Random Molecular Transport around Biological Membranes
Keywords:reaction-diffusion, spherical, stochastic process, Gauss function
The spatio-temporal delivery of essential substances across biological membrane is critical to its survival and the wellbeing of the owner-organism. The process presupposes a permeable soft membrane and the transport are marked by reaction and diffusion phenomena. The spherical configuration of many biological membranes informs the present study on the reaction-diffusion phenomena around spherical membranes, with probability current. The diffusion equation describing the ensemble of reacting molecules around such membranes holds well in elucidating the delivery of drugs across biological cells.
Brown B.S. â€œBiological Membranesâ€,Available online: www.biochemistry.org/portals/0/education/docs/basc 08_full.pdf (accessed on 13-03-2015)
Ostro, M.E. The Lively Membranes, Cambridge University Press, 1983.
Introduction to biological membranes, Available online: http://themedicalbiochemistrypage .org/membranes .php#composition (accessed on 13-03-2015).
Milsom, D.W., â€œBiological membranesâ€, Biological Sciences Review, 6(4), 16-20,1994.
Membrane permeability, Available online: http://www.dartmouth.edu/~cbbc/courses/bio15/ 2004 W/slides/L04.pdf (accessed on 14-03-2015).
Warren B., Shinpei O,â€Fusion in phospholipid spherical membranesâ€, The Journal of Membrane Biology, Volume 23, Issue 1, pp 385-401,1975.
Bosezzi, D; Rosenberg G., Formalizing Spherical membrane structures and membranes proteins population, Available online: http://link.springer.com/chapter/10.1007%2F11963516_2#page-2 (accessed on 10-02-2015).
Haslach , H. W.; Humphrey, J. D., â€œDynamics of biological soft tissue and rubber: internally pressurized spherical membranes surrounded by a fluidâ€, International Journal of Non-Linear Mechanics, Volume 39, Issue 3,399â€“420,2004.
Kenkre VM, Kumar N., â€œNonlinearity in bacterial population dynamics: proposal for experiments for the observation of abrupt transitions in patchesâ€, Proc Natl. Acad. Sci., 105:18752â€“7, 2008.
Volpert A.I.; Volpert VA. â€œApplications of the rotation theory of vector fields to the study of wave solutions of parabolic equationsâ€, Trans Moscow Math Soc., 52:59â€“108, 1990.
Brillinger, D. R., â€œA Particle Migrating Randomly on a Sphereâ€, Journal of Theoretical Probability, Vol. 10, No. 2, 429-443, 1997.
Nicholson C., â€œDiffusion and related transport mechanisms in brain tissueâ€, Rep. Prog. Phys., 64,815â€“884, 2001
LefÃ¨vre J, Mangin J-F., â€œA Reaction-Diffusion Model of Human Brain Developmentâ€, PLoS Comput Biol., 6(4), 2010 , e1000749. doi:10.1371/journal.pcbi.1000749,
Amatore, C.; Oleinick,A.; Klymenko,O.V.; Svir,I., â€œTheory of Long-Range Diffusion of Proteins on a Spherical Biological Membrane: Application to Protein Cluster Formation and Actin-Comet Tail Growthâ€, Chemphyschem, , Vol.10,1586-1592, 2009.
V. Volpert , S. Petrovskii ,â€Reactionâ€“diffusion waves in biologyâ€, Physics of Life Reviews ,6,267â€“310, 2009.
Chaudhry QA, Morgenstern R, Hanke M, and Dreij K(2012), Influence of Biological Cell Geometry on Reaction and Diffusion Simulation, Available online: http://www.diva-portal.org/smash/get /diva 2:516281/FULLTEXT01.pdf (accessed on 22-03-2015)
Radek, E, S; Chapman, J.; Philip K..M. , A practical guide to stochastic simulations of reaction-diffusion processes, Available online: http://people.maths.ox.ac.uk/erban/Education/ StochReacDiff.pdf
Nzerem F E. Orumie C.U., â€œStochastic description of the dynamics of thrombo-embolus in an arterial compartmentâ€, International Journal of Applied Mathematical Sciences ,3(1)(2015) 6-11, doi; 10.14419/ijams.v3i1.4062
Gregoire, N., Anne D. W.,â€œReaction-diffusion systemsâ€, Scholarpedia, 2(9):1475, 2007. doi:10.4249/scholarpedia.1475
Klemens F., Reactions-Diffusion Equations, Available online: http://www.damtp. cam.ac.uk/ research/apde/teaching/ CamRD2010.pdf (accessed on 22-03- 2015 )
Diffusion and Reaction, Available online: https://www.scribd.com/doc/189241200/Chapter12-Diffusion-Reaction , (accessed on 22-02- 2015 )
Effects of Transport Limitations on Rates of Solid-Catalyzed Reactions, Available online: http://authors.library.caltech.edu /25070/7/FundChemReaxEngCh6.pdf (accessed on 18-03-2015).
Krishna, M. G; Joseph S; Supurna, S., â€œBrownian motion on a sphere: distribution of solid anglesâ€ J. Phys. A: Math. Gen., 33,5965â€“5971, 2000.
K. Schulten and I. Kosztin, Lectures in Theoretical Biophysics, Available online: www.ks.uiuc.edu/Services/Class/NSM.pdf (accessed on 22-10-2014)
BÃ¼low, Thomas, "Spherical Diffusion". Technical Reports (CIS). Paper 718, 2001.http://repository.upenn.edu/cis_reports/718
Abhijit G., Joseph S., Supurna S., A â€œGaussian" for diffusion on the sphere, Available online: arXiv:1303.1278 [cond.mat.stat-mech], (accessed on 22-03-2015).
Chapman-Kolmogorov equation for continuous paths: Fokker-Plank equation, Available online: http://www.pd.infn.it/~orlandin/fisica_sis_comp/fokker_plank.pdf.(accessed on 12-09-2014)
Pabitra, N.S., Non-Gaussian Statistics and Anomalous Diffusion in Porous Media, Available online: http://biomedphys.sgu.ru/Files/LIB/Springer/Processes%20with%20LongRange%20Correlatio/10.NonGaussian%20Statistics %20and%20Anomalous%20diffusion %20in%20Porous%20Media.pdf (accessed on 22-10-2014)
Fabio M.; Kepa R-M. Stochastic simulations of minimal self-reproducing cellular systems, Available online: DOI: 10.1098/rstb .2007.2071 (accessed on 22-03-2015)
Gillespie, D.T., â€œA general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys., 22, 403â€“434, 1976, doi:10.1016/0021-9991(76)90041-3
Available online: http://www.pharmpress.com/files/docs/MolBiopharmaceutics_ sample.pdf (accessed on 18-03-2015)
Thielle Modulus, Available online: http://en.wikipedia.org/wiki/Thiele_modulus (accessed on 22-03-2015)
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