The influence of initial placement of molecular or
ion substance is investigated on the diffusion fluxes across the cell membrane.
The diffusion fluxes and recovery curves are obtained by considering both the
singlespot and double-spot concentrations inside the cell membrane. The
results show that the additional concentration inside the membrane reduces the
net fluxes at the cell interior as well as the exterior. In addition, it is
found that the change in diffusion flux at the two outer walls of the membrane
by the two-spot concentrations in the cell membrane is weaker than that of the
single-spot concentration at the center. The variation of the influence of
initial locations of the molecular concentrations inside the cell membrane on
the diffusion fluxes is also discussed. This result can be applied to the
diffusion process in avascular collagenous tissues.
Cite this paper
Jung, B. and Ki, D. (2014) Influence of initial molecular substance on the diffusion flux across cell membranes. Advances in Bioscience and Biotechnology
, 169-176. doi: 10.4236/abb.2014.53021
 Berg, H.C. and Purcell, E.M. (1967) A method for separating according to mass a mixture of macromolecules or small particles suspended in a fluid, I. Theory. Proceedings of the National Academy of Sciences USA, 58, 862-869. http://dx.doi.org/10.1073/pnas.58.3.862
 Berg, H.C. and Purcell, E.M. (1977) Physics of chemoreception. Biophysical Journal, 20, 193-219. http://dx.doi.org/10.1016/S0006-3495(77)85544-6
 Iwasa, Y. and Teramoto, E. (1984) Branching-diffusion model of the formation of a population’s distributional pattern. Journal of Mathematical Biology, 19, 109-124. http://dx.doi.org/10.1007/BF00275934
 Berg, H.C. (1993) Random walks in biology. Expanded Edition, Princeton University Press, Princeton.
 Jones, D.S. and Sleeman, B.D. (2000) Differential equations and mathematical biology. Chapman & Hall, London.
 Murray, J.D. (2001) Mathematical biology, vol. I: An introduction. 3rd Edition, Springer, Berlin.
 Caputo, M. and Cametti, C. (2007) Diffusion with memory in two cases of biological interest. Journal of Theoretical Biology, 254, 697-703. http://dx.doi.org/10.1016/j.jtbi.2008.06.021
 Niklas, K.J. and Spatz, H.-C. (2012) Plant physics. The University of Chicago Press, Chicago. http://dx.doi.org/10.7208/chicago/9780226586342.001.0001
 Herman, I.P. (2008) Physics of human body. Springer, Berlin.
 Truskey, G.A., Yuan, F. and Katz, D.F. (2004) Transport phenomena in biological systems. Pearson Prentice Hall, Upper Saddle River.
 Ermentrout, G.B. and Terman, D.H. (2010) Mathematical foundations of neuroscience. Springer, Berlin. http://dx.doi.org/10.1007/978-0-387-87708-2
 Murray, J.D. (2003) Mathematical biology, vol. II: Spatial models and biomedical applications. 3rd Edition, Springer, Berlin.
 Danckwerts, P.V. (1951) Absorption by simultaneous diffusion and chemical reaction into particles of various shapes and into falling drops. Transactions of the faraday society, 47, 1014-1023. http://dx.doi.org/10.1039/tf9514701014
 Crank, J. (1975) The mathematics of diffusion. 2nd Edition. Oxford University Press, Oxford.
 Jackson, M.B. (2006) Molecular and cellular biophysics. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511754869
 Scherer, P.O.J. and Fischer, S.F. (2010) Theoretical molecular biophysics. Springer, Berlin. http://dx.doi.org/10.1007/978-3-540-85610-8
 Leddy, H.A., Haider, M.A. and Guilak, F. (2006) Diffusional anisotropy in collagenous tissues: Fluorescence imaging of continuous point photobleaching. Biophysical Journal, 91, 311-316. http://dx.doi.org/10.1529/biophysj.105.075283