This review examines intermittent target search strategies, which combine phases of slow motion, allowing the searcher to detect the target, and phases of fast motion during which targets cannot be detected. We first show that intermittent search strategies are actually widely observed at various scales. At the macroscopic scale, this is for example the case of animals looking for food ; at the microscopic scale, intermittent transport patterns are involved in reaction pathway of DNA binding proteins as well as in intracellular transport. Second, we introduce generic stochastic models, which show that intermittent strategies are efficient strategies, which enable to minimize the search time. This suggests that the intrinsic efficiency of intermittent search strategies could justify their frequent observation in nature. Last, beyond these modeling aspects, we propose that intermittent strategies could be used also in a broader context to design and accelerate search processes.

Vaccine-induced high-avidity IgA can protect against bacterial enteropathogens by directly neutralizing virulence factors or by poorly defined mechanisms that physically impede bacterial interactions with the gut tissues ('immune exclusion'). IgA-mediated cross-linking clumps bacteria in the gut lumen and is critical for protection against infection by non-typhoidal Salmonella enterica subspecies enterica serovar Typhimurium (S. Typhimurium). However, classical agglutination, which was thought to drive this process, is efficient only at high pathogen densities (≥10 non-motile bacteria per gram). In typical infections, much lower densities (10-10 colony-forming units per gram) of rapidly dividing bacteria are present in the gut lumen. Here we show that a different physical process drives formation of clumps in vivo: IgA-mediated cross-linking enchains daughter cells, preventing their separation after division, and clumping is therefore dependent on growth. Enchained growth is effective at all realistic pathogen densities, and accelerates pathogen clearance from the gut lumen. Furthermore, IgA enchains plasmid-donor and -recipient clones into separate clumps, impeding conjugative plasmid transfer in vivo. Enchained growth is therefore a mechanism by which IgA can disarm and clear potentially invasive species from the intestinal lumen without requiring high pathogen densities, inflammation or bacterial killing. Furthermore, our results reveal an untapped potential for oral vaccines in combating the spread of antimicrobial resistance.

The restriction endonuclease EcoRV can rapidly locate a short recognition site within long non-cognate DNA using ‘facilitated diffusion’. This process has long been attributed to a sliding mechanism, in which the enzyme first binds to the DNA via nonspecific interaction and then moves along the DNA by 1D diffusion. Recent studies, however, provided evidence that 3D translocations (hopping/jumping) also help EcoRV to locate its target site. Here we report the first direct observation of sliding and jumping of individual EcoRV molecules along nonspecific DNA. Using fluorescence microscopy, we could distinguish between a slow 1D diffusion of the enzyme and a fast translocation mechanism that was demonstrated to stem from 3D jumps. Salt effects on both sliding and jumping were investigated, and we developed numerical simulations to account for both the jump frequency and the jump length distribution. We deduced from our study the 1D diffusion coefficient of EcoRV, and we estimated the number of jumps occurring during an interaction event with nonspecific DNA. Our results substantiate that sliding alternates with hopping/jumping during the facilitated diffusion of EcoRV and, furthermore, set up a framework for the investigation of target site location by other DNA-binding proteins.

The cell cytoskeleton is a striking example of an 'active' medium driven out-of-equilibrium by ATP hydrolysis 1 . Such activity has been shown to have a spectacular impact on the mechanical and rheological properties of the cellular medium 2-10 , as well as on its transport properties 11-14 : a generic tracer particle freely diffuses as in a standard equilibrium medium, but also intermittently binds with random interaction times to motor proteins, which perform active ballistic excursions along cytoskeletal filaments. Here, we propose an analytical model of transport-limited reactions in active media, and show quantitatively how active transport can enhance reactivity for large enough tracers such as vesicles. We derive analytically the average interaction time with motor proteins that optimizes the reaction rate, and reveal remarkable universal features of the optimal configuration. We discuss why active transport may be beneficial in various biological examples: cell cytoskeleton, membranes and lamellipodia, and tubular structures such as axons 1 . Various motor proteins such as kinesins or myosins are able to convert the chemical fuel provided by ATP into mechanical work by interacting with the semiflexible oriented filaments (mainly F-actin and microtubules) of the cytoskeleton 1 . As many molecules or larger cellular organelles such as vesicles, lysosomes or mitochondria, hereafter referred to as tracer particles, can randomly bind and unbind to motors, the overall transport of a tracer in the cell can be described as alternating phases of standard diffusive transport and phases of active directed transport powered by motor proteins 1,15,16 . Active transport in cells has been extensively studied both experimentally, for instance by single-particle tracking methods 11,12 , and theoretically by evaluating the mean displacement of a tracer 13,17 , or stationary concentration profiles 14 . On the other hand, most cell functions are regulated by coordinated chemical reactions that involve low concentrations of reactants (such as ribosomes or vesicles carrying targeted proteins), and are therefore limited by transport. However, up to now a general quantitative analysis of the impact of active transport on reaction kinetics in cells, and more generally in generic active media, is still missing, even though a few specific examples have been tackled 18 . Here, we propose an analytical model that enables us to determine for the first time the kinetic constant of transportlimited reactions in active media.The model relies on the idea of intermittent dynamics introduced in the context of search processes [19][20][21][22][23][24][25][26][27] . We consider a tracer particle evolving in a d-dimensional space (in practice d = 1, 2, 3) that exhibits thermal diffusion phases of diffusion coefficient D (denoted phases 1), randomly interrupted by ballistic excursions bound to motors (referred to as phases 2) of constant velocity v and direction pointing in the solid angle ω v (Fig. 1a). The distribution of the filaments' orie...

Lévy flights are known to be optimal search strategies in the particular case of revisitable targets. In the relevant situation of non revisitable targets, we propose an alternative model of bidimensional search processes, which explicitly relies on the widely observed intermittent behavior of foraging animals. We show analytically that intermittent strategies can minimize the search time, and therefore do constitute real optimal strategies. We study two representative modes of target detection, and determine which features of the search time are robust and do not depend on the specific characteristics of detection mechanisms. In particular, both modes lead to a global minimum of the search time as a function of the typical times spent in each state, for the same optimal duration of the ballistic phase. This last quantity could be a universal feature of bidimensional intermittent search strategies.

We present an exact calculation of the mean first-passage time to a small target on the surface of a 2D or 3D spherical domain, for a molecule performing surface-mediated diffusion. This minimal model of interfacial reactions, which explicitly takes into account the combination of surface and bulk diffusion, shows the importance of correlations induced by the coupling of the switching dynamics to the geometry of the confinement, ignored so far. Interestingly, our results show that, in the context of interfacial systems in confinement, the reaction time can be minimized as a function of the desorption rate from the surface, which puts forward a general mechanism of enhancement and regulation of chemical and biological reactivity. PACS numbers:Among reactions limited by transport, interfacial reactions, for which molecules react on target sites located on the surface of the confining domain [1], play an important role in situations as various as heterogeneous catalysis [2], reactions in porous media or biochemical reactions on DNA [3] and in vesicular systems [4][5][6]. Besides being a problem of great practical importance, the modeling of such systems raises two types of theoretical issues: (i) to determine the impact of geometrical parameters of the confining domain, such as the volume, on reaction kinetics, and (ii) to account for the reactive trajectories which combine bulk and surface-mediated diffusion phases due to the affinity of the molecules for the surface (see fig.1).The point (i) has been studied in the case of a perfectly reflecting surface [6-10] and a universal scaling with the confining volume was found for the mean first-passage time (MFPT) to a reactive target [11,12]. On the other hand, reactive paths of point (ii) can be described as trajectories involving two states, one adsorbed on the surface and one desorbed in the bulk. Such two-state paths have been studied in the broader context of intermittent search strategies under the hypothesis that the times spent in each state are controlled by an internal clock independent of any geometrical parameter [13][14][15]. In most cases, the sojourn times in each state have been assumed to be exponentially distributed [14], with the notable exception of Levy [16] and deterministic laws [17,18].However, in the case of interfacial reactions in confinement, the time spent in a bulk excursion is controlled by the statistics of return to the surface and therefore by the geometry of the confining domain [19][20][21][22]. Hence, this return time is not an external parameter but is generated by the very dynamics of the diffusing molecule in confinement. As a result, the usual methods to calculate mean search times for intermittent processes only provide a mean-field (MF) approximation of the reaction time which completely ignores the correlations induced by the coupling of the switching dynamics to the geometry of the confinement (see [14] for review, and more recently [23]).Here we calculate exactly in the representative example of a spherical confining domain...

Bacteriophage transfer (lysogenic conversion) promotes bacterial virulence evolution. There is limited understanding of the factors that determine lysogenic conversion dynamics within infected hosts. A murine Typhimurium (Tm) diarrhea model was used to study the transfer of SopEΦ, a prophage from Tm SL1344, toTm ATCC14028S. Gut inflammation and enteric disease triggered >55% lysogenic conversion of ATCC14028S within 3 days. Without inflammation, SopEΦ transfer was reduced by up to 10-fold. This was because inflammation (e.g., reactive oxygen species, reactive nitrogen species, hypochlorite) triggers the bacterial SOS response, boosts expression of the phage antirepressor Tum, and thereby promotes free phage production and subsequent transfer. Mucosal vaccination prevented a dense intestinal Tm population from inducing inflammation and consequently abolished SopEΦ transfer. Vaccination may be a general strategy for blocking pathogen evolution that requires disease-driven transfer of temperate bacteriophages.

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.