Geometry-controlled kinetics

Estimating mean first passage time of biased random walks with short relaxation time on complex networks

Biased random walk has been studied extensively over the past decade especially in the transport and communication networks communities. The mean first passage time (MFPT) of a biased random walk is an important performance indicator in those domains. While the fundamental matrix approach gives precise solution to MFPT, the computation is expensive and the solution lacks interpretability. Other approaches based on the Mean Field Theory relate MFPT to the node degree alone. However, nodes with the same degree may have very different local weight distribution, which may result in vastly different MFPT. We derive an approximate bound to the MFPT of biased random walk with short relaxation time on complex network where the biases are controlled by arbitrarily assigned node weights. We show that the MFPT of a node in this general case is closely related to not only its node degree, but also its local weight distribution. The MFPTs obtained from computer simulations also agree with the new theoretical analysis. Our result enables fast estimation of MFPT, which is useful especially to differentiate between nodes that have very different local node weight distribution even though they share the same node degrees.

Single-molecule diffusion in a periodic potential at a solid-liquid interface

We used single-molecule tracking experiments to observe the motion of small hydrophobic fluorescent molecules at the interface between water and a solid surface that exhibited periodic chemical patterns. The dynamics were characterized by non-ergodic, continuous time random walk statistics. The step-size distributions displayed enhanced probability of steps to periodic distances, consistent with theoretical predictions for diffusion in an atomic/molecular scale periodic potential. Surprisingly, this general behavior was observed here for surfaces exhibiting characteristic length scales three orders of magnitude larger than atomic/molecular dimensions, and may provide a new way to understand and control solid-liquid interfacial diffusion for molecular targeting applications.

Importance of crowding in signaling, genetic, and metabolic networks

It is now well established that the cell is a highly crowded environment. Yet, the effects of crowding on the dynamics of signaling pathways, gene regulation networks, and metabolic networks are still largely unknown. Crowding can alter both molecular diffusion and the equilibria of biomolecular reactions. In this chapter, we first discuss how diffusion can affect biochemical networks. Diffusion of transcription factors can increase noise in gene expression, while diffusion of proteins between intracellular compartments or between cells can reduce concentration fluctuations. In push-pull networks diffusion can impede information transmission, while in multisite protein modification networks diffusion can qualitatively change the macroscopic response of the system, such as the loss or emergence of bistability. Moreover, diffusion can directly change the metabolic flux. We describe how crowding affects diffusion, and thus how all these phenomena are influenced by crowding. Yet, a potentially more important effect of crowding on biochemical networks is mediated via the shift in the equilibria of bimolecular reactions, and we provide computational evidence that supports this idea. Finally, we discuss how the effects of crowding can be incorporated in models of biochemical networks.

Relevance and limitations of crowding, fractal, and polymer models to describe nuclear architecture

Chromosome architecture plays an essential role for all nuclear functions, and its physical description has attracted considerable interest over the last few years among the biophysics community. These researches at the frontiers of physics and biology have been stimulated by the demand for quantitative analysis of molecular biology experiments, which provide comprehensive data on chromosome folding, or of live cell imaging experiments that enable researchers to visualize selected chromosome loci in living or fixed cells. In this review our goal is to survey several nonmutually exclusive models that have emerged to describe the folding of DNA in the nucleus, the dynamics of proteins in the nucleoplasm, or the movements of chromosome loci. We focus on three classes of models, namely molecular crowding, fractal, and polymer models, draw comparisons, and discuss their merits and limitations in the context of chromosome structure and dynamics, or nuclear protein navigation in the nucleoplasm. Finally, we identify future challenges in the roadmap to a unified model of the nuclear environment.

Adaptation dynamics in densely clustered chemoreceptors

In many sensory systems, transmembrane receptors are spatially organized in large clusters. Such arrangement may facilitate signal amplification and the integration of multiple stimuli. However, this organization likely also affects the kinetics of signaling since the cytoplasmic enzymes that modulate the activity of the receptors must localize to the cluster prior to receptor modification. Here we examine how these spatial considerations shape signaling dynamics at rest and in response to stimuli. As a model system, we use the chemotaxis pathway of Escherichia coli, a canonical system for the study of how organisms sense, respond, and adapt to environmental stimuli. In bacterial chemotaxis, adaptation is mediated by two enzymes that localize to the clustered receptors and modulate their activity through methylation-demethylation. Using a novel stochastic simulation, we show that distributive receptor methylation is necessary for successful adaptation to stimulus and also leads to large fluctuations in receptor activity in the steady state. These fluctuations arise from noise in the number of localized enzymes combined with saturated modification kinetics between the localized enzymes and the receptor substrate. An analytical model explains how saturated enzyme kinetics and large fluctuations can coexist with an adapted state robust to variation in the expression levels of the pathway constituents, a key requirement to ensure the functionality of individual cells within a population. This contrasts with the well-mixed covalent modification system studied by Goldbeter and Koshland in which mean activity becomes ultrasensitive to protein abundances when the enzymes operate at saturation. Large fluctuations in receptor activity have been quantified experimentally and may benefit the cell by enhancing its ability to explore empty environments and track shallow nutrient gradients. Here we clarify the mechanistic relationship of these large fluctuations to well-studied aspects of the chemotaxis system, precise adaptation and functional robustness.

Control of logic gates by dichotomous noise in energetic and entropic systems

We consider the stochastic response of a nonlinear dynamical system towards a combination of input signals. The response can assume binary values if the state of the system is considered to be the output and the system can make transitions between two states separated by an energetic or entropic barrier. We show how the input-output correspondence can be controlled by an external exponentially correlated dichotomous noise optimizing the logical response which exhibits a maximum at an intermediate value of correlation time. This resonance manifests itself as a "logical" resonance correlation effect and sets the condition for performance of the stochastic system as a logic gate. The role of asymmetry of the dichotomous noise is examined and the results on numerical simulations are correlated with a two-state model using a master equation approach.

Disentangling sources of anomalous diffusion

We show that some important properties of subdiffusion of unknown origin (including ones of mixed origins) can be easily assessed when finding the "fundamental moment" of the corresponding random process, i.e., the one which is additive in time. In subordinated processes, the index of the fundamental moment is inherited from the parent process and its time dependence from the leading one. In models of a particle's motion in disordered potentials, the index is governed by the structural part of the disorder while the time dependence is given by its energetic part.

Uniform asymptotic approximation of diffusion to a small target

The problem of the time required for a diffusing molecule, within a large bounded domain, to first locate a small target is prevalent in biological modeling. Here we study this problem for a small spherical target. We develop uniform in time asymptotic expansions in the target radius of the solution to the corresponding diffusion equation. Our approach is based on combining expansions of a long-time approximation of the solution, involving the first eigenvalue and eigenfunction of the Laplacian, with expansions of a short-time correction calculated by a pseudopotential approximation. These expansions allow the calculation of corresponding expansions of the first passage time density for the diffusing molecule to find the target. We demonstrate the accuracy of our method in approximating the first passage time density and related statistics for the spherically symmetric problem where the domain is a large concentric sphere about a small target centered at the origin.

Exploration and trapping of mortal random walkers

Exploration and trapping properties of random walkers that may evanesce at any time as they walk have seen very little treatment in the literature, and yet a finite lifetime is a frequent occurrence, and its effects on a number of random walk properties may be profound. For instance, whereas the average number of distinct sites visited by an immortal walker grows with time without bound, that of a mortal walker may, depending on dimensionality and rate of evanescence, remain finite or keep growing with the passage of time. This number can in turn be used to calculate other classic quantities such as the survival probability of a target surrounded by diffusing traps. If the traps are immortal, the survival probability will vanish with increasing time. However, if the traps are evanescent, the target may be spared a certain death. We analytically calculate a number of basic and broadly used quantities for evanescent random walkers.

Modeling and simulation of biological systems from image data

This essay provides an introduction to the terminology, concepts, methods, and challenges of image-based modeling in biology. Image-based modeling and simulation aims at using systematic, quantitative image data to build predictive models of biological systems that can be simulated with a computer. This allows one to disentangle molecular mechanisms from effects of shape and geometry. Questions like "what is the functional role of shape" or "how are biological shapes generated and regulated" can be addressed in the framework of image-based systems biology. The combination of image quantification, model building, and computer simulation is illustrated here using the example of diffusion in the endoplasmic reticulum.

Origin of the hub spectral dimension in scale-free networks

The return-to-origin probability and the first-passage-time distribution are essential quantities for understanding transport phenomena in diverse systems. The behaviors of these quantities typically depend on the spectral dimension d(s). However, it was recently revealed that in scale-free networks these quantities show a crossover between two power-law regimes characterized by d(s) and the so-called hub spectral dimension d(s)((hub)) due to the heterogeneity of connectivities of each node. To understand the origin of d(s)((hub)) from a theoretical perspective, we study a random walk problem on hierarchical scale-free networks by using the renormalization group (RG) approach. Under the RG transformation, not only the system size but also the degree of each node changes due to the scale-free nature of the degree distribution. We show that the anomalous behavior of random walks involving the hub spectral dimension d(s)((hub)) is induced by the conservation of the power-law degree distribution under the RG transformation.

Encounter times in overlapping domains: application to epidemic spread in a population of territorial animals

We develop an analytical method to calculate encounter times of two random walkers in one dimension when each individual is segregated in its own spatial domain and shares with its neighbor only a fraction of the available space, finding very good agreement with numerically exact calculations. We model a population of susceptible and infected territorial individuals with this spatial arrangement, and which may transmit an epidemic when they meet. We apply the results on encounter times to determine analytically the macroscopic propagation speed of the epidemic as a function of the microscopic characteristics: the confining geometry, the animal diffusion constant, and the infection transmission probability.

In vivo facilitated diffusion model

Under dilute in vitro conditions transcription factors rapidly locate their target sequence on DNA by using the facilitated diffusion mechanism. However, whether this strategy of alternating between three-dimensional bulk diffusion and one-dimensional sliding along the DNA contour is still beneficial in the crowded interior of cells is highly disputed. Here we use a simple model for the bacterial genome inside the cell and present a semi-analytical model for the in vivo target search of transcription factors within the facilitated diffusion framework. Without having to resort to extensive simulations we determine the mean search time of a lac repressor in a living E. coli cell by including parameters deduced from experimental measurements. The results agree very well with experimental findings, and thus the facilitated diffusion picture emerges as a quantitative approach to gene regulation in living bacteria cells. Furthermore we see that the search time is not very sensitive to the parameters characterizing the DNA configuration and that the cell seems to operate very close to optimal conditions for target localization. Local searches as implied by the colocalization mechanism are only found to mildly accelerate the mean search time within our model.

Enhanced transport through desorption-mediated diffusion

We present a master equation approach to the study of the bulk-mediated surface diffusion mechanism in a three-dimensional confined domain. The proposed scheme allowed us to evaluate analytically a number of magnitudes that were used to characterize the efficiency of the bulk-mediated surface transport mechanism, for instance, the mean escape time from the domain, and the mean number of distinct visited sites on the confined domain boundary.

Spatial log-periodic oscillations of first-passage observables in fractals

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.

Quenching dynamics in CdSe nanoparticles: surface-induced defects upon dilution

We have analyzed the decays of the fluorescence of colloidal CdSe quantum dots (QDs) suspensions during dilution and titration by the ligands. A ligand shell made of a combination of trioctylphosphine (TOP), oleylamine (OA), and stearic acid (SA) stabilizes the as-synthesized QDs. The composition of the shell was analyzed and quantified using high resolution liquid state 1H nuclear magnetic resonance (NMR) spectroscopy. A quenching of the fluorescence of the QDs is observed upon removal of the ligands by diluting the stock solution of the QDs. The fluorescence is restored by the addition of TOP. We analyze the results by assuming a binomial distribution of quenchers among the QDs and predict a linear trend in the time-resolved fluorescence decays. We have used a nonparametric analysis to show that for our QDs, 3.0 ± 0.1 quenching sites per QD on average are revealed by the removal of TOP. We moreover show that the quenching rates of the quenching sites add up. The decay per quenching site can be compared with the decay at saturation of the dilution effect. This provides a value of 2.88 ± 0.02 for the number of quenchers per QD. We extract the quenching dynamics of one site. It appears to be a process with a distribution of rates that does not involve the ligands.

Logic gates for entropic transport

We consider a Brownian particle that is confined in a two-dimensional enclosure and driven by a combination of input signals. It has been shown that the logic gates can be formed by considering the state of the particle experiencing an entropic barrier as the output signal. For a consistent logical output, it is necessary to optimize the strength of the noise driving the particle for a given system size. The variation of the logical output behavior exhibits a turnover at an optimal value of system size parameter, implying a size resonance condition in entropic transport. The role of a transverse bias field used to tune the transport between the entropy dominated regime and the energy dominated regime is elucidated.

First passages in bounded domains: when is the mean first passage time meaningful?

We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(ω) distribution of the random variable ω=τ(1)/(τ(1)+τ(2)), which is a measure for how similar the first passage times τ(1) and τ(2) are of two independent realizations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(ω) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(ω), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.

First passage time for random walks in heterogeneous networks

The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous networks, is not yet fully understood. Here, we study, both analytically and numerically, the scaling behavior of the FPT distribution to a given target node, averaged over all starting nodes. We find that random walks arrive quickly at a local hub, and therefore, the FPT distribution shows a crossover with respect to time from fast decay behavior (induced from the attractive effect to the hub) to slow decay behavior (caused by the exploring of the entire system). Moreover, the mean FPT is independent of the degree of the target node in the case of compact exploration. These theoretical results justify the necessity of using a random jump protocol (empirically used in search engines) and provide guidelines for designing an effective network to make information quickly accessible.

A fractal model for nuclear organization: current evidence and biological implications

Chromatin is a multiscale structure on which transcription, replication, recombination and repair of the genome occur. To fully understand any of these processes at the molecular level under physiological conditions, a clear picture of the polymorphic and dynamic organization of chromatin in the eukaryotic nucleus is required. Recent studies indicate that a fractal model of chromatin architecture is consistent with both the reaction-diffusion properties of chromatin interacting proteins and with structural data on chromatin interminglement. In this study, we provide a critical overview of the experimental evidence that support a fractal organization of chromatin. On this basis, we discuss the functional implications of a fractal chromatin model for biological processes and propose future experiments to probe chromatin organization further that should allow to strongly support or invalidate the fractal hypothesis.

Setup for single-particle orbit tracking: artifacts and corrections

We report on an experimental setup for single-particle orbit tracking, which allows following fluorescent nanoparticles for more than 10 min with a temporal resolution of 4 ms and a dynamic position accuracy of better than 10 nm. On a model sample--20 nm sized fluorescent polymer beads in glycerol--we will illustrate how artifacts caused by unavoidable experimental shortcomings (might) obscure the experimental result and how misinterpretations can be prevented.

Non-Markovian polymer reaction kinetics

Describing the kinetics of polymer reactions, such as the formation of loops and hairpins in nucleic acids or polypeptides, is complicated by the structural dynamics of their chains. Although both intramolecular reactions, such as cyclization, and intermolecular reactions have been studied extensively, both experimentally and theoretically, there is to date no exact explicit analytical treatment of transport-limited polymer reaction kinetics, even in the case of the simplest (Rouse) model of monomers connected by linear springs. We introduce a new analytical approach to calculate the mean reaction time of polymer reactions that encompasses the non-Markovian dynamics of monomer motion. This requires that the conformational statistics of the polymer at the very instant of reaction be determined, which provides, as a by-product, new information on the reaction path. We show that the typical reactive conformation of the polymer is more extended than the equilibrium conformation, which leads to reaction times significantly shorter than predicted by the existing classical Markovian theory.

Interfacial effects on nanoconfined diffusive mass transport regimes

A hierarchical multiscale modeling approach, incorporating molecular dynamics and finite element techniques, is used to study parametrically diffusion regimes through nanoconfined fluid. Novel parameters that determine the character of the diffusion regime and diffusion kinetics within the nanoscale confined fluids is established by exploring diffusion where the interface effects at the solid surface are important. New diffusion transport characteristics are established when nanochannel confining dimension approaches 3-4 sizes of diffusing molecules, which also marks peripheries of the non-fickian transport regime.

Geometry-induced bursting dynamics in gene expression

In prokaryotes and eukaryotes, genes are transcribed stochastically according to various temporal patterns that range from simple first-order kinetics to marked bursts, resulting in temporal and cell-to-cell variations of mRNA and protein levels. Here, we consider the effect of the transport of regulatory molecules on the noise in gene expression by taking into account explicitly the dynamics of a finite number of transcription factors confined in the cell. We calculate analytically time-dependent correlation functions of mRNA levels for a wide range of transport mechanisms and find that in the limit of small-transcription-factor copy number, the results differ significantly from standard approaches, which ignore confinement. It is shown how such dynamical quantities, which can now be obtained experimentally, can be used to identify the underlying mechanisms of transcription. Of particular importance, it is demonstrated that the geometry of transcription-factor trajectories in the cellular environment plays a key role in transcription kinetics, and can intrinsically generate the observed various transcription patterns ranging from simple first-order kinetics to bursts.

The membrane environment can promote or suppress bistability in cell signaling networks

Many key biochemical reactions that mediate signal transduction in cells occur at the cell membrane, yet how the two-dimensional membrane environment influences the collective behavior of signaling networks is poorly understood. We study models of two topologically different signaling pathways that exhibit bistability, examining the effects of reduced protein mobility and increased concentration at the membrane, as well as effects due to differences in spatiotemporal correlations between the membrane environment and three-dimensional cytoplasm. The two model networks represent the distributive enzymatic modification of a protein at multiple sites and the positive feedback-mediated activation of a protein. In both cases, we find that confining proteins to a membrane-like environment can markedly alter the emergent dynamics. For the distributive protein modification network, increased concentration promotes bistability through enhanced protein-protein binding, while lower mobility and membrane-enhanced spatiotemporal correlations suppress bistability. For the positive feedback-mediated activation network, confinement to a membrane environment enhances protein activation, which can induce bistability or stabilize a monostable, active state. Importantly, the influence of the membrane environment on signaling dynamics can be qualitatively different for signaling modules with different network topologies.

Entropic dynamical hysteresis in a driven system

We show that the application of a time periodic field driving a Brownian particle between the two lobes of a two-dimensional bilobal enclosure results in a hysteresis loop in the variation of integrated probability of residence of the particle as a function of the field. The confinement of the particle is characterized by symmetry breaking of the hysteresis loop, and the area of the loop exhibits a turnover with variation of frequency of the field. This dynamical hysteresis is geometry controlled, entropic in nature, and amenable to theoretical analysis with a two-state model.

Optimizing persistent random searches

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.

Protein sorting and membrane-mediated interactions

Sorting of membrane proteins is of vital importance for living cells. Indeed, roughly one-third of a eukaryotic cell's proteome consists of peripheral and transmembrane proteins. These need to be properly distributed and dynamically maintained at distinct locations in the compartmentalized cell, and one may wonder how proteins determine where, when, and how to travel to reach a specific organelle. While specific binary interactions between proteins have been invoked in explaining the trafficking and sorting processes, a more active role of lipids in this context has become visible in recent years. In particular, membrane-mediated interactions have been suggested to serve as a robust physicochemical mechanism to facilitate protein sorting. Here, we will review some recent insights into these aspects.

Intra-nuclear mobility and target search mechanisms of transcription factors: a single-molecule perspective on gene expression

Precise expression of specific genes in time and space is at the basis of cellular viability as well as correct development of organisms. Understanding the mechanisms of gene regulation is fundamental and still one of the great challenges for biology. Gene expression is regulated also by specific transcription factors that recognize and bind to specific DNA sequences. Transcription factors dynamics, and especially the way they sample the nucleoplasmic space during the search for their specific target in the genome, are a key aspect for regulation and it has been puzzling researchers for forty years. The scope of this review is to give a state-of-the-art perspective over the intra-nuclear mobility and the target search mechanisms of specific transcription factors at the molecular level. Going through the seminal biochemical experiments that have raised the first questions about target localization and the theoretical grounds concerning target search processes, we describe the most recent experimental achievements and current challenges in understanding transcription factors dynamics and interactions with DNA using in vitro assays as well as in live prokaryotic and eukaryotic cells. This article is part of a Special Issue entitled: Nuclear Transport and RNA Processing.

Exact calculations of first-passage quantities on recursive networks

We present general methods to exactly calculate mean first-passage quantities on self-similar networks defined recursively. In particular, we calculate the mean first-passage time and the splitting probabilities associated to a source and one or several targets; averaged quantities over a given set of sources (e.g., same-connectivity nodes) are also derived. The exact estimate of such quantities highlights the dependency of first-passage processes with respect to the source-target distance, which has recently revealed to be a key parameter in characterizing transport in complex media. We explicitly perform calculations for different classes of recursive networks [finitely ramified fractals, scale-free (trans)fractals, nonfractals, mixtures between fractals and nonfractals, nondecimable hierarchical graphs] of arbitrary size. Our approach unifies and significantly extends the available results in the field.

Classes of fast and specific search mechanisms for proteins on DNA

Problems of search and recognition appear over different scales in biological systems. In this review we focus on the challenges posed by interactions between proteins, in particular transcription factors, and DNA and possible mechanisms which allow for fast and selective target location. Initially we argue that DNA-binding proteins can be classified, broadly, into three distinct classes which we illustrate using experimental data. Each class calls for a different search process and we discuss the possible application of different search mechanisms proposed over the years to each class. The main thrust of this review is a new mechanism which is based on barrier discrimination. We introduce the model and analyze in detail its consequences. It is shown that this mechanism applies to all classes of transcription factors and can lead to a fast and specific search. Moreover, it is shown that the mechanism has interesting transient features which allow for stability at the target despite rapid binding and unbinding of the transcription factor from the target.

Thermal and mechanical denaturation properties of a DNA model with three sites per nucleotide

In this paper, we show that the coarse grain model for DNA, which has been proposed recently by Knotts et al. [J. Chem. Phys. 126, 084901 (2007)], can be adapted to describe the thermal and mechanical denaturation of long DNA sequences by adjusting slightly the base pairing contribution. The adjusted model leads to (i) critical temperatures for long homogeneous sequences that are in good agreement with both experimental ones and those obtained from statistical models, (ii) a realistic step-like denaturation behaviour for long inhomogeneous sequences, and (iii) critical forces at ambient temperature of the order of 10 pN, close to measured values. The adjusted model furthermore supports the conclusion that the thermal denaturation of long homogeneous sequences corresponds to a first-order phase transition and yields a critical exponent for the critical force equal to σ = 0.70. This model is both geometrically and energetically realistic, in the sense that the helical structure and the grooves, where most proteins bind, are satisfactorily reproduced, while the energy and the force required to break a base pair lie in the expected range. It therefore represents a promising tool for studying the dynamics of DNA-protein specific interactions at an unprecedented detail level.

Theoretical and computational modeling of target-site search kinetics in vitro and in vivo

Access to genetically encoded data depends on the dynamics of DNA-binding proteins searching for specific target sites in the genome. This search process is thought to occur by facilitated diffusion-a combination of three-dimensional diffusion and one-dimensional sliding. Although facilitated diffusion is capable of significantly speeding up the search in vitro, the importance of this mechanism in vivo remains unclear. We use numeric simulations and analytical theory to model the target-search dynamics of DNA-binding proteins under a wide range of conditions. Our models reproduce experimental measurements of search-rate enhancement within bulk in vitro experiments, as well as the target search time for transcription factors measured in vivo. We find that facilitated diffusion can accelerate the search process only for a limited range of parameters and only under dilute DNA conditions. We address the role of DNA configuration and confinement, demonstrating that facilitated diffusion does not speed up the search on coiled versus straight DNA. Furthermore, we show that, under in vivo conditions, the search process becomes effectively diffusive and is independent of DNA configuration. We believe our results cast in a new light the role of facilitated diffusion in DNA targeting kinetics within the cell.

Langevin dynamics, entropic crowding, and stochastic cloaking

We consider a pack of independent probes--within a spatially inhomogeneous thermal bath consisting of a vast number of randomly moving particles--which are subjected to an external force. The stochastic dynamics of the probes are governed by Langevin's equation. The probes attain a steady state distribution which, in general, is different than the concentration of the particles in the spatially inhomogeneous thermal bath. In this paper we explore the state of "entropic crowding" in which the probes' distribution and the particles' concentration coincide--thus yielding maximal relative entropies of one with respect to the other. Entropic crowding can be attained by two scenarios which are analyzed in detail: (i) "entropically crowding thermal baths"--in which the particles crowd uniformly around the probes; (ii) "entropically crowding Langevin forces"--in which the probes crowd uniformly amongst the particles. Entropic crowding is equivalent to the optimal stochastic cloaking of the probes within the spatially inhomogeneous thermal bath.

Close or connected: distance and connectivity effects on transport in networks

We develop an analytical approach that provides the dependence of the mean first-passage time (MFPT) for random walks on complex networks both on the target connectivity and on the source-target distance. Our approach puts forward two strongly different behaviors depending on the type-compact or non compact-of the random walk. In the case of non compact exploration, we show that the MFPT scales linearly with the inverse connectivity of the target and is largely independent of the starting point. On the contrary, in the compact case, the MFPT is controlled by the source-target distance, and we find that unexpectedly the target connectivity becomes irrelevant for remote targets.

Solute diffusion is hindered in the mitochondrial matrix

Intracellular chemical reactions generally constitute reaction-diffusion systems located inside nanostructured compartments like the cytosol, nucleus, endoplasmic reticulum, Golgi, and mitochondrion. Understanding the properties of such systems requires quantitative information about solute diffusion. Here we present a novel approach that allows determination of the solvent-dependent solute diffusion constant (D(solvent)) inside cell compartments with an experimentally quantifiable nanostructure. In essence, our method consists of the matching of synthetic fluorescence recovery after photobleaching (FRAP) curves, generated by a mathematical model with a realistic nanostructure, and experimental FRAP data. As a proof of principle, we assessed D(solvent) of a monomeric fluorescent protein (AcGFP1) and its tandem fusion (AcGFP1(2)) in the mitochondrial matrix of HEK293 cells. Our results demonstrate that diffusion of both proteins is substantially slowed by barriers in the mitochondrial matrix (cristae), suggesting that cells can control the dynamics of biochemical reactions in this compartment by modifying its nanostructure.

Universality classes of first-passage-time distribution in confined media

We study the first-passage time (FPT) distribution to a target site for a random walker evolving in a bounded domain. We show that in the limit of large volume of the confining domain, this distribution falls into universality classes indexed by the walk dimension d(w) and the fractal dimension d(f) of the medium, which have been recently identified previously [Bénichou et al., Nat. Chem. 2, 472 (2010)]. We present in this paper a complete derivation of these universal distributions, discuss extensively the range of applicability of the results, and extend the method to continuous-time random walks. This analysis puts forward the importance of the geometry, and in particular the position of the starting point, in first-passage statistics. Analytical results are validated by numerical simulations, applied to various models of transport in disordered media, which illustrate the universality classes of the FPT distribution.

Facilitated diffusion of proteins on chromatin

We present a theoretical model of facilitated diffusion of proteins in the cell nucleus. This model, which takes into account the successive binding and unbinding events of proteins to DNA, relies on a fractal description of the chromatin which has been recently evidenced experimentally. Facilitated diffusion is shown quantitatively to be favorable for a fast localization of a target locus by a transcription factor and even to enable the minimization of the search time by tuning the affinity of the transcription factor with DNA. This study shows the robustness of the facilitated diffusion mechanism, invoked so far only for linear conformations of DNA.

Response to targeted perturbations for random walks on networks

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.

Light-scattering technologies for field carcinogenesis detection: a modality for endoscopic prescreening

Colonoscopy has revolutionized colorectal cancer (CRC) screening resulting in a decrease in both CRC mortality and incidence. Despite this, CRC still ranks as the second leading cause of cancer deaths among Americans underscoring the need to both increase availability and accuracy of colonoscopy. The latter considerations provide the impetus for much of the current research into adjunctive imaging technologies. Recent advances in improving detection of dysplasia that have translated into clinical practice include high-definition scopes, narrow-band imaging, and chromo-endoscopy. Another major direction of research into improving endoscopy is determining histology of lesions in situ (“optical biopsy”) with confocal endomicroscopy, fluorescence and elastic scattering spectroscopy. All these techniques are of great promise in improving delivery of endoscopy but, to date, have not addressed the potentially more important hurdle associated with logistic challenges of providing accurate CRC screening for the entire at-risk population.

Optimal reaction time for surface-mediated diffusion

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. 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.