Surface Tensions between Active Fluids and Solid Interfaces: Bare vs Dressed.

We analyze the surface tension exerted at the interface between an active fluid and a solid boundary in terms of tangential forces. Focusing on active systems known to possess an equation of state for the pressure, we show that interfacial forces are of a more complex nature. Using a number of macroscopic setups, we show that the surface tension is a combination of an equation-of-state abiding part and of setup-dependent contributions. The latter arise from generic setup-dependent steady currents which "dress" the measurement of the "bare" surface tension. The former shares interesting properties with its equilibrium counterpart, and can be used to generalize the Young-Laplace law to active systems. Finally, we show how a suitably designed probe can directly access this bare surface tension, which can also be computed using a generalized virial formula.

Activated Escape of a Self-Propelled Particle from a Metastable State.

We study the noise-driven escape of active Brownian particles (ABPs) and run-and-tumble particles (RTPs) from confining potentials. In the small noise limit, we provide an exact expression for the escape rate in terms of a variational problem in any dimension. For RTPs in one dimension, we obtain an explicit solution, including the first subleading correction. In two dimensions we solve the escape from a quadratic well for both RTPs and ABPs. In contrast to the equilibrium problem we find that the escape rate depends explicitly on the full shape of the potential barrier, and not only on its height. This leads to a host of unusual behaviors. For example, when a particle is trapped between two barriers it may preferentially escape over the higher one. Moreover, as the self-propulsion speed is varied, the escape route may discontinuously switch from one barrier to the other, leading to a dynamical phase transition.

How does the DNA sequence affect the Hill curve of transcriptional response?

The Hill coefficient is often used as a direct measure of the cooperativity of binding processes. It is an essential tool for probing properties of reactions in many biochemical systems. Here, we analyze existing experimental data and demonstrate that the Hill coefficient characterizing the binding of transcription factors to their cognate sites can in fact be larger than one-the standard indication of cooperativity-even in the absence of any standard cooperative binding mechanism. We demonstrate that this effect occurs due to the disordered binding energy of transcription factors to the DNA molecule and the steric repulsion between the different copies of the transcription factor. We show that the enhanced Hill coefficient implies a significant reduction in the number of copies of the transcription factors which is needed to occupy a cognate site and, in many cases, can explain existing estimates for number of copies of the transcription factors in cells.

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.

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.

Searching fast for a target on DNA without falling to traps.

Genomic expression depends critically on both the ability of regulatory proteins to locate specific target sites on DNA within seconds and on the formation of long-lived (many minutes) complexes between these proteins and the DNA. Equilibrium experiments show that indeed regulatory proteins bind tightly to their target site. However, they also find strong binding to other nonspecific sites which act as traps that can dramatically increase the time needed to locate the target. This gives rise to a conflict between the speed and stability requirements. Here we suggest a simple mechanism which can resolve this long-standing paradox.

Nonequilibrium phase transitions in the extraction of membrane tubes by molecular motors.

The extraction of membrane tubes by molecular motors is known to play an important role for the transport properties of eukaryotic cells. By studying a generic class of models for the tube extraction, we discover a rich phase diagram. In particular we show that the density of motors along the tube can exhibit shocks, inverse shocks, and plateaux, depending on parameters which could in principle be probed experimentally. In addition the phase diagram exhibits interesting reentrant behavior.

Dynamics of DNA melting.

The dynamics of loops at the DNA denaturation transition is studied. A scaling argument is used to evaluate the asymptotic behavior of the autocorrelation function of the state of complementary bases (either open or closed). The long-time asymptotic behavior of the autocorrelation function is expressed in terms of the entropy exponent, c, of a loop. The validity of the scaling argument is tested using a microscopic model of an isolated loop and a toy model of interacting loops. This suggests a method for measuring the entropy exponent using single-molecule experiments such as fluorescence correlation spectroscopy.

Loop dynamics in DNA denaturation.

The dynamics of a loop in DNA molecules at the denaturation transition is studied by scaling arguments and numerical simulations. The autocorrelation function of the state of complementary bases (either closed or open) is calculated. The long-time decay of the autocorrelation function is expressed in terms of the loop exponent c both for homopolymers and heteropolymers. This suggests an experimental method for measuring the exponent c using florescence correlation spectroscopy.

Collective dynamics of interacting molecular motors.

The collective dynamics of N interacting processive molecular motors are considered theoretically when an external force is applied to the leading motor. We show, using a discrete lattice model, that the force-velocity curves strongly depend on the effective dynamic interactions between motors and differ significantly from those of a simple approach where the motors equally share the force. Moreover, they become essentially independent of the number of motors if N is large enough (N> or approximately 5 for conventional kinesin). We show that a two-state ratchet model has a very similar behavior to that of the coarse-grained lattice model with effective interactions. The general picture is unaffected by motor attachment and detachment events.

Pause point spectra in DNA constant-force unzipping.

Under constant applied force, the separation of double-stranded DNA into two single strands is known to proceed through a series of pauses and jumps. Given experimental traces of constant-force unzipping, we present a method whereby the locations of pause points can be extracted in the form of a pause point spectrum. A simple theoretical model of DNA constant-force unzipping is presented, which generates theoretical pause point spectra through Monte Carlo simulation of the unzipping process. The locations of peaks in the experimental and theoretical pause point spectra are found to be nearly coincident below 6000 basepairs for unzipping the bacteriophage lambda-genome. The model only requires the sequence, temperature, and a set of empirical basepair binding and stacking energy parameters, and the good agreement with experiment suggests that pause point locations are primarily determined by the DNA sequence. The model is also used to predict pause point spectra for the bacteriophage phi X174 genome. The algorithm for extracting the pause point spectrum might also be useful for studying related systems which exhibit pausing behavior such as molecular motors.

Measurement of the phase diagram of DNA unzipping in the temperature-force plane.

We separate double stranded lambda phage DNA by applying a fixed force at a constant temperature ranging from 15 to 50 degrees C, and measure the minimum force required to separate the two strands. The measurements also offer information on the free energy of double stranded DNA (dsDNA) at temperatures where dsDNA does not thermally denature in the absence of force. While parts of the phase diagram can be explained using existing models and free energy parameters, others deviate significantly. Possible reasons for the deviations between theory and experiment are considered.

Disorder and nonconservation in a driven diffusive system.

We consider a disordered asymmetric exclusion process in which randomly chosen sites do not conserve particle number. The model is motivated by features of many interacting molecular motors such as RNA polymerases. We solve the steady state exactly in the two limits of infinite and vanishing nonconserving rates. The first limit is used as an approximation to large but finite rates and allows the study of Griffiths singularities in a nonequilibrium steady state despite the absence of any transition in the pure model. The disorder is also shown to induce a stretched exponential decay of system density with stretching exponent phi=2/5 .

Phase-separation transition in one-dimensional driven models.

A class of models of two-species driven diffusive systems which is shown to exhibit phase separation in d=1 dimensions is introduced. Unlike previously studied models exhibiting similar phenomena, here the relative density of the two species is fluctuating within the macroscopic domain of the phase separtated state. The nature of the phase transition from the homogeneous to the phase-separated state is discussed in view of a recently introduced criterion for phase separation in one-dimensional driven systems.

Griffiths singularities in unbinding of strongly disordered polymers.

Griffiths singularities occurring in the unbinding of strongly disordered heteropolymers are studied. A model with two randomly distributed binding energies, -1 and -v, is introduced and studied analytically by analyzing the Lee-Yang zeros of the partition sum. It is demonstrated that in the limit v--> infinity the model exhibits a Griffiths type singularity at a temperature T(G)=O(1) corresponding to melting of long homogeneous domains of the low binding energy. For finite v>>1 the model is expected to exhibit an additional, unbinding, transition at a high temperature T(M)=O(v).

Interstrand distance distribution of DNA near melting.

The distance distribution between complementary base pairs of the two strands of a DNA molecule is studied near the melting transition. Scaling arguments are presented for a generalized Poland-Scheraga-type model that includes self-avoiding interactions. At the transition temperature and for a large distance r, the distribution decays as 1/r(kappa) with kappa=1+(c-2)/nu. Here nu is the self-avoiding walk correlation length exponent and c is the exponent associated with the entropy of an open loop in the chain. Results for the distribution function just below the melting point are also presented. Numerical simulations that fully take into account the self-avoiding interactions are in good agreement with the scaling approach.

Criterion for phase separation in one-dimensional driven systems.

A general criterion for the existence of phase separation in driven density-conserving one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zero-range processes. The criterion is verified in all cases where analytical results are available, and predictions for other models are provided.

Ordering dynamics of the driven lattice-gas model.

The evolution of a two-dimensional driven lattice-gas model is studied on an LxxL(y) lattice. Scaling arguments and extensive numerical simulations are used to show that starting from random initial configuration the model evolves via two stages: (a) an early stage in which alternating stripes of particles and vacancies are formed along the direction y of the driving field, and (b) a stripe coarsening stage, in which the number of stripes is reduced and their average width increases. The number of stripes formed at the end of the first stage is shown to be a function of L(x)/L(straight phi)(y), with straight phi approximately 0.2. Thus, depending on this parameter, the resulting state could be either single or multistriped. In the second, stripe coarsening stage, the coarsening time is found to be proportional to L(y), becoming infinitely long in the thermodynamic limit. This implies that the multistriped state is thermodynamically stable. The results put previous studies of the model in a more general framework.

Search for correlates of protective immunity conferred by anthrax vaccine.

Vaccination by anthrax protective antigen (PA)-based vaccines requires multiple immunization, underlying the need to develop more efficacious vaccines or alternative vaccination regimens. In spite of the vast use of PA-based vaccines, the definition of a marker for protective immunity is still lacking. Here we describe studies designed to help define such markers. To this end we have immunized guinea pigs by different methods and monitored the immune response and the corresponding extent of protection against a lethal challenge with anthrax spores. Active immunization was performed by a single injection using one of two methods: (i) vaccination with decreasing amounts of PA and (ii) vaccination with constant amounts of PA that had been thermally inactivated for increasing periods. In both studies a direct correlation between survival and neutralizing-antibody titer was found (r(2) = 0.92 and 0.95, respectively). Most significantly, in the two protocols a similar neutralizing-antibody titer range provided 50% protection. Furthermore, in a complementary study involving passive transfer of PA hyperimmune sera to naive animals, a similar correlation between neutralizing-antibody titers and protection was found. In all three immunization studies, neutralization titers of at least 300 were sufficient to confer protection against a dose of 40 50% lethal doses (LD(50)) of virulent anthrax spores of the Vollum strain. Such consistency in the correlation of protective immunity with anti-PA antibody titers was not observed for antibody titers determined by an enzyme-linked immunosorbent assay. Taken together, these results clearly demonstrate that neutralizing antibodies to PA constitute a major component of the protective immunity against anthrax and suggest that this parameter could be used as a surrogate marker for protection.

Why is the DNA denaturation transition first order?

We study a model for the denaturation transition of DNA in which the molecules are considered as being composed of a sequence of alternating bound segments and denaturated loops. We take into account the excluded-volume interactions between denaturated loops and the rest of the chain by exploiting recent results on scaling properties of polymer networks of arbitrary topology. The phase transition is found to be first order in d = 2 dimensions and above, in agreement with experiments and at variance with previous theoretical results, in which only excluded-volume interactions within denaturated loops were taken into account. Our results agree with recent numerical simulations.