Fractional cable models for spiny neuronal dendrites

Article


Henry, B. I., Langlands, Trevor and Wearne, S. L.. 2008. "Fractional cable models for spiny neuronal dendrites." Physical Review Letters. 100 (12), pp. 1-4. https://doi.org/10.1103/PhysRevLett.100.128103
Article Title

Fractional cable models for spiny neuronal dendrites

ERA Journal ID1019
Article CategoryArticle
AuthorsHenry, B. I. (Author), Langlands, Trevor (Author) and Wearne, S. L. (Author)
Journal TitlePhysical Review Letters
Journal Citation100 (12), pp. 1-4
Number of Pages4
Year2008
Place of PublicationUnited States
ISSN0031-9007
1079-7114
1092-0145
Digital Object Identifier (DOI)https://doi.org/10.1103/PhysRevLett.100.128103
Web Address (URL)http://link.aps.org/doi/10.1103/PhysRevLett.100.128103
Abstract

Cable equations with fractional order temporal operators are introduced to model electrotonic properties of spiny neuronal dendrites. These equations are derived from Nernst-Planck equations with fractional order operators to model the anomalous subdiffusion that arises from trapping properties of dendritic spines. The fractional cable models predict that postsynaptic potentials propagating along dendrites with larger spine densities can arrive at the soma faster and be sustained at higher levels over longer times. Calibration and validation of the models should provide new insight into the functional implications of altered neuronal spine densities, a hallmark of normal aging and many neurodegenerative disorders.

Keywordsanomalous subdiffusion, fractional cable model, spiny dendrites
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 2020490510. Stochastic analysis and modelling
490410. Partial differential equations
490102. Biological mathematics
Public Notes

File reproduced in accordance with the copyright policy of the publisher/author.

Byline AffiliationsUniversity of New South Wales
Icahn School of Medicine at Mount Sinai, United States
Permalink -

https://research.usq.edu.au/item/9z196/fractional-cable-models-for-spiny-neuronal-dendrites

Download files


Accepted Version
  • 1971
    total views
  • 467
    total downloads
  • 2
    views this month
  • 4
    downloads this month

Export as

Related outputs

Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations
Osman, Sheelan and Langlands, Trevor. 2022. "Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations." Fractional Calculus and Applied Analysis. 25 (6), pp. 2166-2192. https://doi.org/10.1007/s13540-022-00096-2
Connecting community online and through partnership: A reflective piece
Pickstone, Leigh, Sharma, Ekta, King, Rachel, Galligan, Linda and Langlands, Trevor. 2022. "Connecting community online and through partnership: A reflective piece." International Journal for Students as Partners. 6 (2), pp. 114-120. https://doi.org/10.15173/ijsap.v6i2.4825
Modern artificial intelligence model development for undergraduate student performance prediction: an investigation on engineering mathematics courses
Deo, Ravinesh C., Yaseen, Zaher Mundher, Al-Ansari, Nadhir, Nguyen-Huy, Thong, Langlands, Trevor and Galligan, Linda. 2020. "Modern artificial intelligence model development for undergraduate student performance prediction: an investigation on engineering mathematics courses." IEEE Access. 8, pp. 136697-136724. https://doi.org/10.1109/ACCESS.2020.3010938
An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations
Osman, S. A and Langlands, T. A. M.. 2019. "An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations." Applied Mathematics and Computation. 348, pp. 609-626. https://doi.org/10.1016/j.amc.2018.12.015
From stochastic processes to numerical methods: a new scheme for solving reaction subdiffusion fractional partial differential equations
Angstmann, C. N., Donnelly, I. C., Henry, B. I., Jacobs, B. A., Langlands, T. A. M. and Nichols, J. A.. 2016. "From stochastic processes to numerical methods: a new scheme for solving reaction subdiffusion fractional partial differential equations." Journal of Computational Physics. 307, pp. 508-534. https://doi.org/10.1016/j.jcp.2015.11.053
Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions
Langlands, Trevor, Henry, B. I. and Wearne, S. L.. 2009. "Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions." Journal of Mathematical Biology. 59 (6), pp. 761-808. https://doi.org/10.1007/s00285-009-0251-1
A mathematical model for the proliferation, accumulation and spread of pathogenic proteins along neuronal pathways with locally anomalous trapping
Angstmann, C. N., Donnelly, I. C., Henry, B. I. and Langlands, T. A. M.. 2016. "A mathematical model for the proliferation, accumulation and spread of pathogenic proteins along neuronal pathways with locally anomalous trapping." Mathematical Modelling of Natural Phenomena (MMNP). 11 (3), pp. 142-156. https://doi.org/10.1051/mmnp/20161139
Generalized continuous time random walks, master equations, and fractional Fokker-Planck equations
Angstmann, C. N., Donnelly, I. C., Henry, B. I., Langlands, T. A. M. and Straka, P.. 2015. "Generalized continuous time random walks, master equations, and fractional Fokker-Planck equations." SIAM Journal on Applied Mathematics. 75 (4), pp. 1445-1468. https://doi.org/10.1137/15M1011299
Continuous-time random walks on networks with vertex- and time-dependent forcing
Angstmann, C. N., Donnelly, I. C., Henry, B. I. and Langlands, T. A. M.. 2013. "Continuous-time random walks on networks with vertex- and time-dependent forcing." Physical Review E. 88 (2). https://doi.org/10.1103/PhysRevE.88.022811
Fractional cable equation models for anomalous electrodiffusion in nerve cells: finite domain solutions
Langlands, T. A. M., Henry, B. I. and Wearne, S. L.. 2011. "Fractional cable equation models for anomalous electrodiffusion in nerve cells: finite domain solutions." SIAM Journal on Applied Mathematics. 71 (4), pp. 1168-1203. https://doi.org/10.1137/090775920
Fractional diffusion in force fields, fractional electro-diffusion and fractional chemotaxis diffusion
Langlands, Trevor, Henry, Bruce and Straka, Peter. 2010. "Fractional diffusion in force fields, fractional electro-diffusion and fractional chemotaxis diffusion." Henry, Bruce and Roberts, John (ed.) Dynamics Days Asia Pacific 6 Conference (DDAP6). Sydney, Australia 12 - 14 Jul 2010 Sydney, Australia.
Anomalous subdiffusion with multispecies linear reaction dynamics
Langlands, Trevor, Henry, B. I. and Wearne, S. L.. 2008. "Anomalous subdiffusion with multispecies linear reaction dynamics." Physical Review B: Covering condensed matter and materials physics. 77, pp. 1-9. https://doi.org/10.1103/PhysRevE.77.021111
Turing pattern formation with fractional diffusion and fractional reactions
Langlands, T. A. M., Henry, B. I. and Wearne, S. L.. 2006. "Turing pattern formation with fractional diffusion and fractional reactions." Journal of Physics: Condensed Matter. 19 (6), pp. 065115 -065134. https://doi.org/10.1088/0953-8984/19/6/065115
Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations
Henry, B. I., Langlands, Trevor and Wearne, S. L.. 2006. "Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations." Physical Review E. 74 (3), pp. 1-15. https://doi.org/10.1103/PhysRevE.74.031116
Solution of a modified fractional diffusion equation
Langlands, T. A. M.. 2006. "Solution of a modified fractional diffusion equation." Physica A: Statistical Mechanics and its Applications. 367, pp. 136-144. https://doi.org/10.1016/j.physa.2005.12.012
Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces
Henry, B. I., Langlands, T. A. M. and Straka, P.. 2010. "Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces." Physical Review Letters. 105 (17), pp. 17062-1-170602-4. https://doi.org/10.1103/PhysRevLett.105.170602
Fractional chemotaxis diffusion equations
Langlands, T. A. M. and Henry, B. I.. 2010. "Fractional chemotaxis diffusion equations." Physical Review E. 81 (5), pp. 1-12. https://doi.org/10.1103/PhysRevE.81.051102
Optimal targeting of hepatitis C virus treatment among injecting drug users to those not enrolled in methadone maintenance programs
Zeiler, Irmgard, Langlands, Trevor, Murray, John M. and Ritter, Alison. 2010. "Optimal targeting of hepatitis C virus treatment among injecting drug users to those not enrolled in methadone maintenance programs." Drug and Alcohol Dependence. 110 (3), pp. 228-233. https://doi.org/10.1016/j.drugalcdep.2010.03.006
An introduction to fractional diffusion
Henry, B. I., Langlands, Trevor and Straka, P.. 2010. "An introduction to fractional diffusion." Dewar, Robert L. and Detering, Frank (ed.) 22nd Canberra International Physics Summer School. Canberra, Australia 08 - 19 Dec 2008 Singapore. https://doi.org/10.1142/9789814277327_0002