Tunable nonequilibrium dynamics of field quenches in spin ice

We present nonequilibrium physics in spin ice as a unique setting that combines kinematic constraints, emergent topological defects, and magnetic long-range Coulomb interactions. In spin ice, magnetic frustration leads to highly degenerate yet locally constrained ground states. Together, they form a highly unusual magnetic state—a “Coulomb phase”—whose excitations are point-like defects—magnetic monopoles—in the absence of which effectively no dynamics is possible. Hence, when they are sparse at low temperature, dynamics becomes very sluggish. When quenching the system from a monopole-rich to a monopole-poor state, a wealth of dynamical phenomena occur, the exposition of which is the subject of this article. Most notably, we find reaction diffusion behavior, slow dynamics owing to kinematic constraints, as well as a regime corresponding to the deposition of interacting dimers on a honeycomb lattice. We also identify potential avenues for detecting the magnetic monopoles in a regime of slow-moving monopoles. The interest in this model system is further enhanced by its large degree of tunability and the ease of probing it in experiment: With varying magnetic fields at different temperatures, geometric properties—including even the effective dimensionality of the system—can be varied. By monitoring magnetization, spin correlations or zero-field NMR, the dynamical properties of the system can be extracted in considerable detail. This establishes spin ice as a laboratory of choice for the study of tunable, slow dynamics.The nature and origin of unusual—in particular, slow—dynamics in disorder-free systems (1) are among the most fascinating aspects of disciplines as diverse as the physics of structural glasses and polymers (2), chemical reactions, and biological matter (3). Kinetically constrained models, following the original idea by Fredrickson and Andersen (4), represent one paradigm in which unusual dynamics is generated by short-distance ingredients alone without disorder (5). Another is provided by reaction-diffusion systems, in which spatial and temporal fluctuations feed off each other to provide a wide variety of dynamical phenomena (6) especially due to the slow decay of long wavelength fluctuations.Spin ice systems (7) allow combining both aspects, thanks to the nature of their emergent topological excitations, which take the form of magnetic monopoles (8, 9) with long-range Coulomb interactions. The ground-state correlations in these localized spin systems lead to kinematic constraints in the reaction-diffusion behavior of these mobile excitations (10, 11, 12).Understanding the dynamics of spin ice systems, and in particular proposing new ways to probe their out-of-equilibrium properties, is of direct experimental relevance. For instance, modeling the emergent excitations near equilibrium (13, 14) allowed gaining insight on the observed spin freezing at low temperatures (15, 16) and explaining in part the time scales measured in zero-field NMR (17). Despite the fast-paced progress, several open questions remain unanswered, in particular concerning the behavior of spin ice materials far from equilibrium, as evidenced for instance by recent low-temperature magnetic relaxation experiments (18–20).In this article, we study the strongly out-of-equilibrium behavior following a quench from a monopole-rich to a monopole-poor regime by means of varying an applied magnetic field. We uncover a wide range of dynamical regimes and we provide a theoretical understanding of their origin. We show that the initial evolution maps onto a deposition of dimers on a honeycomb lattice, in the presence of long-range Coulomb interactions between the “vacancies” (i.e., the uncovered sites). The long-time behavior can instead be understood as a dynamical arrest owing to the appearance of field-induced energy barriers to monopole motion. This regime can be seen as similar to conventional spin ice, but with a monopole hopping time exponentially sensitive to temperature: We have a Coulomb liquid in which time can pass arbitrarily slowly.We discuss how to probe these phenomena in experiment, showing how by monitoring magnetization, spin correlations, or zero-field NMR the dynamical properties of the system can be extracted in detail.Overall, this richness and versatility establish spin ice as a laboratory of choice for the study of slow dynamics arising from an interplay of frustration (local constraints), topological defects (monopoles), and magnetic long-range Coulomb interactions.     

Axis-dependent anisotropy in protein unfolding from integrated nonequilibrium single-molecule experiments, analysis, and simulation

We present a comprehensive study that integrates experimental and theoretical nonequilibrium techniques to map energy landscapes along well defined pull-axis specific coordinates to elucidate mechanisms of protein unfolding. Single-molecule force-extension experiments along two different axes of photoactive yellow protein combined with nonequilibrium statistical mechanical analysis and atomistic simulation reveal energetic and mechanistic anisotropy. Steered molecular dynamics simulations and free-energy curves constructed from the experimental results reveal that unfolding along one axis exhibits a transition-state-like feature where six hydrogen bonds break simultaneously with weak interactions observed during further unfolding. The other axis exhibits a constant (unpeaked) force profile indicative of a noncooperative transition, with enthalpic (e.g., H-bond) interactions being broken throughout the unfolding process. Striking qualitative agreement was found between the force-extension curves derived from steered molecular dynamics calculations and the equilibrium free-energy curves obtained by Jarzynski–Hummer–Szabo analysis of the nonequilibrium work data. The anisotropy persists beyond pulling distances of more than twice the initial dimensions of the folded protein, indicating a rich energy landscape to the mechanically fully unfolded state. Our findings challenge the notion that cooperative unfolding is a universal feature in protein stability.     

Free energy landscapes for initiation and branching of protein aggregation

Experiments on artificial multidomain protein constructs have probed the early stages of aggregation processes, but structural details of the species that initiate aggregation remain elusive. Using the associative-memory, water-mediated, structure and energy model known as AWSEM, a transferable coarse-grained protein model, we performed simulations of fused constructs composed of up to four copies of the Titin I27 domain or its mutant I27* (I59E). Free energy calculations enable us to quantify the conditions under which such multidomain constructs will spontaneously misfold. Consistent with experimental results, the dimer of I27 is found to be the smallest spontaneously misfolding construct. Our results show how structurally distinct misfolded states can be stabilized under different thermodynamic conditions, and this result provides a plausible link between the single-molecule misfolding experiments under native conditions and aggregation experiments under denaturing conditions. The conditions for spontaneous misfolding are determined by the interplay among temperature, effective local protein concentration, and the strength of the interdomain interactions. Above the folding temperature, fusing additional domains to the monomer destabilizes the native state, and the entropically stabilized amyloid-like state is favored. Because it is primarily energetically stabilized, the domain-swapped state is more likely to be important under native conditions. Both protofibril-like and branching structures are found in annealing simulations starting from extended structures, and these structures suggest a possible connection between the existence of multiple amyloidogenic segments in each domain and the formation of branched, amorphous aggregates as opposed to linear fibrillar structures.Mature fibrils are a most striking feature of protein aggregation-related diseases, but how these structures relate to disease pathology remains an open question (1–4). Recent evidence supports the notion that in some cases fibers are by-products of a process that starts with oligomers that are themselves toxic and pathogenic. It is then vitally important to understand the early stages of aggregation that are invisible to many experimental techniques. Molecular simulations can be useful for proposing candidate misfolded structures and other oligomeric species. These initial seeds may or may not end up becoming incorporated into a fiber or an amorphous, nonfibrillar aggregate. In this study, we show how free energy calculations using a coarse-grained protein model can be used to determine the minimal number of domains needed for a fused construct to spontaneously misfold under different thermodynamic conditions. These simulations based on a transferable potential capable of low-resolution structure prediction (5, 6) also allow us to obtain detailed information about the misfolded structures, which can serve as the bridge between low oligomeric species and insoluble aggregates.The fundamental question of how individual protein domains fold to nearly unique structures in a short amount of time has been answered in the form of the Principle of minimal frustration (7), and a quantitative understanding of this critical self-organization process has grown out of the framework of the energy landscape theory (ELT) of protein folding (8). Although initially these ideas were investigated using analytical models (9) and further tested with relatively simple lattice models (10), the degree of detail and realism of the models that have now been optimized using ELT makes them useful for practical tasks such as de novo prediction of protein structures (5) and prediction of binding interfaces (6). Protein folding theory provides a solid framework on which to build our understanding of misfolding (11). Misfolding and aggregation are bigger problems when the concentration of protein domains is high. Many proteins in nature are, in fact, multidomain proteins (12), consisting of multiple covalently linked but (semi)independently folding domains. In such systems, the local concentration of protein domains is always high because of their covalent linkages. Artificial multidomain protein constructs are therefore good systems for probing the early stages of aggregation.The question of the size of the smallest thermodynamically stable misfolded species is fundamental to understanding the aggregation process as a whole. Despite the experimental difficulties, recent progress has been made using isolated artificial multidomain protein constructs (13). Using these constructs allows the experimentalist to control precisely the number of interacting domains. These low-oligomer misfolding experiments differ from aggregation experiments where only the average concentration of a sample is fixed. In aggregation experiments, the structural and thermodynamic details of the transiently populated species that seed aggregation are hidden beneath a cascade of events. Aggregation experiments that monitor the concentration of macroscopic aggregates in bulk (12, 14) typically observe a lag phase and then a fast growth phase after aggregation has been seeded. The size of the critical initiating species can be roughly inferred by repeating these types of experiments using constructs with a variable number of domains, but the wide range of time and spatial scales involved makes these inferences nontrivial. In this study we focus our attention on systems that have been studied in aggregation experiments, but use simulation techniques that are more akin to studies using isolated fused constructs in hopes that we can make a connection between these two levels of observation.Previously, equilibrium simulations using a lattice model with the Miyazawa–Jernigan potential (15) have suggested that the melting temperature decreases as the concentration increases, and misfolding is entropically driven near the folding temperature of a single chain. Off-lattice native structure-based models have also been used to probe the folding of multidomain proteins (16) as well as to understand the biophysical consequences of tethering in multidomain proteins (17). An early use of lattice models for studying the initial stages of aggregation yielded a phase diagram including six phases with varying degrees of order present at different temperatures and concentrations (18). The state-of-the-art coarse-grained models used to study protein aggregation have been reviewed recently (19). Here we investigate the equilibrium thermodynamics of multidomain protein folding and misfolding using an optimized, transferable, and coarse-grained protein force field named AWSEM for associative-memory, water-mediated, structure and energy model. We recently used AWSEM to clarify the multidomain protein misfolding at the level of a single pair of neighboring domains (20). In this paper, we extend our study of the I27 protein to larger constructs with up to four domains. We study how the free energy landscape changes as the number of domains increases. We quantify the relative stability between the native and the misfolded states via equilibrium umbrella sampling (21) simulations to infer the minimal number of domains needed for spontaneous misfolding under different conditions of temperature and strength of interdomain interactions. We also perform simulated annealing simulations to characterize the possible misfolded structures of oligomers. Our analysis suggests a connection between the existence of multiple amyloidogenic segments per domain and a preference for forming amorphous branched aggregates as opposed to linear, fibril-like structures.     

地理景观特征与鼠疫关系的研究概述

鼠疫是由鼠疫耶尔森菌引起的人兽共患的烈性传染病,鼠疫生态地理景观是形成自然疫源地的重要因素。疫源地地理景观类型多样,结构复杂,探讨地理景观特征与鼠疫的关系及其相关的研究技术,对阐明各类疫源地的适宜生境、鉴别地理生态环境系统的脆弱性及预防鼠疫的发生流行具有重要作用。     

Ecosystem service bundles for analyzing tradeoffs in diverse landscapes

A key challenge of ecosystem management is determining how to manage multiple ecosystem services across landscapes. Enhancing important provisioning ecosystem services, such as food and timber, often leads to tradeoffs between regulating and cultural ecosystem services, such as nutrient cycling, flood protection, and tourism. We developed a framework for analyzing the provision of multiple ecosystem services across landscapes and present an empirical demonstration of ecosystem service bundles, sets of services that appear together repeatedly. Ecosystem service bundles were identified by analyzing the spatial patterns of 12 ecosystem services in a mixed-use landscape consisting of 137 municipalities in Quebec, Canada. We identified six types of ecosystem service bundles and were able to link these bundles to areas on the landscape characterized by distinct social–ecological dynamics. Our results show landscape-scale tradeoffs between provisioning and almost all regulating and cultural ecosystem services, and they show that a greater diversity of ecosystem services is positively correlated with the provision of regulating ecosystem services. Ecosystem service-bundle analysis can identify areas on a landscape where ecosystem management has produced exceptionally desirable or undesirable sets of ecosystem services.     

Better outcomes for pest pressure,insecticide use,and yield in less intensive agricultural landscapes

Agricultural systems have been continuously intensified to meet rising demand for agricultural products. However, there are increasing concerns that larger, more connected crop fields and loss of seminatural areas exacerbate pest pressure, but findings to date have been inconclusive. Even less is known about whether increased pest pressure results in measurable effects for farmers, such as increased insecticide use and decreased crop yield. Using extensive spatiotemporal data sampled every 2 to 3 d throughout five growing seasons in 373 cotton fields, we show that pests immigrated earlier and were more likely to occur in larger cotton fields embedded in landscapes with little seminatural area (<10%). Earlier pest immigration resulted in earlier spraying that was further linked to more sprays per season. Importantly, crop yield was the lowest in these intensified landscapes. Our results demonstrate that both environmental conservation and production objectives can be achieved in conventional agriculture by decreasing field sizes and maintaining seminatural vegetation in the surrounding landscapes.

There are increasing concerns that the rapid loss of seminatural areas and larger sizes and connectance of crop fields in the past several decades have made them more susceptible to pest outbreaks, thereby requiring greater insecticide uses (1–3). Meehan et al. (1) estimated that landscape simplification at the county scale was associated with increased insecticide application to 1.4 million hectares in a seven-state region of the United States and an associated increase in direct costs of between US$34 and US$103 million. Global market value of crop protection chemicals is projected to increase from US$50.62 billion in 2017 to US$68.82 billion by the end of 2025, mainly due to a growing demand for insecticides (4). This is an alarming issue, not only because of an increase in farm costs due to insecticide spraying but also because of increasing pest resistance and secondary incursion as well as increased insecticide exposure in surrounding areas negatively affecting air, soil, and water quality; biodiversity; ecosystem processes; and human health (5, 6).There are several reasons why pest and insecticide pressure may be exacerbated in larger fields and in simple landscapes (low proportion of seminatural area). Simple landscapes can shorten the time and increase the frequency of pest immigration by increasing the amount and connectivity of crop resources to the pest, while simultaneously decreasing abundances of their natural enemies (7). Island biogeography theory (8) and the resource concentration hypothesis (9) set the framework for the mechanisms of increased pest pressure with increased field sizes, particularly if pests have large dispersal distances and high reproductive rate (10). In addition, natural enemies of crop pests may be restricted mainly to the edges of fields, thus limiting any effective biocontrol in the interior of large fields (10).Despite this growing theoretical knowledge, it remains to be demonstrated in a real-world situation how local and landscape factors drive pest immigration and dynamics in crop fields. Management measures to reduce pest immigration might require lower investment and deliver better outcomes than managing for conservation biocontrol, but they have largely been overlooked (ref. 11, but see refs. 12 and 13). Previous studies that related landscape effects to pest pressure found inconsistent results (see syntheses in refs. 14 and 15). Moreover, the majority of these studies do not extend their findings to measures relevant to farmers, such as the consequences of pest management (insecticide spraying) and crop yield (16, 17). A handful of studies that measured landscape-dependent insecticide spraying did this at too coarse a scale (county rather than field data) to be directly applicable for farmers and decision making (1, 2, 18, 19). This is a major obstacle in the adoption of management recommendations, and therefore, it is essential to focus research on variables of interest and at relevant spatial and temporal scales in order to bridge the gap between field experiments, policy, and on the ground actions (16).Here, we take advantage of a unique field-level crop, pest, insecticide, and yield dataset from 626 cotton field-season combinations on the Darling Downs, Queensland, Australia, studied from 2010 to 2015 (373 fields, some of which were sampled over several seasons, SI Appendix, Fig. S1). The data have high temporal resolution of the main cotton pest (mirids, Hemiptera: Heteroptera) sampling at two to three times per week throughout each crop season, allowing us to estimate the time of pest immigration and their dynamics in the field. The field-level observations allowed for the investigation of a link between agricultural intensification and insecticide use, while accounting for pest populations and estimating overall implications for yield. Furthermore, using data sampled over multiple seasons is uncommon (17), increases confidence in the results, and is important given inconsistencies in the previous findings over time (18).Finally, the data were collected by an agronomic consultancy company, with no economic ties to insecticide sales (see Materials and Methods). This company is contracted by farmers to conduct surveys of pests and to provide recommendations on insecticide spraying based on industry standard economic thresholds [a pest population density at which control is recommended (20)]. These field-level decisions made according to the advice provided by the same company in our study minimized any possible effect of exogenous confounding variables which could have influenced insecticide use, such as the farmer’s knowledge, skills, income, perception of pest risk, and the possibility of more frequent insecticide applications at larger farms due to economies of scales (21).     

Force fluctuations and polymerization dynamics of intracellular microtubules

Microtubules are highly dynamic biopolymer filaments involved in a wide variety of biological processes including cell division, migration, and intracellular transport. Microtubules are very rigid and form a stiff structural scaffold that resists deformation. However, despite their rigidity, inside of cells they typically exhibit significant bends on all length scales. Here, we investigate the origin of these bends using a Fourier analysis approach to quantify their length and time dependence. We show that, in cultured animal cells, bending is suppressed by the surrounding elastic cytoskeleton, and even large intracellular forces only cause significant bending fluctuations on short length scales. However, these lateral bending fluctuations also naturally cause fluctuations in the orientation of the microtubule tip. During growth, these tip fluctuations lead to microtubule bends that are frozen-in by the surrounding elastic network. This results in a persistent random walk of the microtubule, with a small apparent persistence length of approximately 30 microm, approximately 100 times smaller than that resulting from thermal fluctuations alone. Thus, large nonthermal forces govern the growth of microtubules and can explain the highly curved shapes observed in the microtubule cytoskeleton of living cells.     

Mechanism of enhanced mechanical stability of a minimal RNA kissing complex elucidated by nonequilibrium molecular dynamics simulations

An RNA kissing loop from the Moloney murine leukemia virus (MMLV) exhibits unusual mechanical stability despite having only two intermolecular base pairs. Mutations at this junction have been shown to destabilize genome dimerization, with concomitant reductions in viral packaging efficiency and infectivity. Optical tweezers experiments have shown that it requires as much force to break the MMLV kissing-loop complex as is required to unfold an 11-bp RNA hairpin [Li PTX, Bustamante C, Tinoco I (2006) Proc Natl Acad Sci USA 103:15847-15852]. Using nonequilibrium all-atom molecular dynamics simulations, we have developed a detailed model for the kinetic intermediates of the force-induced dissociation of the MMLV dimerization initiation site kissing loop. Two hundred and eight dissociation events were simulated (approximately 16 μs total simulation time) under conditions of constant applied external force, which we use to construct a Markov state model for kissing-loop dissociation. We find that the complex undergoes a conformational rearrangement, which allows for equal distribution of the applied force among all of the intermolecular hydrogen bonds, which is intrinsically more stable than the sequential unzipping of an ordinary hairpin. Stacking interactions with adjacent, unpaired loop adenines further stabilize the complex by increasing the repair rate of partially broken H-bonds. These stacking interactions are prominently featured in the transition state, which requires additional coordinates orthogonal to the end-to-end extension to be uniquely identified. We propose that these stabilizing features explain the unusual stability of other retroviral kissing-loop complexes such as the HIV dimerization site.     

Topography of funneled landscapes determines the thermodynamics and kinetics of protein folding

The energy landscape approach has played a fundamental role in advancing our understanding of protein folding. Here, we quantify protein folding energy landscapes by exploring the underlying density of states. We identify three quantities essential for characterizing landscape topography: the stabilizing energy gap between the native and nonnative ensembles δE, the energetic roughness ΔE, and the scale of landscape measured by the entropy S. We show that the dimensionless ratio between the gap, roughness, and entropy of the system accurately predicts the thermodynamics, as well as the kinetics of folding. Large Λ implies that the energy gap (or landscape slope towards the native state) is dominant, leading to more funneled landscapes. We investigate the role of topological and energetic roughness for proteins of different sizes and for proteins of the same size, but with different structural topologies. The landscape topography ratio Λ is shown to be monotonically correlated with the thermodynamic stability against trapping, as characterized by the ratio of folding temperature versus trapping temperature. Furthermore, Λ also monotonically correlates with the folding kinetic rates. These results provide the quantitative bridge between the landscape topography and experimental folding measurements.     

Signatures and control of strong-field dynamics in a complex system

Controlling chemical reactions by light, i.e., the selective making and breaking of chemical bonds in a desired way with strong-field lasers, is a long-held dream in science. An essential step toward achieving this goal is to understand the interactions of atomic and molecular systems with intense laser light. The main focus of experiments that were performed thus far was on quantum-state population changes. Phase-shaped laser pulses were used to control the population of final states, also, by making use of quantum interference of different pathways. However, the quantum-mechanical phase of these final states, governing the system’s response and thus the subsequent temporal evolution and dynamics of the system, was not systematically analyzed. Here, we demonstrate a generalized phase-control concept for complex systems in the liquid phase. In this scheme, the intensity of a control laser pulse acts as a control knob to manipulate the quantum-mechanical phase evolution of excited states. This control manifests itself in the phase of the molecule’s dipole response accessible via its absorption spectrum. As reported here, the shape of a broad molecular absorption band is significantly modified for laser pulse intensities ranging from the weak perturbative to the strong-field regime. This generalized phase-control concept provides a powerful tool to interpret and understand the strong-field dynamics and control of large molecules in external pulsed laser fields.Can we find universal concepts to understand and control the response of atoms and molecules in interactions with strong laser fields? This question is at the heart of a vast number of experiments in time-resolved spectroscopy (1–30). The wide range of light sources spanning the spectral range from the X-ray (e.g., free-electron laser sources, synchrotrons) over the visible (conventional laser systems) to the far-infrared regime and covering the temporal range from nanosecond down to attosecond time scales created a wealth of new physics insight into quantum mechanisms, however mostly of simple systems in the gas phase (1–4). In chemistry, the generation of femtosecond laser pulses enabled the investigation of wave packet dynamics in molecules, as the induced vibrations occur on these time scales. Experiments focusing on, for instance, dissociation reactions, atom transfer, isomerization, or solvation dynamics have led to a deeper understanding of chemical bonds and their breakage dynamics and have opened and established the field of femtochemistry (5, 6). The aim is not only to study the light−matter interaction, but to use the obtained understanding of the processes to control the dynamics in complex molecules and, in the future, even to be able to control chemical reactions (7–10). Shaping the amplitude and phase of femtosecond laser pulses has been used, for example, to control the shape of wavefunctions in atomic systems (11) or to control and optimize the single-photon and multiphoton fluorescence in atoms such as cesium (12) and complex systems, e.g., dye molecules (13). Shaped pulses are also used in time-resolved coherent anti-Stokes Raman scattering (14–16) or 2D spectroscopy (17, 18). Adaptive shaping of the pulses via feedback control even allows the optimization of dynamical processes, e.g., the relative photodissociation yield of organometallic molecules (19), the relative two-photon fluorescence yield of dye molecules (20), and the energy transfer in light-harvesting molecules (21).However, the strong-field dynamics in complex systems, e.g., in the liquid phase, and its control have only recently moved into scientific focus (22–27). The dynamics of complex systems was thus far studied mainly in perturbative experiments such as transient absorption spectroscopy, which measures the evolution of a system after absorbing a single or a few photons. These experiments mainly measured population dynamics of excited states, without gaining access to the phases of the excited wavefunction coefficients. Even the phase-sensitive method of 2D/3D spectroscopy (28, 29), which evolved out of transient absorption spectroscopy, probes the perturbative third- or fifth-order response of the system and has not yet been used to systematically understand the strong-field response of a complex system. However, an important ingredient in approaching the ultimate goal of controlling chemistry is to get access to the phase of quantum-state coefficients and to analyze systematically the phase of the system’s response. In recent work, the phase of the dipole response after excitation was measured and controlled in a simple system, namely gaseous helium (31, 32). Transient absorption experiments were performed using extreme-UV attosecond pulses and 7-fs short visible to near-infrared (VIS/NIR) pulses, and the absorption was measured as a function of the time delay. The intensity of the femtosecond pulse could be varied in addition to the time delay. Thereby, the dipole response was systematically investigated as a function of the laser pulse intensity, ranging from the weak perturbative to the strong-field regime. Modifications of the absorption line shapes of helium from Fano to Lorentzian profiles and vice versa were observed with increasing VIS/NIR pulse intensity. These changes can be explained by an induced phase shift of the dipole response that is caused by the femtosecond pulse. Thus, the laser pulse intensity can be used as a control knob to modify the system’s response in a desired manner. In this work, we present the generalization of an atomic strong-field phase-control concept to complex systems in the liquid phase.     

A framework for generating and analyzing movement paths on ecological landscapes

The movement paths of individuals over landscapes are basically represented by sequences of points (x_i, y_i) occurring at times t_i. Theoretically, these points can be viewed as being generated by stochastic processes that in the simplest cases are Gaussian random walks on featureless landscapes. Generalizations have been made of walks that (i) take place on landscapes with features, (ii) have correlated distributions of velocity and direction of movement in each time interval, (iii) are Lévy processes in which distance or waiting-time (time-between steps) distributions have infinite moments, or (iv) have paths bounded in space and time. We begin by demonstrating that rather mild truncations of fat-tailed step-size distributions have a dramatic effect on dispersion of organisms, where such truncations naturally arise in real walks of organisms bounded by space and, more generally, influenced by the interactions of physiological, behavioral, and ecological factors with landscape features. These generalizations permit not only increased realism and hence greater accuracy in constructing movement pathways, but also provide a biogeographically detailed epistemological framework for interpreting movement patterns in all organisms, whether tossed in the wind or willfully driven. We illustrate the utility of our framework by demonstrating how fission–fusion herding behavior arises among individuals endeavoring to satisfy both nutritional and safety demands in heterogeneous environments. We conclude with a brief discussion of potential methods that can be used to solve the inverse problem of identifying putative causal factors driving movement behavior on known landscapes, leaving details to references in the literature.     

Social network models predict movement and connectivity in ecological landscapes

Network analysis is on the rise across scientific disciplines because of its ability to reveal complex, and often emergent, patterns and dynamics. Nonetheless, a growing concern in network analysis is the use of limited data for constructing networks. This concern is strikingly relevant to ecology and conservation biology, where network analysis is used to infer connectivity across landscapes. In this context, movement among patches is the crucial parameter for interpreting connectivity but because of the difficulty of collecting reliable movement data, most network analysis proceeds with only indirect information on movement across landscapes rather than using observed movement to construct networks. Statistical models developed for social networks provide promising alternatives for landscape network construction because they can leverage limited movement information to predict linkages. Using two mark-recapture datasets on individual movement and connectivity across landscapes, we test whether commonly used network constructions for interpreting connectivity can predict actual linkages and network structure, and we contrast these approaches to social network models. We find that currently applied network constructions for assessing connectivity consistently, and substantially, overpredict actual connectivity, resulting in considerable overestimation of metapopulation lifetime. Furthermore, social network models provide accurate predictions of network structure, and can do so with remarkably limited data on movement. Social network models offer a flexible and powerful way for not only understanding the factors influencing connectivity but also for providing more reliable estimates of connectivity and metapopulation persistence in the face of limited data.     

The movement ecology and dynamics of plant communities in fragmented landscapes

A conceptual model of movement ecology has recently been advanced to explain all movement by considering the interaction of four elements: internal state, motion capacity, navigation capacities, and external factors. We modified this framework to generate predictions for species richness dynamics of fragmented plant communities and tested them in experimental landscapes across a 7-year time series. We found that two external factors, dispersal vectors and habitat features, affected species colonization and recolonization in habitat fragments and their effects varied and depended on motion capacity. Bird-dispersed species richness showed connectivity effects that reached an asymptote over time, but no edge effects, whereas wind-dispersed species richness showed steadily accumulating edge and connectivity effects, with no indication of an asymptote. Unassisted species also showed increasing differences caused by connectivity over time, whereas edges had no effect. Our limited use of proxies for movement ecology (e.g., dispersal mode as a proxy for motion capacity) resulted in moderate predictive power for communities and, in some cases, highlighted the importance of a more complete understanding of movement ecology for predicting how landscape conservation actions affect plant community dynamics.     

Evolutionary dynamics,evolutionary forces,and robustness: A nonequilibrium statistical mechanics perspective

Any realistic evolutionary theory has to consider 1) the dynamics of organisms that reproduce and possess heritable traits, 2) the appearance of stochastic variations in these traits, and 3) the selection of those organisms that better survive and reproduce. These elements shape the “evolutionary forces” that characterize the evolutionary dynamics. Here, we introduce a general model of reproduction–variation–selection dynamics. By treating these dynamics as a nonequilibrium thermodynamic process, we make precise the notion of the forces that characterize evolution. One of these forces, in particular, can be associated with the robustness of reproduction to variations. Some of the detailed predictions of our model can be tested by quantitative laboratory experiments, similar to those performed in the past on evolving populations of proteins or viruses.

A conventional view of evolutionary dynamics is based on three essential elements (1): 1) organism reproduction with imperfect heredity; 2) variations, including mutations, which are typically introduced by the reproduction process; and 3) selection, which acts within a population and allows some variant species to survive and reproduce, while eliminating others. When considering variations, a sizeable fraction of evolutionary biology is focused on genetic and epigenetic variations. However, variations upon which selection acts are occurring on multiple levels, and involve many entities, traits, and behaviors that are usually encapsulated by a rather imprecise concept of phenotype (2, 3). Regarding selection, many phenotypic aspects contribute to long-term survival and reproduction. Two instances are the interactions between the organisms (e.g., sexual reproduction, predation, competition and cooperation, and social organization) and the interactions with biotic and abiotic environmental factors (e.g., the presence of other species or the inorganic composition of a certain habitat), whose changes span multiple spatiotemporal scales.The main role of (necessarily) simplistic mathematical models of evolution is to analyze the possible outcomes of evolution and to explore the assumptions that generate these outcomes. In this way, one hopes to clarify some essential concepts used by evolutionary narratives. In the present work, we formulate a simple model that incorporates the three essential elements described above. Consequently, we call the evolutionary dynamics described by this model the reproduction–variation–selection (RVS) dynamics. In formulating the model, we seek both simplicity and generality. For the sake of generality, we specify neither the particular nature of the hereditary variables nor that of the related variations: They can be genetic, epigenetic, or phenotypic. For the sake of simplicity, we assume large population sizes and the presence of a constant environment. By building a theoretical framework inspired by nonequilibrium statistical mechanics (4–7), we can study this dynamics in its generality. In fact, we can clearly define the notion of evolutionary force and explicate its relation to reproduction, variations, and selection. Because of the simplicity of the model, we are able to get analytical expressions for different force terms, and to perform explicit analyses of the role played by them. In particular, we uncover an evolutionary force within the RVS dynamics that can engender robustness of reproduction to variations, without any explicit selection for this trait. By adding restraining assumptions to the model, we can also make simple predictions about the behavior of population robustness during the RVS dynamics. Lastly, we compare our predictions with the results of laboratory experiments on populations of evolving viruses.     

Coevolutionary information,protein folding landscapes,and the thermodynamics of natural selection

The energy landscape used by nature over evolutionary timescales to select protein sequences is essentially the same as the one that folds these sequences into functioning proteins, sometimes in microseconds. We show that genomic data, physical coarse-grained free energy functions, and family-specific information theoretic models can be combined to give consistent estimates of energy landscape characteristics of natural proteins. One such characteristic is the effective temperature T_sel at which these foldable sequences have been selected in sequence space by evolution. T_sel quantifies the importance of folded-state energetics and structural specificity for molecular evolution. Across all protein families studied, our estimates for T_sel are well below the experimental folding temperatures, indicating that the energy landscapes of natural foldable proteins are strongly funneled toward the native state.The physics and natural history of proteins are inextricably intertwined (1, 2). The cooperative manner in which proteins find their way to a folded structure is the result of proteins having undergone natural selection and not typical of random polymers (3, 4). Likewise, the requirement that most proteins must fold to function is a strong constraint on their phylogeny. The unavoidable random mutation events that proteins have undergone throughout their evolution have provided countless numbers of physicochemical experiments on folding landscapes. Thus, the evolutionary patterns of proteins found through comparative sequence analysis can be used to understand protein structure and energetics. In this paper, we compare the information content in the correlated changes that have occurred in protein sequences of common ancestry with energies from a transferable energy function to quantify the influence of maintaining foldability on molecular evolution.     

Potential landscape and flux framework of nonequilibrium networks: robustness, dissipation, and coherence of biochemical oscillations

We established a theoretical framework for studying nonequilibrium networks with two distinct natures essential for characterizing the global probabilistic dynamics: the underlying potential landscape and the corresponding curl flux. We applied the idea to a biochemical oscillation network and found that the underlying potential landscape for the oscillation limit cycle has a distinct closed ring valley (Mexican hat-like) shape when the fluctuations are small. This global landscape structure leads to attractions of the system to the ring valley. On the ring, we found that the nonequilibrium flux is the driving force for oscillations. Therefore, both structured landscape and flux are needed to guarantee a robust oscillating network. The barrier height separating the oscillation ring and other areas derived from the landscape topography is shown to be correlated with the escaping time from the limit cycle attractor and provides a quantitative measure of the robustness for the network. The landscape becomes shallower and the closed ring valley shape structure becomes weaker (lower barrier height) with larger fluctuations. We observe that the period and the amplitude of the oscillations are more dispersed and oscillations become less coherent when the fluctuations increase. We also found that the entropy production of the whole network, characterizing the dissipation costs from the combined effects of both landscapes and fluxes, decreases when the fluctuations decrease. Therefore, less dissipation leads to more robust networks. Our approach is quite general and applicable to other networks, dynamical systems, and biological evolution. It can help in designing robust networks.