Different parts of this project involves collaborative work with NIH scientists, in which sophisticated mathematical tools or an acquaintance with theoretical methods in the physical sciences are required for the research. Mainly these methods require an intimate acquaintance with techniques developed in statistical physics. To rationalize data on the partioning of PEG-3400 in the alpha-hemolysin channel as a function of function of polymer concentration we have developed a theory of polymer partitioning in cylindrical pores in non-ideal polymer solutions. The theory explains the highly nonlinear increase of partitioning with polymer concentration which has been observed in experiments. We discovered a very general property of particle dynamics in channels and similar systems, namely that the distributions of times spent in the channel by particles traversing the channel in opposite directions are always identical in spite of the fact that the translocation probabilities may be quite different. We developed an approach to extract information related to molecular transitions (e.g., protein folding, ligand dissociation, DNA unzipping) from single-molecule force experiments based on Kramers'theory of diffusive barrier crossing. The theory has been applied to experimental data on nanopore unzipping of individual DNA hairpin molecules. We have obtained simple analytical expressions for the time-dependent rate coefficients of diffusion-influenced reactions in the presence of spherically symmetric potentials. These should prove useful in the analysis of experimental data for essentially irreversible reactions such as fluorescence quenching.

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Krueger, Frank; Spampinato, Maria Vittoria; Pardini, Matteo et al. (2008) Integral calculus problem solving: an fMRI investigation. Neuroreport 19:1095-9