Integrating Molecular Models Into CryoEM Heterogeneity Analysis Using Scalable High-resolution Deep Gaussian Mixture Models

Resolving the structural variability of proteins is often key to understanding the structure–function relationship of those macromolecular machines. Single particle analysis using Cryogenic electron microscopy (CryoEM), combined with machine learning algorithms, provides a way to reveal the dynamics within the protein system from noisy micrographs. Here, we introduce an improved computational method that uses Gaussian mixture models for protein structure representation and deep neural networks for conformation space embedding. By integrating information from molecular models into the heterogeneity analysis, we can analyze continuous protein conformational changes using structural information at the frequency of 1/3 Å⁻¹, and present the results in a more interpretable form.     

Effective Genetic-Risk Prediction Using Mixed Models

For predicting genetic risk, we propose a statistical approach that is specifically adapted to dealing with the challenges imposed by disease phenotypes and case-control sampling. Our approach (termed Genetic Risk Scores Inference [GeRSI]), combines the power of fixed-effects models (which estimate and aggregate the effects of single SNPs) and random-effects models (which rely primarily on whole-genome similarities between individuals) within the framework of the widely used liability-threshold model. We demonstrate in extensive simulation that GeRSI produces predictions that are consistently superior to current state-of-the-art approaches. When applying GeRSI to seven phenotypes from the Wellcome Trust Case Control Consortium (WTCCC) study, we confirm that the use of random effects is most beneficial for diseases that are known to be highly polygenic: hypertension (HT) and bipolar disorder (BD). For HT, there are no significant associations in the WTCCC data. The fixed-effects model yields an area under the ROC curve (AUC) of 54%, whereas GeRSI improves it to 59%. For BD, using GeRSI improves the AUC from 55% to 62%. For individuals ranked at the top 10% of BD risk predictions, using GeRSI substantially increases the BD relative risk from 1.4 to 2.5.     

Mesenteric Artery Contraction and Relaxation Studies Using Automated Wire Myography

Proximal resistance vessels, such as the mesenteric arteries, contribute substantially to the peripheral resistance. These small vessels of between 100-400 μm in diameter function primarily in directing blood flow to various organs according to the overall requirements of the body. The rat mesenteric artery has a diameter greater than 100 μm. The myography technique, first described by Mulvay and Halpern¹, was based on the method proposed by Bevan and Osher². The technique provides information about small vessels under isometric conditions, where substantial shortening of the muscle preparation is prevented. Since force production and sensitivity of vessels to different agonists is dependent on the extent of stretch, according to active tension-length relation, it is essential to conduct contraction studies under isometric conditions to prevent compliance of the mounting wires. Stainless steel wires are preferred to tungsten wires because of oxidation of the latter, which affects recorded responses³.The technique allows for the comparison of agonist-induced contractions of mounted vessels to obtain evidence for normal function of vascular smooth muscle cell receptors.We have shown in several studies that isolated mesenteric arteries that are contracted with phenylyephrine relax upon addition of cumulative concentrations of extracellular calcium (Ca²⁺_e). The findings led us to conclude that perivascular sensory nerves, which express the G protein-coupled Ca²⁺-sensing receptor (CaR), mediate this vasorelaxation response. Using an automated wire myography method, we show here that mesenteric arteries from Wistar, Dahl salt-sensitive(DS) and Dahl salt-resistant (DR) rats respond differently to Ca²⁺_e. Tissues from Wistar rats showed higher Ca²⁺-sensitivity compared to those from DR and DS. Reduced CaR expression in mesenteric arteries from DS rats correlates with reduced Ca²⁺_e-induced relaxation of isolated, pre-contracted arteries. The data suggest that the CaR is required for relaxation of mesenteric arteries under increased adrenergic tone, as occurs in hypertension, and indicate an inherent defect in the CaR signaling pathway in Dahl animals, which is much more severe in DS.The method is useful in determining vascular reactivity ex vivo in mesenteric resistance arteries and similar small blood vessels and comparisons between different agonists and/or antagonists can be easily and consistently assessed side-by-side^6,7,8.Download video file.^{(48M, mov)}     

Integrating Multiple Distribution Models to Guide Conservation Efforts of an Endangered Toad

Species distribution models are used for numerous purposes such as predicting changes in species’ ranges and identifying biodiversity hotspots. Although implications of distribution models for conservation are often implicit, few studies use these tools explicitly to inform conservation efforts. Herein, we illustrate how multiple distribution models developed using distinct sets of environmental variables can be integrated to aid in identification sites for use in conservation. We focus on the endangered arroyo toad (Anaxyrus californicus), which relies on open, sandy streams and surrounding floodplains in southern California, USA, and northern Baja California, Mexico. Declines of the species are largely attributed to habitat degradation associated with vegetation encroachment, invasive predators, and altered hydrologic regimes. We had three main goals: 1) develop a model of potential habitat for arroyo toads, based on long-term environmental variables and all available locality data; 2) develop a model of the species’ current habitat by incorporating recent remotely-sensed variables and only using recent locality data; and 3) integrate results of both models to identify sites that may be employed in conservation efforts. We used a machine learning technique, Random Forests, to develop the models, focused on riparian zones in southern California. We identified 14.37% and 10.50% of our study area as potential and current habitat for the arroyo toad, respectively. Generally, inclusion of remotely-sensed variables reduced modeled suitability of sites, thus many areas modeled as potential habitat were not modeled as current habitat. We propose such sites could be made suitable for arroyo toads through active management, increasing current habitat by up to 67.02%. Our general approach can be employed to guide conservation efforts of virtually any species with sufficient data necessary to develop appropriate distribution models.     

Modelling Cultivar Mixtures Using SEIR Compartmental Models

A SEIR (susceptible, exposed, infectious, removed) compartmental model is constructed to represent disease progress in a two cultivar mixture. The concept of the spore pool is the means by which inoculum exchange between the constituent cultivars is represented. Infection frequencies for each cultivar are permitted to vary with that cultivar's susceptible fraction according to a power-law relationship. For each cultivar, new additions to the susceptible class balance deaths from the removed class so that the total leaf area of all four SEIR classes remains constant. It is shown that an equilibrium with non-zero diseased classes exists in a certain parameter regime. A numerical stability analysis is performed using the model equations linearised about this equilibrium. The effects of changing induced resistance parameters within the model are demonstrated graphically. It is also demonstrated that the proportion of susceptibles as a function of mixture composition has an optimum in the regime where nontrivial equilibria exist, a feature of practical interest provided that equilibrium is reached within a growing season.     

Network Reconstruction Using Nonparametric Additive ODE Models

Network representations of biological systems are widespread and reconstructing unknown networks from data is a focal problem for computational biologists. For example, the series of biochemical reactions in a metabolic pathway can be represented as a network, with nodes corresponding to metabolites and edges linking reactants to products. In a different context, regulatory relationships among genes are commonly represented as directed networks with edges pointing from influential genes to their targets. Reconstructing such networks from data is a challenging problem receiving much attention in the literature. There is a particular need for approaches tailored to time-series data and not reliant on direct intervention experiments, as the former are often more readily available. In this paper, we introduce an approach to reconstructing directed networks based on dynamic systems models. Our approach generalizes commonly used ODE models based on linear or nonlinear dynamics by extending the functional class for the functions involved from parametric to nonparametric models. Concomitantly we limit the complexity by imposing an additive structure on the estimated slope functions. Thus the submodel associated with each node is a sum of univariate functions. These univariate component functions form the basis for a novel coupling metric that we define in order to quantify the strength of proposed relationships and hence rank potential edges. We show the utility of the method by reconstructing networks using simulated data from computational models for the glycolytic pathway of Lactocaccus Lactis and a gene network regulating the pluripotency of mouse embryonic stem cells. For purposes of comparison, we also assess reconstruction performance using gene networks from the DREAM challenges. We compare our method to those that similarly rely on dynamic systems models and use the results to attempt to disentangle the distinct roles of linearity, sparsity, and derivative estimation.     

Riboswitch Detection Using Profile Hidden Markov Models

Background  

Riboswitches are a type of noncoding RNA that regulate gene expression by switching from one structural conformation to another on ligand binding. The various classes of riboswitches discovered so far are differentiated by the ligand, which on binding induces a conformational switch. Every class of riboswitch is characterized by an aptamer domain, which provides the site for ligand binding, and an expression platform that undergoes conformational change on ligand binding. The sequence and structure of the aptamer domain is highly conserved in riboswitches belonging to the same class. We propose a method for fast and accurate identification of riboswitches using profile Hidden Markov Models (pHMM). Our method exploits the high degree of sequence conservation that characterizes the aptamer domain.     

Cross-Scale Numerical Simulations Using Discrete Particle Models

Abstract

We propose a concept for a homogenous computational model in carrying out cross-scale numerical experiments on liquids. The model employs the particle paradigm and comprises three types of simulation techniques: molecular dynamics (MD), dissipative particle dynamics (DPD) and smoothed particle hydrodynamics (SPH). With respect to the definition of the collision operator, this model may work in different hierarchical spatial and time scales as: MD in the atomistic scale, DPD in the mesoscale and SPH in the macroscale. The optimal computational efficiency of the three types of cross-scale experiments are estimated in dependence on: the system size N-where N is the number of particles-and the number of processors P employed for computer simulation. For the three-hierarchical-stage, as embodied in the MD-DPD-SPH model, the efficiency is proportional to N ^8/7 but its dependence on P is different for each of the three types of cross-scale experiments. The problem of matching the different scales is discussed.     

Integrating Evolution into Ecological Modelling: Accommodating Phenotypic Changes in Agent Based Models

Evolutionary change is a characteristic of living organisms and forms one of the ways in which species adapt to changed conditions. However, most ecological models do not incorporate this ubiquitous phenomenon. We have developed a model that takes a ‘phenotypic gambit’ approach and focuses on changes in the frequency of phenotypes (which differ in timing of breeding and fecundity) within a population, using, as an example, seasonal breeding. Fitness per phenotype calculated as the individual’s contribution to population growth on an annual basis coincide with the population dynamics per phenotype. Simplified model variants were explored to examine whether the complexity included in the model is justified. Outputs from the spatially implicit model underestimated the number of individuals across all phenotypes. When no phenotype transitions are included (i.e. offspring always inherit their parent’s phenotype) numbers of all individuals are always underestimated. We conclude that by using a phenotypic gambit approach evolutionary dynamics can be incorporated into individual based models, and that all that is required is an understanding of the probability of offspring inheriting the parental phenotype.     

Mechanism Study of Pulsus Paradoxus Using Mechanical Models

Pulsus paradoxus is an exaggeration of the normal inspiratory decrease in systolic blood pressure. Despite a century of attempts to explain this sign consensus is still lacking. To solve the controversy and reveal the exact mechanism, we reexamined the characteristic anatomic arrangement of the circulation system in the chest and designed these mechanical models based on related hydromechanic principles. Model 1 was designed to observe the primary influence of respiratory intrathoracic pressure change (RIPC) on systemic and pulmonary venous return systems (SVR and PVR) respectively. Model 2, as an equivalent mechanical model of septal swing, was to study the secondary influence of RIPC on the motion of the interventriclar septum (IVS), which might be the direct cause for pulsus paradoxus. Model 1 demonstrated that the simulated RIPC had different influence on the simulated SVR and PVR. It increased the volume of the simulated right ventricle (SRV) when the internal pressure was kept constant (8.16 cmH₂O), while it had the opposite effect on PVR. Model 2 revealed the three major factors determining the respiratory displacement of IVS in normal and different pathophysiological conditions: the magnitude of RIPC, the pressure difference between the two ventricles and the intrapericardial pressure. Our models demonstrate that the different anatomical arrangement of the two venous return systems leads to a different effect of RIPC on right and left ventricles, and thus a pressure gradient across IVS that tends to shift IVS left- and rightwards. When the leftward displacement of IVS reaches a considerable amplitude in some pathologic condition such as cardiac tamponade, the pulsus paradoxus occurs.     

Integrating Life Stages into Ecological Niche Models: A Case Study on Tiger Beetles

Detailed understanding of a species’ natural history and environmental needs across spatial scales is a primary requisite for effective conservation planning, particularly for species with complex life cycles in which different life stages occupy different niches and respond to the environment at different scales. However, niche models applied to conservation often neglect early life stages and are mostly performed at broad spatial scales. Using the endangered heath tiger beetle (Cicindela sylvatica) as a model species, we relate presence/absence and abundance data of locally dispersing adults and sedentary larvae to abiotic and biotic variables measured in a multiscale approach within the geographic extent relevant to active conservation management. At the scale of hundreds of meters, fine-grained abiotic conditions (i.e., vegetation structure) are fundamental determinants of the occurrence of both life stages, whereas the effect of biotic factors is mostly contained in the abiotic signature. The combination of dense heath vegetation and bare ground areas is thus the first requirement for the species’ preservation, provided that accessibility to the suitable habitat is ensured. At a smaller scale (centimetres), the influence of abiotic factors on larval occurrence becomes negligible, suggesting the existence of important additional variables acting within larval proximity. Sustained significant correlations between neighbouring larvae in the models provide an indication of the potential impact of neighbourhood crowding on the larval niche within a few centimetres. Since the species spends the majority of its life cycle in the larval stage, it is essential to consider the hierarchical abiotic and biotic processes affecting the larvae when designing practical conservation guidelines for the species. This underlines the necessity for a more critical evaluation of the consequences of disregarding niche variation between life stages when estimating niches and addressing effective conservation measures for species with complex life cycles.     

利用“复杂性”解说经济生态发展模式

前言在研究生态经济问题时,常常感到理论上的虚弱,不能从理论上解说生态经济这一庞大、复杂的综合体是如何由生态、经济的相互作用衍变而成的。在生态和经济的复杂性的尺度上我们能把握多少?我们对于生态、经济关系能否及时调控和调控到什么程度?等等,如能从理论上给这些问题作出说明,相信会对生态经济理论及实践都有裨益。为此,我们对生态经济系统作了简化,只讨论了工业增长、农业增长和环境质量三者间的相互作用并用微分方程组表述,试定量说明生态系统、经济系统的复合系统的复杂性和发展。生态系统的复杂性自牛顿建立牛顿力学以来,尽管经典物理     

Identity-by-Descent Matrix Decomposition Using Latent Ancestral Allele Models

Genetic linkage and association studies are empowered by proper modeling of relatedness among individuals. Such relatedness can be inferred from marker and/or pedigree information. In this study, the genetic relatedness among n inbred individuals at a particular locus is expressed as an n × n square matrix Q. The elements of Q are identity-by-descent probabilities, that is, probabilities that two individuals share an allele descended from a common ancestor. In this representation the definition of the ancestral alleles and their number remains implicit. For human inspection and further analysis, an explicit representation in terms of the ancestral allele origin and the number of alleles is desirable. To this purpose, we decompose the matrix Q by a latent class model with K classes (latent ancestral alleles). Let P be an n × K matrix with assignment probabilities of n individuals to K classes constrained such that every element is nonnegative and each row sums to 1. The problem then amounts to approximating Q by PP^T, while disregarding the diagonal elements. This is not an eigenvalue problem because of the constraints on P. An efficient algorithm for calculating P is provided. We indicate the potential utility of the latent ancestral allele model. For representative locus-specific Q matrices constructed for a set of maize inbreds, the proposed model recovered the known ancestry.HIGH-THROUGHPUT techniques allow extensive genotyping of individuals for thousands of SNP markers (Gibbs et al. 2003) and thereby provide accurate information about the genetic diversity within a population at many chromosomal loci. If two individuals within this population carry the same DNA sequence at a locus, and this sequence can be traced to the same common ancestor, the individuals are said to be identical by descent (IBD) for this segment (Chapman and Thompson 2003). Quite often, however, the ancestral source of a chromosomal segment is ambiguous and thus IBD relationships between haplotypes are given as probabilities. Various methods have been described to estimate the IBD probability of pairs of chromosomal segments (Meuwissen and Goddard 2001; Leutenegger et al. 2003). When pedigree relationships are known, these can be included to estimate IBD probabilities (Wang et al. 1995; Heath 1997; George et al. 2000; Meuwissen and Goddard 2000; Besnier and Carlborg 2007).In quantitative genetic analysis we seek to find and characterize associations between the large number of SNPs that are now available for many organisms and phenotypic variation for traits of interest (e.g., grain yield and time to flowering). Many current methods developed for this purpose make use of IBD information. For example, a locus-specific matrix of IBD probabilities can be incorporated into restricted maximum-likelihood (REML) procedures for fine mapping quantitative trait loci (Bink and Meuwissen 2004) as well as for marker-based genetic evaluation (Fernando and Grossman 1989) using mixed models. The IBD matrix takes the role of a covariance matrix in the REML procedure.Other approaches, however, require that chromosome segments (also referred to here as haplotypes or alleles) are assigned to independent ancestors. These approaches include regression approaches with genetic predictors (Malosetti et al. 2006) and Bayesian oligo-allelic approaches that sample the ancestral origin of each chromosomal segment (Heath 1997; Uimari and Sillanpaa 2001; Bink et al. 2008a). In the IBD matrix representation the ancestral alleles and their number remain implicit. For these approaches, the locus-specific matrix of IBD probabilities must therefore be decomposed into a matrix that links the chromosomal segments to independent ancestral alleles. This decomposition is addressed in this article.The individuals that we consider in this article are inbred. For n inbred individuals the IBD matrix at a given chromosomal position is thus n × n, because there is no need to distinguish between identical chromosomes. In diploid, outbred populations, each individual would be represented by two haplotypes (alleles) and the matrix would be 2n × 2n (Fernando and Grossman 1989). This is feasible if any phase ambiguity can be resolved. From now on, the term “individual” thus means chromosomal segment or haplotype. Analogously, ancestor will be shorthand for ancestral allele (ancestral haplotype).We propose two models of IBD matrix decomposition, a simple threshold model (TIBD) and a more sophisticated latent ancestral allele model (LAAM), that provide (1) an estimate of the number of independent ancestral alleles, (2) a concise, easy-to-interpret, summary of the relatedness, (3) an explicit (probabilistic) representation of the descent of alleles, and (4) the ability to sample alleles for each individual from a set of ancestral alleles in such a way that the probability that a pair of individuals shares the same allele corresponds to their IBD probability.The last two features of the model are essential for its use in Bayesian oligo-allelic approaches to quantitative trait locus (QTL) analysis (Uimari and Sillanpaa 2001; Bink et al. 2008a).     

Quantifying Food Web Flows Using Linear Inverse Models

The quantitative mapping of food web flows based on empirical data is a crucial yet difficult task in ecology. The difficulty arises from the under-sampling of food webs, because most data sets are incomplete and uncertain. In this article, we review methods to quantify food web flows based on empirical data using linear inverse models (LIM). The food web in a LIM is described as a linear function of its flows, which are estimated from empirical data by inverse modeling. The under-sampling of food webs implies that infinitely many different solutions exist that are consistent with a given data set. The existing approaches to food web LIM select a single solution from this infinite set by invoking additional assumptions: either a specific selection criterion that has no solid ecological basis is used or the data set is artificially upgraded by assigning fixed values to, for example, physiological parameters. Here, we advance a likelihood approach (LA) that follows a different solution philosophy. Rather than singling out one particular solution, the LA generates a large set of possible solutions from which the marginal probability density function (mPDF) of each flow and correlations between flows can be derived. The LA is exemplified with an example model of a soil food web and is made available in the open-source R-software. Moreover, we show how stoichiometric data, stable isotope signatures, and fatty acid compositions can be included in the LIM to alleviate the under-sampling problem. Overall, LIM prove to be a powerful tool in food web research, which can bridge the gap between empirical data and the analysis of food web structures.