Long-term retention of antigens in germinal centers is controlled by the spatial organization of the follicular dendritic cell network.

Germinal centers (GCs) require sustained availability of antigens to promote antibody affinity maturation against pathogens and vaccines. A key source of antigens for GC B cells are immune complexes (ICs) displayed on follicular dendritic cells (FDCs). Here we show that FDC spatial organization regulates antigen dynamics in the GC. We identify heterogeneity within the FDC network. While the entire light zone (LZ) FDC network captures ICs initially, only the central cells of the network function as the antigen reservoir, where different antigens arriving from subsequent immunizations colocalize. Mechanistically, central LZ FDCs constitutively express subtly higher CR2 membrane densities than peripheral LZ FDCs, which strongly increases the IC retention half-life. Even though repeated immunizations gradually saturate central FDCs, B cell responses remain efficient because new antigens partially displace old ones. These results reveal the principles shaping antigen display on FDCs during the GC reaction.

Manipulating the selection forces during affinity maturation to generate cross-reactive HIV antibodies.

Generation of potent antibodies by a mutation-selection process called affinity maturation is a key component of effective immune responses. Antibodies that protect against highly mutable pathogens must neutralize diverse strains. Developing effective immunization strategies to drive their evolution requires understanding how affinity maturation happens in an environment where variants of the same antigen are present. We present an in silico model of affinity maturation driven by antigen variants which reveals that induction of cross-reactive antibodies often occurs with low probability because conflicting selection forces, imposed by different antigen variants, can frustrate affinity maturation. We describe how variables such as temporal pattern of antigen administration influence the outcome of this frustrated evolutionary process. Our calculations predict, and experiments in mice with variant gp120 constructs of the HIV envelope protein confirm, that sequential immunization with antigen variants is preferred over a cocktail for induction of cross-reactive antibodies focused on the shared CD4 binding site epitope.

Immune cells use active tugging forces to distinguish affinity and accelerate evolution.

Cells are known to exert forces to sense their physical surroundings for guidance of motion and fate decisions. Here, we propose that cells might do mechanical work to drive their own evolution, taking inspiration from the adaptive immune system. Growing evidence indicates that immune B cells-capable of rapid Darwinian evolution-use cytoskeletal forces to actively extract antigens from other cells' surfaces. To elucidate the evolutionary significance of force usage, we develop a theory of tug-of-war antigen extraction that maps receptor binding characteristics to clonal reproductive fitness, revealing physical determinants of selection strength. This framework unifies mechanosensing and affinity-discrimination capabilities of evolving cells: Pulling against stiff antigen tethers enhances discrimination stringency at the expense of absolute extraction. As a consequence, active force usage can accelerate adaptation but may also cause extinction of cell populations, resulting in an optimal range of pulling strength that matches molecular rupture forces observed in cells. Our work suggests that nonequilibrium, physical extraction of environmental signals can make biological systems more evolvable at a moderate energy cost.

Tuning environmental timescales to evolve and maintain generalists.

Natural environments can present diverse challenges, but some genotypes remain fit across many environments. Such "generalists" can be hard to evolve, outcompeted by specialists fitter in any particular environment. Here, inspired by the search for broadly neutralizing antibodies during B cell affinity maturation, we demonstrate that environmental changes on an intermediate timescale can reliably evolve generalists, even when faster or slower environmental changes are unable to do so. We find that changing environments on timescales comparable with evolutionary transients in a population enhance the rate of evolving generalists from specialists, without enhancing the reverse process. The yield of generalists is further increased in more complex dynamic environments, such as a "chirp" of increasing frequency. Our work offers design principles for how nonequilibrium fitness "seascapes" can dynamically funnel populations to genotypes unobtainable in static environments.

Roadmap on biology in time varying environments.

Biological organisms experience constantly changing environments, from sudden changes in physiology brought about by feeding, to the regular rising and setting of the Sun, to ecological changes over evolutionary timescales. Living organisms have evolved to thrive in this changing world but the general principles by which organisms shape and are shaped by time varying environments remain elusive. Our understanding is particularly poor in the intermediate regime with no separation of timescales, where the environment changes on the same timescale as the physiological or evolutionary response. Experiments to systematically characterize the response to dynamic environments are challenging since such environments are inherently high dimensional. This roadmap deals with the unique role played by time varying environments in biological phenomena across scales, from physiology to evolution, seeking to emphasize the commonalities and the challenges faced in this emerging area of research.

Aging-induced fragility of the immune system.

The adaptive and innate branches of the vertebrate immune system work in close collaboration to protect organisms from harmful pathogens. As an organism ages its immune system undergoes immunosenescence, characterized by declined performance or malfunction in either immune branch, which can lead to disease and death. In this study we develop a mathematical framework of coupled innate and adaptive immune responses, namely the integrated immune branch (IIB) model. This model describes dynamics of immune components in both branches, uses a shape-space representation to encode pathogen-specific immune memory, and exhibits three steady states - health, septic death, and chronic inflammation - qualitatively similar to clinically-observed immune outcomes. In this model, the immune system (initialized in the health state) is subjected to a sequence of pathogen encounters, and we use the number of prior pathogen encounters as a proxy for the "age" of the immune system. We find that repeated pathogen encounters may trigger a fragility in which any encounter with a novel pathogen will cause the system to irreversibly switch from health to chronic inflammation. This transition is consistent with the onset of "inflammaging", a condition observed in aged individuals who experience chronic low-grade inflammation even in the absence of pathogens. The IIB model predicts that the onset of chronic inflammation strongly depends on the history of encountered pathogens; the timing of onset differs drastically when the same set of infections occurs in a different order. Lastly, the coupling between the innate and adaptive immune branches generates a trade-off between rapid pathogen clearance and a delayed onset of immunosenescence. Overall, by considering the complex feedback between immune compartments, our work suggests potential mechanisms for immunosenescence and provides a theoretical framework at the system level and on the scale of an organism's lifetime to account for clinical observations.

Verifying Negative Sentences.

In the long history of psycholinguistic research on verifying negative sentences, an often-reported finding is that participants take longer to correctly judge negative sentences true than false, while being faster to judge their positive counterparts true (e.g. Clark & Chase, Cogn Psychol 3(3):472-517, 1972; Carpenter & Just, Psychol Rev 82(1):45-73, 1975). While many linguists and psycholinguists have strongly advocated the idea that the costs and complexity of negation can be explained by appeal to context, context-based approaches have not been able to provide a satisfying account of this polarity*truth-value interaction. By contrast, the alternative theory of negation processing, which says that negation is processed by separately representing the positive, does provide a plausible account. Our proposals provide a means for reconciliation between the two views since we argue that negation is a strong cue to a positive context. Here we present our account of why and when negation is often apparently processed via the positive. We review many of the factors that are seen to be at play in sentence verification involving negation. We present evidence that participants' adoption of the positive-first procedure in sentence-picture verification tasks is conditioned by context.

Evolving generalists in switching rugged landscapes.

Evolving systems, be it an antibody repertoire in the face of mutating pathogens or a microbial population exposed to varied antibiotics, constantly search for adaptive solutions in time-varying fitness landscapes. Generalists refer to genotypes that remain fit across diverse selective pressures; while multi-drug resistant microbes are undesired yet prevalent, broadly-neutralizing antibodies are much wanted but rare. However, little is known about under what conditions such generalists with a high capacity to adapt can be efficiently discovered by evolution. In addition, can epistasis-the source of landscape ruggedness and path constraints-play a different role, if the environment varies in a non-random way? We present a generative model to estimate the propensity of evolving generalists in rugged landscapes that are tunably related and alternating relatively slowly. We find that environmental cycling can substantially facilitate the search for fit generalists by dynamically enlarging their effective basins of attraction. Importantly, these high performers are most likely to emerge at intermediate levels of ruggedness and environmental relatedness. Our approach allows one to estimate correlations across environments from the topography of experimental fitness landscapes. Our work provides a conceptual framework to study evolution in time-correlated complex environments, and offers statistical understanding that suggests general strategies for eliciting broadly neutralizing antibodies or preventing microbes from evolving multi-drug resistance.

Active Tuning of Synaptic Patterns Enhances Immune Discrimination.

Immune cells learn about their antigenic targets using tactile sense: a self-organized motif named immunological synapse forms between an immune cell and an antigen-presenting cell (APC) during recognition. Via synapses, immune cells apply mechanical pulling forces to selectively extract antigen (Ag) from APCs. Curiously, depending on its stage of development, a B lymphocyte exhibits distinct synaptic patterns and uses force at different strength and timing, which appears to strongly impact its ability to distinguish Ag affinities. We use a statistical-mechanical model to study how the experimentally observed synaptic architectures can originate from normal cytoskeletal forces coupled to the lateral organization of mobile receptors, and show how this active regulation scheme, collective in nature, may enhance the efficiency and capacity of discrimination.

Optimal Sequential Immunization Can Focus Antibody Responses against Diversity Loss and Distraction.

Affinity maturation is a Darwinian process in which B lymphocytes evolve potent antibodies to encountered antigens and generate immune memory. Highly mutable complex pathogens present an immense antigenic diversity that continues to challenge natural immunity and vaccine design. Induction of broadly neutralizing antibodies (bnAbs) against this diversity by vaccination likely requires multiple exposures to distinct but related antigen variants, and yet how affinity maturation advances under such complex stimulation remains poorly understood. To fill the gap, we present an in silico model of affinity maturation to examine two realistic new aspects pertinent to vaccine development: loss in B cell diversity across successive immunization periods against different variants, and the presence of distracting epitopes that entropically disfavor the evolution of bnAbs. We find these new factors, which introduce additional selection pressures and constraints, significantly influence antibody breadth development, in a way that depends crucially on the temporal pattern of immunization (or selection forces). Curiously, a less diverse B cell seed may even favor the expansion and dominance of cross-reactive clones, but only when conflicting selection forces are presented in series rather than in a mixture. Moreover, the level of frustration due to evolutionary conflict dictates the degree of distraction. We further describe how antigenic histories select evolutionary paths of B cell lineages and determine the predominant mode of antibody responses. Sequential immunization with mutationally distant variants is shown to robustly induce bnAbs that focus on conserved elements of the target epitope, by thwarting strain-specific and distracted lineages. An optimal range of antigen dose underlies a fine balance between efficient adaptation and persistent reaction. These findings provide mechanistic guides to aid in design of vaccine strategies against fast mutating pathogens.

The effects of somatic hypermutation on neutralization and binding in the PGT121 family of broadly neutralizing HIV antibodies.

Broadly neutralizing HIV antibodies (bnAbs) are typically highly somatically mutated, raising doubts as to whether they can be elicited by vaccination. We used 454 sequencing and designed a novel phylogenetic method to model lineage evolution of the bnAbs PGT121-134 and found a positive correlation between the level of somatic hypermutation (SHM) and the development of neutralization breadth and potency. Strikingly, putative intermediates were characterized that show approximately half the mutation level of PGT121-134 but were still capable of neutralizing roughly 40-80% of PGT121-134 sensitive viruses in a 74-virus panel at median titers between 15- and 3-fold higher than PGT121-134. Such antibodies with lower levels of SHM may be more amenable to elicitation through vaccination while still providing noteworthy coverage. Binding characterization indicated a preference of inferred intermediates for native Env binding over monomeric gp120, suggesting that the PGT121-134 lineage may have been selected for binding to native Env at some point during maturation. Analysis of glycan-dependent neutralization for inferred intermediates identified additional adjacent glycans that comprise the epitope and suggests changes in glycan dependency or recognition over the course of affinity maturation for this lineage. Finally, patterns of neutralization of inferred bnAb intermediates suggest hypotheses as to how SHM may lead to potent and broad HIV neutralization and provide important clues for immunogen design.

Active contractility in actomyosin networks.

Contractile forces are essential for many developmental processes involving cell shape change and tissue deformation. Recent experiments on reconstituted actomyosin networks, the major component of the contractile machinery, have shown that active contractility occurs above a threshold motor concentration and within a window of cross-link concentration. We present a microscopic dynamic model that incorporates two essential aspects of actomyosin self-organization: the asymmetric load response of individual actin filaments and the correlated motor-driven events mimicking myosin-induced filament sliding. Using computer simulations, we examine how the concentration and susceptibility of motors contribute to their collective behavior and interplay with the network connectivity to regulate macroscopic contractility. Our model is shown to capture the formation and dynamics of contractile structures and agree with the observed dependence of active contractility on microscopic parameters, including the contractility onset. Cooperative action of load-resisting motors in a force-percolating structure integrates local contraction/buckling events into a global contractile state via an active coarsening process, in contrast to the flow transition driven by uncorrelated kicks of susceptible motors.

On the spontaneous collective motion of active matter.

Spontaneous directed motion, a hallmark of cell biology, is unusual in classical statistical physics. Here we study, using both numerical and analytical methods, organized motion in models of the cytoskeleton in which constituents are driven by energy-consuming motors. Although systems driven by small-step motors are described by an effective temperature and are thus quiescent, at higher order in step size, both homogeneous and inhomogeneous, flowing and oscillating behavior emerges. Motors that respond with a negative susceptibility to imposed forces lead to an apparent negative-temperature system in which beautiful structures form resembling the asters seen in cell division.

Microscopic theory of the glassy dynamics of passive and active network materials.

Signatures of glassy dynamics have been identified experimentally for a rich variety of materials in which molecular networks provide rigidity. Here we present a theoretical framework to study the glassy behavior of both passive and active network materials. We construct a general microscopic network model that incorporates nonlinear elasticity of individual filaments and steric constraints due to crowding. Based on constructive analogies between structural glass forming liquids and random field Ising magnets implemented using a heterogeneous self-consistent phonon method, our scheme provides a microscopic approach to determine the mismatch surface tension and the configurational entropy, which compete in determining the barrier for structural rearrangements within the random first order transition theory of escape from a local energy minimum. The influence of crosslinking on the fragility of inorganic network glass formers is recapitulated by the model. For active network materials, the mapping, which correlates the glassy characteristics to the network architecture and properties of nonequilibrium motor processes, is shown to capture several key experimental observations on the cytoskeleton of living cells: Highly connected tense networks behave as strong glass formers; intense motor action promotes reconfiguration. The fact that our model assuming a negative motor susceptibility predicts the latter suggests that on average the motorized processes in living cells do resist the imposed mechanical load. Our calculations also identify a spinodal point where simultaneously the mismatch penalty vanishes and the mechanical stability of amorphous packing disappears.

Active patterning and asymmetric transport in a model actomyosin network.

Cytoskeletal networks, which are essentially motor-filament assemblies, play a major role in many developmental processes involving structural remodeling and shape changes. These are achieved by nonequilibrium self-organization processes that generate functional patterns and drive intracellular transport. We construct a minimal physical model that incorporates the coupling between nonlinear elastic responses of individual filaments and force-dependent motor action. By performing stochastic simulations we show that the interplay of motor processes, described as driving anti-correlated motion of the network vertices, and the network connectivity, which determines the percolation character of the structure, can indeed capture the dynamical and structural cooperativity which gives rise to diverse patterns observed experimentally. The buckling instability of individual filaments is found to play a key role in localizing collapse events due to local force imbalance. Motor-driven buckling-induced node aggregation provides a dynamic mechanism that stabilizes the two-dimensional patterns below the apparent static percolation limit. Coordinated motor action is also shown to suppress random thermal noise on large time scales, the two-dimensional configuration that the system starts with thus remaining planar during the structural development. By carrying out similar simulations on a three-dimensional anchored network, we find that the myosin-driven isotropic contraction of a well-connected actin network, when combined with mechanical anchoring that confers directionality to the collective motion, may represent a novel mechanism of intracellular transport, as revealed by chromosome translocation in the starfish oocyte.

Modeling and Simulation of the Hysteretic Behavior of Concrete under Cyclic Tension-Compression Using the Smeared Crack Approach.

Concrete structures under wind and earthquake loads will experience tensile and compressive stress reversals. It is very important to accurately reproduce the hysteretic behavior and energy dissipation of concrete materials under cyclic tension-compression for the safety evaluation of concrete structures. A hysteretic model for concrete under cyclic tension-compression is proposed in the framework of smeared crack theory. Based on the crack surface opening-closing mechanism, the relationship between crack surface stress and cracking strain is constructed in a local coordinate system. Linear loading-unloading paths are used and the partial unloading-reloading condition is considered. The hysteretic curves in the model are controlled by two parameters: the initial closing stress and the complete closing stress, which can be determined by the test results. Comparison with several experimental results shows that the model is capable of simulating the cracking process and hysteretic behavior of concrete. In addition, the model is proven to be able to reproduce the damage evolution, energy dissipation, and stiffness recovery caused by crack closure during the cyclic tension-compression. The proposed model can be applied to the nonlinear analysis of real concrete structures under complex cyclic loads.

Multiple phase transitions shape biodiversity of a migrating population.

In a wide variety of natural systems, closely related microbial strains coexist stably, resulting in high levels of fine-scale biodiversity. However, the mechanisms that stabilize this coexistence are not fully understood. Spatial heterogeneity is one common stabilizing mechanism, but the rate at which organisms disperse throughout the heterogeneous environment may strongly impact the stabilizing effect that heterogeneity can provide. An intriguing example is the gut microbiome, where active mechanisms affect the movement of microbes and potentially maintain diversity. We investigate how biodiversity is affected by migration rate using a simple evolutionary model with heterogeneous selection pressure. We find that the biodiversity-migration rate relationship is shaped by multiple phase transitions, including a reentrant phase transition to coexistence. At each transition, an ecotype goes extinct and dynamics exhibit critical slowing down (CSD). CSD is encoded in the statistics of fluctuations due to demographic noise-this may provide an experimental means for detecting and altering impending extinction.

Tensegrity and motor-driven effective interactions in a model cytoskeleton.

Actomyosin networks are major structural components of the cell. They provide mechanical integrity and allow dynamic remodeling of eukaryotic cells, self-organizing into the diverse patterns essential for development. We provide a theoretical framework to investigate the intricate interplay between local force generation, network connectivity, and collective action of molecular motors. This framework is capable of accommodating both regular and heterogeneous pattern formation, arrested coarsening and macroscopic contraction in a unified manner. We model the actomyosin system as a motorized cat's cradle consisting of a crosslinked network of nonlinear elastic filaments subjected to spatially anti-correlated motor kicks acting on motorized (fibril) crosslinks. The phase diagram suggests there can be arrested phase separation which provides a natural explanation for the aggregation and coalescence of actomyosin condensates. Simulation studies confirm the theoretical picture that a nonequilibrium many-body system driven by correlated motor kicks can behave as if it were at an effective equilibrium, but with modified interactions that account for the correlation of the motor driven motions of the actively bonded nodes. Regular aster patterns are observed both in Brownian dynamics simulations at effective equilibrium and in the complete stochastic simulations. The results show that large-scale contraction requires correlated kicking.