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.     

Integrating Developmental Theory and Methodology: Using Derivatives to Articulate Change Theories,Models, and Inferences

Matching theories about growth, development, and change to appropriate statistical models can present a challenge, which can result in misuse, misinterpretation, and underutilization of different analytical approaches. We discuss the use of derivatives: the change of a construct with respect to the change in another construct. Derivatives provide a common language linking developmental theory and statistical methods. Conceptualizing change in terms of derivatives allows precise translation of theory into method and highlights commonly overlooked models of change. A wide variety of models can be understood in terms of the level, velocity, and acceleration of constructs: the zeroth, first, and second derivatives, respectively. We introduce the language of derivatives, and highlight the conceptually differing questions that can be addressed in developmental studies. A substantive example is presented to demonstrate how common and unfamiliar statistical methodology can be understood as addressing relations between differing pairs of derivatives.     

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)}     

Using Species Distribution Models For Fungi

Species distribution models (SDMs) are an emerging tool in the study of fungi, and their use is expanding across species and research topics. To summarise progress to date and to highlight important considerations for future users, we review 283 studies that apply SDMs to fungi. We found that macrofungi, lichens, and pathogenic microfungi are most often studied. While many studies only aim to model species response to environmental covariates, the use of SDMs for explicitly predicting fungal occurrence in space and time is growing. Many studies collect fungal occurrence data, but the use of pre-collected records from reference collections and citizen science programs is increasing. Challenges of applying SDMs to fungi include detection and sampling biases, and uncertainties in identification and taxonomy. Further, finding environmental covariates at appropriate spatial and temporal scales is important, as fungi can respond to fine-scale environmental patterns. Fine-scale covariate data can be difficult to gather across space, but we show remote-sensing measurements are viable for fungi SDMs. For those fungi interacting with host species, host information is also important, and can be used as covariates in SDMs. We also highlight that competition among fungi, and dispersal, can affect observed distributions, with the latter particularly prominent for invasive fungi. We show how one can account for these processes in models, when suitable data are available. Finally, we note that environmental DNA records create new opportunities and challenges for future modelling efforts, and discuss the difficulties in predicting invasions and climate change impacts. The application of SDMs to fungi has already provided interesting lessons on how to adapt modelling tools for specific questions, and fungi will continue to be relevant test subjects for further technical development of SDMs.     

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.     

Integrating Crop Growth Models with Whole Genome Prediction through Approximate Bayesian Computation

Genomic selection, enabled by whole genome prediction (WGP) methods, is revolutionizing plant breeding. Existing WGP methods have been shown to deliver accurate predictions in the most common settings, such as prediction of across environment performance for traits with additive gene effects. However, prediction of traits with non-additive gene effects and prediction of genotype by environment interaction (G×E), continues to be challenging. Previous attempts to increase prediction accuracy for these particularly difficult tasks employed prediction methods that are purely statistical in nature. Augmenting the statistical methods with biological knowledge has been largely overlooked thus far. Crop growth models (CGMs) attempt to represent the impact of functional relationships between plant physiology and the environment in the formation of yield and similar output traits of interest. Thus, they can explain the impact of G×E and certain types of non-additive gene effects on the expressed phenotype. Approximate Bayesian computation (ABC), a novel and powerful computational procedure, allows the incorporation of CGMs directly into the estimation of whole genome marker effects in WGP. Here we provide a proof of concept study for this novel approach and demonstrate its use with synthetic data sets. We show that this novel approach can be considerably more accurate than the benchmark WGP method GBLUP in predicting performance in environments represented in the estimation set as well as in previously unobserved environments for traits determined by non-additive gene effects. We conclude that this proof of concept demonstrates that using ABC for incorporating biological knowledge in the form of CGMs into WGP is a very promising and novel approach to improving prediction accuracy for some of the most challenging scenarios in plant breeding and applied genetics.     

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.     

Inferring Adaptive Introgression Using Hidden Markov Models

Adaptive introgression—the flow of adaptive genetic variation between species or populations—has attracted significant interest in recent years and it has been implicated in a number of cases of adaptation, from pesticide resistance and immunity, to local adaptation. Despite this, methods for identification of adaptive introgression from population genomic data are lacking. Here, we present Ancestry_HMM-S, a hidden Markov model-based method for identifying genes undergoing adaptive introgression and quantifying the strength of selection acting on them. Through extensive validation, we show that this method performs well on moderately sized data sets for realistic population and selection parameters. We apply Ancestry_HMM-S to a data set of an admixed Drosophila melanogaster population from South Africa and we identify 17 loci which show signatures of adaptive introgression, four of which have previously been shown to confer resistance to insecticides. Ancestry_HMM-S provides a powerful method for inferring adaptive introgression in data sets that are typically collected when studying admixed populations. This method will enable powerful insights into the genetic consequences of admixture across diverse populations. Ancestry_HMM-S can be downloaded from https://github.com/jesvedberg/Ancestry_HMM-S/.     

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.     

Exploring Migration Data Using Interval-Censored Time-to-Event Models

Abstract: Ecologists and wildlife biologists rely on periodic observation of radiocollared animals to study habitat use, survival, movement, and migration, resulting in response times (e.g., mortality and migration) known only to occur within an interval of time. We illustrate methods for analyzing interval-censored data using data on the timing of fall migration (from spring-summer-fall to winter ranges) for white-tailed deer (Odocoileus virginianus) in northern Minnesota, USA, during years 1991–1992 to 2005–2006. We compare both nonparametric and parametric methods for estimating the cumulative distribution function of migration times, and we suggest a parametric (cure rate) model that accounts for conditional (facultative) migrators as a potential alternative to traditional parametric models. Lastly, we illustrate methods for exploring the effect of environmental covariates on migration timing. Models with time-dependent covariates (snow depth, temp) were sensitive to the treatment of the data (as interval-censored or known event times), suggesting the need to account for interval-censoring when modeling the effect of these covariates.     

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.