Markovian and non-Markovian protein sequence evolution: aggregated Markov process models

Over the years, there have been claims that evolution proceeds according to systematically different processes over different timescales and that protein evolution behaves in a non-Markovian manner. On the other hand, Markov models are fundamental to many applications in evolutionary studies. Apparent non-Markovian or time-dependent behavior has been attributed to influence of the genetic code at short timescales and dominance of physicochemical properties of the amino acids at long timescales. However, any long time period is simply the accumulation of many short time periods, and it remains unclear why evolution should appear to act systematically differently across the range of timescales studied. We show that the observed time-dependent behavior can be explained qualitatively by modeling protein sequence evolution as an aggregated Markov process (AMP): a time-homogeneous Markovian substitution model observed only at the level of the amino acids encoded by the protein-coding DNA sequence. The study of AMPs sheds new light on the relationship between amino acid-level and codon-level models of sequence evolution, and our results suggest that protein evolution should be modeled at the codon level rather than using amino acid substitution models.     

Molecular models of the Mojave rattlesnake (Crotalus scutulatus scutulatus) venom metalloproteinases reveal a structural basis for differences in hemorrhagic activities

Rattlesnake venom can differ in composition and in metalloproteinase-associated activities. The molecular basis for this intra-species variation in Crotalus scutulatus scutulatus (Mojave rattlesnake) remains an enigma. To understand the molecular basis for intra-species variation of metalloproteinase-associated activities, we modeled the three-dimensional structures of four metalloproteinases based on the amino acid sequence of four variations of the proteinase domain of the C. s. scutulatus metalloproteinase gene (GP1, GP2, GP3, and GP4). For comparative purposes, we modeled the atrolysin metalloproteinases of C. atrox as well. All molecular models shared the same topology. While the atrolysin metalloproteinase molecular models contained highly conserved substrate binding sites, the Mojave rattlesnake metalloproteinases showed higher structural divergence when superimposed onto each other. The highest structural divergence among the four C. s. scutulatus molecular models was located at the northern cleft wall and the S’₁-pocket of the substrate binding site, molecular regions that modulate substrate selectivity. Molecular dynamics and field potential maps for each C. s. scutulatus metalloproteinase model demonstrated that the non-hemorrhagic metalloproteinases (GP2 and GP3) contain highly basic molecular and field potential surfaces while the hemorrhagic metalloproteinases GP1 and atrolysin C showed extensive acidic field potential maps and shallow but less dynamic active site pockets. Hence, differences in the spatial arrangement of the northern cleft wall, the S’₁-pocket, and the physico-chemical environment surrounding the catalytic site contribute to differences in metalloproteinase activities in the Mojave rattlesnake. Our results provide a structural basis for variation of metalloproteinase-associated activities in the rattlesnake venom of the Mojave rattlesnake.     

REVIEW: Optimality models in the age of experimental evolution and genomics

Optimality models have been used to predict evolution of many properties of organisms. They typically neglect genetic details, whether by necessity or design. This omission is a common source of criticism, and although this limitation of optimality is widely acknowledged, it has mostly been defended rather than evaluated for its impact. Experimental adaptation of model organisms provides a new arena for testing optimality models and for simultaneously integrating genetics. First, an experimental context with a well‐researched organism allows dissection of the evolutionary process to identify causes of model failure – whether the model is wrong about genetics or selection. Second, optimality models provide a meaningful context for the process and mechanics of evolution, and thus may be used to elicit realistic genetic bases of adaptation – an especially useful augmentation to well‐researched genetic systems. A few studies of microbes have begun to pioneer this new direction. Incompatibility between the assumed and actual genetics has been demonstrated to be the cause of model failure in some cases. More interestingly, evolution at the phenotypic level has sometimes matched prediction even though the adaptive mutations defy mechanisms established by decades of classic genetic studies. Integration of experimental evolutionary tests with genetics heralds a new wave for optimality models and their extensions that does not merely emphasize the forces driving evolution.     

Behaviour of simple population models under ecological processes

The two most popular and extensively-used discrete models of population growth display the generic bifurcation structure of a hierarchy of period-doubling sequence to chaos with increasing growth rates. In this paper we show that these two models, though they belong to a general class of one-dimensional maps, show very different dynamics when important ecological processes such as immigration and emigration/depletion, are considered. It is important that ecologists recognize the differences between these models before using them to describe their data—or develop optimization strategies—based on these models.     

DNA进化马尔可夫过程模型的评价与推广

本文对ＤＮＡ序列进化过程中核苷酸替代的随机模型进行了评价,对替代速率在时间和空间上不恒定的情形进行了考察和推广。Ｌａｎａｖｅ等（１９８４）曾提出一个模型,宣称对替代的模式未做任何假定,但事实上我们证明它假定替代过程是可逆的。运用２－ｐ、４－ｐ和６－ｐ模型进行的计算表明替代速度在位点间的差异会造成估计的替代数严重偏低,并且替代数越大,偏差也越大。替代模式在位点间的差异也会造成估计值偏低,但偏差不严重     

Numerical algorithms for estimation and calculation of parameters in modeling pest population dynamics and evolution of resistance

Computational simulation models can provide a way of understanding and predicting insect population dynamics and evolution of resistance, but the usefulness of such models depends on generating or estimating the values of key parameters. In this paper, we describe four numerical algorithms generating or estimating key parameters for simulating four different processes within such models. First, we describe a novel method to generate an offspring genotype table for one- or two-locus genetic models for simulating evolution of resistance, and how this method can be extended to create offspring genotype tables for models with more than two loci. Second, we describe how we use a generalized inverse matrix to find a least-squares solution to an over-determined linear system for estimation of parameters in probit models of kill rates. This algorithm can also be used for the estimation of parameters of Freundlich adsorption isotherms. Third, we describe a simple algorithm to randomly select initial frequencies of genotypes either without any special constraints or with some pre-selected frequencies. Also we give a simple method to calculate the “stable” Hardy–Weinberg equilibrium proportions that would result from these initial frequencies. Fourth we describe how the problem of estimating the intrinsic rate of natural increase of a population can be converted to a root-finding problem and how the bisection algorithm can then be used to find the rate. We implemented all these algorithms using MATLAB and Python code; the key statements in both codes consist of only a few commands and are given in the appendices. The results of numerical experiments are also provided to demonstrate that our algorithms are valid and efficient.     

Karyotype evolution of the Asterids insights from the first genome sequences of the family Cornaceae

Cornaceae is a core representative family in Cornales, the earliest branching lineage in the Asterids on the life tree of angiosperms. This family includes the only genus Cornus, a group of ~55 species. These species occur widely in Northern Hemisphere and have been used as resources for horticultural ornaments, medicinal and industrial manufacturing. However, no any genome sequences are available for this family. Here, we reported a chromosome­level genome for Cornus controversa. This was generated using high-fidelity plus Hi–C sequencing, and totally ~771.80 Mb assembled sequences and 39,886 protein-coding genes were obtained. We provided evidence for a whole-genome duplication event (WGD) unique to C. controversa. The evolutionary features of this genome indicated that the expanded and unique genes might have contributed to response to stress, stimulus and defense. By using chromosome-level syntenic blocks shared between eight living genomes, we found high degrees of genomic diversification from the ancestral core-eudicot genome to the present-day genomes, suggesting an important role of WGD in genomic plasticity that leads to speciation and diversification. These results provide foundational insights on the evolutionary history of Cornaceae, as well as on the Asterids diversification.     

Modeling of a propagation mechanism of infectious prion protein; a hexamer as the minimum infectious unit

To construct a new model of the propagation mechanism of infectious scrapie-type prion protein (PrP(Sc)), here we conducted a disruption simulation of a PrP(Sc) nonamer using structure-based molecular dynamics simulation method based on a hypothetical PrP(Sc) model structure. The simulation results showed that the nonamer disrupted in cooperative manners into monomers via two significant intermediate states: (1) a nonamer with a partially unfolded surface trimer and (2) a hexamer and three monomers. Dimers and trimers were rarely observed. Then, we propose a new PrP(Sc) propagation mechanism where a hexamer plays an essential role as a minimum infectious unit.     

Prediction of protein structural class for the twilight zone sequences

Structural class characterizes the overall folding type of a protein or its domain. This paper develops an accurate method for in silico prediction of structural classes from low homology (twilight zone) protein sequences. The proposed LLSC-PRED method applies linear logistic regression classifier and a custom-designed, feature-based sequence representation to provide predictions. The main advantages of the LLSC-PRED are the comprehensive representation that includes 58 features describing composition and physicochemical properties of the sequences and transparency of the prediction model. The representation also includes predicted secondary structure content, thus for the first time exploring synergy between these two related predictions. Based on tests performed with a large set of 1673 twilight zone domains, the LLSC-PRED's prediction accuracy, which equals over 62%, is shown to be better than accuracy of over a dozen recently published competing in silico methods and similar to accuracy of other, non-transparent classifiers that use the proposed representation.     

Genetic diversity and models of viral evolution for the hepatitis C virus

In this review we discuss the application of theoretical frameworks to the interpretation of viral gene sequence data, with particular reference to the hepatitis C virus (HCV). The increasing availability of such data means that it is now possible (and necessary) to proceed from simple qualitative models of viral evolution, to more quantitative frameworks based on statistical inference, notably population genetics and molecular phylogenetics. We argue that these approaches are invaluable tools to the virologist and are essential for understanding the dynamics of viral infection and the outcome of therapeutic strategies. We use several recent HCV data-sets to illustrate the methods.     

Genes that determine flower color: the role of regulatory changes in the evolution of phenotypic adaptations

A central goal of evolutionary genetics is to trace the causal pathway between mutations at particular genes and adaptation at the phenotypic level. The proximate objective is to identify adaptations through the analysis of molecular sequence data from specific candidate genes or their regulatory elements. In this paper, we consider the molecular evolution of floral color in the morning glory genus (Ipomoea) as a model for relating molecular and phenotypic evolution. To begin, flower color variation usually conforms to simple Mendelian transmission, thus facilitating genetic and molecular analyses. Population genetic studies of flower color polymorphisms in the common morning glory (Ipomoea purpurea) have shown that some morphs are subject to complex patterns of selection. Striking differences in floral color and morphology are also associated with speciation in the genus Ipomoea. The molecular bases for these adaptive shifts can be dissected because the biosynthetic pathways that determine floral pigmentation are well understood and many of the genes of flavonoid biosynthesis have been isolated and extensively studied. We present a comparative analysis of the level of gene expression in Ipomoea for several key genes in flavonoid biosynthesis. Specifically we ask: how frequently are adaptive shifts in flower color phenotypes associated with changes in regulation of gene expression versus mutations in structural genes? The results of this study show that most species differences in this crucial phenotype are associated with changes in the regulation of gene expression.     

Examination of structural stability and phase transitions in constant-pressure first-principles molecular dynamics simulations

Constant-pressure first-principles molecular dynamics (FPMD) simulation is a powerful tool for investigations of structures in crystals. However, it needs enourmous computations so that highly accurate calculations for electronic states cannot be employed at present. In this report, we examined the reliability and applicability of constant-pressure FPMD in the study of structural properties under this limitation. Crystalline silicon was employed as a benchmark to perform constant-pressure FPMD simulations (with a deformable simulation cell). It is found that, in high pressure (metallic) phases, crystalline symmetry is broken with the present simulation conditions. Several structural transformations were realized by compression and decompression, but they are not entirely consistent with experiment. We discuss this discrepancy and conclude that the number of k point sampling in the Brillouin zone is crucial. It is recommended that constant-pressure FPMD is employed to explore candidate structures for unknown solid phases at present computational resources.     

Divergent microsatellite evolution in the human and chimpanzee lineages

Comparison of the complete human genome sequence to one of its closest relatives, the chimpanzee genome, provides a unique opportunity for exploring recent evolutionary events affecting the microsatellites in these species. A simple assumption on microsatellite distribution is that the total length of perfect repeats is constant compared to that of imperfect ones regardless of the repeat sequence. In this paper, we show that this is valid for most of the chimpanzee genome but not for a number of human chromosomes. Our results suggest accelerated evolution of microsatellites in the human genome relative to the chimpanzee lineage.     

Evaluation of the current models for the evolution of bacterial DNA uptake signal sequences

Current opinion considers two main hypotheses for the evolutionary origin of uptake signal sequences in bacteria: one model regards the uptake signal sequence (USS) as the result of biased gene conversion, whereas the second model views the USS as a molecular tag that evolved as an adaptation. In this article, we present various computational models that implement specific versions of those hypotheses. Those models show that the two hypothesis are not necessarily as opposed to each other as may appear at first glance.     

Target selection and annotation for the structural genomics of the amidohydrolase and enolase superfamilies

To study the substrate specificity of enzymes, we use the amidohydrolase and enolase superfamilies as model systems; members of these superfamilies share a common TIM barrel fold and catalyze a wide range of chemical reactions. Here, we describe a collaboration between the Enzyme Specificity Consortium (ENSPEC) and the New York SGX Research Center for Structural Genomics (NYSGXRC) that aims to maximize the structural coverage of the amidohydrolase and enolase superfamilies. Using sequence- and structure-based protein comparisons, we first selected 535 target proteins from a variety of genomes for high-throughput structure determination by X-ray crystallography; 63 of these targets were not previously annotated as superfamily members. To date, 20 unique amidohydrolase and 41 unique enolase structures have been determined, increasing the fraction of sequences in the two superfamilies that can be modeled based on at least 30% sequence identity from 45% to 73%. We present case studies of proteins related to uronate isomerase (an amidohydrolase superfamily member) and mandelate racemase (an enolase superfamily member), to illustrate how this structure-focused approach can be used to generate hypotheses about sequence–structure–function relationships. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Bridging the gap between theory and data in ecological models

In September 2011, the University of Essex, UK, hosted an interdisciplinary conference, Mathematical and Theoretical Ecology 2011 (MATE 2011), with the theme of ‘Linking models with ecological processes’. The aim of the meeting was to create discussion and debate between modellers and empiricists working in ecology. A wide range of topics were discussed at the meeting including evolutionary and community models of ecosystem structure, epidemiological models, non-linear models of population dynamics, spatiotemporal models, individual and collective movement behaviour, and applications of ecological models to engineering problems. In this introductory article, we provide a report of the MATE 2011 meeting, and briefly review the most recent relevant research in the fields of mathematical and theoretical ecology. We introduce and summarise the eight contributed articles that were selected for this special issue. The diverse range of topics and the wide range of mathematical, statistical and computational tools used illustrate the broad appeal and depth of research in the rich field of mathematical and theoretical ecology.     

Crystallography, evolution, and the structure of viruses

My undergraduate education in mathematics and physics was a good grounding for graduate studies in crystallographic studies of small organic molecules. As a postdoctoral fellow in Minnesota, I learned how to program an early electronic computer for crystallographic calculations. I then joined Max Perutz, excited to use my skills in the determination of the first protein structures. The results were even more fascinating than the development of techniques and provided inspiration for starting my own laboratory at Purdue University. My first studies on dehydrogenases established the conservation of nucleotide-binding structures. Having thus established myself as an independent scientist, I could start on my most cherished ambition of studying the structure of viruses. About a decade later, my laboratory had produced the structure of a small RNA plant virus and then, in another six years, the first structure of a human common cold virus. Many more virus structures followed, but soon it became essential to supplement crystallography with electron microscopy to investigate viral assembly, viral infection of cells, and neutralization of viruses by antibodies. A major guide in all these studies was the discovery of evolution at the molecular level. The conservation of three-dimensional structure has been a recurring theme, from my experiences with Max Perutz in the study of hemoglobin to the recognition of the conserved nucleotide-binding fold and to the recognition of the jelly roll fold in the capsid protein of a large variety of viruses.     

The discovery of novel and selective fatty acid binding protein 4 inhibitors by virtual screening and biological evaluation

Adipocyte fatty acid binding protein (AFABP, FABP4) has been proven to be a potential therapeutic target for diabetes, atherosclerosis and inflammation-related diseases. In this study, a series of new scaffolds of small molecule inhibitors of FABP4 were identified by virtual screening and were validated by a bioassay. Fifty selected compounds were tested, which led to the discovery of seven hits. Structural similarity-based searches were then performed based on the hits and led to the identification of one high affinity compound 33b (K_i = 0.29 ± 0.07 μM, ΔT_m = 8.5 °C). This compound’s effective blockade of inflammatory response was further validated by its ability to suppress pro-inflammatory cytokines induced by lipopolysaccharide (LPS) stimulation. Molecular dynamics simulation (MD) and mutagenesis studies validated key residues for its inhibitory potency and thus provide an important clue for the further development of drugs.