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

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Abstract

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.

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Notes

  1. The quantity p (x, t) dx is the probabiliy of finding the particle in a surface element dx centered at x at time t.

References

  • Andrsfalvy, B.K., Smith, M.A., Borchardt, T., Sprengel, R., Magee, J. C. (2003). Impaired regulation of synaptic strength in hippocampal neurons from glur1-deficient mice. The Journal of Physiology, 552(1), 35–45.

    Article  Google Scholar 

  • Ashby, M., Maier, S., Nishimune, A., Henley, J. (2006). Lateral diffusion drives constitutive exchange of ampa receptors at dendritic spines and is regulated by spine morphology. Journal of Neuroscience, 26(26), 7046–7055.

    Article  CAS  PubMed  Google Scholar 

  • Biess, A., Korkotian, E., Holcman, D. (2007). Diffusion in a dendritic spine: The role of geometry. Physical Review E, 021922, 76.

    Google Scholar 

  • Borgdorff, A., & Choquet, D. (2002). Regulation of ampa receptor lateral movements. Nature, 417, 649–653.

    Article  CAS  PubMed  Google Scholar 

  • Bressloff, P.C., & Earnshaw, B.A. (2007). Diffusion-trapping model of receptor trafficking in dendrites. Physical Review E, 75(041915).

  • Calhoun, D., & Helzel, C. (2009). A finite volume method for solving parabolic equations on logically cartesian curved surface meshes. SIAM Journal on Scientific Computing, 31(6).

  • Cautres, R., Herbin, R., Hubert, F. (2004). The lions domain decomposition algorithm on non matching cell-centered nite volume meshes. IMA Journal of Numerical Analysis, 24(3), 465–490.

    Article  Google Scholar 

  • Choquet, D. (2010). Fast ampar trafficking for a high-frequency synaptic transmission. European Journal of Neuroscience, 32, 250–260.

    Article  PubMed  Google Scholar 

  • Choquet, D., & Triller, A. (2003). The role of receptor diffusion in the organization of the postsynaptic membrane. Nature Reviews Neuroscience, 4, 251–265.

    Article  CAS  PubMed  Google Scholar 

  • Dyhkin, E.B. (1965). Markov Processes I,II, Springer Verlag.

  • Ehlers, M.D., Heine, M., Groc, L., Lee, M.-C., Choquet, D. (2007). Diffusional trapping of glur1 ampa receptors by input-specific synaptic activity. Neuron, 54(3), 447–460.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Fischer, M., Kaech, S., Knutti, D., Matus, A. (1998). Rapid actin-based plasticity in dendritic spines. Neuron, 20(5), 847–854.

    Article  CAS  PubMed  Google Scholar 

  • Geuzaine, C., & Remacle, J.-F. (2009). Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering, 79(11), 1309–1331.

    Article  Google Scholar 

  • Giannone, G., Hosy, E., Levet, F., Constals, A., Schulze, K., Sobolevsky, A., Rosconi, M., Gouaux, E., Tamp, R., Choquet, D., Cogne, L. (2010). Dynamic superresolution imaging of endogenous proteins on living cells at ultra-high density. Biophysical Journal, 99(4), 1303–1310.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Guyer, J.E., Wheeler, D., Fipy, Warren, J.A. (2009). Partial differential equations with python. Computing in Science and Engineering, 11(3), 6–15.

    Article  CAS  Google Scholar 

  • Harris, K.M.(P.I.). (2012). Synapse web. http://synapses.clm.utexas.edu/anatomy/Ca1pyrmd/radiatum/index.stm. See K21 and K18.

  • Harris, K.M., & Stevens, J.K. (1989). Dendritic spines of ca1 pyramidal cells in the rat hippocampus: serial electron microscopy with reference to their biophysical characteristics. Journal of Neuroscience, 9, 2982–2997.

    CAS  PubMed  Google Scholar 

  • Heine, M., Groc, L., Frischknecht, R., Bque, J.C., Lounis, B., Rumbaugh, G., Huganir, R., Cognet, L., Choquet, D. (2008). Surface mobility of postsynaptic ampars tunes synaptic transmission. Science, 320(5873), 201–205.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Holcman, D., & Schuss, Z. (2004). Escape through a small opening: Receptor trafficking in a synaptic membrane. Journal of Statistical Physics, 117(5/6), 975–1014.

    Article  Google Scholar 

  • Holcman, D., & Schuss, Z. (2011). Diffusion laws in dendritic spines. Journal of Mathematical Neuroscience, 1(10).

  • Holcman, D., Korkotian, E., Segal, M. (2005). Calcium dynamics in dendritic spines, modeling and experiments. Cell Calcium, 37(5), 467–475. Calcium in the function of the nervous system: New implications.

    Article  CAS  PubMed  Google Scholar 

  • Holcman, D., Singer, A., Schuss, Z. (2006). Narrow escape, part ii: The circular disk. Journal of Statistical Physics, 122(3), 465–489.

    Article  Google Scholar 

  • Holmes, W. R. (1990). Is the function of dendritic spines to concentrate calcium? Brain Research, 519(1-2), 338–342.

    Article  CAS  PubMed  Google Scholar 

  • Hugel, S., Abegg, M., de Paola, V., Caroni, P., Gahwiler, B., McKinney, R. (2009). Dendritic spine morphology determines membrane-associated protein exchange between dendritic shafts and spine heads. Cerebral Cortex, 19(3), 697–702.

    Article  PubMed  Google Scholar 

  • Jaskolski, F., & Henley, J.M. (2009). Synaptic receptor trafficking: The lateral point of view. Neuroscience, 158, 19–24.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Kieri, E. (2011). Accuracy aspects of the reaction-diffusion master equation on unstructured meshes. Uppsala Universitet.

  • Lynch, G., & Baudry, M. (1984). The biochemistry of memory: A new and specific hypothesis. Science, 224, 1057–1063.

    Article  CAS  PubMed  Google Scholar 

  • Makino, H., & Malinow, R. (2009). Ampa receptor incorporation into synapses during ltp: the role of lateral movement and exocytosis. Neuron, 64, 381-390.

    Google Scholar 

  • Masugi-Tokita, M., Tarusawa, E., Watanabe, M., Molnár, E., Fujimoto, K., Shigemoto, R. (2007). Number and density of ampa receptors in individual synapses in the rat cerebellum as revealed by sds-digested freeze-fracture replica labeling. The Journal of Neuroscience, 27(8), 2135–2144.

    Article  CAS  PubMed  Google Scholar 

  • Newpher, T.M., & Ehlers, M.D. (2008). Glutamate receptor dynamics in dendritic microdomains. Neuron, 58(4), 472–497.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Nicholson, D., Trana, R., Katz, Y., Kath, W., Spruston, N., Geinisman, Y. (2006). Distance-dependent differences in synapse number and ampa receptor expression in hippocampal ca1 pyramidal neurons. Neuron, 50, 431–442.

    Article  CAS  PubMed  Google Scholar 

  • Noguchi, J., Matsuzaki, M., Ellis-Davies, G.C.R., Kasai, H. (2005). Spine-neck geometry determines nmda receptor-dependent ca2+ signaling in dendrites. Neuron, 4, 609–622.

    Article  Google Scholar 

  • OBrien, R.J., Kamboj, S., Ehlers, M.D., Rosen, K.R., Fischbach, G.D., Huganir, R.L. (1998). Activity-dependent modulation of synaptic ampa receptor accumulation. Neuron, 21(5), 1067–1078.

    Article  CAS  Google Scholar 

  • Opazo, P., Labrecque, S., Tigaret, C., Frouin, A., Wiseman, P., De Koninck, P., Choquetl, D. (2010). Camkii triggers the diffusional trapping of surface ampars through phosphorylation of stargazin. Neuron, 67(2), 239–252.

    Article  CAS  PubMed  Google Scholar 

  • Pike, L.J. (2003). Lipid rafts bringing order to chaos. Journal of Lipid Research, 44(4), 655–667.

    Article  CAS  PubMed  Google Scholar 

  • Renner, M., Choquet, D.l., Triller, A. (2009). Control of the postsynaptic membrane viscosity. The Journal of Neuroscience, 29(9), 2926–2937.

    Article  CAS  PubMed  Google Scholar 

  • Sabatini, B.L., Maravall, M., Svoboda, K. (2001). Ca(2+) signaling in dendritic spines. Current Opinion Neurobiology, 11(3), 349–56.

    Article  CAS  Google Scholar 

  • Santamaria, F., Wils, S., De Schutter, E., Augustine, G. J. (2006). Anomalous diffusion in purkinje cell dendrites caused by spines. Neuron, 52(4), 635–648.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Schuss, Z. (1980). Theory and applications of stochastic differential equations. Wiley.

  • Schuss, Z. (2010). Theory and applications of stochastic processes: an analytical approach. Springer.

  • Schuss, Z., Singer, A., Holcman, D. (2007). The narrow escape problem for diffusion in cellular microdomains. PNAS, 104(41), 16098–16103.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Sheng, M., & Jong Kim, M. (2002). Postsynaptic signaling and plasticity mechanisms. Science, 298(25), 776–780.

    Article  CAS  PubMed  Google Scholar 

  • Sheng, M., & Lee, S.H. (2001). Ampa receptor trafficking and the control of synaptic transmission. Cell, 105(7), 825–828.

    Article  CAS  PubMed  Google Scholar 

  • Simons, K., & Toomre, D. (2000). Lipid rafts and signal transduction. Nature Reviews Molecular Cell Biology, 1(1), 31–39.

    Article  CAS  PubMed  Google Scholar 

  • Singer, S.J., & Nicolson, G. (1972). The fluid mosaic model of the structure of cell membranes. Science, 175(4023), 720–731.

    Article  CAS  PubMed  Google Scholar 

  • Svoboda, K., Tank, D.W., Denk, W. (1996). Direct measurement of coupling between dendritic spines and shafts. Science, 272(5262), 716–719.

    Article  CAS  PubMed  Google Scholar 

  • Tardin, C., Cognet, L., Bats, C., Lounis, B., Choquet, D. (2003). Direct imaging of lateral movements of ampa receptors inside synapses. The EMBO Journal, 22(18), 4656–4665.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Triller, A., & Choquet, D. (2008). New concepts in synaptic biology derived from single-molecule imaging. Neuron, 59(3), 359–374.

    Article  CAS  PubMed  Google Scholar 

  • Yudowski, G.A., Puthenveedu, M.A., Leonoudakis, D., Panicker, S., Thorn, K.S., Beattie, E.C., von Zastrow, M. (2007). Real-time imaging of discrete exocytic events mediating surface delivery of ampa receptors. The Journal of Neuroscience, 27(41), 11112–11121.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

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Authors and Affiliations

  1. Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA, USA

    Cory M. Simon

  2. Theoretical Neurobiology, University of Antwerp, Antwerp, Belgium

    Iain Hepburn & Erik De Schutter

  3. Computational Neuroscience Unit, Okinawa Institute of Science and Technology, Onna-son, Okinawa, Japan

    Iain Hepburn, Weiliang Chen & Erik De Schutter

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  1. Cory M. Simon
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Correspondence to Cory M. Simon.

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Action Editor: Arnd Roth

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Simon, C.M., Hepburn, I., Chen, W. et al. The role of dendritic spine morphology in the compartmentalization and delivery of surface receptors. J Comput Neurosci 36, 483–497 (2014). https://doi.org/10.1007/s10827-013-0482-4

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