Calcium dynamics in dendritic spines, modeling and experiments

A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics

Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either (1) top-down and interpretable, but not flexible enough to account for experimental data, or (2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit to data. To avoid the shortcomings of these approaches, we present a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to predict plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model also predicts that in vivo-like spike timing irregularity strongly shapes plasticity outcome. This geometrical readout modelling approach can be readily applied to other excitatory or inhibitory synapses to discover their synaptic plasticity rules.

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.

Noise Helps Optimization Escape From Saddle Points in the Synaptic Plasticity

Numerous experimental studies suggest that noise is inherent in the human brain. However, the functional importance of noise remains unknown. n particular, from a computational perspective, such stochasticity is potentially harmful to brain function. In machine learning, a large number of saddle points are surrounded by high error plateaus and give the illusion of the existence of local minimum. As a result, being trapped in the saddle points can dramatically impair learning and adding noise will attack such saddle point problems in high-dimensional optimization, especially under the strict saddle condition. Motivated by these arguments, we propose one biologically plausible noise structure and demonstrate that noise can efficiently improve the optimization performance of spiking neural networks based on stochastic gradient descent. The strict saddle condition for synaptic plasticity is deduced, and under such conditions, noise can help optimization escape from saddle points on high dimensional domains. The theoretical results explain the stochasticity of synapses and guide us on how to make use of noise. In addition, we provide biological interpretations of proposed noise structures from two points: one based on the free energy principle in neuroscience and another based on observations of in vivo experiments. Our simulation results manifest that in the learning and test phase, the accuracy of synaptic sampling with noise is almost 20% higher than that without noise for synthesis dataset, and the gain in accuracy with/without noise is at least 10% for the MNIST and CIFAR-10 dataset. Our study provides a new learning framework for the brain and sheds new light on deep noisy spiking neural networks.

Resonance induced by coupling diversity in globally coupled bistable oscillators

We investigate the collective response of an ensemble of bistable oscillators to an external periodic signal, where the coupling strength between oscillators is diverse. We find that there exists an optimal level of coupling diversity, at which the collective response of the system can be largely improved, i.e., resonance induced by coupling diversity. We also observe that the system splits into three oscillation clusters when this resonance happens. We finally propose a reduced model based on the three oscillation clusters, which can well predict the collective response of the system.

Spinogenesis in spinal cord motor neurons following pharmacological lesions to the rat motor cortex

INTRODUCTION

Motor function is impaired in multiple neurological diseases associated with corticospinal tract degeneration. Motor impairment has been linked to plastic changes at both the presynaptic and postsynaptic levels. However, there is no evidence of changes in information transmission from the cortex to spinal motor neurons.

METHODS

We used kainic acid to induce stereotactic lesions to the primary motor cortex of female adult rats. Fifteen days later, we evaluated motor function with the BBB scale and the rotarod and determined the density of thin, stubby, and mushroom spines of motor neurons from a thoracolumbar segment of the spinal cord. Spinophilin, synaptophysin, and β iii-tubulin expression was also measured.

RESULTS

Pharmacological lesions resulted in poor motor performance. Spine density and the proportion of thin and stubby spines were greater. We also observed increased expression of the 3 proteins analysed.

CONCLUSION

The clinical symptoms of neurological damage secondary to Wallerian degeneration of the corticospinal tract are associated with spontaneous, compensatory plastic changes at the synaptic level. Based on these findings, spontaneous plasticity is a factor to consider when designing more efficient strategies in the early phase of rehabilitation.

The role of dendritic spine morphology in the compartmentalization and delivery of surface receptors

Since AMPA receptors are major molecular players in both short- and long-term plasticity, it is important to identify the time-scales of and factors affecting the lateral diffusion of AMPARs on the dendrite surface. Using a mathematical model, we study how the dendritic spine morphology affects two processes: (1) compartmentalization of the surface receptors in a single spine to retain local chemistry and (2) the delivery of receptors to the post-synaptic density (PSD) of spines via lateral diffusion following insertion onto the dendrite shaft. Computing the mean first passage time (MFPT) of surface receptors on a sample of real spine morphologies revealed that a constricted neck and bulbous head serve to compartmentalize receptors, consistent with previous works. The residence time of a Brownian diffusing receptor on the membrane of a single spine was computed to be ∼ 5 s. We found that the location of the PSD corresponds to the location at which the maximum MFPT occurs, the position that maximizes the residence time of a diffusing receptor. Meanwhile, the same geometric features of the spine that compartmentalize receptors inhibit the recruitment of AMPARs via lateral diffusion from dendrite insertion sites. Spines with narrow necks will trap a smaller fraction of diffusing receptors in the their PSD when considering competition for receptors between the spines, suggesting that ideal geometrical features involve a tradeoff depending on the intent of compartmentalizing the current receptor pool or recruiting new AMPARs in the PSD. The ultimate distribution of receptors among the spine PSDs by lateral diffusion from the dendrite shaft is an interplay between the insertion location and the shape and locations of both the spines and their PSDs. The time-scale for delivery of receptors to the PSD of spines via lateral diffusion was computed to be ∼ 60 s.

Control of flux by narrow passages and hidden targets in cellular biology

Critical biological processes, such as synaptic plasticity and transmission, activation of genes by transcription factors, or double-strained DNA break repair, are controlled by diffusion in structures that have both large and small spatial scales. These may be small binding sites inside or on the surface of the cell, or narrow passages between subcellular compartments. The great disparity in spatial scales is the key to controlling cell function by structure. We report here recent progress on resolving analytical and numerical difficulties in extracting properties from experimental data, from biophysical models, and from Brownian dynamics simulations of diffusion in multi-scale structures. This progress is achieved by developing an analytical approximation methodology for solving the model equations. The reported results are applied to analysis and simulations of subcellular processes and to the quantification of their biological functions.

Calcium signalling in astroglia

Astroglia possess excitability based on movements of Ca(2+) ions between intracellular compartments and plasmalemmal Ca(2+) fluxes. This "Ca(2+) excitability" is controlled by several families of proteins located in the plasma membrane, within the cytosol and in the intracellular organelles, most notably in the endoplasmic reticulum (ER) and mitochondria. Accumulation of cytosolic Ca(2+) can be caused by the entry of Ca(2+) from the extracellular space through ionotropic receptors and store-operated channels expressed in astrocytes. Plasmalemmal Ca(2+) ATP-ase and sodium-calcium exchanger extrude cytosolic Ca(2+) to the extracellular space; the exchanger can also operate in reverse, depending of the intercellular Na(+) concentration, to deliver Ca(2+) to the cytosol. The ER internal store possesses inositol 1,4,5-trisphosphate receptors which can be activated upon stimulation of astrocytes through a multiple plasma membrane metabotropic G-protein coupled receptors. This leads to release of Ca(2+) from the ER and its elevation in the cytosol, the level of which can be modulated by mitochondria. The mitochondrial uniporter takes up Ca(2+) into the matrix, while free Ca(2+) exits the matrix through the mitochondrial Na(+)/Ca(2+) exchanger as well as via transient openings of the mitochondrial permeability transition pore. One of the prominent consequences of astroglial Ca(2+) excitability is gliotransmission, a release of transmitters from astroglia which can lead to signalling to adjacent neurones.

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.

Colocalization of protein kinase A with adenylyl cyclase enhances protein kinase A activity during induction of long-lasting long-term-potentiation

The ability of neurons to differentially respond to specific temporal and spatial input patterns underlies information storage in neural circuits. One means of achieving spatial specificity is to restrict signaling molecules to particular subcellular compartments using anchoring molecules such as A-Kinase Anchoring Proteins (AKAPs). Disruption of protein kinase A (PKA) anchoring to AKAPs impairs a PKA-dependent form of long term potentiation (LTP) in the hippocampus. To investigate the role of localized PKA signaling in LTP, we developed a stochastic reaction-diffusion model of the signaling pathways leading to PKA activation in CA1 pyramidal neurons. Simulations investigated whether the role of anchoring is to locate kinases near molecules that activate them, or near their target molecules. The results show that anchoring PKA with adenylyl cyclase (which produces cAMP that activates PKA) produces significantly greater PKA activity, and phosphorylation of both inhibitor-1 and AMPA receptor GluR1 subunit on S845, than when PKA is anchored apart from adenylyl cyclase. The spatial microdomain of cAMP was smaller than that of PKA suggesting that anchoring PKA near its source of cAMP is critical because inactivation by phosphodiesterase limits diffusion of cAMP. The prediction that the role of anchoring is to colocalize PKA near adenylyl cyclase was confirmed by experimentally rescuing the deficit in LTP produced by disruption of PKA anchoring using phosphodiesterase inhibitors. Additional experiments confirm the model prediction that disruption of anchoring impairs S845 phosphorylation produced by forskolin-induced synaptic potentiation. Collectively, these results show that locating PKA near adenylyl cyclase is a critical function of anchoring.

The hippocampus is a part of the cerebral cortex involved in formation of certain types of long term memories. Activity-dependent change in the strength of neuronal connections in the hippocampus, known as synaptic plasticity, is one mechanism used to store memories. The ability to form crisp and distinguishable memories of different events implies that learning produces plasticity of specific and distinct subsets of synapses within each neuron. Synaptic activity leads to production of intracellular signaling molecules, which ultimately cause changes in the properties of the synapses. The requirement for synaptic specificity seems incompatible with the diffusibility of intracellular signaling molecules. Anchoring proteins restrict signaling molecules to particular subcellular compartments thereby combating the indiscriminate spread of intracellular signaling molecules. To investigate whether the critical function of anchoring proteins is to localize proteins near their activators or their targets, we developed a stochastic reaction-diffusion model of signaling pathways leading to synaptic plasticity in hippocampal neurons. Simulations demonstrate that colocalizing proteins with their activator molecules is more important due to inactivation mechanisms that limit the spatial extent of the activator molecules.

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.

One-dimensional description of diffusion in a tube of abruptly changing diameter: Boundary homogenization based approach

Reduction of three-dimensional (3D) description of diffusion in a tube of variable cross section to an approximate one-dimensional (1D) description has been studied in detail previously only in tubes of slowly varying diameter. Here we discuss an effective 1D description in the opposite limiting case when the tube diameter changes abruptly, i.e., in a tube composed of any number of cylindrical sections of different diameters. The key step of our approach is an approximate description of the particle transitions between the wide and narrow parts of the tube as trapping by partially absorbing boundaries with appropriately chosen trapping rates. Boundary homogenization is used to determine the trapping rate for transitions from the wide part of the tube to the narrow one. This trapping rate is then used in combination with the condition of detailed balance to find the trapping rate for transitions in the opposite direction, from the narrow part of the tube to the wide one. Comparison with numerical solution of the 3D diffusion equation allows us to test the approximate 1D description and to establish the conditions of its applicability. We find that suggested 1D description works quite well when the wide part of the tube is not too short, whereas the length of the narrow part can be arbitrary. Taking advantage of this description in the problem of escape of diffusing particle from a cylindrical cavity through a cylindrical tunnel we can lift restricting assumptions accepted in earlier theories: We can consider the particle motion in the tunnel and in the cavity on an equal footing, i.e., we can relax the assumption of fast intracavity relaxation used in all earlier theories. As a consequence, the dependence of the escape kinetics on the particle initial position in the system can be analyzed. Moreover, using the 1D description we can analyze the escape kinetics at an arbitrary tunnel radius, whereas all earlier theories are based on the assumption that the tunnel is narrow.

Escape from cavity through narrow tunnel

The paper deals with a diffusing particle that escapes from a cavity to the outer world through a narrow cylindrical tunnel. We derive expressions for the Laplace transforms of the particle survival probability, its lifetime probability density, and the mean lifetime. These results show how the quantities of interest depend on the geometric parameters (the cavity volume and the tunnel length and radius) and the particle diffusion coefficients in the cavity and in the tunnel. Earlier suggested expressions for the mean lifetime, which correspond to different escape scenarios, are contained in our result as special cases. In contrast to these expressions, our formula predicts correct asymptotic behavior of the mean lifetime in the absence of the cavity or tunnel. To test the accuracy of our approximate theory we compare the mean lifetime, the lifetime probability density, and the survival probability (the latter two are obtained by inverting their Laplace transforms numerically) with corresponding quantities found by solving numerically the three-dimensional diffusion equation, assuming that the cavity is a sphere and that the particle has the same diffusion coefficient in the cavity and in the tunnel. Comparison shows excellent agreement between the analytical and numerical results over a broad range of the geometric parameters of the problem.

Roles of mGluR5 in synaptic function and plasticity of the mouse thalamocortical pathway

The group I metabotropic glutamate receptor 5 (mGluR5) has been implicated in the development of cortical sensory maps. However, its precise roles in the synaptic function and plasticity of thalamocortical (TC) connections remain unknown. Here we first show that in mGluR5 knockout (KO) mice bred onto a C57BL6 background cytoarchitectonic differentiation into barrels is missing, but the representations for large whiskers are identifiable as clusters of TC afferents. The altered dendritic morphology of cortical layer IV spiny stellate neurons in mGluR5 KO mice implicates a role for mGluR5 in the dendritic morphogenesis of excitatory neurons. Next, in vivo single-unit recordings of whisker-evoked activity in mGluR5 KO adults demonstrated a preserved topographical organization of the whisker representation, but a significantly diminished temporal discrimination of center to surround whiskers in the responses of individual neurons. To evaluate synaptic function at TC synapses in mGluR5 KO mice, whole-cell voltage-clamp recording was conducted in acute TC brain slices prepared from postnatal day 4-11 mice. At mGluR5 KO TC synapses, N-methyl-D-aspartate (NMDA) currents decayed faster and synaptic strength was more easily reduced, but more difficult to strengthen by Hebbian-type pairing protocols, despite a normal developmental increase in alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR)-mediated currents and presynaptic function. We have therefore demonstrated that mGluR5 is required for synaptic function/plasticity at TC synapses as barrels are forming, and we propose that these functional alterations at the TC synapse are the basis of the abnormal anatomical and functional development of the somatosensory cortex in the mGluR5 KO mouse.

Dendritic spine morphology determines membrane-associated protein exchange between dendritic shafts and spine heads

The purpose of this study was to examine whether variability in the shape of dendritic spines affects protein movement within the plasma membrane. Using a combination of confocal microscopy and the fluorescence loss in photobleaching technique in living hippocampal CA1 pyramidal neurons expressing membrane-linked GFP, we observed a clear correlation between spine shape parameters and the diffusion and compartmentalization of membrane-associated proteins. The kinetics of membrane-linked GFP exchange between the dendritic shaft and the spine head compartment were slower in dendritic spines with long necks and/or large heads than in those with short necks and/or small heads. Furthermore, when the spine area was reduced by eliciting epileptiform activity, the kinetics of protein exchange between the spine compartments exhibited a concomitant decrease. As synaptic plasticity is considered to involve the dynamic flux by lateral diffusion of membrane-bound proteins into and out of the synapse, our data suggest that spine shape represents an important parameter in the susceptibility of synapses to undergo plastic change.

IQ-motif proteins influence intracellular free Ca2+ in hippocampal neurons through their interactions with calmodulin

Calmodulin (CaM) is most recognized for its role in activating Ca(2+)-CaM-dependent enzymes following increased intracellular Ca(2+). However, CaM's high intracellular concentration indicates CaM has the potential to play a significant role as a Ca(2+) buffer. Neurogranin (Ng) is a small neuronal IQ-motif-containing protein that accelerates Ca(2+) dissociation from CaM. In cells that contain high concentrations of both Ng and CaM, like CA1 pyramidal neurons, we hypothesize that the accelerated Ca(2+) dissociation from CaM by Ng decreases the buffering capacity of CaM and thereby shapes the transient dynamics of intracellular free Ca(2+). We examined this hypothesis using a mathematical model constructed on the known biochemistry of Ng and confirmed the simulation results with Ca(2+) imaging data in the literature. In a single-compartment model that contains no Ca(2+) extrusion mechanism, Ng increased the steady-state free Ca(2+). However, in the presence of a Ca(2+) extrusion mechanism, Ng accelerated the decay rate of free Ca(2+) through its ability to increase the Ca(2+) dissociation from CaM, which in turn becomes subject to Ca(2+) extrusion. Interestingly, PEP-19, another neuronal IQ-motif protein that accelerates both Ca(2+) association and dissociation from CaM, appears to have the opposite impact than that of Ng on free Ca(2+). As such, Ng may regulate, in addition to the Ca(2+)-CaM-dependent process, Ca(2+)-sensitive enzymes by influencing the buffering capacity of CaM and subsequently free Ca(2+) levels. We examined the relative impact of these Ng-induced effects in the induction of synaptic plasticity.

Opposing functions of CREB and MKK1 synergistically regulate the geometry of dendritic spines in visual cortex

Most excitatory inputs onto pyramidal neurons are made on dendritic spines. The geometry of dendritic spines modulates synaptic function; yet we know little regarding the molecular signals that regulate spine geometry. Here we report that neurons coordinately regulate the geometry of spines to compensate for variability in spine number, by a process requiring the transcription factor CREB and the kinase MKK1. We find that CREB function is induced, whereas MKK1 is inhibited, by activity blockade. To obtain evidence that CREB and MKK1 regulate dendritic spine geometry in vivo, we coexpressed green fluorescent protein and dominant negative CREB or MKK1 in pyramidal neurons of the intact rat visual cortex. Spines on apical dendrites of layer 3 neurons were then characterized by confocal microscopy. We find that CREB and MKK1 regulate spine geometry in opposite ways. MKK1 is required to reduce spine head size when spine density is high, whereas CREB is required to enlarge spines when spine density is low. Our data suggest that CREB and MKK1 might function as complementary negative feedback mechanisms to maintain synaptic drive within bounds.

A role for synaptopodin and the spine apparatus in hippocampal synaptic plasticity

Spines are considered sites of synaptic plasticity in the brain and are capable of remodeling their shape and size. A molecule thathas been implicated in spine plasticity is the actin-associated protein synaptopodin. This article will review a series of studies aimed at elucidating the role of synaptopodin in the rodent brain. First, the developmental expression of synaptopodin mRNA and protein were studied; secondly, the subcellular localization of synaptopodin in hippocampal principal neurons was analyzed using confocal microscopy as well as electron microscopy and immunogold labelling; and, finally, the functional role of synaptopodin was investigated using a synaptopodin-deficient mouse. The results of these studies are: (1) synaptopodin expression byhippocampal principal neurons develops during the first postnatal weeks and increases in parallel with the maturation of spines in the hippocampus. (2) Synaptopodin is sorted to the spine compartment, where it is tightly associated with the spine apparatus, an enigmatic organelle believed to be involved in calcium storage or local protein synthesis. (3) Synaptopodin-deficient mice generated by gene targeting are viable but lack the spine apparatus organelle. These mice show deficitsin synaptic plasticity as well as impaired learning and memory. Taken together, these data implicate synaptopodin and the spine apparatus in the regulation of synaptic plasticity in the hippocampus. Future studies will be aimed at finding the molecular link between synaptopodin, the spine apparatus organelle, and synaptic plasticity.

Perisynaptic organization of plasma membrane calcium pumps in cerebellar cortex

Calcium, a ubiquitous intracellular messenger, regulates numerous intracellular signaling pathways. To permit specificity of signal transduction and prevent unwanted cross-talk between pathways, sites of calcium entry in neurons are localized to specific membrane domains. To test whether Ca(2+) extrusion pumps might exhibit analogous compartmentalization, we used immunohistochemistry to determine the subcellular localization of the two main plasma membrane Ca(2+)-ATPase (PMCA) isoforms in the cortex of the rat cerebellum. We find that both PMCA2 and PMCA3 are targeted to distinct compartments within the plasma membrane. In the molecular layer, both isoforms were at highest levels within synaptic profiles, but PMCA2 was postsynaptic and PMCA3 was presynaptic. Moreover, inside these compartments, both pumps exhibited nonuniform distributions. These data imply that cerebellar neurons possess remarkably effective mechanisms to target and restrict PMCA2 and -3 to specific membrane domains, raising the possibility that calcium pumps contribute to local Ca(2+) signaling.

Spatially confined diffusion of calcium in dendrites of hippocampal neurons revealed by flash photolysis of caged calcium

The extent of diffusion of a locally evoked calcium surge in dendrites of cultured hippocampal neurons was studied by flash photolysis of caged EGTA. Cells were transfected with pDsRed for visualization, preincubated with caged NP-EGTA (AM) and Fluo-4 (AM) at room temperature and imaged in a PASCAL confocal microscope. Pulses of UV laser light within an active sphere of about 1 micro m(2) produced a rise of Fluo-4 fluorescence transients in dendrites which peaked at 1 ms and decayed exponentially with a fast (8-10 ms) time constant. A slower decay component was uncovered following incubation with thapsigargin. Lateral diffusion of [Ca(2+)]i did not vary significantly among different size dendrites being symmetric and reaching about 3-3.5 micro mm at a diffusion rate of 0.8 micro mm/ms on both sides of the photolysis center. Fluo-4 was also replaced by the membrane-bound Fluo-NOMO (AM) or by the 'heavy' Calcium Green dextran (CGd) loaded through a patch pipette. Similar rates of diffusion were found in these cases, indicating that the diffusion is not of the dye complexed to calcium but of genuine free calcium ions. Interestingly, presence of a dendritic spine at the focus of photolysis significantly reduced [Ca(2+)]i spread while the focal transient remained unaffected. Finally, [Ca(2+)]i diffused about twice as far from the photolysis sphere in glass tubes of a similar diameter to that of a dendrite, indicating that intrinsic calcium uptake mechanisms in the dendrite determine the diffusion of calcium away from its original site of rise.

Main determinants of presynaptic Ca2+ dynamics at individual mossy fiber-CA3 pyramidal cell synapses

Synaptic transmission between hippocampal mossy fibers (MFs) and CA3 pyramidal cells exhibits remarkable use-dependent plasticity. The underlying presynaptic mechanisms, however, remain poorly understood. Here, we have used fluorescent Ca2+ indicators Fluo-4, Fluo-5F, and Oregon Green BAPTA-1 to investigate Ca2+ dynamics in individual giant MF boutons (MFBs) in area CA3 traced from the somata of granule cells held in whole-cell mode. In an individual MFB, a single action potential induces a brief peak of free Ca2+ (estimated in the range of 8-9 microm) followed by an elevation to approximately 320 nm, which slowly decays to its resting level of approximately 110 nm. Changes in the somatic membrane potential influence presynaptic Ca2+ entry at proximal MFBs in the hilus. This influence decays with distance along the axon, with a length constant of approximately 200 microm. In giant MFBs in CA3, progressive saturation of endogenous Ca2+ buffers during repetitive spiking amplifies rapid Ca2+ peaks and the residual Ca2+ severalfold, suggesting a causal link to synaptic facilitation. We find that internal Ca2+ stores contribute to maintaining the low resting Ca2+ providing approximately 22% of the buffering/extrusion capacity of giant MFBs. Rapid Ca2+ release from stores represents up to 20% of the presynaptic Ca2+ transient evoked by a brief train of action potentials. The results identify the main components of presynaptic Ca2+ dynamics at this important cortical synapse.

Transition rate prefactors for systems of many degrees of freedom

When a minimum on the potential energy surface is surrounded by multiple saddle points with similar energy barriers, the transition pathways with greater prefactors are more important than those that have similar energy barriers but smaller prefactors. In this paper, we present a theoretical formulation for the prefactors, computing the probabilities for transition paths from a minimum to its surrounding saddle points. We apply this formulation to a system of 2 degrees of freedom and a system of 14 degrees of freedom. The first is Brownian motion in a two-dimensional potential whose global anharmonicities play a dominant role in determining the transition rates. The second is a Lennard-Jones (LJ) cluster of seven particles in two dimensions. Low lying transition states of the LJ cluster, which can be reached directly from a minimum without passing through another minimum, are identified without any presumption of their characteristics nor of the product states they lead to. The probabilities are computed for paths going from an equilibrium ensemble of states near a given minimum to the surrounding transition states. These probabilities are directly related to the prefactors in the rate formula. This determination of the rate prefactors includes all anharmonicities, near or far from transition states, which are pertinent in the very sophisticated energy landscape of LJ clusters and in many other complex systems.

Physiological roles of spine motility: development, plasticity and disorders

The vast majority of excitatory connections in the hippocampus are made on dendritic spines. Both dendritic spines and molecules within the membrane are able to move, but the physiological role of these movements is unclear. In the developing brain, spines show highly dynamic behaviour thought to facilitate new synaptic connections. Dynamic movements also occur in adults but the role of this movement is unclear. We have studied the effects of the most important excitatory neurotransmitter, glutamate, and found receptor activation to enhance movement of molecules within the spine membrane. This action of glutamate may be important in regulating the trafficking of neurotransmitter receptors that mediate change in synaptic function. In addition, we have studied the dynamic interactions between pre- and postsynaptic structures labelled with FM 4-64 and a membrane-targeted GFP (green fluorescent protein), respectively, in hippocampal slice cultures under conditions of increased activity, such as epilepsy. Our findings suggest a novel form of activity-dependent synaptic plasticity where spontaneous glutamate release is sufficient to trigger changes in the hippocampal microcircuitry by attracting neighbouring spines responsive to an enhanced level of extracellular glutamate.