamate binding. The model reproduced optical recordings using calcium indicator dyes and showed that without the dye the free intracellular calcium concentration transient was much higher than predicted from the fluorescent signal. Excitatory postsynaptic potentials induced large, long-lasting calcium gradients across the postsynaptic density, which activated CaM. When glutamate was released at the synapse 10 ms before an action potential occurred, simulating activity patterns that strengthen hippocampal synapses, the calcium gradient and activation of CaM in the postsynaptic density were much greater than when the order was reversed, a condition that decreases synaptic strengths, suggesting a possible mechanism underlying the induction of long-term changes in synaptic strength. The spatial and temporal mechanisms for selectivity in CaM activation demonstrated here could be used in other signaling pathways.

Diffusion in a dendritic spine: the role of geometry

Dendritic spines, the sites where excitatory synapses are made in most neurons, can dynamically regulate diffusing molecules by changing their shape. We present here a combination of theory, simulations, and experiments to quantify the diffusion time course in dendritic spines. We derive analytical formulas and compared them to Brownian simulations for the mean sojourn time a diffusing molecule stays inside a dendritic spine when either the molecule can reenter the spine head or not, once it is located in the spine neck. We show that the spine length is the fundamental regulatory geometrical parameter for the diffusion decay rate in the neck only. By changing the spine length, dendritic spines can be dynamically coupled or uncoupled to their parent dendrites, which regulates diffusion, and this property makes them unique structures, different from static dendrites.

Synaptic plasticity in vitro and in silico: insights into an intracellular signaling maze

Synaptic plasticity provides a record of neuronal activity and is a likely basis for memory. The early apparent simplicity of the process of synaptic plasticity has been lost in a flood of experimental data that now implicates some 200 signaling molecules in cellular memory. It is now clear that these signaling networks perform surprisingly sophisticated cellular decisions that weigh factors such as input patterns, location of stimulus, history of activity, and context. Computer models have followed experiments into this maze of molecular detail, often matching closely with their experimental counterparts, but perhaps losing simplicity in the process. Here, we suggest that the merger of models and experiment have begun to restore the earlier simplicity by outlining a few key functional roles for signaling networks in synaptic plasticity. In this review, we discuss the current state of understanding of synaptic plasticity in terms of models and experiments.

Calcium dynamics in dendritic spines, modeling and experiments

Dendritic spines are microstructures, about one femtoliter in volume, where excitatory synapses are made with incoming afferents, in most neurons of the vertebrate brain. The spine contains all the molecular constituents of the postsynaptic side of the synapse, as well as a contractile element that can cause its movement in space. It also contains calcium handling machineries to allow fast buffering of excess calcium that influx through voltage and NMDA gated channels. The spine is connected to the dendrite through a thin neck that serves as a variable barrier between the spine head and the parent dendrite. We review a novel modeling approach that is more suitable for the accurate description of the stochastic behavior of individual molecules in microstructures. Using this approach, we predict the calcium handling ability of the spine in complex situations associated with synaptic activity, spine motility and plasticity.

Survival probability of diffusion with trapping in cellular neurobiology

The problem of diffusion with absorption and trapping sites arises in the theory of molecular signaling inside and on the membranes of biological cells. In particular, this problem arises in the case of spine-dendrite communication, where the number of calcium ions, modeled as random particles, is regulated across the spine microstructure by pumps, which play the role of killing sites, while the end of the dendritic shaft is an absorbing boundary. We develop a general mathematical framework for diffusion in the presence of absorption and killing sites and apply it to the computation of the time-dependent survival probability of ions. We also compute the ratio of the number of absorbed particles at a specific location to the number of killed particles. We show that the ratio depends on the distribution of killing sites. The biological consequence is that the position of the pumps regulates the fraction of calcium ions that reach the dendrite.

Stochastic chemical reactions in microdomains

Traditional chemical kinetics may be inappropriate to describe chemical reactions in microdomains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a master-diffusion equation for the joint probability density of a mobile reactant and the number of bound substrate in a confined domain. We use the equation to calculate the fluctuations in the number of bound substrate molecules as a function of initial reactant distribution. A second model is presented based on a Markov description of the binding and unbinding and on the mean first passage time of a molecule to a small portion of the boundary. These models can be used for the description of noise due to gating of ionic channels by random binding and unbinding of ligands in biological sensor cells, such as olfactory cilia, photoreceptors, hair cells in the cochlea.

Dynamic regulation of spine-dendrite coupling in cultured hippocampal neurons

We investigated the role of dendritic spine morphology in spine-dendrite calcium communication using novel experimental and theoretical approaches. A transient rise in [Ca2+]i was produced in individual spine heads of Fluo-4-loaded cultured hippocampal neurons by flash photolysis of caged calcium. Following flash photolysis in the spine head, a delayed [Ca2+]i transient was detected in the parent dendrites of only short, but not long, spines. Delayed elevated fluorescence in the dendrite of the short spines was also seen with a membrane-bound fluorophore and fluorescence recovery from bleaching of a calcium-bound fluorophore had a much slower kinetics, indicating that the dendritic fluorescence change reflects a genuine diffusion of free [Ca2+]i from the spine head to the parent dendrite. Calcium diffusion between spine head and the parent dendrite was regulated by calcium stores as well as by a Na-Ca exchanger. Spine length varied with the recent history of the [Ca2+]i variations in the spine, such that small numbers of calcium transients resulted in elongation of spines whereas large numbers of calcium transients caused shrinkage of the spines. Consequently, spine elongation resulted in a complete isolation of the spine from the dendrite, while shrinkage caused an enhanced coupling with the parent dendrite. These studies highlight a dynamically regulated coupling between a dendritic spine head and its parent dendrite.