A minimal model of intermittent search in dimension two

We propose and analyse a model of bidimensional search processes, explicitly relying on the widely observed intermittent behaviour of foraging animals, which involves a searcher enjoying minimal orientational and temporal memory skills. We show analytically that, in the case of non-revisitable targets, intermittent strategies can minimize the search time, and therefore constitute real optimal strategies, as opposed to Levy flights strategy which are optimal only in the particular case of revisitable targets. Two representative modes of target detection are presented, and they allow us to determine which characteristics of the optimal strategy are robust and do not depend on the specific characteristics of detection mechanisms. In particular, our study tends to show that the optimal duration of the ballistic phase is a universal feature of bidimensional intermittent search strategies. Last, by comparing the results of our minimal model to systematic search strategies, we show that if temporal and orientational memory skills speed up the search, they do not change the order of magnitude of the search time.

[1]  F Bartumeus,et al.  Optimizing the encounter rate in biological interactions: Lévy versus Brownian strategies. , 2002, Physical review letters.

[2]  S. Redner.  A guide to first-passage processes , 2001 .

[3]  E. B. Huey.  The Psychology And Pedagogy Of Reading , 1908 .

[4]  Germinal Cocho,et al.  Scale-free foraging by primates emerges from their interaction with a complex environment , 2006, Proceedings of the Royal Society B: Biological Sciences.

[5]  O Bénichou,et al.  Optimal search strategies for hidden targets. , 2005, Physical review letters.

[6]  Mathieu Coppey,et al.  Intermittent search strategies: When losing time becomes efficient , 2006 .

[7]  Sidney Redner,et al.  A guide to first-passage processes , 2001 .

[8]  L. Mirny,et al.  Kinetics of protein-DNA interaction: facilitated target location in sequence-dependent potential. , 2004, Biophysical journal.

[9]  G M Viswanathan,et al.  Optimization of random searches on regular lattices. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Noam Agmon,et al.  Residence time distribution of a Brownian particle , 1998 .

[11]  Margaret Floy Washburn,et al.  The Psychology And Pedagogy Of Reading , 1908 .

[12]  P. A. Prince,et al.  Lévy flight search patterns of wandering albatrosses , 1996, Nature.

[13]  Stephen A. Rice.  Diffusion-limited reactions , 1985 .

[14]  M. Moreau,et al.  Averaged residence times of stochastic motions in bounded domains , 2005 .

[15]  KARL PEARSON,et al.  The Problem of the Random Walk , 1905, Nature.

[16]  W. J. Bell.  Searching Behaviour: The Behavioural Ecology of Finding Resources , 1991 .

[17]  J. Marko,et al.  How do site-specific DNA-binding proteins find their targets? , 2004, Nucleic acids research.

[18]  D. Kramer,et al.  The Behavioral Ecology of Intermittent Locomotion1 , 2001 .

[19]  M. Shlesinger,et al.  Beyond Brownian motion , 1996 .

[20]  O Bénichou,et al.  Two-dimensional intermittent search processes: An alternative to Lévy flight strategies. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Ralf Metzler,et al.  Target search of N sliding proteins on a DNA. , 2005, Biophysical journal.

[22]  S. Blanco,et al.  An invariance property of diffusive random walks , 2019, 1902.07080.

[23]  Marcos C. Santos,et al.  Dynamical robustness of Lévy search strategies. , 2003, Physical review letters.

[24]  Ralf Metzler,et al.  Optimal target search on a fast-folding polymer chain with volume exchange. , 2005, Physical review letters.

[25]  A. Mazzolo,et al.  Properties of diffusive random walks in bounded domains , 2004 .

[26]  H. Stanley,et al.  Optimizing the success of random searches , 1999, Nature.

[27]  O. Bénichou,et al.  Kinetics of target site localization of a protein on DNA: a stochastic approach. , 2004, Biophysical journal.

[28]  Huan-Xiang Zhou,et al.  Enhancement of association rates by nonspecific binding to DNA and cell membranes. , 2004, Physical review letters.