Localization Transitions in Biological Media 
 David R. Nelson 
Lyman Laboratory, Harvard University
Cambridge, Massachusetts  02138
nelson@cmts.harvard.edu

 

 Recent developments in the dynamics and statistical mechanics of biological systems are explored.  The first example concerns the time evolution of spatial fluctuations in inhomogeneous biological systems, e.g., growing bacteria with both diffusion and convection.  Spatial environmental heterogeneities, such a random distribution of nutrients or sunlight, are modelled by quenched disorder in the growth rate.  We find a transition separating localized and extended eigenfunctions of the linearized growth operator at a critical convection threshold. In the limit of high convection velocity, the linearized growth problem exhibits singular scaling with superdiffusive spreading transverse to the flow direction.  We also discuss related results for biased random walks of detachable motor proteins and unzipping of DNA duplexes in the presence of quenched random disorder.

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