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The Scientific World Journal
Volume 2014, Article ID 150826, 8 pages
Research Article

Diagrammatic Analysis of Nonhomogeneous Diffusion

Sección Biofísica, Facultad de Ciencias, Universidad de la República, Iguá Esq. Mataojo, 11400 Montevideo, Uruguay

Received 5 November 2014; Accepted 13 December 2014; Published 31 December 2014

Academic Editor: Boris Martinac

Copyright © 2014 Julio A. Hernández. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By virtue of its complexity, realistic approaches to describe diffusion in cellular media require the employment of computational methods. Among others, this type of studies has shown that the apparent diffusion coefficient of a macromolecular solute through a cytoplasmic-like medium exhibits a power-law dependence with the excluded volume. Power laws are ubiquitous findings in diverse systems, such as metabolic processes, population dynamics, and communication networks, and have been the object of many interpretative formal approaches. This study introduces a diagrammatic algorithm, inspired in previous ones employed to analyze multicyclic chemical systems, to derive expressions for nonhomogeneous diffusion coefficients and to study the effects of volume exclusion. A most noteworthy result of this work is that midsize diagrams of nonhomogeneous diffusion are already able to exhibit an approximate power-law dependence of the diffusion coefficient with the excluded volume. The employment of the diagrammatic method for the analysis of simple situations may thus prove useful to interpret some properties of larger network systems.