Molecular Modeling of the Misfolded Insulin Subunit and Amyloid Fibril

Insulin, a small hormone protein comprising 51 residues in two disulfide-linked polypeptide chains, adopts a predominantly α-helical conformation in its native state. It readily undergoes protein misfolding and aggregates into amyloid fibrils under a variety of conditions. Insulin is a unique model system in which to study protein fibrillization, since its three disulfide bridges are retained in the fibrillar state and thus limit the conformational space available to the polypeptide chains during misfolding and fibrillization. Taking into account this unique conformational restriction, we modeled possible monomeric subunits of the insulin amyloid fibrils using β-solenoid folds, namely, the β-helix and β-roll. Both models agreed with currently available biophysical data. We performed molecular dynamics simulations, which allowed some limited insights into the relative structural stability, suggesting that the β-roll subunit model may be more stable than the β-helix subunit model. We also constructed β-solenoid-based insulin fibril models and conducted fiber diffraction simulation to identify plausible fibril architectures of insulin amyloid. A comparison of simulated fiber diffraction patterns of the fibril models to the experimental insulin x-ray fiber diffraction data suggests that the model fibers composed of six twisted β-roll protofilaments provide the most reasonable fit to available experimental diffraction patterns and previous biophysical studies.     

On the problems of the evolutionary optimization of life history. II. To justification of optimization criterion for nonlinear Leslie model

The paper considers the problems in the adaptive evolution of life-history traits for individuals in the nonlinear Leslie model of age-structured population. The possibility to predict adaptation results as the values of organism’s traits (properties) that provide for the maximum of a certain function of traits (optimization criterion) is studied. An ideal criterion of this type is Darwinian fitness as a characteristic of vital success of an individual. Criticism of the optimization approach is associated with the fact that it does not take into account the changes in the environment (in a broad sense) caused by evolution, thereby leading to losses in the adequacy of the criterion. In addition, the justification for this criterion under stationary conditions is not usually rigorous. It has been suggested to overcome these objections in terms of the adaptive dynamics theory using the concept of invasive fitness. The reasons are given that favor the application of the average number of offspring for an individual, R _L , as an optimization criterion in the nonlinear Leslie model. According to the theory of quantitative genetics, the selection for fertility (that is, for a set of correlated quantitative traits determined by both multiple loci and the environment) leads to an increase in R _L . In terms of adaptive dynamics, the maximum R _L corresponds to the evolutionary stability and, in certain cases, convergent stability of the values for traits. The search for evolutionarily stable values on the background of limited resources for reproduction is a problem of linear programming.     

Evolutionary Capacitance and Control of Protein Stability in Protein-Protein Interaction Networks

In addition to their biological function, protein complexes reduce the exposure of the constituent proteins to the risk of undesired oligomerization by reducing the concentration of the free monomeric state. We interpret this reduced risk as a stabilization of the functional state of the protein. We estimate that protein-protein interactions can account for of additional stabilization; a substantial contribution to intrinsic stability. We hypothesize that proteins in the interaction network act as evolutionary capacitors which allows their binding partners to explore regions of the sequence space which correspond to less stable proteins. In the interaction network of baker''s yeast, we find that statistically proteins that receive higher energetic benefits from the interaction network are more likely to misfold. A simplified fitness landscape wherein the fitness of an organism is inversely proportional to the total concentration of unfolded proteins provides an evolutionary justification for the proposed trends. We conclude by outlining clear biophysical experiments to test our predictions.     

Monitoring protein stability <Emphasis Type="Italic">in vivo</Emphasis>

Reduced protein stability in vivo is a prerequisite to aggregation. While this is merely a nuisance factor in recombinant protein production, it holds a serious impact for man. This review focuses on specific approaches to selectively determine the solubility and/or stability of a target protein within the complex cellular environment using different detection techniques. Noninvasive techniques mapping folding/misfolding events on a fast time scale can be used to unravel the complexity and dynamics of the protein aggregation process and factors altering protein solubility in vivo. The development of approaches to screen for folding and solubility in vivo should facilitate the identification of potential components that improve protein solubility and/or modulate misfolding and aggregation and may provide a therapeutic benefit.     

Inhibition of mTOR affects protein stability of OGT

Autophagy regulates cellular homeostasis through degradation of aged or damaged subcellular organelles and components. Interestingly, autophagy-deficient beta cells, for example Atg7-mutant mice, exhibited hypoinsulinemia and hyperglycemia. Also, autophagy response is diminished in heart of diabetic mice. These results implied that autophagy and diabetes are closely connected and affect each other. Although protein O-GlcNAcylation is up-regulated in hyperglycemia and diabetes, and O-GlcNAcylated proteins play an important role in metabolism and nutrient sensing, little is known whether autophagy affects O-GlcNAc modification and vice versa. In this study, we suppressed the action of mTOR by treatment of mTOR catalytic inhibitors (PP242 and Torin1) to induce autophagic flux. Results showed a decrease in global O-GlcNAcylation, which is due to decreased OGT protein and increased OGA protein. Interestingly, knockdown of ATG genes or blocking of lysosomal degradation enhanced protein stability of OGT. In addition, when proteasomal inhibitor was treated together with mTOR inhibitor, protein level of OGT almost recovered to control level. These data suggest that mTOR inhibition is a more efficient way to reduce protein level of OGT rather than that of CHX treatment. We also showed that not only proteasomal degradation regulated OGT stability but autophagic degradation also affected OGT stability in part. We concluded that mTOR signaling regulates protein O-GlcNAc modification through adjustment of OGT stability.     

Formal Darwinism

Two questions are raised for Grafen’s formal darwinism project of aligning evolutionary dynamics under natural selection with the optimization of phenotypes for individuals of a population. The first question concerns mean fitness maximization during frequency-dependent selection; in such selection regimes, not only is mean fitness typically not maximized but it is implausible that any parameter closely related to fitness is being maximized. The second question concerns whether natural selection on inclusive fitness differences can be regarded as individual selection or whether it leads to a departure from the central motivation that led to the formal darwinism project, viz., to show that “Darwinian” evolution through individual selection leads to “good design” or phenotypic adaptation through trait optimization.     

Species interactions constrain adaptation and preserve ecological stability in an experimental microbial community

Species loss within a microbial community can increase resource availability and spur adaptive evolution. Environmental shifts that cause species loss or fluctuations in community composition are expected to become more common, so it is important to understand the evolutionary forces that shape the stability and function of the emergent community. Here we study experimental cultures of a simple, ecologically stable community of Saccharomyces cerevisiae and Lactobacillus plantarum, in order to understand how the presence or absence of a species impacts coexistence over evolutionary timescales. We found that evolution in coculture led to drastically altered evolutionary outcomes for L. plantarum, but not S. cerevisiae. Both monoculture- and co-culture-evolved L. plantarum evolved dozens of mutations over 925 generations of evolution, but only L. plantarum that had evolved in isolation from S. cerevisiae lost the capacity to coexist with S. cerevisiae. We find that the evolutionary loss of ecological stability corresponds with fitness differences between monoculture-evolved L. plantarum and S. cerevisiae and genetic changes that repeatedly evolve across the replicate populations of L. plantarum. This work shows how coevolution within a community can prevent destabilising evolution in individual species, thereby preserving ecological diversity and stability, despite rapid adaptation.Subject terms: Evolution, Microbial ecology     

Fixation probabilities in evolutionary game dynamics with a two-strategy game in finite diploid populations

Fixation processes in evolutionary game dynamics in finite diploid populations are investigated. Traditionally, frequency dependent evolutionary dynamics is modeled as deterministic replicator dynamics. This implies that the infinite size of the population is assumed implicitly. In nature, however, population sizes are finite. Recently, stochastic processes in finite populations have been introduced in order to study finite size effects in evolutionary game dynamics. One of the most significant studies on evolutionary dynamics in finite populations was carried out by Nowak et al. which describes “one-third law” [Nowak, et al., 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646-650]. It states that under weak selection, if the fitness of strategy α is greater than that of strategy β when α has a frequency , strategy α fixates in a β-population with selective advantage. In their study, it is assumed that the inheritance of strategies is asexual, i.e. the population is haploid. In this study, we apply their framework to a diploid population that plays a two-strategy game with two ESSs (a bistable game). The fixation probability of a mutant allele in this diploid population is derived. A “three-tenth law” for a completely recessive mutant allele and a “two-fifth law” for a completely dominant mutant allele are found; other cases are also discussed.     

Dynamical Phase Transitions Reveal Amyloid-like States on Protein Folding Landscapes

Developing an understanding of protein misfolding processes presents a crucial challenge for unlocking the mysteries of human disease. In this article, we present our observations of β-sheet-rich misfolded states on a number of protein dynamical landscapes investigated through molecular dynamics simulation and Markov state models. We employ a nonequilibrium statistical mechanical theory to identify the glassy states in a protein’s dynamics, and we discuss the nonnative, β-sheet-rich states that play a distinct role in the slowest dynamics within seven protein folding systems. We highlight the fundamental similarity between these states and the amyloid structures responsible for many neurodegenerative diseases, and we discuss potential consequences for mechanisms of protein aggregation and intermolecular amyloid formation.     

Neural networks enable efficient and accurate simulation-based inference of evolutionary parameters from adaptation dynamics

The rate of adaptive evolution depends on the rate at which beneficial mutations are introduced into a population and the fitness effects of those mutations. The rate of beneficial mutations and their expected fitness effects is often difficult to empirically quantify. As these 2 parameters determine the pace of evolutionary change in a population, the dynamics of adaptive evolution may enable inference of their values. Copy number variants (CNVs) are a pervasive source of heritable variation that can facilitate rapid adaptive evolution. Previously, we developed a locus-specific fluorescent CNV reporter to quantify CNV dynamics in evolving populations maintained in nutrient-limiting conditions using chemostats. Here, we use CNV adaptation dynamics to estimate the rate at which beneficial CNVs are introduced through de novo mutation and their fitness effects using simulation-based likelihood–free inference approaches. We tested the suitability of 2 evolutionary models: a standard Wright–Fisher model and a chemostat model. We evaluated 2 likelihood-free inference algorithms: the well-established Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) algorithm, and the recently developed Neural Posterior Estimation (NPE) algorithm, which applies an artificial neural network to directly estimate the posterior distribution. By systematically evaluating the suitability of different inference methods and models, we show that NPE has several advantages over ABC-SMC and that a Wright–Fisher evolutionary model suffices in most cases. Using our validated inference framework, we estimate the CNV formation rate at the GAP1 locus in the yeast Saccharomyces cerevisiae to be 10^−4.7 to 10⁻⁴ CNVs per cell division and a fitness coefficient of 0.04 to 0.1 per generation for GAP1 CNVs in glutamine-limited chemostats. We experimentally validated our inference-based estimates using 2 distinct experimental methods—barcode lineage tracking and pairwise fitness assays—which provide independent confirmation of the accuracy of our approach. Our results are consistent with a beneficial CNV supply rate that is 10-fold greater than the estimated rates of beneficial single-nucleotide mutations, explaining the outsized importance of CNVs in rapid adaptive evolution. More generally, our study demonstrates the utility of novel neural network–based likelihood–free inference methods for inferring the rates and effects of evolutionary processes from empirical data with possible applications ranging from tumor to viral evolution.

This study shows that simulation-based inference of evolutionary dynamics using neural networks can yield parameter values for fitness and mutation rate that are difficult to determine experimentally, including those of copy number variants (CNVs) during experimental adaptive evolution of yeast.     

Fluctuation domains in adaptive evolution

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains-parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource.     

One-third rules with equality: Second-order evolutionary stability conditions in finite populations

The one-third law of evolutionary dynamics [Nowak et al. 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 246-650] describes a robustness criterion for evolution in a finite population: If at an A-frequency of 1/3, the fitness of an A player is greater (smaller) than the fitness of a B player, then a single A mutant that appears in a population of otherwise all B has a fixation probability greater (smaller) than the neutral threshold 1/N, the inverse population size. We examine the case where at an A-frequency of 1/3, the fitness of an A player is exactly equal to the fitness of a B player. We find that in this case the relative magnitude of the cross payoffs matters: If the payoff of A against B is larger (smaller) than the payoff of B against A, then a single A mutant has a fixation probability larger (smaller) than 1/N. If the cross payoffs coincide, we are in the special case of a partnership game, where the deviation cost from an inefficient equilibrium is exactly balanced by the potential gain of switching to the payoff dominant equilibrium. We show that in this case the fixation probability of A is lower than 1/N. Finally, we illustrate our findings by a language game with differentiated costs of signals.     

Mutation-selection equilibrium in games with multiple strategies

In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process in well-mixed populations, but almost identical results are found for the Wright-Fisher and Pairwise Comparison processes. Surprisingly simple conditions specify whether a strategy is more abundant on average than 1/n, or than another strategy, in the mutation-selection equilibrium. We find one condition that holds for low mutation rate and another condition that holds for high mutation rate. A linear combination of these two conditions holds for any mutation rate. Our results allow a complete characterization of n×n games in the limit of weak selection.     

Fitness,inclusive fitness,and optimization

Individual-as-maximizing agent analogies result in a simple understanding of the functioning of the biological world. Identifying the conditions under which individuals can be regarded as fitness maximizing agents is thus of considerable interest to biologists. Here, we compare different concepts of fitness maximization, and discuss within a single framework the relationship between Hamilton’s (J Theor Biol 7:1–16, 1964) model of social interactions, Grafen’s (J Evol Biol 20:1243–1254, 2007a) formal Darwinism project, and the idea of evolutionary stable strategies. We distinguish cases where phenotypic effects are additive separable or not, the latter not being covered by Grafen’s analysis. In both cases it is possible to define a maximand, in the form of an objective function ?(z), whose argument is the phenotype of an individual and whose derivative is proportional to Hamilton’s inclusive fitness effect. However, this maximand can be identified with the expression for fecundity or fitness only in the case of additive separable phenotypic effects, making individual-as-maximizing agent analogies unattractive (although formally correct) under general situations of social interactions. We also feel that there is an inconsistency in Grafen’s characterization of the solution of his maximization program by use of inclusive fitness arguments. His results are in conflict with those on evolutionary stable strategies obtained by applying inclusive fitness theory, and can be repaired only by changing the definition of the problem.     

Experimental Evolution of Legionella pneumophila in Mouse Macrophages Leads to Strains with Altered Determinants of Environmental Survival

The Gram-negative bacterium, Legionella pneumophila, is a protozoan parasite and accidental intracellular pathogen of humans. We propose a model in which cycling through multiple protozoan hosts in the environment holds L. pneumophila in a state of evolutionary stasis as a broad host-range pathogen. Using an experimental evolution approach, we tested this hypothesis by restricting L. pneumophila to growth within mouse macrophages for hundreds of generations. Whole-genome resequencing and high-throughput genotyping identified several parallel adaptive mutations and population dynamics that led to improved replication within macrophages. Based on these results, we provide a detailed view of the population dynamics of an experimentally evolving bacterial population, punctuated by frequent instances of transient clonal interference and selective sweeps. Non-synonymous point mutations in the flagellar regulator, fleN, resulted in increased uptake and broadly increased replication in both macrophages and amoebae. Mutations in multiple steps of the lysine biosynthesis pathway were also independently isolated, resulting in lysine auxotrophy and reduced replication in amoebae. These results demonstrate that under laboratory conditions, host restriction is sufficient to rapidly modify L. pneumophila fitness and host range. We hypothesize that, in the environment, host cycling prevents L. pneumophila host-specialization by maintaining pathways that are deleterious for growth in macrophages and other hosts.     

Dynamical Phase Transitions Reveal Amyloid-like States on Protein Folding Landscapes

Developing an understanding of protein misfolding processes presents a crucial challenge for unlocking the mysteries of human disease. In this article, we present our observations of β-sheet-rich misfolded states on a number of protein dynamical landscapes investigated through molecular dynamics simulation and Markov state models. We employ a nonequilibrium statistical mechanical theory to identify the glassy states in a protein’s dynamics, and we discuss the nonnative, β-sheet-rich states that play a distinct role in the slowest dynamics within seven protein folding systems. We highlight the fundamental similarity between these states and the amyloid structures responsible for many neurodegenerative diseases, and we discuss potential consequences for mechanisms of protein aggregation and intermolecular amyloid formation.     

Mutation-selection equilibrium in games with mixed strategies

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an n×n payoff matrix. Players can use mixed strategies, which are given by the vector (p₁,…,p_n). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S_n. We study evolutionary dynamics in a well-mixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutation-selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dove game. We prove general statements about the relationship between games with pure and with mixed strategies.     

A stochastic model of evolutionary dynamics with deterministic large-population asymptotics

An evolutionary birth-death process is proposed as a model of evolutionary dynamics. Agents residing in a continuous spatial environment X, play a game G, with a continuous strategy set S, against other agents in the environment. The agents’ positions and strategies continuously change in response to other agents and to random effects. Agents spawn asexually at rates that depend on their current fitness, and agents die at rates that depend on their local population density. Agents’ individual evolutionary trajectories in X and S are governed by a system of stochastic ODEs. When the number of agents is large and distributed in a smooth density on (X,S), the collective dynamics of the entire population is governed by a certain (deterministic) PDE, which we call a fitness-diffusion equation.     

Recombination Accelerates Adaptation on a Large-Scale Empirical Fitness Landscape in HIV-1

Recombination has the potential to facilitate adaptation. In spite of the substantial body of theory on the impact of recombination on the evolutionary dynamics of adapting populations, empirical evidence to test these theories is still scarce. We examined the effect of recombination on adaptation on a large-scale empirical fitness landscape in HIV-1 based on in vitro fitness measurements. Our results indicate that recombination substantially increases the rate of adaptation under a wide range of parameter values for population size, mutation rate and recombination rate. The accelerating effect of recombination is stronger for intermediate mutation rates but increases in a monotonic way with the recombination rates and population sizes that we examined. We also found that both fitness effects of individual mutations and epistatic fitness interactions cause recombination to accelerate adaptation. The estimated epistasis in the adapting populations is significantly negative. Our results highlight the importance of recombination in the evolution of HIV-I.