Redundancy, extreme statistics and geometrical optics of Brownian motion: Comment on "Redundancy principle and the role of extreme statistics in molecular and cellular biology" by Z. Schuss et al.

The authors of [1] promote the idea that many diffusion-limited reaction processes in molecular and cellular biology are determined by extreme effects. That is, the reaction kinetics is controlled not by the typical time for a reactant to reach a reaction site, but rather, by the time for the first of many particles to arrive. If the number of reactants is very large, there can be a profound difference between the typical arrival time and the first arrival time. As argued in [1], this difference has striking implications for the kinetics of a wide variety of diffusion-limited reactions. To appreciate the origin of these extreme effects, it is helpful to start with a simple example. Consider the average time for a diffusing particle in one dimension, initially at L > 0, to first reach a target that is located at the origin—the first-passage time. As is well known, the particle is sure to eventually reach the target, but the average first-passage time is infinite [2,3]. This dichotomy is one of reason why diffusion processes are so fascinating, both from the theoretical and the practical perspective. Physically, this divergent first-passage time stems from the contribution of trajectories that wander arbitrarily far from the target before eventually reaching it. Mathematically, the divergence arises because the distribution of first-passage times,

• Publication year

  2019

• Venue

  Physics of Life Reviews

• Publication date

  2019-03-01

• Fields of study

  Biology, Medicine, Physics

• Identifiers
  DOI 10.1016/j.plrev.2019.01.020PMID 30718199
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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