The subdiffusive targeting problem

Journal of Physical Chemistry B

Volumn 112, Issue 14, 2008, Pages 4283-4289

  Eaves, Joel D ^a   Reichman, David R ^a  

^a Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LIVING CELLS; MEAN-SQUARED DISPLACEMENT (MSD);

ENZYME;

ARTICLE; BIOCHEMISTRY; CHEMICAL MODEL; DIFFUSION; KINETICS; MATHEMATICS; METABOLISM; MOLECULAR EVOLUTION;

BIOCHEMISTRY; DIFFUSION; ENZYMES; EVOLUTION, MOLECULAR; KINETICS; MATHEMATICS; MODELS, CHEMICAL;

EID: 46449100191     PISSN: 15206106     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp0749017     Document Type: Article

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23. Assuming, of course, that the second cumulant of the jump length distribution is also finite. There is currently no experimental evidence to suggest otherwise.
24. 22 Although our master equations are almost identical, our method of analysis leads to different conclusions. In particular, our eq 27 coincides with their eq 8 only if we allow P̃(ε, s) to be non-analytic, which would violate consistency. More specifically, both the boundary condition and subdiffusion equation are explicit asymptotic expressions for long time scales and large length scales and must be independent of the lattice spacing. The physical requirement that we do not allow random walkers to start on the origin arises naturally from the analysis of eq 24. However, the boundary conditions in eq 27, ref 22, and ref 14 are equivalent when walkers do not begin at the origin. Although our approach allows for the derivation of corrections to the Fokker-Planck equation from fast spatial fluctuations, as in ref 16, such corrections have little bearing on asymptotically slow dynamics. Indeed, the continuum limit is not useful if there are rapid spatial or temporal fluctuations. It is not presently clear how the differences in the boundary conditions would alter the picture of targeting in biological problems in the terms of weak ergodicity breaking, as presented in ref 22. This is a topic worthy of further investigation.