ISSN:
1522-9602
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Abstract The concentration of a diffusible substanceA(x, t) in a semi-infinite geometry is studied for the set of reversible reactionsA+B i ⇆C i ;i=1...n, whereB i andC i are assumed to be associated with non-diffusible biological structures. Assuming chemical equilibrium prevails throughout for each reaction, it is shown that a single uncoupled partial differential equation is sufficient to specifyA(x, t) and indirectlyB i (x, t) andC i (x, t) as well: $$\left[ {1 + \sum\limits_i {\frac{{K_i \beta _i }}{{\left( {1 + K_i A} \right)^2 }}} } \right]\frac{{\partial A}}{{\partial t}} = D_A \frac{{\partial ^2 A}}{{\partial x^2 }}$$ whereK i is the chemical equilibrium constant of theith reaction, β1 is concentration of binding sites of theith species (i.e.B i+C i) andD A is the usual diffusion constant forA. Numerical solutions for boundary conditions amenable to the Boltzman transformation are presented and the range of parameters established over which the uniqueness and convergence of the solutions can be proven.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02476875
Permalink