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From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate (ATP). Moreover, chromatin motion varies with genomic coordinate, pointing towards a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers non-equilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward disentangling active and passive mechanisms of folding, we discuss a data-driven approach to discern if and how active processes affect genome organization.

Fluctuation-induced forces (FIFs) are prevalent in nature, covering a plethora of phenomena spanning biophysics to cosmology. The common ingredients are: (i) A fluctuating medium that can be described by a probability distribution; and (ii) External objects whose presence constrains (or somehow modifies) these fluctuations. The overall strength of the interaction is proportional to the magnitude of undistorted fluctuations; while its range is set by the extent of correlations of the fluctuations. In this Chapter we focus on some interesting cases when the interactions are long–ranged and arise from scale free fluctuations. We first discuss the universality of FIF in equilibrium (set by $k_B T$ and $\hbar$ for thermal and quantum fluctuations) using tools from statistical mechanics and field-theory. The dependence of FIF on boundary shapes is explored next in the context of polymers; and finally we conclude by considering FIF in non-equilibrium settings with conservation laws.

We study how walls confining active fluids interact with asymmetric passive objects placed in their bulk. We show that the objects experience non-conservative long-ranged forces mediated by the active bath. To leading order, these forces can be computed using a generalized image theorem. The walls repel asymmetric objects, irrespective of their microscopic properties or their orientations. For circular cavities, we demonstrate how this may lead to the localization of asymmetric objects in the center of the cavity, something impossible for symmetric ones.

We discuss and analyze the properties of Casimir forces acting between nonreciprocal objects in thermal equilibrium. By starting from the fluctuation-dissipation theorem and splitting the force into those arising from individual sources, we show that if all temperatures are equal, the resulting force is reciprocal and is derivable as the gradient of a Casimir (free) energy. While the expression for the free energy is identical to the one for reciprocal objects, there are several distinct features: To leading order in reflections, the free energy can be decomposed as the sum of two terms, the first corresponding to two reciprocal objects, and the second corresponding to two anti-reciprocal objects. The first term is negative and typically yields attraction, while the second can have either sign. For the case of two objects that are each other's mirror images, the second term is positive and yields repulsion. The sum of terms can lead to overall repulsive forces, in agreement with previous observations. Stable configurations, ruled out for reciprocal cases, appear possible for nonreciprocal objects. We show that for three objects, a three-body free energy exists, indicating that previously found persistent heat currents in situations of three objects cannot be used to produce persistent torques.

The Casimir force provides a striking example of the effects of quantum fluctuations in a mesoscopic system. Because it arises from the objects' electromagnetic response, the necessary calculations in quantum field theory are most naturally expressed in terms of electromagnetic scattering from each object. In this review we illustrate a variety of such techniques, with a focus on those that can be expressed in terms of surface effects, including both idealized boundary conditions and their physical realization in terms of material properties., Comment: 29 pages, 2 figures; invited contribution to Annual Reviews in Nuclear and Particle Science; v2: minor editing of version for publication

First proposed as an empirical rule over half a century ago, the Richards growth equation has been frequently invoked in population modeling and pandemic forecasting. Central to this model is the advent of a fractional exponent $\gamma$, typically fitted to the data. While various motivations for this non-analytical form have been proposed, it is still considered foremost an empirical fitting procedure. Here, we find that Richards-like growth laws emerge naturally from generic analytical growth rules in a distributed population, upon inclusion of {\bf (i)} migration (spatial diffusion) amongst different locales, and {\bf (ii)} stochasticity in the growth rate, also known as "seascape noise." The latter leads to a wide (power-law) distribution in local population number that, while smoothened through the former, can still result in a fractional growth law for the overall population. This justification of the Richards growth law thus provides a testable connection to the distribution of constituents of the population., Comment: 12 pages, 7 figures

There still are no effective long-term protective vaccines against viruses that continuously evolve under immune pressure such as seasonal influenza, which has caused, and can cause, devastating epidemics in the human population. For finding such a broadly protective immunization strategy it is useful to know how easily the virus can escape via mutation from specific antibody responses. This information is encoded in the fitness landscape of the viral proteins (i.e., knowledge of the viral fitness as a function of sequence). Here we present a computational method to infer the intrinsic mutational fitness landscape of influenza-like evolving antigens from yearly sequence data. We test inference performance with computer-generated sequence data that are based on stochastic simulations mimicking basic features of immune-driven viral evolution. Although the numerically simulated model does create a phylogeny based on the allowed mutations, the inference scheme does not use this information. This provides a contrast to other methods that rely on reconstruction of phylogenetic trees. Our method just needs a sufficient number of samples over multiple years. With our method we are able to infer single-as well as pairwise mutational fitness effects from the simulated sequence time series for short antigenic proteins. Our fitness inference approach may have potential future use for design of immunization protocols by identifying intrinsically vulnerable immune target combinations on antigens that evolve under immune-driven selection. This approach may in the future be applied to influenza and other novel viruses such as SARS-CoV-2, which evolves and, like influenza, might continue to escape the natural and vaccine-mediated immune pressures.

We study Eigen’s model of quasi-species (Eigen in Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58(10):465, 1971), characterized by sequences that replicate with a specified fitness and mutate independently at single sites. The evolution of the population vector in time is then closely related to that of quantum spins in imaginary time. We employ multiple perspectives and tools from interacting quantum systems to examine growth and collapse of realistic viral populations, specifically considering excessive mutations in certain HIV proteins. All approaches used, including the simplest perturbation theory, give consistent results.

Persistent motion of passive asymmetric bodies in non-equilibrium media has been experimentally observed in a variety of settings. However, fundamental constraints on the efficiency of such motion are not fully explored. Understanding such limits, and ways to circumvent them, is important for efficient utilization of energy stored in agitated surroundings for purposes of taxis and transport. Here, we examine such issues in the context of erratic movements of a passive asymmetric dumbbell driven by non-equilibrium noise. For uncorrelated (white) noise, we find a (non-Boltzmann) joint probability distribution for the velocity and orientation, which indicates that the dumbbell preferentially moves along its symmetry axis. The dumbbell thus behaves as an Ornstein–Uhlenbeck walker, a prototype of active matter. Exploring the efficiency of this active motion, we show that in the over-damped limit, the persistence length l of the dumbbell is bound from above by half its mean size, while the propulsion speed v∥ is proportional to its inverse size. The persistence length can be increased by exploiting inertial effects beyond the over-damped regime, but this improvement always comes at the price of smaller propulsion speeds. This limitation is explained by noting that the diffusivity of a dumbbell, related to the product v∥ l, is always less than that of its components, thus severely constraining the usefulness of passive dumbbells as active particles.

Arguments based on symmetry and thermodynamics may suggest the existence of a ratchet-like lateral Casimir force between two plates at different temperatures and with broken inversion symmetry. We find that this is not sufficient, and at least one plate must be made of nonreciprocal material. This setup operates as a heat engine by transforming heat radiation into mechanical force. Although the ratio of the lateral force to heat transfer in the near field regime diverges inversely with the plates separation, $d$, an Onsager symmetry, which we extend to nonreciprocal plates, limits the engine efficiency to the Carnot value $\eta_c$. The optimal velocity of operation in the far field is of the order of $c\eta_c$, where $c$ is the speed of light. In the near field regime, this velocity can be reduced to the order of $\bar\omega d \eta_c$, where $\bar\omega$ is a typical material frequency., Comment: V2 and V3 Minor corrections

We show that disordered boundaries destroy bulk phase separation in scalar active systems in dimension $d, Comment: 18 pages, 11 figures

We study the impact of a random quenched potentials and torques on scalar active matter. Microscopic simulations reveal that motility-induced phase separation is replaced in two-dimensions by an asymptotically homogeneous phase with anomalous long-ranged correlations and non-vanishing steady-state currents. Using a combination of phenomenological models and a field-theoretical treatment, we show the existence of a lower-critical dimension, $d_c=4$, below which phase separation is only observed for systems smaller than an Imry-Ma length-scale. We identify a weak-disorder regime in which the structure factor scales as $S(q) \sim 1/q^2$ which accounts for our numerics. In $d=2$ we predict that, at larger scales, the behaviour should cross over to a strong-disorder regime. In $d>2$, these two regimes exist separately, depending on the strength of the potential., 14 pages, 8 figures

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wavefunction amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: phase transitions which are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions which are continuous become governed by new critical exponents. We introduce a more general class of models which encompasses both cases, and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies., Comment: 10 pages, 9 figures

Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed population with logistic growth at each location, subject to "seascape" noise, wherein the population's fitness randomly varies with {\it location and time}. Despite its simplicity, the model actually incorporates variants of directed percolation, and directed polymers in random media, within a mean-field perspective. Probability distributions of the population can be computed self-consistently; and the extinction transition is shown to exhibit novel critical behavior with exponents dependent on the ratio of the strengths of migration and noise amplitudes. The results are compared and contrasted with the more conventional choice of demographic noise due to stochastic changes in reproduction.

Quantum and thermal fluctuations of electromagnetic waves are the cornerstone of quantum and statistical physics, and inherent to such phenomena as thermal radiation and van der Waals forces. While the basic principles are the material of elementary texts, recent experimental and technological advances have made it necessary to come to terms with counterintuitive consequences of electromagnetic fluctuations at short scales -- in the so called {\it near-field} regime. We focus on three manifestations of such behavior: {\bf (i)} The Stefan--Boltzmann law describes thermal radiation from macroscopic bodies, but fails to account for magnitude, polarization and coherence of radiation from small objects (say compared to the skin depth). {\bf (ii)} The heat transfer between two bodies at similar close proximity is dominated by evanescent waves, and can be several orders of magnitude larger than the classical contribution due to propagating waves. {\bf (iii)} Casimir/van der Waals interactions are a dominant force between objects at sub-micron separation; the non-equilibrium analogs of this force (for objects at different temperatures) have not been sufficiently explored (at least experimentally). To explore these phenomena we introduce the tool of fluctuational quantum electrodynamics (QED) originally introduced by Rytov in the 1950s. Combined with a scattering formalism, this enables studies of heat radiation and transfer, equilibrium and non-equilibrium forces for objects of different material properties, shapes, separations and arrangements., Comment: accepted for publication in Annual Reviews of Condensed Matter Physics

How does removal of sites by a random walk lead to blockage of percolation? To study this problem of correlated site percolation, we consider a random walk (RW) of $N=uL^d$ steps on a $d$-dimensional hypercubic lattice of size $L^d$ (with periodic boundaries). We systematically explore dependence of the probability $��_d(L,u)$ of percolation (existence of a spanning cluster) of sites not removed by the RW on $L$ and $u$. The concentration of unvisited sites decays exponentially with increasing $u$, while the visited sites are highly correlated -- their correlations decaying with the distance $r$ as $1/r^{d-2}$ (in $d>2$). Upon increasing $L$, the percolation probability $��_d(L,u)$ approaches a step function, jumping from 1 to 0 when $u$ crosses a percolation threshold $u_c$ that is close to 3 for all $3\le d\le6$. Within numerical accuracy, the correlation length associated with percolation diverges with exponents consistent with $��=2/(d-2)$. There is no percolation threshold at the lower critical dimension of $d=2$, with the percolation probability approaching a smooth function $��_2(\infty,u)>0$., RevTex, 12 pages, 13 figures

International audience; The effects of quenched disorder on a single and many active run-and-tumble particles is studied in one dimension. For a single particle, we consider both the steady-state distribution and the particle's dynamics subject to disorder in three parameters: a bounded external potential, the particle's speed, and its tumbling rate. We show that in the case of a disordered potential, the behavior is like an equilibrium particle diffusing on a random force landscape, implying a dynamics that is logarithmically slow in time. In the situations of disorder in the speed or tumbling rate, we find that the particle generically exhibits diffusive motion, although particular choices of the disorder may lead to anomalous diffusion. Based on the single-particle results, we find that in a system with many interacting particles, disorder in the potential leads to strong clustering. We characterize the clustering in two different regimes depending on the system size and show that the mean cluster size scales with the system size, in contrast to non-disordered systems.

Directed Percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has appeared as a generic model for the evolutionary/ecological dynamics of competing bacterial populations. Range expansion -- the stochastic reproduction of bacteria competing for space to be occupied by their progeny -- leads to a fluctuating and rough growth front, which is known from experiment and simulation to affect the underlying critical behavior of the DP transition. In this work, we employ symmetry arguments to construct a pair of non-linear stochastic partial differential equations describing the co-evolution of surface roughness with the composition field of DP. Macroscopic manifestations (phenomenology) of these equations on growth patterns and genealogical tracks of range expansion are discussed; followed by a renormalization group analysis of possible scaling behaviors at the DP transition., 13+9 pages, 5+5 figures, 1 table

Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational symmetry. Deformations, e.g. by a bulge or indentation, break symmetry and can pin a pattern. We adapt methods of conformal mapping and perturbation theory to examine how curvature inhomogeneities select and pin patterns, and confirm the results numerically. The theory provides an analogy to quantum mechanics in a geometry-dependent potential and yields intuitive implications for cell membranes, tissues, thin films, and noise-induced quasipatterns., substantial re-write of arXiv:1710.00103

During infection by the human immunodeficiency virus (HIV), mutations accumulate in the intra-host viral population due to selection imposed by host T cell responses. The timescales at which HIV residues acquire mutations in a host range from days to years, correlating with their diversity in the global population of hosts, and with the relative strengths at which different regions of the HIV sequence are targeted by the host. In recent years, “fitness landscapes” of HIV proteins have been estimated from the global HIV sequence diversity, and stochastic simulations ofin silicoHIV infection, using these inferred landscapes, were shown to generate escape mutations whose locations and relative timescales correlate with those measured in patients with known T cell responses. These results suggest that the residue-specific fitness costs and epistatic interactions in the inferred landscapes encode useful information allowing for predictions of the dynamics of HIV mutations; however, currently available computational approaches to HIV dynamics that make use of realistic fitness landscapes are limited to these fixed-population-size stochastic simulations, which require many simulation runs and do not provide further insight as to why certain mutations tend to arise in a given host and for a given sequence background. In this paper, we introduce and examine an alternative approach, which we designate the evolutionary mean-field (EMF) method. EMF is an approximate high-recombination-rate model of HIV replication and mutation, in whose limit the dynamics of a large, diverse population of HIV sequences becomes computationally tractable. EMF takes as input the fitness landscape of an HIV protein, the locations and strengths of a host’s T cell responses, and the infecting HIV strain(s), and outputs a set of time-dependent “effective fitnesses” and frequencies of mutation at each HIV residue over time. Importantly, the effective fitnesses depend crucially on the fitness costs, epistatic interactions, and time-varying sequence background, thus automatically encoding how their combined effect influences the tendency for an HIV residue to mutate, in a time-dependent manner. As a proof of principle, we apply EMF to the dynamics of the p24 gag protein infecting a host whose T cell responses are known, and show how features of the fitness landscape, relative strengths of host T cell responses, and the sequence background impact the locations and time course of HIV escape mutations, which is consistent with previous work employing stochastic simulations. Furthermore, we show how features of longer-term HIV dynamics, specifically reversions, may be described in terms of these effective fitnesses, and also quantify the mean fitness and site entropy of the intra-host population over time. Finally, we introduce a stochastic population dynamics extension of EMF, where population size changes depend crucially on the fitness of strains existing in the population at each time, unlike prior stochastic simulation approaches with a fixed population size or a time-varying one that is externally defined. The EMF method offers an alternative framework for studying how genetic-level attributes of the virus and host immune response impact both the evolutionary and population dynamics of HIV, in a computationally tractable way.Author summaryFitness landscapes of HIV proteins have recently been inferred from HIV sequence diversity in the global population of hosts, and have been used in simulations ofin silicoHIV infection to predict the locations and relative timescales of mutations arising in hosts with known immune responses. However, computational approaches to HIV dynamics using realistic fitness landscapes are currently limited to these fixed-population-size stochastic simulations, which require many simulation runs and do not provide further insight as to why certain mutations tend to arise in a given host and for a given sequence background. Here, we introduce an alternative approach designated the evolutionary mean-field (EMF) method, which is an approximate high-recombination-rate model of HIV dynamics. It takes as input an HIV fitness landscape, the locations and strengths of a host’s immune responses, and the infecting HIV strain(s), and outputs a set of time-dependent “effective fitnesses” and frequencies of mutation at each HIV residue over time. We apply EMF on an example to show how features of the fitness landscape, relative strengths of host immune responses, and the HIV sequence background modify the effective fitnesses and hence the locations and time course of HIV mutations. We also develop a stochastic population dynamics extension of EMF where population size changes depend crucially on the fitness of strains existing in the population at each time. The EMF method enables more detailed study of how genetic-level attributes of the virus and host immune response shape the evolutionary and population dynamics of HIV, in a computationally tractable way.

Ensembles of biological and artificial microswimmers produce long-range velocity fields with strong nonequilibrium fluctuations, which result in dramatic increase diffusivity of embedded particles (tracers). While such enhanced diffusivity may point to enhanced mixing of the fluid, a rigorous quantification of the mixing efficiency requires analysis of pair dispersion of tracers, rather than simple one-particle diffusivity. Here, we calculate analytically the scale-dependent coefficient of relative diffusivity of passive tracers embedded in a dilute suspension of run-and-tumble microswimmers. Although each tracer is subject to strong fluctuations resulting in large absolute diffusivity, the small-scale relative dispersion is suppressed due to the correlations in fluid velocity which are relevant when the inter-tracers separation is below the persistence length of the swimmers motion. Our results suggest that the reorientation of swimming direction plays an important role in biological mixing and should be accounted in design of potential active matter devices capable of effective fluid mixing at microscale., Comment: 9 pages, 3 figures

Perturbations of fluid media can give rise to non-equilibrium dynamics, which may, in turn, cause motion of immersed inclusions or tracer particles. We consider perturbations ("activations") that are local in space and time, of a fluid density which is conserved, and study the resulting diffusiophoretic phenomena that emerge at a large distance. Specifically, we consider cases where the perturbations propagate diffusively, providing examples from passive and active matter for which this is expected to be the case. Activations can, for instance, be realized by sudden and local changes in interaction potentials of the medium or by local changes in its activity. Various analytical results are provided for the case of confinement by two parallel walls. We investigate the possibility of extracting work from inclusions, which are moving through the activated fluid. Furthermore, we show that a time-dependent density profile, created via suitable activation protocols, allows for the conveyance of inclusions along controlled and stable trajectories. In contrast, in states with a steady density, inclusions cannot be held at stable positions, reminiscent of Earnshaw's theorem of electrostatics. We expect these findings to be applicable in a range of experimental systems. The phenomena described here are argued to be distinct from other forms of phoresis such as thermophoresis., NSF (DMR-1708280)

We consider localization of a random walk (RW) when attracted or repelled by multiple extended manifolds of different dimensionalities. In particular, we consider a RW near a rectangular wedge in two dimensions, where the (zero-dimensional) corner and the (one-dimensional) wall have competing localization properties. This model applies also (as cross section) to an ideal polymer attracted to the surface or edge of a rectangular wedge in three dimensions. More generally, we consider (d-1)- and (d-2)-dimensional manifolds in d-dimensional space, where attractive interactions are (fully or marginally) relevant. The RW can then be in one of four phases where it is localized to neither, one, or both manifolds. The four phases merge at a special multicritical point where (away from the manifolds) the RW spreads diffusively. Extensive numerical analyses on two-dimensional RWs confined inside or outside a rectangular wedge confirm general features expected from a continuum theory, but also exhibit unexpected attributes, such as a reentrant localization to the corner while repelled by it.

Non-equilibrium systems are known to exhibit long-ranged correlations due to conservation of quantities like density or momentum. This, in turn, leads to long-ranged fluctuation-induced (Casimir) forces, predicted to arise in a variety of non-equilibrium settings. Here, we study such forces, which arise transiently between parallel plates or compact inclusions in a gas of particles, following a change ("quench") in temperature or activity of the medium. Analytical calculations, as well as numerical simulations of passive or active Brownian particles, indicate two distinct forces: (i) The immediate effect of the quench is adsorption or desorption of particles of the medium to the immersed objects, which in turn initiates a front of relaxing (mean) density. This leads to time-dependent {\it density-induced forces}. (ii) A long-term effect of the quench is that density fluctuations are modified, manifested as transient (long-ranged) (pair-)correlations that relax diffusively to their (short-ranged) steady-state limit. As a result, transient {\it fluctuation-induced forces} emerge. We discuss the properties of fluctuation-induced and density-induced forces as regards universality, relaxation as a function of time, and scaling with distance between objects. Their distinct signatures allow us to distinguish the two types of forces in simulation data. Finally, we propose several scenarios for their experimental observation., Comment: - Added Journal reference and DOI - Modified title - Fixed minor typos - Added plot of Eq. (32) [16 pages, 11 figures]

T cell receptors (TCRs) bind foreign or self-peptides attached to major histocompatibility complex (MHC) molecules, and the strength of this interaction determines T cell activation. Optimizing the ability of T cells to recognize a diversity of foreign peptides yet be tolerant of self-peptides is crucial for the adaptive immune system to properly function. This is achieved by selection of T cells in the thymus, where immature T cells expressing unique, stochastically generated TCRs interact with a large number of self-peptide-MHC; if a TCR does not bind strongly enough to any self-peptide-MHC, or too strongly with at least one self-peptide-MHC, the T cell dies. Past theoretical work cast thymic selection as an extreme value problem, and characterized the statistical enrichment or depletion of amino acids in the post-selection TCR repertoire, showing how T cells are selected to be able to specifically recognize peptides derived from diverse pathogens, yet have limited self-reactivity. Here, we investigate how the degree of enrichment is modified by nonuniform contacts that a TCR makes with peptide-MHC. Specifically, we were motivated by recent experiments showing that amino acids at certain positions of a TCR sequence have large effects on thymic selection outcomes, and crystal structure data that reveal a nonuniform contact profile between a TCR and its peptide-MHC ligand. Using a representative TCR contact profile as an illustration, we show via simulations that the degree of enrichment now varies by position according to the contact profile, and, importantly, it depends on the implementation of nonuniform contacts during thymic selection. We explain these nontrivial results analytically. Our study has implications for understanding the selection forces that shape the functionality of the post-selection TCR repertoire., 10 pages, 4 figures, submitted to Phys. Rev. E

© 2019 Elsevier Ltd When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic spatial wandering of both genetic lineages and the boundaries between genetically segregated sectors. Laboratory experiments on microbial range expansions have shown that this stochastic wandering, transverse to the front, is superdiffusive due to the front's growing roughness, implying much faster loss of genetic diversity than predicted by simple flat front diffusive models. We study the evolutionary consequences of this superdiffusive wandering using two complementary numerical models of range expansions: the stepping stone model, and a new interpretation of the model of directed paths in random media, in the context of a roughening population front. Through these approaches we compute statistics for the times since common ancestry for pairs of individuals with a given spatial separation at the front, and we explore how environmental heterogeneities can locally suppress these superdiffusive fluctuations.

The enormous genetic diversity and mutability of HIV has prevented effective control of this virus by natural immune responses or vaccination. Evolution of the circulating HIV population has thus occurred in response to diverse, ultimately ineffective, immune selection pressures that randomly change from host to host. We show that the interplay between the diversity of human immune responses and the ways that HIV mutates to evade them results in distinct sets of sequences defined by similar collectively coupled mutations. Scaling laws that relate these sets of sequences resemble those observed in linguistics and other branches of inquiry, and dynamics reminiscent of neural networks are observed. Like neural networks that store memories of past stimulation, the circulating HIV population stores memories of host-pathogen combat won by the virus. We describe an exactly solvable model that captures the main qualitative features of the sets of sequences and a simple mechanistic model for the origin of the observed scaling laws. Our results define collective mutational pathways used by HIV to evade human immune responses, which could guide vaccine design.

A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a repulsive wedge. The well-known mapping between the statistical mechanics of an ideal polymer and the quantum problem of a particle in a potential is then used to analyze the singular behavior of the unbinding transition of the polymer. The divergence of the localization length is found to be governed by an exponent that varies continuously with the angle (when reflex). Numerical treatment of the discrete (lattice) version of such an adsorption problem confirms this behavior.

We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles, but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or cone), when the polymer is repelled by the obstacles, or is marginally attracted to it (close to the depinning transition where the absorption length is infinite). In such cases, the separation $h$ between obstacles is the only relevant macroscopic length scale, and the polymer mediated force equals ${\cal A} \, k_{B}T/h$, where $T$ is temperature. The amplitude ${\cal A}$ is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of ${\cal A}$, which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find ${\cal A}=0$ for ideal polymers at the adsorption transition point, irrespective of shapes of the obstacles, i.e. at this special point there is no polymer-mediated force between obstacles (scale-free or not)., Comment: RevTeX, 10 pages, 10 figures

The Casimir--Polder interaction between an anisotropic particle and a surface is orientation dependent. We study novel orientational effects that arise due to curvature of the surface for distances much smaller than the radii of curvature by employing a derivative expansion. For nanoparticles we derive a general short distance expansion of the interaction potential in terms of their dipolar polarizabilities. Explicit results are presented for nano-spheroids made of SiO$_2$ and gold, both at zero and at finite temperatures. The preferred orientation of the particle is strongly dependent on curvature, temperature, as well as material properties., Comment: 9 pages, 10 encapsulated figures

In addition to an innate immune system that battles pathogens in a nonspecific fashion, higher organisms, such as humans, possess an adaptive immune system to combat diverse (and evolving) microbial pathogens. Remarkably, the adaptive immune system mounts pathogen-specific responses, which can be recalled upon reinfection with the same pathogen. It is difficult to see how the adaptive immune system can be preprogrammed to respond specifically to a vast and unknown set of pathogens. Although major advances have been made in understanding pertinent molecular and cellular phenomena, the precise principles that govern many aspects of an immune response are largely unknown. We discuss complementary approaches from statistical mechanics and cell biology that can shed light on how key components of the adaptive immune system, T cells, develop to enable pathogen-specific responses against many diverse pathogens. The mechanistic understanding that emerges has implications for how host genetics may influence the development of T cells with differing responses to the human immunodeficiency virus (HIV) infection., Ragon Institute of MGH, MIT and Harvard, National Institutes of Health (U.S.) (Grant 1PO1-AI071195-01), National Science Foundation (U.S.) (Grant DMR-12-06323), National Institutes of Health (U.S.) (Director's Pioneer Award)

Strategies to elicit Abs that can neutralize diverse strains of a highly mutable pathogen are likely to result in a potent vaccine. Broadly neutralizing Abs (bnAbs) against HIV have been isolated from patients, proving that the human immune system can evolve them. Using computer simulations and theory, we study immunization with diverse mixtures of variant antigens (Ags). Our results show that particular choices for the number of variant Ags and the mutational distances separating them maximize the probability of inducing bnAbs. The variant Ags represent potentially conflicting selection forces that can frustrate the Darwinian evolutionary process of affinity maturation. An intermediate level of frustration maximizes the chance of evolving bnAbs. A simple model makes vivid the origin of this principle of optimal frustration. Our results, combined with past studies, suggest that an appropriately chosen permutation of immunization with an optimally designed mixture (using the principles that we describe) and sequential immunization with variant Ags that are separated by relatively large mutational distances may best promote the evolution of bnAbs.

We study, from first principles, the pressure exerted by an active fluid of spherical particles on general boundaries in two dimensions. We show that, despite the non-uniform pressure along curved walls, an equation of state is recovered upon a proper spatial averaging. This holds even in the presence of pairwise interactions between particles or when asymmetric walls induce ratchet currents, which are accompanied by spontaneous shear stresses on the walls. For flexible obstacles, the pressure inhomogeneities lead to a modulational instability as well as to the spontaneous motion of short semi-flexible filaments. Finally, we relate the force exerted on objects immersed in active baths to the particle flux they generate around them., 6 pages, 5 figures and 8 pages of supplementary information

We use a derivative expansion for gently curved surfaces to compute the leading and the next-to-leading curvature corrections to the Casimir-Polder interaction between a polarizable small particle and a non-planar surface. While our methods apply to any homogeneous and isotropic surface, explicit results are presented here for perfect conductors. We show that the derivative expansion of the Casimir-Polder potential follows from a resummation of its perturbative series, for small in-plane momenta. We consider the retarded, non-retarded and classical high temperature limits., Comment: 6 pages, 1 Figure