Random Molecular Transport around Biological Membranes
Keywords:
reaction-diffusion, spherical, stochastic process, Gauss functionAbstract
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.
References
Brown B.S. “Biological 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., “Biological 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., “Dynamics of biological soft tissue and rubber: internally pressurized spherical membranes surrounded by a fluidâ€, International Journal of Non-Linear Mechanics, Volume 39, Issue 3,399–420,2004.
Kenkre VM, Kumar N., “Nonlinearity in bacterial population dynamics: proposal for experiments for the observation of abrupt transitions in patchesâ€, Proc Natl. Acad. Sci., 105:18752–7, 2008.
Volpert A.I.; Volpert VA. “Applications of the rotation theory of vector fields to the study of wave solutions of parabolic equationsâ€, Trans Moscow Math Soc., 52:59–108, 1990.
Brillinger, D. R., “A Particle Migrating Randomly on a Sphereâ€, Journal of Theoretical Probability, Vol. 10, No. 2, 429-443, 1997.
Nicholson C., “Diffusion and related transport mechanisms in brain tissueâ€, Rep. Prog. Phys., 64,815–884, 2001
Lefèvre J, Mangin J-F., “A 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., “Theory 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€Reaction–diffusion waves in biologyâ€, Physics of Life Reviews ,6,267–310, 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., “Stochastic 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.,“Reaction-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., “Brownian motion on a sphere: distribution of solid angles†J. Phys. A: Math. Gen., 33,5965–5971, 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)
Bülow, Thomas, "Spherical Diffusion". Technical Reports (CIS). Paper 718, 2001.http://repository.upenn.edu/cis_reports/718
Abhijit G., Joseph S., Supurna S., A “Gaussian" 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., “A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys., 22, 403–434, 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)
Downloads
Published
Issue
Section
License
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.
