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.

[1]  R. Nicoll,et al.  AMPA Receptor Trafficking at Excitatory Synapses , 2003, Neuron.

[2]  M Segal,et al.  Release of calcium from stores alters the morphology of dendritic spines in cultured hippocampal neurons. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[3]  F. Crick.  Do dendritic spines twitch? , 1982, Trends in Neurosciences.

[4]  David Holcman,et al.  Survival probability of diffusion with trapping in cellular neurobiology. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  M. Segal,et al.  Spike-Associated Fast Contraction of Dendritic Spines in Cultured Hippocampal Neurons , 2001, Neuron.

[6]  D. Holcman,et al.  Dwell time of a Brownian molecule in a microdomain with traps and a small hole on the boundary. , 2007, The Journal of chemical physics.

[7]  D Holcman,et al.  Calcium dynamics in dendritic spines and spine motility. , 2004, Biophysical journal.

[8]  Hillel Adesnik,et al.  Photoinactivation of Native AMPA Receptors Reveals Their Real-Time Trafficking , 2005, Neuron.

[9]  K. Ibuki,et al.  Improved Velocity Distribution Applied to Fokker–Planck–Kramers Equation Treatment for Dynamics of Diffusion-Controlled Reactions in Two Dimensions , 2003 .

[10]  Pico Caroni,et al.  Dendritic spine morphology determines membrane-associated protein exchange between dendritic shafts and spine heads. , 2009, Cerebral cortex.

[11]  David Holcman,et al.  Brownian Motion in Dire Straits , 2012, Multiscale Model. Simul..

[12]  Michael J. Ward,et al.  Strong Localized Perturbations of Eigenvalue Problems , 1993, SIAM J. Appl. Math..

[13]  David Holcman,et al.  Modeling Calcium Dynamics in Dendritic Spines , 2005, SIAM J. Appl. Math..

[14]  Sebastian Pascarelle,et al.  Unusual spectral energy distribution of a galaxy previously reported to be at redshift 6.68 , 2000, Nature.

[15]  R. Yuste,et al.  Regulation of Spine Calcium Dynamics by Rapid Spine Motility Materials and Methods , 2022 .

[16]  J. Bourne,et al.  Balancing structure and function at hippocampal dendritic spines. , 2008, Annual review of neuroscience.

[17]  Z. Schuss,et al.  Narrow Escape, Part II: The Circular Disk , 2004, math-ph/0412050.

[18]  D Holcman,et al.  Calcium dynamics in dendritic spines, modeling and experiments. , 2005, Cell calcium.

[19]  C. Hoogenraad,et al.  Actin in dendritic spines: connecting dynamics to function , 2010, The Journal of cell biology.

[20]  Michael J. Ward,et al.  Summing Logarithmic Expansions for Singularly Perturbed Eigenvalue Problems , 1993, SIAM J. Appl. Math..

[21]  R. Malenka,et al.  AMPA receptor trafficking and synaptic plasticity. , 2002, Annual review of neuroscience.

[22]  Roberto Malinow,et al.  AMPA receptor trafficking and long-term potentiation. , 2003, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[23]  Michael J. Ward,et al.  An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part II: The Sphere , 2010, Multiscale Model. Simul..

[24]  M. Ehlers,et al.  Spine microdomains for postsynaptic signaling and plasticity. , 2009, Trends in cell biology.

[25]  Z. Schuss,et al.  Escape Through a Small Opening: Receptor Trafficking in a Synaptic Membrane , 2004 .

[26]  A. Triller,et al.  The role of receptor diffusion in the organization of the postsynaptic membrane , 2003, Nature Reviews Neuroscience.

[27]  Paul C Bressloff,et al.  Biophysical Model of AMPA Receptor Trafficking and Its Regulation during Long-Term Potentiation/Long-Term Depression , 2006, The Journal of Neuroscience.

[28]  Alexander M Berezhkovskii,et al.  Escape from cavity through narrow tunnel. , 2009, The Journal of chemical physics.

[29]  Paul C Bressloff,et al.  A dynamic corral model of receptor trafficking at a synapse. , 2009, Biophysical journal.

[30]  David Holcman,et al.  Dynamic regulation of spine–dendrite coupling in cultured hippocampal neurons , 2004, The European journal of neuroscience.

[31]  D A Lauffenburger,et al.  Analysis of intracellular receptor/ligand sorting. Calculation of mean surface and bulk diffusion times within a sphere. , 1986, Biophysical journal.

[32]  David Holcman,et al.  Modeling synaptic dynamics driven by receptor lateral diffusion. , 2006, Biophysical journal.

[33]  J. Henley,et al.  Lateral Diffusion Drives Constitutive Exchange of AMPA Receptors at Dendritic Spines and Is Regulated by Spine Morphology , 2006, The Journal of Neuroscience.

[34]  I. Kupka,et al.  Some questions related to modeling in cellular biology , 2010 .

[35]  Z. Schuss,et al.  The narrow escape problem for diffusion in cellular microdomains , 2007, Proceedings of the National Academy of Sciences.

[36]  David Holcman,et al.  Erratum: Narrow escape through a funnel and effective diffusion on a crowded membrane [Phys. Rev. E 84, 021906 (2011)] , 2012 .

[37]  Bernard J. Matkowsky,et al.  Uniform expansion of the transition rate in Kramers' problem , 1984 .

[38]  E. V. D. Velde,et al.  The onset of thermal runaway in partially insulated or cooled reactors , 1992 .

[39]  Rafael Yuste,et al.  From form to function: calcium compartmentalization in dendritic spines , 2000, Nature Neuroscience.

[40]  Z. Schuss,et al.  Narrow Escape, Part III: Non-Smooth Domains and Riemann Surfaces , 2006 .

[41]  Dane M. Chetkovich,et al.  Stargazin regulates synaptic targeting of AMPA receptors by two distinct mechanisms , 2000, Nature.

[42]  R. Yuste,et al.  Mechanisms of Calcium Decay Kinetics in Hippocampal Spines: Role of Spine Calcium Pumps and Calcium Diffusion through the Spine Neck in Biochemical Compartmentalization , 2000, The Journal of Neuroscience.

[43]  Michael J. Ward,et al.  Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps , 2005, European Journal of Applied Mathematics.

[44]  Association Rates of Diffusion-Controlled Reactions in Two Dimensions , 1985 .

[45]  D Holcman,et al.  Diffusion in a dendritic spine: the role of geometry. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  K. Harris,et al.  Dendritic spines of rat cerebellar Purkinje cells: serial electron microscopy with reference to their biophysical characteristics , 1988, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[47]  Z. Schuss,et al.  Narrow escape and leakage of Brownian particles. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Bernardo L Sabatini,et al.  Neuronal Activity Regulates Diffusion Across the Neck of Dendritic Spines , 2005, Science.

[49]  Daniel Coombs,et al.  Diffusion on a Sphere with Localized Traps: Mean First Passage Time, Eigenvalue Asymptotics, and Fekete Points , 2009, SIAM J. Appl. Math..

[50]  C. Hoogenraad,et al.  The postsynaptic architecture of excitatory synapses: a more quantitative view. , 2007, Annual review of biochemistry.

[51]  Z. Schuss,et al.  Diffusion through a cluster of small windows and flux regulation in microdomains , 2008 .

[52]  R. Eisenberg,et al.  Narrow Escape, Part I , 2004, math-ph/0412048.

[53]  M. Segal,et al.  Dendritic spine density and LTP induction in cultured hippocampal slices. , 1997, Journal of neurophysiology.

[54]  M. Segal,et al.  Morphological plasticity in dendritic spines of cultured hippocampal neurons , 1996, Neuroscience.

[55]  E. R. Rang.  Narrow Escape. , 1965, Science.

[56]  Paul C Bressloff,et al.  Cable theory of protein receptor trafficking in a dendritic tree. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[57]  Z. Schuss,et al.  Diffusion escape through a cluster of small absorbing windows , 2008 .

[58]  K. Svoboda,et al.  Rapid spine delivery and redistribution of AMPA receptors after synaptic NMDA receptor activation. , 1999, Science.

[59]  Z. Schuss,et al.  Narrow escape through a funnel and effective diffusion on a crowded membrane. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  Roberto Malinow,et al.  AMPA Receptor Incorporation into Synapses during LTP: The Role of Lateral Movement and Exocytosis , 2009, Neuron.

[61]  D W Tank,et al.  Direct Measurement of Coupling Between Dendritic Spines and Shafts , 1996, Science.

[62]  D. Choquet,et al.  Regulation of AMPA receptor lateral movements , 2002, Nature.