Diffusion model, biological

Box models and box-diffusion models have few degrees of freedom and they must describe physical, chemical, and biological processes very crudely. They are based on empirical relations rather than on first principles. Nevertheless, the simple models have been useful for obtaining some general features of the carbon cycle and retain some important roles in carbon cycle research (Craig and Holmen, 1995 Craig et al, 1997 Siegenthaler and joos, 1992). 

Meanwhile, computational methods have reached a level of sophistication that makes them an important complement to experimental work. These methods take into account the inhomogeneities of the bilayer, and present molecular details contrary to the continuum models like the classical solubility-diffusion model. The first solutes for which permeation through (polymeric) membranes was described using MD simulations were small molecules like methane and helium [128]. Soon after this, the passage of biologically more interesting molecules like water and protons [129,130] and sodium and chloride ions [131] over lipid membranes was considered. We will come back to this later in this section. 

Diamond KR, Farrell TJ, Patterson MS. Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence. Physics in Medicine and Biology 2003,48, 4135 1149. 

The radiolysis of aqueous solutions has a clearer picture compared to other liquids. The characterization of ion induced phenomena in aqueous solutions has been a subject for theoretical approaches because the prediction is necessary from the calculation, for example, DNA damages in biological system. In place of the kinetic diffusion model, Monte Carlo methods have been also applied to ion beam radiolysis and recent status was reported [62]. 

The low molecular weight of NO may allow rapid movement in aqueous environments. Molecules larger than NO have much lower diffusion coefficients and rates of spread. Models to describe the kinetic and concentration profiles for NO have been developed, based on diffusion models used to describe heat conduction in solids. These models show NO concentrations to be a function of the rate of formation, diffusion coefficient, distance from the source and time. Close to a production source, perhaps within a radius of 10/rm, concentrations reach a steady state within a few hundred ms of release. This is an order of magnitude faster than the measured biological half-life of NO, so that metabolism of NO in vivo should not significantly affect these concentration gradients... 

Key words Mathematical model, Chemotaxis, Reaction-diffusion, Systems biology, Virtual cell... 

Complex Systems are systems that comprise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous formation of distinctive temporal, spatial or functional stmctures. Models of such systems can be successfully mapped onto quite diverse real-life situations like the climate, the coherent emission of light from lasers, chemical reaction-diffusion systems, biological cellular networks, the dynamics of stock markets and of the internet, earthquake statistics and prediction, freeway traffic, the human brain, or the formation of opinions in social systems, to name just some of the popular applications. 

Kondo, S., Miura, T. (2010). Reaction-diffusion model as a framework for understanding biological pattern formation. Science, 329,1616-1620. 

Lyons, M.J., Harrison, L.G., Lakowski, B.C., Lacalli, T.C (1990). Reaction diffusion modelling of biological pattern formation application to the embryogenesis of Drosophila melanogaster. Canadian Journal of Physics, Vol.68, pp. 772-777. 

Nagata, W., Harrison, L.G., Wehner, S. (2003). Reaction-diffusion models of growing plant tips bifurcations on hemispheres. Bulletin of Mathematical Biology, Vol.65, pp. 571-607. 

ESR microscopy (at X-band) has been applied to a variety of materials including in situ studies of the oxidation of coals defects in diamonds radio-metric dosimeters polymer swelling and to the diffusion of oxygen in model biological systems. The resolution of ESR imaging depends on the field gradient and line width, and the best resolution to date from an X-band imager is 1 pm. 

Hydrated bilayers containing one or more lipid components are commonly employed as models for biological membranes. These model systems exhibit a multiplicity of structural phases that are not observed in biological membranes. In the state that is analogous to fluid biological membranes, the liquid crystal or La bilayer phase present above the main bilayer phase transition temperature, Ta, the lipid hydrocarbon chains are conforma-tionally disordered and fluid ( melted ), and the lipids diffuse in the plane of the bilayer. At temperatures well below Ta, hydrated bilayers exist in the gel, or Lp, state in which the mostly all-trans chains are collectively tilted and pack in a regular two-dimensional... 

---