Commentary: New mathematical physics needed for life sciences

Holcman, David; Schuss, Z.

doi:10.1063/pt.3.3036

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Smoluchowski's Limit Of Langevin's Equation1

Introduction1

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2017

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(2 citation statements)

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“…Smoluchowski has shown [3] that as → γ ∞ the trajectories x(t) of the Langevin equation (13) converge in probability to these of the Smoluchowski equation…”

Section: Smoluchowski's Limit Of Langevin's Equationmentioning

confidence: 99%

“…Nowadays, 100 years after Smoluchowski, the field of stochastic modeling has matured into molecular biophysics and physiology and brought with it a plethora of new mathematical problems [13]. A particularly fruitful direction is that of calculating the MFPT of a Smoluchowski trajectory to a small target, the so-called narrow escape problem.…”

Section: Introductionmentioning

confidence: 99%

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100 years after Smoluchowski: stochastic processes in cell biology

Holcman

Schuss

2017

J. Phys. A: Math. Theor.

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100 years after Smoluchowski introduces his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from large number (tens of thousands) of single molecular trajectories or to study the diffusive motion of molecules, proteins or receptors. Stochastic modeling is a new step in large data analysis that serves extracting cell biology concepts. We review here the Smoluchowski's approach to stochastic processes and provide several applications for coarse-graining diffusion, studying polymer models for understanding nuclear organization and finally, we discuss the stochastic jump dynamics of telomeres across cell division and stochastic gene regulation.

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“…Smoluchowski has shown [3] that as → γ ∞ the trajectories x(t) of the Langevin equation (13) converge in probability to these of the Smoluchowski equation…”

Section: Smoluchowski's Limit Of Langevin's Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%