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Cell movement has essential functions in development, immunity, and cancer. Various cell migration patterns have been reported, but no general rule has emerged so far. Here, we show on the basis of experimental data in vitro and in vivo that cell persistence, which quantifies the straightness of trajectories, is robustly coupled to cell migration speed. We suggest that this universal coupling constitutes a generic law of cell migration, which originates in the advection of polarity cues by an actin cytoskeleton undergoing flows at the cellular scale. Our analysis relies on a theoretical model that we validate by measuring the persistence of cells upon modulation of actin flow speeds and upon optogenetic manipulation of the binding of an actin regulator to actin filaments. Beyond the quantitative prediction of the coupling, the model yields a generic phase diagram of cellular trajectories, which recapitulates the full range of observed migration patterns., (Copyright © 2015 Elsevier Inc. All rights reserved.)

In somatic cells, the position of the cell centroid is dictated by the centrosome. The centrosome is instrumental in nucleus positioning, the two structures being physically connected. Mouse oocytes have no centrosomes, yet harbour centrally located nuclei. We demonstrate how oocytes define their geometric centre in the absence of centrosomes. Using live imaging of oocytes, knockout for the formin 2 actin nucleator, with off-centred nuclei, together with optical trapping and modelling, we discover an unprecedented mode of nucleus positioning. We document how active diffusion of actin-coated vesicles, driven by myosin Vb, generates a pressure gradient and a propulsion force sufficient to move the oocyte nucleus. It promotes fluidization of the cytoplasm, contributing to nucleus directional movement towards the centre. Our results highlight the potential of active diffusion, a prominent source of intracellular transport, able to move large organelles such as nuclei, providing in vivo evidence of its biological function.

3D amoeboid cell migration is central to many developmental and disease-related processes such as cancer metastasis. Here, we identify a unique prototypic amoeboid cell migration mode in early zebrafish embryos, termed stable-bleb migration. Stable-bleb cells display an invariant polarized balloon-like shape with exceptional migration speed and persistence. Progenitor cells can be reversibly transformed into stable-bleb cells irrespective of their primary fate and motile characteristics by increasing myosin II activity through biochemical or mechanical stimuli. Using a combination of theory and experiments, we show that, in stable-bleb cells, cortical contractility fluctuations trigger a stochastic switch into amoeboid motility, and a positive feedback between cortical flows and gradients in contractility maintains stable-bleb cell polarization. We further show that rearward cortical flows drive stable-bleb cell migration in various adhesive and non-adhesive environments, unraveling a highly versatile amoeboid migration phenotype., (Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.)

The mesenchymal-amoeboid transition (MAT) was proposed as a mechanism for cancer cells to adapt their migration mode to their environment. While the molecular pathways involved in this transition are well documented, the role of the microenvironment in the MAT is still poorly understood. Here, we investigated how confinement and adhesion affect this transition. We report that, in the absence of focal adhesions and under conditions of confinement, mesenchymal cells can spontaneously switch to a fast amoeboid migration phenotype. We identified two main types of fast migration--one involving a local protrusion and a second involving a myosin-II-dependent mechanical instability of the cell cortex that leads to a global cortical flow. Interestingly, transformed cells are more prone to adopt this fast migration mode. Finally, we propose a generic model that explains migration transitions and predicts a phase diagram of migration phenotypes based on three main control parameters: confinement, adhesion, and contractility., (Copyright © 2015 Elsevier Inc. All rights reserved.)

Cell mechanics control the outcome of cell division. In mitosis, external forces applied on a stiff cortex direct spindle orientation and morphogenesis. During oocyte meiosis on the contrary, spindle positioning depends on cortex softening. How changes in cortical organization induce cortex softening has not yet been addressed. Furthermore, the range of tension that allows spindle migration remains unknown. Here, using artificial manipulation of mouse oocyte cortex as well as theoretical modelling, we show that cortical tension has to be tightly regulated to allow off-center spindle positioning: a too low or too high cortical tension both lead to unsuccessful spindle migration. We demonstrate that the decrease in cortical tension required for spindle positioning is fine-tuned by a branched F-actin network that triggers the delocalization of myosin-II from the cortex, which sheds new light on the interplay between actin network architecture and cortex tension.

Many physiological and pathological processes involve directed cell motion. In general, migrating cells are represented with a polarized morphology with extending and retracting protrusions at the leading edge. However, cell motion is a more complex phenomenon. Cells show heterogeneous morphologies and high protrusive dynamics is not always related to cell shape. This prevents the quantitative prediction of cell motion and the identification of cellular mechanisms setting directionality. Here we discuss the importance of protrusion fluctuations in directed cell motion. We show how their spatiotemporal distribution and dynamics determine the fluctuations and directions of cell motion for NIH3T3 fibroblasts plated on micro-patterned adhesive ratchets. (1) We introduce efficient protrusions and direction index which capture short-term cell motility over hours: these new read-outs allow the prediction of parameters characteristic for the long-term motion of cells over days. The results may have important implications for the study of biological phenomena where directed cell migration is involved, in morphogenesis and in cancer.

Podosomes are mechanosensitive adhesion cell structures that are capable of applying protrusive forces onto the extracellular environment. We have recently developed a method dedicated to the evaluation of the nanoscale forces that podosomes generate to protrude into the extracellular matrix. It consists in measuring by atomic force microscopy (AFM) the nanometer deformations produced by macrophages on a compliant Formvar membrane and has been called protrusion force microscopy (PFM). Here we perform time-lapse PFM experiments and investigate spatial correlations of force dynamics between podosome pairs. We use an automated procedure based on finite element simulations that extends the analysis of PFM experimental data to take into account podosome architecture and organization. We show that protrusion force varies in a synchronous manner for podosome first neighbors, a result that correlates with phase synchrony of core F-actin temporal oscillations. This dynamic spatial coordination between podosomes suggests a short-range interaction that regulates their mechanical activity.

We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence on the applied force, and show quantitatively that such negative differential mobility (NDM), observed in various physical contexts, is controlled by both the density and diffusion time scale of the obstacles. Our study unifies recent numerical and analytical results obtained in specific regimes, and makes it possible to determine analytically the region of the full parameter space where NDM occurs. These results suggest that NDM could be a generic feature of biased (or active) transport in crowded environments.

Podosomes are adhesion structures formed in monocyte-derived cells. They are F-actin-rich columns perpendicular to the substrate surrounded by a ring of integrins. Here, to measure podosome protrusive forces, we designed an innovative experimental setup named protrusion force microscopy (PFM), which consists in measuring by atomic force microscopy the deformation induced by living cells onto a compliant Formvar sheet. By quantifying the heights of protrusions made by podosomes onto Formvar sheets, we estimate that a single podosome generates a protrusion force that increases with the stiffness of the substratum, which is a hallmark of mechanosensing activity. We show that the protrusive force generated at podosomes oscillates with a constant period and requires combined actomyosin contraction and actin polymerization. Finally, we elaborate a model to explain the mechanical and oscillatory activities of podosomes. Thus, PFM shows that podosomes are mechanosensing cell structures exerting a protrusive force.

We consider the dynamics and the cyclization kinetics of Gaussian semiflexible chains, in which the interaction potential tends to align successive bonds. We provide asymptotic expressions for the cyclization time, for the eigenvalues and eigenfunctions, and for the mean square displacement at all time and length scales, with explicit dependence on the capture radius, on the positions of the reactive monomers in the chain, and on the finite number of beads. For the cyclization kinetics, we take into account non-Markovian effects by calculating the distribution of reactive conformations of the polymer, which are not taken into account in the classical Wilemski-Fixman theory. Comparison with numerical simulations confirms the accuracy of this non-Markovian theory.

Cell migration is a crucial event during development and in disease. Mechanical constraints and chemical gradients can contribute to the establishment of cell direction, but their respective roles remain poorly understood. Using a microfabricated topographical ratchet, we show that the nucleus dictates the direction of cell movement through mechanical guidance by its environment. We demonstrate that this direction can be tuned by combining the topographical ratchet with a biochemical gradient of fibronectin adhesion. We report competition and cooperation between the two external cues. We also quantitatively compare the measurements associated with the trajectory of a model that treats cells as fluctuating particles trapped in a periodic asymmetric potential. We show that the cell nucleus contributes to the strength of the trap, whereas cell protrusions guided by the adhesive gradients add a constant tunable bias to the direction of cell motion., (Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

We consider a discrete model in which a tracer performs a random walk biased by an external force, in a dense bath of particles performing symmetric random walks constrained by hard-core interactions. We reveal the emergence of a striking velocity anomaly in confined geometries: in quasi-1D systems such as stripes or capillaries, the velocity of the tracer displays a long-lived plateau before ultimately dropping to a lower value. We develop an analytical solution that quantitatively accounts for this intriguing behavior. Our analysis suggests that such a velocity anomaly could be a generic feature of driven dynamics in quasi-1D crowded systems.

Semiflexible polymer rings whose bonds obey both angular and dihedral restrictions [M. Dolgushev and A. Blumen, J. Chem. Phys. 138, 204902 (2013)], are treated under exact closure constraints. This allows us to obtain semianalytic results for their dynamics, based on sets of Langevin equations. The dihedral restrictions clearly manifest themselves in the behavior of the mean-square monomer displacement. The determination of the equilibrium ring conformations shows that the dihedral constraints influence the ring curvature, leading to compact folded structures. The method for imposing such constraints in Gaussian systems is very general and it allows to account for heterogeneous (site-dependent) restrictions. We show it by considering rings in which one site differs from the others.

Many physiological phenomena involve directional cell migration. It is usually attributed to chemical gradients in vivo. Recently, other cues have been shown to guide cells in vitro, including stiffness/adhesion gradients or micropatterned adhesive motifs. However, the cellular mechanism leading to these biased migrations remains unknown, and, often, even the direction of motion is unpredictable. In this study, we show the key role of fluctuating protrusions on ratchet-like structures in driving NIH3T3 cell migration. We identified the concept of efficient protrusion and an associated direction index. Our analysis of the protrusion statistics facilitated the quantitative prediction of cell trajectories in all investigated conditions. We varied the external cues by changing the adhesive patterns. We also modified the internal cues using drug treatments, which modified the protrusion activity. Stochasticity affects the short- and long-term steps. We developed a theoretical model showing that an asymmetry in the protrusion fluctuations is sufficient for predicting all measures associated with the long-term motion, which can be described as a biased persistent random walk., (Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

We derive exact expressions of the mean first-passage time to a bulk target for a random searcher that performs boundary-mediated diffusion in a circular domain. Although nonintuitive for bulk targets, it is found that boundary excursions, if fast enough, can minimize the search time. A scaling analysis generalizes these findings to domains of arbitrary shapes and underlines their robustness. Overall, these results provide a generic mechanism of optimization of search kinetics in interfacial systems, which could have important implications in chemical physics. In the context of animal behavior sciences, it shows that following the boundaries of a domain can accelerate a search process, and therefore suggests that thigmotactism could be a kinetically efficient behavior.

Gene regulation relies on transcription factors (TFs) exploring the nucleus searching their targets. So far, most studies have focused on how fast TFs diffuse, underestimating the role of nuclear architecture. We implemented a single-molecule tracking assay to determine TFs dynamics. We found that c-Myc is a global explorer of the nucleus. In contrast, the positive transcription elongation factor P-TEFb is a local explorer that oversamples its environment. Consequently, each c-Myc molecule is equally available for all nuclear sites while P-TEFb reaches its targets in a position-dependent manner. Our observations are consistent with a model in which the exploration geometry of TFs is restrained by their interactions with nuclear structures and not by exclusion. The geometry-controlled kinetics of TFs target-search illustrates the influence of nuclear architecture on gene regulation, and has strong implications on how proteins react in the nucleus and how their function can be regulated in space and time.

The cover time is defined as the time needed for a random walker to visit every site of a confined domain. Here, we focus on persistent random walks, which provide a minimal model of random walks with short-range memory. We derive the exact expression of the mean cover time of a one-dimensional lattice by such a persistent random walk, both for periodic and reflecting boundary conditions.

We present a continuum level analytical model of a droplet of active contractile fluid consisting of filaments and motors. We calculate the steady state flows that result from a splayed polarisation of the filaments. We account for interaction with the external medium by imposing a viscous friction at the fixed droplet boundary. We then show that the droplet has non-zero force dipole and quadrupole moments, the latter of which is essential for self-propelled motion of the droplet at low Reynolds' number. Therefore, this calculation describes a simple mechanism for the motility of a droplet of active contractile fluid embedded in a three-dimensional environment, which is relevant to cell migration in confinement (for example, embedded within a gel or tissue). Our analytical results predict how the system depends on various parameters such as the effective friction coefficient, the phenomenological activity parameter and the splay of the imposed polarisation.

We consider the mean territory covered by a particle that performs surface-mediated diffusion inside a spherical confining domain (in two and three dimensions) before exit through an opening on the surface. This quantity can be expressed in terms of the splitting probability between two targets on the surface. We derive a general formula that relates this splitting probability to the mean first passage time to a single target that has been recently calculated for such a surface-mediated diffusion process. This formula is exact for pointlike targets and is shown to be accurate for extended targets. The mean covered territory is then found and analyzed for an arbitrary extension of the exit region in both two- and three-dimensional spherical domains.

Recent molecular dynamics simulations of glass-forming liquids revealed superdiffusive fluctuations associated with the position of a tracer particle (TP) driven by an external force. Such an anomalous response, whose mechanism remains elusive, has been observed up to now only in systems close to their glass transition, suggesting that this could be one of its hallmarks. Here, we show that the presence of superdiffusion is in actual fact much more general, provided that the system is crowded and geometrically confined. We present and solve analytically a minimal model consisting of a driven TP in a dense, crowded medium in which the motion of particles is mediated by the diffusion of packing defects, called vacancies. For such nonglass-forming systems, our analysis predicts a long-lived superdiffusion which ultimately crosses over to giant diffusive behavior. We find that this trait is present in confined geometries, for example long capillaries and stripes, and emerges as a universal response of crowded environments to an external force. These findings are confirmed by numerical simulations of systems as varied as lattice gases, dense liquids, and granular fluids.

In the absence of environmental cues, a migrating cell performs an isotropic random motion. Recently, the breaking of this isotropy has been observed when cells move in the presence of asymmetric adhesive patterns. However, up to now the mechanisms at work to direct cell migration in such environments remain unknown. Here, we show that a nonadhesive surface with asymmetric microgeometry consisting of dense arrays of tilted micropillars can direct cell motion. Our analysis reveals that most features of cell trajectories, including the bias, can be reproduced by a simple model of active Brownian particle in a ratchet potential, which we suggest originates from a generic elastic interaction of the cell body with the environment. The observed guiding effect, independent of adhesion, is therefore robust and could be used to direct cell migration both in vitro and in vivo.

Dendritic cells (DCs) constitute a complex cell population that resides in both peripheral tissues and lymphoid organs. Their major function in tissues is to patrol their environment in search of danger-associated antigens to transport to lymph nodes and present to T lymphocytes. This process constitutes the first step of the adaptive immune response and relies on specific DC properties, including a high endocytic capacity as well as efficient motility in confined three-dimensional environments. Although cell motility has been widely studied, little is known on how the geometric characteristics of the environment influence DC migration and function. In this review, we give an overview of the basic physical principles and molecular mechanisms that control DC migration under confinement and discuss how such mechanisms impact the environment-patrolling capacity of DCs., (© 2013 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.)

Animal cells actively generate contractile stress in the actin cortex, a thin actin network beneath the cell membrane, to facilitate shape changes during processes like cytokinesis and motility. On the microscopic scale, this stress is generated by myosin molecular motors, which bind to actin cytoskeletal filaments and use chemical energy to exert pulling forces. To decipher the physical basis for the regulation of cell shape changes, here, we use a cell-like system with a cortex anchored to the outside or inside of a liposome membrane. This system enables us to dissect the interplay between motor pulling forces, cortex-membrane anchoring, and network connectivity. We show that cortices on the outside of liposomes either spontaneously rupture and relax built-up mechanical stress by peeling away around the liposome or actively compress and crush the liposome. The decision between peeling and crushing depends on the cortical tension determined by the amount of motors and also on the connectivity of the cortex and its attachment to the membrane. Membrane anchoring strongly affects the morphology of cortex contraction inside liposomes: cortices contract inward when weakly attached, whereas they contract toward the membrane when strongly attached. We propose a physical model based on a balance of active tension and mechanical resistance to rupture. Our findings show how membrane attachment and network connectivity are able to regulate actin cortex remodeling and membrane-shape changes for cell polarization.

Directionality of information flow through neuronal networks is sustained at cellular level by polarized neurons. However, specific targeting or anchoring motifs responsible for polarized distribution on the neuronal surface have only been identified for a few neuronal G-protein-coupled receptors (GPCRs). Here, through mutational and pharmacological modifications of the conformational state of two model GPCRs, the axonal CB1R cannabinoid and the somatodendritic SSTR2 somatostatin receptors, we show important conformation-dependent variations in polarized distribution. The underlying mechanisms include lower efficiency of conformation-dependent GPCR endocytosis in axons, compared with dendrites, particularly at moderate activation levels, as well as endocytosis-dependent transcytotic delivery of GPCRs from the somatodendritic domain to distal axonal portions, shown by using compartmentalized microfluidic devices. Kinetic modeling predicted that GPCR distribution polarity is highly regulated by steady-state endocytosis, which is conformation dependent and is able to regulate the relative amount of GPCRs targeted to axons and that axonally polarized distribution is an intermediary phenotype that appears at moderate basal activation levels. Indeed, we experimentally show that gradual changes in basal activation-dependent endocytosis lead to highly correlated shifts of polarized GPCR distribution on the neuronal surface, which can even result in a fully reversed polarized distribution of naturally somatodendritic or axonal GPCRs. In conclusion, polarized distribution of neuronal GPCRs may have a pharmacologically controllable component, which, in the absence of dominant targeting motifs, could even represent the principal regulator of sub-neuronal distribution. Consequently, chronic modifications of basal GPCR activation by therapeutic or abused drugs may lead to previously unanticipated changes in brain function through perturbation of polarized GPCR distribution on the neuronal surface.

At mitosis onset, cortical tension increases and cells round up, ensuring correct spindle morphogenesis and orientation. Thus, cortical tension sets up the geometric requirements of cell division. On the contrary, cortical tension decreases during meiotic divisions in mouse oocytes, a puzzling observation because oocytes are round cells, stable in shape, that actively position their spindles. We investigated the pathway leading to reduction in cortical tension and its significance for spindle positioning. We document a previously uncharacterized Arp2/3-dependent thickening of the cortical F-actin essential for first meiotic spindle migration to the cortex. Using micropipette aspiration, we show that cortical tension decreases during meiosis I, resulting from myosin-II exclusion from the cortex, and that cortical F-actin thickening promotes cortical plasticity. These events soften and relax the cortex. They are triggered by the Mos-MAPK pathway and coordinated temporally. Artificial cortex stiffening and theoretical modelling demonstrate that a soft cortex is essential for meiotic spindle positioning.

We study a minimal model of active transport in crowded single-file environments which generalizes the emblematic model of single-file diffusion to the case when the tracer particle (TP) performs either an autonomous directed motion or is biased by an external force, while all other particles of the environment (bath) perform unbiased diffusions. We derive explicit expressions, valid in the limit of high density of bath particles, of the full distribution P((n))(X) of the TP position and of all its cumulants, for arbitrary values of the bias f and for any time n. Our analysis reveals striking features, such as the anomalous scaling [proportionality] √[n] of all cumulants, the equality of cumulants of the same parity characteristic of a Skellam distribution and a convergence to a Gaussian distribution in spite of asymmetric density profiles of bath particles. Altogether, our results provide the full statistics of the TP position and set the basis for a refined analysis of real trajectories of active particles in crowded single-file environments.

We investigate theoretically the physics of diffusion-limited intramolecular polymer reactions. The present work completes and goes beyond a previous study [T. Guérin, O. Bénichou, and R. Voituriez, Nat. Chem. 4, 568 (2012)] that showed that the distribution of the polymer conformations at the very instant of reaction plays a key role in the cyclization kinetics, and takes explicitly into account the non-Markovian nature of the reactant motion. Here, we present in detail this non-Markovian theory, and compare it explicitly with existing Markovian theories and with numerical stochastic simulations. A large focus is made on the description of the non-equilibrium reactive conformations, with both numerical and analytical tools. We show that the reactive conformations are elongated and are characterized by a spectrum with a slowly decreasing tail, implying that the monomers that neighbor the reactive monomers are significantly shifted at the instant of reaction. We complete the study by deriving explicit formulas for the reaction rates in the Markovian Wilemski-Fixman theory when the reactants are located in arbitrary positions in the chain. We also give a simple scaling argument to understand the existence of two regimes in the reaction time, that come from two possible behaviors of monomer motion, which can be either diffusive or subdiffusive.

For transport processes in geometrically restricted domains, the mean first-passage time (MFPT) admits a general scaling dependence on space parameters for diffusion, anomalous diffusion, and diffusion in disordered or fractal media. For transport in self-similar fractal structures, we obtain an expression for the source-target distance dependence of the MFPT that exhibits both the leading power-law behavior, depending on the Hausdorff and spectral dimension of the fractal, as well as small log-periodic oscillations that are a clear and definitive signal of the underlying fractal structure. We also present refined numerical results for the Sierpinski gasket that confirm this oscillatory behavior.

We use a stochastic approach to show how Taylor dispersion is affected by kinetic processes of adsorption and desorption onto surfaces. A general theory is developed, from which we derive explicitly the dispersion coefficients of canonical examples such as Poiseuille flows in planar and cylindrical geometries, in both constant and sinusoidal velocity fields. These results open the way for the measurement of adsorption and desorption rate constants using stationary flows and molecular sorting using the stochastic resonance of the adsorption and desorption processes with the oscillatory velocity field.

Cell migration plays a major role in many fundamental biological processes, such as morphogenesis, tumor metastasis, and wound healing. As they anchor and pull on their surroundings, adhering cells actively probe the stiffness of their environment. Current understanding is that traction forces exerted by cells arise mainly at mechanotransduction sites, called focal adhesions, whose size seems to be correlated to the force exerted by cells on their underlying substrate, at least during their initial stages. In fact, our data show by direct measurements that the buildup of traction forces is faster for larger substrate stiffness, and that the stress measured at adhesion sites depends on substrate rigidity. Our results, backed by a phenomenological model based on active gel theory, suggest that rigidity-sensing is mediated by a large-scale mechanism originating in the cytoskeleton instead of a local one. We show that large-scale mechanosensing leads to an adaptative response of cell migration to stiffness gradients. In response to a step boundary in rigidity, we observe not only that cells migrate preferentially toward stiffer substrates, but also that this response is optimal in a narrow range of rigidities. Taken together, these findings lead to unique insights into the regulation of cell response to external mechanical cues and provide evidence for a cytoskeleton-based rigidity-sensing mechanism.

We consider a minimal model of persistent random searcher with a short range memory. We calculate exactly for such a searcher the mean first-passage time to a target in a bounded domain and find that it admits a nontrivial minimum as function of the persistence length. This reveals an optimal search strategy which differs markedly from the simple ballistic motion obtained in the case of Poisson distributed targets. Our results show that the distribution of targets plays a crucial role in the random search problem. In particular, in the biologically relevant cases of either a single target or regular patterns of targets, we find that, in strong contrast to repeated statements in the literature, persistent random walks with exponential distribution of excursion lengths can minimize the search time, and in that sense perform better than any Levy walk.

We present a model of cell motility generated by actomyosin contraction of the cell cortex. We identify, analytically, dynamical instabilities of the cortex and show that they yield steady-state cortical flows, which, in turn, can induce cell migration in three-dimensional environments. This mechanism relies on the regulation of contractility by myosin, whose transport is explicitly taken into account in the model. Theoretical predictions are compared to experimental data of tumor cells migrating in three-dimensional matrigel and suggest that this mechanism could be a general mode of cell migration in three-dimensional environments., (Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

We introduce a general framework, applicable to a broad class of random walks on networks, that quantifies the response of the mean first-passage time to a target node to a local perturbation of the network, both in the context of attacks (damaged link) or strategies of transport enhancement (added link). This approach enables to determine explicitly the dependence of this response on geometric parameters (such as the network size and the localization of the perturbation) and on the intensity of the perturbation. In particular, it is showed that the relative variation of the mean first-passage time is independent of the network size, and remains significant in the large size limit. Furthermore, in the case of noncompact exploration of the network, it is found that a targeted perturbation keeps a substantial impact on transport properties for any localization of the damaged link.

An increasing number of experimental studies employ single particle tracking to probe the physical environment in complex systems. We here propose and discuss what we believe are new methods to analyze the time series of the particle traces, in particular, for subdiffusion phenomena. We discuss the statistical properties of mean maximal excursions (MMEs), i.e., the maximal distance covered by a test particle up to time t. Compared to traditional methods focusing on the mean-squared displacement we show that the MME analysis performs better in the determination of the anomalous diffusion exponent. We also demonstrate that combination of regular moments with moments of the MME method provides additional criteria to determine the exact physical nature of the underlying stochastic subdiffusion processes. We put the methods to test using experimental data as well as simulated time series from different models for normal and anomalous dynamics such as diffusion on fractals, continuous time random walks, and fractional Brownian motion., (Copyright (c) 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

In this communication, we show that the residence time of a Brownian particle, defined as the cumulative time spent in a given region of space, can be optimized as a function of the diffusion coefficient. We discuss the relevance of this effect to several schematic experimental situations classified in nature--random or deterministic--both of the observation time and of the starting position of the Brownian particle.

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 authors study an intermittent search process combining diffusion and "teleportation" phases in a d-dimensional spherical continuous system and in a regular lattice. The searcher alternates diffusive phases, during which targets can be discovered, and fast phases (teleportation) which randomly relocate the searcher, but do not allow for target detection. The authors show that this alternation can be favorable for minimizing the time of first discovery, and that this time can be optimized by a convenient choice of the mean waiting times of each motion phase. The optimal search strategy is explicitly derived in the continuous case and in the lattice case. Arguments are given to show that much more general intermittent motions do provide optimal search strategies in d dimensions. These results can be useful in the context of heterogeneous catalysis or in various biological examples of transport through membrane pores.

For diffusion-limited reversible A+A<==>B reactions we reexamine two fundamental concepts of classical chemical kinetics-the notion of "chemical equilibrium" and the "law of mass action." We consider a general model with distance-dependent reaction rates, such that any pair of A particles, performing standard random walks on sites of a d-dimensional lattice and being at a distance mu apart of each other at time moment t, may associate forming a B particle at the rate k+(mu). In turn, any randomly moving B particle may spontaneously dissociate at the rate k-(lambda) into a geminate pair of As "born" at a distance lambda apart of each other. Within a formally exact approach based on Gardiner's Poisson representation method we show that the asymptotic t=infinity state attained by such diffusion-limited reactions is generally not a true thermodynamic equilibrium, but rather a nonequilibrium steady state, and that the law of mass action is invalid. The classical concepts hold only in case when the ratio k+(mu)k-(mu) does not depend on mu for any mu.