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要旨:
The first half of this review describes the development in mathematical
models of Brownian motion after Einsteins and Smoluchowskis seminal
papers and current applications to optical tweezers. This instrument of
choice among single-molecule biophysicists is also an instrument of such
precision that it requires an understanding of Brownian motion beyond
Einsteins and Smoluchowskis for its calibration, and can measure effects
not present in their theories. This is illustrated with some applications,
current and potential. It is also shown how addition of a controlled forced
motion on the nano-scale of the thermal motion of the tweezed object can
improve the calibration of the instrument in general, and make calibration
possible also in complex surroundings. The second half of the present re-
view, starting with Sect. 9, describes the co-evolution of biological motility
models with models of Brownian motion, including recent results for how to
derive cell-type-specific motility models from experimental cell trajectories.
