Spiny Dendrites Research Articles

Anomalous diffusion and dynamics of fluorescence recovery after photobleaching in the random-comb model.

We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ,P(ℓ)∼ℓ^{-(1+α)} (α>0). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems.

Galerkin finite element method and error analysis for the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. These equations can be derived from the Nernst-Planck equation for electro-diffusion in smooth homogeneous cylinders. Fractional cable equations are introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, a Galerkin finite element method(GFEM) is presented for the numerical simulation of the fractional cable equation(FCE) involving two integro-differential operators. The proposed method is based on a semi-discrete finite difference approximation in time and Galerkin finite element method in space. We prove that the numerical solution converges to the exact solution with order O(?+hl+1) for the lth-order finite element method. Further, a novel Galerkin finite element approximation for improving the order of convergence is also proposed. Finally, some numerical results are given to demonstrate the theoretical analysis. The results show that the numerical solution obtained by the improved Galerkin finite element approximation converges to the exact solution with order O(?2+hl+1).

Zooming in on the small: the plasticity of striatal dendritic spines in L-DOPA-induced dyskinesia.

The spiny dendrites of striatal projection neurons integrate synaptic inputs of different origins to regulate movement. It has long been known that these dendrites lose spines and display atrophic features in Parkinson's disease (PD), but the significance of these morphological changes has remained unknown. Some recent studies reveal a remarkable structural plasticity of striatal spines in parkinsonian rodents treated with L-3,4-dihydroxyphenylalanine (L-DOPA), and they demonstrate an association between this plasticity and the development of dyskinesia. These studies used different approaches and animal models, which possibly explains why they emphasize different plastic changes as being most closely linked to dyskinesia (such as a growth of new spines in neurons of the indirect pathway, or a loss of spines in neurons of the direct pathway, or the appearance of spines with aberrant synaptic features). Clearly, further investigations are required to reconcile these intriguing findings and integrate them in a coherent pathophysiological model. Nevertheless, these studies may mark the beginning of a new era for dyskinesia research. In addition to addressing neurochemical and molecular events that trigger involuntary movements, there is a need to better understand the long-lasting structural reorganization of cells and circuits that maintain the brain in a "dyskinesia-prone" state. This may lead to the identification of new efficacious approaches to prevent the complications of dopaminergic therapies in PD.

Maturation of cortical circuits requires Semaphorin 7A.

Abnormal cortical circuits underlie some cognitive and psychiatric disorders, yet the molecular signals that generate normal cortical networks remain poorly understood. Semaphorin 7A (Sema7A) is an atypical member of the semaphorin family that is GPI-linked, expressed principally postnatally, and enriched in sensory cortex. Significantly, SEMA7A is deleted in individuals with 15q24 microdeletion syndrome, characterized by developmental delay, autism, and sensory perceptual deficits. We studied the role that Sema7A plays in establishing functional cortical circuitry in mouse somatosensory barrel cortex. We found that Sema7A is expressed in spiny stellate cells and GABAergic interneurons and that its absence disrupts barrel cytoarchitecture, reduces asymmetrical orientation of spiny stellate cell dendrites, and functionally impairs thalamocortically evoked synaptic responses, with reduced feed-forward GABAergic inhibition. These data identify Sema7A as a regulator of thalamocortical and local circuit development in layer 4 and provide a molecular handle that can be used to explore the coordinated generation of excitatory and inhibitory cortical circuits.

Musical Representation of Dendritic Spine Distribution: A New Exploratory Tool

Dendritic spines are small protrusions along the dendrites of many types of neurons in the central nervous system and represent the major target of excitatory synapses. For this reason, numerous anatomical, physiological and computational studies have focused on these structures. In the cerebral cortex the most abundant and characteristic neuronal type are pyramidal cells (about 85 % of all neurons) and their dendritic spines are the main postsynaptic target of excitatory glutamatergic synapses. Thus, our understanding of the synaptic organization of the cerebral cortex largely depends on the knowledge regarding synaptic inputs to dendritic spines of pyramidal cells. Much of the structural data on dendritic spines produced by modern neuroscience involves the quantitative analysis of image stacks from light and electron microscopy, using standard statistical and mathematical tools and software developed to this end. Here, we present a new method with musical feedback for exploring dendritic spine morphology and distribution patterns in pyramidal neurons. We demonstrate that audio analysis of spiny dendrites with apparently similar morphology may “sound” quite different, revealing anatomical substrates that are not apparent from simple visual inspection. These morphological/music translations may serve as a guide for further mathematical analysis of the design of the pyramidal neurons and of spiny dendrites in general.Electronic Supplementary MaterialThe online version of this article (doi:10.1007/s12021-013-9195-0) contains supplementary material, which is available to authorized users.

Dendritic signal transmission induced by intracellular charge inhomogeneities

Signal propagation in neuronal dendrites represents the basis for interneuron communication and information processing in the brain. Here we take into account charge inhomogeneities arising in the vicinity of ion channels in cytoplasm and obtain a modified cable equation. We show that charge inhomogeneities acting on a millisecond time scale can lead to the appearance of propagating waves with wavelengths of hundreds of micrometers. They correspond to a certain frequency band predicting the appearance of resonant properties in brain neuron signaling. We also show that membrane potential in spiny dendrites obeys the modified cable equation suggesting a crucial role of the spines in dendritic subthreshold resonance.

VolRoverN: Enhancing Surface and Volumetric Reconstruction for Realistic Dynamical Simulation of Cellular and Subcellular Function

Establishing meaningful relationships between cellular structure and function requires accurate morphological reconstructions. In particular, there is an unmet need for high quality surface reconstructions to model subcellular and synaptic interactions among neurons and glia at nanometer resolution. We address this need with VolRoverN, a software package that produces accurate, efficient, and automated 3D surface reconstructions from stacked 2D contour tracings. While many techniques and tools have been developed in the past for 3D visualization of cellular structure, the reconstructions from VolRoverN meet specific quality criteria that are important for dynamical simulations. These criteria include manifoldness, water-tightness, lack of self- and object-object-intersections, and geometric accuracy. These enhanced surface reconstructions are readily extensible to any cell type and are used here on spiny dendrites with complex morphology and axons from mature rat hippocampal area CA1. Both spatially realistic surface reconstructions and reduced skeletonizations are produced and formatted by VolRoverN for easy input into analysis software packages for neurophysiological simulations at multiple spatial and temporal scales ranging from ion electro-diffusion to electrical cable models.

Contrasting distribution of physiological cell types in different regions of the bed nucleus of the stria terminalis

We characterized the electroresponsive and morphological properties of neurons in the bed nucleus of the stria terminalis (BNST). Previously, Rainnie and colleagues distinguished three cell types in the anterolateral region of BNST (BNST-AL): low-threshold bursting cells (LTB; type II) and regular spiking neurons that display time-dependent (RS; type I) or fast (fIR; type III) inward rectification in the hyperpolarizing direction (Hammack SE, Mania I, Rainnie DG. J Neurophysiol 98: 638-56, 2007). We report that the same neuronal types exist in the anteromedial (AM) and anteroventral (AV) regions of BNST. In addition, we observed two hitherto unreported cell types: late-firing (LF) cells, only seen in BNST-AL, that display a conspicuous delay to firing, and spontaneously active (SA) neurons, only present in BNST-AV, firing continuously at rest. However, the feature that most clearly distinguished the three BNST regions was the incidence of LTB cells (approximately 40-70%) and the strength of their bursting behavior (both higher in BNST-AM and AV relative to AL). The incidence of RS cells was similar in the three regions (∼25%), whereas that of fIR cells was higher in BNST-AL (∼25%) than AV or AM (≤8%). With the use of biocytin, two dominant morphological cell classes were identified but they were not consistently related to particular physiological phenotypes. One neuronal class had highly branched and spiny dendrites; the second had longer but poorly branched and sparsely spiny dendrites. Both often exhibited dendritic varicosities. Since LTB cells prevail in BNST, it will be important to determine what inputs set their firing mode (tonic vs. bursting) and in what behavioral states.

Reaction-subdiffusion front propagation in a comblike model of spiny dendrites

Fractional reaction-diffusion equations are derived by exploiting the geometrical similarities between a comb structure and a spiny dendrite. In the framework of the obtained equations, two scenarios of reaction transport in spiny dendrites are explored, where both a linear reaction in spines and nonlinear Fisher-Kolmogorov-Petrovskii-Piskunov reactions along dendrites are considered. In the framework of fractional subdiffusive comb model, we develop a Hamilton-Jacobi approach to estimate the overall velocity of the reaction front propagation. One of the main effects observed is the failure of the front propagation for both scenarios due to either the reaction inside the spines or the interaction of the reaction with the spines. In the first case the spines are the source of reactions, while in the latter case, the spines are a source of a damping mechanism.

Modeling the effects of anomalous diffusion on synaptic plasticity

The diffusion of cytosolic intracellular signals in spiny dendrites is anomalous due to spine trapping [1]. During anomalous diffusion the mean square displacement (MSD) of diffusing molecules follows a power law, MSD ~ tα, with α called the anomalous exponent. We have shown that α depends on the density and structure of spines and could be a general property of all spiny dendrites [2]. Anomalous diffusion affects the spatial spread and temporal concentration profiles of cytosolic molecules, thus potentially affecting the specificity and reliability of synaptic plasticity. Here we study the effect of anomalous diffusion on the spatial and the temporal distribution of signals involved in the expression of long term depression (LTD) in Purkinje cells (PCs). LTD depends on the PKC-MAPK positive feedback cascade. Increased [Ca2+] activates PKC, which in turn activates MAPK. Activated MAPK and [Ca2+] results in production of arachidonic acid which then activates PKC. The activated PKC either further activates MAPK or phosphorylates AMPARs, which are then removed from the synapse [3]. We use the fractional diffusion formulation of anomalous diffusion. In such a framework the diffusion-reaction equation for a given reactant is: ∂αCRi∂tα=γ∇2CRi+fCRi,CRj where α depends on the spine density along the dendrite, γ(t) is the generalized transport coefficient, CRi(t) is the concentration of the reactant Ri and f(CRi, CRj) defines the reaction terms of the specific biochemical reaction. Solving a system of coupled fractional diffusion-reaction equations for [Ca2+], PKC and MAPK is computationally expensive. To address this problem we recently developed a Fractional Integration Toolbox (FIT) [4]. We have solved a simplified LTD model. In this model [Ca2+] does not undergo anomalous diffusion [1]. However, since PKC and MAPK are large proteins, they are susceptible to molecular trapping by spines resulting in anomalous diffusion. Our results show that in spiny dendrites (α < 1) the diffusion of either PKC or MAPK is slower than in the case of diffusion in spineless dendrites (α = 1) (Figure ​(Figure1A).1A). Under anomalous diffusion there is a longer activation of the PKC-MAPK positive feedback loop. Once activated, PKC and MAPK stay activated longer (Figure ​(Figure1B),1B), implying a lower [Ca2+] activation threshold. Thus, anomalous diffusion affects not only the spatial spread of molecules produced during LTD but also the activation threshold of the synaptic plasticity process. Figure 1 Diffusion of PKC along a dendrite with no spines (α = 1) or high spine density (α = 0.4). (A) Spatial profile of PKC at t = 1 sec after release at × = 0, the anomalous diffusing PKC remains longer and with higher amplitude than ...

Comb-like models for transport along spiny dendrites

We suggest a modification of a comb model to describe anomalous transport in spiny dendrites. Geometry of the comb structure consisting of a one-dimensional backbone and lateral branches makes it possible to describe anomalous diffusion, where dynamics inside fingers corresponds to spines, while the backbone describes diffusion along dendrites. The presented analysis establishes that the fractional dynamics in spiny dendrites is controlled by fractal geometry of the comb structure and fractional kinetics inside the spines. Our results show that the transport along spiny dendrites is subdiffusive and depends on the density of spines in agreement with recent experiments.

Observations on the Shapes of Dendrites

The common assumption that dendrites are cylindrical is incorrect. Analyses of spiny stellate cell dendrites reconstructed from serial thin sections of mouse barrels indicates that these dendrites are flattened; the ratio of long to short axes in cross‐sectioned dendritic profiles is typically 2:1. Planes of flattening are unrelated to the orientation of dendritic segments within the brain, bear no relationship to the plane of section, and are unchanged for various estimates of section thickness. Thus, the flattened shape is not due to compression, sectioning artifact, or to inaccuracy of the reconstruction method. 2/3 of spines are emitted from the relatively narrow, ridge‐like regions of the flattened shafts, causing the dendritic cross‐section to resemble bitufted cell bodies that also are elongated along the poles that give rise to their major projections. Apical dendrites of pyramidal cells also exhibit a flattened morphology and preferential distribution of spines. The flattened shape may reflect the in vivo condition, or be an artifact of fixation. If the latter, flattening could be imagined to result from the shrinking of cell membrane around the cytoskeleton and/or from the collapse of particularly delicate cytoskeletal elements within certain dendritic compartments.

Numerical simulation of fractional Cable equation of spiny neuronal dendrites

In this article, numerical study for the fractional Cable equation which is fundamental equations for modeling neuronal dynamics is introduced by using weighted average of finite difference methods. The stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. A simple and an accurate stability criterion valid for different discretization schemes of the fractional derivative and arbitrary weight factor is introduced and checked numerically. Numerical results, figures, and comparisons have been presented to confirm the theoretical results and efficiency of the proposed method.

Contrasting nanoparticle diffusion in branched polymer and particulate solutions: more than just volume fraction

We contrasted the diffusion of gold nanoparticles (AuNPs) in crowded solutions of a randomly branched polymer (dextran) and rigid, spherical particles (silica). The goal was to understand the roles played by the probe size and structure of the crowding agent in determining the probe diffusion. AuNPs of two different sizes (2.5 nm & 10 nm), dextran of molecular weight 70 kDa and silica particles of radius 10 nm were used. Our results indicated that the AuNP diffusion can be described using the bulk viscosity of the matrix and hydrodynamically dextran behaved similar to a soft colloid. In all situations, we observed normal diffusion except for 2.5 nm sized AuNPs in dextran solution at a higher volume fraction. This is caused by transient trapping of particles within the random branches. The results showed the importance of macromolecular architecture in determining the transport properties in intracellular matrix and in cells with spiny dendrites.

Generation of striatal projection neurons extends into the neonatal period in the rat brain

Substantial advances have been made in the last decade on our understanding of the basic physiology underlying neurogenesis in the postnatal mammalian brain. The bulk of the work in this area has been based on analysis of the adult brain. Relatively less is known about the capacity for neurogenesis in specific structures within the neonatal brain. Here we report that the production of medium spiny striatal projection neurons extends into the early neonatal period under normal physiological conditions in the rat brain. Birth-dating of newborn cells with bromodeoxyuridine at postnatal days 0, 2 and 5 showed a peak production close to birth, which sharply declined at the later time-points. Additionally, there was a low-level but stable contribution of neurons with interneuron identity over the same time-period. Importantly, retroviral labelling of new striatal projection neurons with green fluorescent protein showed long-term survival and terminal differentiation with characteristic morphology, including highly elaborated spiny dendrites, and appropriate axonal targeting of the globus pallidus and midbrain. This latent period of striatal neurogenesis in the early neonatal brain represents an interesting target for regenerative approaches aimed at restoring striatal circuitry in perinatal pathologies, such as hypoxic and ischaemic damage associated with cerebral palsy.

The rostral subcommissural ventral pallidum is a mix of ventral pallidal neurons and neurons from adjacent areas: an electrophysiological study

The ventral pallidum (VP) is a part of the ventral striatopallidal system and is involved in reward-related behaviors. The VP is composed of a ventromedial (VPvm) and a dorsolateral (VPdl) subregion, and some rostral-caudal differences are reported. Study of the VP often focuses on the subcommissural VP, typically considered homogenous in spite of known subdivisions. In this work, we used slice electrophysiology combined with immunohistochemistry for marker neuropeptides to test whether the subcommissural VP is functionally homogenous. Using sagittal slices, we show that more lateral levels (2.40 mm) of the subcommissural VP are homogenous but that a more medial slice (1.90 mm) contains two types of neurons. One type, located more caudally, resembles neurons in the lateral subcommissural VP, with long aspiny dendrites, primarily GABAergic input, and characteristic electrophysiological properties, such as depolarized membrane potential and spontaneous action potential discharge. The second type of neuron, located mostly in the rostral subcommissural VP, shows properties that are akin to medium spiny neurons of adjacent regions, including spiny dendrites, major glutamatergic input, hyperpolarized membrane potential, and no spontaneous action potentials. The two types of neurons were present in both the VPvm and VPdl, implying that the mix is not a characteristic of histologically defined subregions. We conclude that at medial levels the rostral subcommissural VP contains a mix of typical ventral pallidal neurons and spiny neurons similar to those in adjacent regions. This observation needs to be considered when interpreting past experiments and designing future experiments in the subcommissural VP.

Neurogliaform cells of amygdala: a source of slow phasic inhibition in the basolateral complex

Synaptic inhibition in the amygdala actively participates in processing emotional information. To improve the understanding of interneurons in amygdala networks it is necessary to characterize the GABAergic cell types, their connectivity and physiological roles. We used a mouse line expressing a green fluorescent protein (GFP) under the neuropeptide Y (NPY) promoter. Paired recordings between presynaptic NPY-GFP-expressing (+) cells and postsynaptic principal neurons (PNs) of the basolateral amygdala (BLA) were performed. The NPY-GFP+ neurons displayed small somata and short dendrites embedded in a cloud of highly arborized axon, suggesting a neurogliaform cell (NGFC) type. We discovered that a NPY-GFP+ cell evoked a GABA(A) receptor-mediated slow inhibitory postsynaptic current (IPSC) in a PN and an autaptic IPSC. The slow kinetics of these IPSCs was likely caused by the low concentration and spillover of extracellular GABA. We also report that NGFCs of the BLA fired action potentials phase-locked to hippocampal theta oscillations in anaesthetized rats. When this firing was re-played in NPY+-NGFCs in vitro, it evoked a transient depression of the IPSCs. Presynaptic GABA(B) receptors and functional depletion of synaptic vesicles determined this short-term plasticity. Synaptic contacts made by recorded NGFCs showed close appositions, and rarely identifiable classical synaptic structures. Thus, we report here a novel interneuron type of the amygdala that generates volume transmission of GABA. The peculiar functional mode of NGFCs makes them unique amongst all GABAergic cell types of the amygdala identified so far.

Organization of the gymnotiform fish pallium in relation to learning and memory: I. Cytoarchitectonics and cellular morphology

The present article examines the anatomical organization of the dorsal telencephalon of two gymnotiform fish: Gymnotus sp. and Apteronotus leptorhynchus. These electric fish use elaborate electrical displays for agonistic and sexual communication. Our study emphasizes mainly pallial divisions: dorsolateral (DL), dorsodorsal (DD), and dorsocentral (DC), previously implicated in social learning dependent on electric signals. We found that the pallial cytoarchitectonics of gymnotiformes are similar to those reported for the commonly studied goldfish, except that DC is larger and better differentiated in gymnotiformes. We identified a new telencephalic region (Dx), located between DL and DC, and describe the morphological and some biochemical properties of its neurons. Most neurons in DL, DD, and DC are glutamatergic with spiny dendrites. However, the size of these cells as well as the orientation and extent of their dendrites vary systematically across these regions. In addition, both DD and DL contained numerous small GABAergic interneurons as well as well-developed GABAergic plexuses. One important and novel observation is that the dendrites of the spiny neurons within all three regions remain confined to their respective territories. We confirm that DL and DC express very high levels of NMDA receptor subunits as well as CaMKIIα, a key downstream effector of this receptor. In contrast, this enzyme is nearly absent in DD, while NMDA receptors are robustly expressed, suggesting different rules for synaptic plasticity across these regions. Remarkably, GABAergic pallial neurons do not express CaMKIIα, in agreement with previously reported results in the cortex of rats.

Effects of noise on models of spiny dendrites

We study the effects of noise in two models of spiny dendrites. Through the introduction of different types of noise to both the Spike-diffuse-spike (SDS) and Baer-Rinzel (BR) models we investigate the change in behaviour of the travelling wave solution present in both deterministic systems, as noise intensity increases. We show that the speed of wave propagation in both the SDS and BR models respectively differs as the noise intensity in the spine heads increases. In contrast the cable is very robust to noise and as such the speed shows very little variation from the deterministic system. We introduce a space-dependent spine density, ρ(x), to the original Baer-Rinzel model and show how this modified model can mimic behaviour (under influence of noise) of both original systems, through variation of one parameter. We also show that the correlation time and length scales of the noise can enhance propagation of travelling wave solutions where the white noise dominates the underlying signal and produces noise induced phenomena.

Imaging Synaptic Protein Dynamics Using Photoactivatable Green Fluorescent Protein

Considerable evidence has accumulated that structural changes in dendritic spines and their synapses are associated with adaptive functional changes in cortical circuits, such as during circuit refinement in young animals and in learning and memory in adults. Understanding the mechanisms of circuit plasticity requires detailed investigation of the structural dynamics of dendritic spines and how they are regulated by neural activity and sensory experience. Studying the dynamic localization of synaptic proteins in dendritic spines and how their stabilization and exchange rates influence spine structural plasticity is also important. This protocol describes imaging approaches to study synaptic protein dynamics in dendritic spines of the rodent cerebral cortex. It gives a strategy for generating photoactivatable green fluorescent protein (PA-GFP)-tagged synaptic proteins and in vitro and in vivo transfection methods for coexpression of these proteins with a spectrally separable cell-filling marker (DsRed-Express). Methods for tracking synaptic protein localization using photoactivation and time-lapse imaging of PA-GFP in spiny pyramidal neuron dendrites are given. A discussion of imaging hardware and software preferences is also included. The methods described here can be used to study the dynamic processes underlying spine synapse development during the formation and plasticity of neural circuits in the mammalian brain.