Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States.

Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub (https://covid19forecasthub.org/) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multimodel ensemble forecast that combined predictions from dozens of groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-wk horizon three to five times larger than when predicting at a 1-wk horizon. This project underscores the role that collaboration and active coordination between governmental public-health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks.

A genome wide dosage suppressor network reveals genomic robustness.

Genomic robustness is the extent to which an organism has evolved to withstand the effects of deleterious mutations. We explored the extent of genomic robustness in budding yeast by genome wide dosage suppressor analysis of 53 conditional lethal mutations in cell division cycle and RNA synthesis related genes, revealing 660 suppressor interactions of which 642 are novel. This collection has several distinctive features, including high co-occurrence of mutant-suppressor pairs within protein modules, highly correlated functions between the pairs and higher diversity of functions among the co-suppressors than previously observed. Dosage suppression of essential genes encoding RNA polymerase subunits and chromosome cohesion complex suggests a surprising degree of functional plasticity of macromolecular complexes, and the existence of numerous degenerate pathways for circumventing the effects of potentially lethal mutations. These results imply that organisms and cancer are likely able to exploit the genomic robustness properties, due the persistence of cryptic gene and pathway functions, to generate variation and adapt to selective pressures.

Assessment of the utility of contact-based restraints in accelerating the prediction of protein structure using molecular dynamics simulations.

Molecular dynamics (MD) simulation is a well-established tool for the computational study of protein structure and dynamics, but its application to the important problem of protein structure prediction remains challenging, in part because extremely long timescales can be required to reach the native structure. Here, we examine the extent to which the use of low-resolution information in the form of residue-residue contacts, which can often be inferred from bioinformatics or experimental studies, can accelerate the determination of protein structure in simulation. We incorporated sets of 62, 31, or 15 contact-based restraints in MD simulations of ubiquitin, a benchmark system known to fold to the native state on the millisecond timescale in unrestrained simulations. One-third of the restrained simulations folded to the native state within a few tens of microseconds-a speedup of over an order of magnitude compared with unrestrained simulations and a demonstration of the potential for limited amounts of structural information to accelerate structure determination. Almost all of the remaining ubiquitin simulations reached near-native conformations within a few tens of microseconds, but remained trapped there, apparently due to the restraints. We discuss potential methodological improvements that would facilitate escape from these near-native traps and allow more simulations to quickly reach the native state. Finally, using a target from the Critical Assessment of protein Structure Prediction (CASP) experiment, we show that distance restraints can improve simulation accuracy: In our simulations, restraints stabilized the native state of the protein, enabling a reasonable structural model to be inferred.

Differential hepatic protein tyrosine nitration of mouse due to aging - effect on mitochondrial energy metabolism, quality control machinery of the endoplasmic reticulum and metabolism of drugs.

Aging is the inevitable fate of life which leads to the gradual loss of functions of different organs and organelles of all living organisms. The liver is no exception. Oxidative damage to proteins and other macromolecules is widely believed to be the primary cause of aging. One form of oxidative damage is tyrosine nitration of proteins, resulting in the potential loss of their functions. In this study, the effect of age on the nitration of tyrosine in mouse liver proteins was examined. Liver proteins from young (19-22 weeks) and old (24 months) C57/BL6 male mice were separated using sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) and electroblotted onto nitrocellulose membranes. Proteins undergoing tyrosine nitration were identified using anti-nitrotyrosine antibody. Three different protein bands were found to contain significantly increased levels of nitrotyrosine in old mice (Wilconxon rank-sum test, p<0.05). Electrospray ionization liquid chromatography tandem mass spectrometry (ESI-LC-MS/MS) was used to identify the proteins in these bands, which included aldehyde dehydrogenase 2, Aldehyde dehydrogenase family 1, subfamily A1, ATP synthase, H(+) transporting, mitochondrial F1 complex, ß subunit, selenium-binding protein 2, and protein disulfide-isomerase precursor. The possible impairment of their functions can lead to altered hepatic activity and have been discussed.

Refinement of protein structure homology models via long, all-atom molecular dynamics simulations.

Accurate computational prediction of protein structure represents a longstanding challenge in molecular biology and structure-based drug design. Although homology modeling techniques are widely used to produce low-resolution models, refining these models to high resolution has proven difficult. With long enough simulations and sufficiently accurate force fields, molecular dynamics (MD) simulations should in principle allow such refinement, but efforts to refine homology models using MD have for the most part yielded disappointing results. It has thus far been unclear whether MD-based refinement is limited primarily by accessible simulation timescales, force field accuracy, or both. Here, we examine MD as a technique for homology model refinement using all-atom simulations, each at least 100 µs long-more than 100 times longer than previous refinement simulations-and a physics-based force field that was recently shown to successfully fold a structurally diverse set of fast-folding proteins. In MD simulations of 24 proteins chosen from the refinement category of recent Critical Assessment of Structure Prediction (CASP) experiments, we find that in most cases, simulations initiated from homology models drift away from the native structure. Comparison with simulations initiated from the native structure suggests that force field accuracy is the primary factor limiting MD-based refinement. This problem can be mitigated to some extent by restricting sampling to the neighborhood of the initial model, leading to structural improvement that, while limited, is roughly comparable to the leading alternative methods.

Computational modeling in systems biology.

Interactions among cellular constituents play a crucial role in overall cellular function and organization. These interactions can be viewed as being complementary to the usual "parts list" of genes and proteins and, in conjunction with the expression states of these parts, are key to a systems level understanding of the cell. Here, we review computational approaches to the understanding of the functional roles of cellular networks, ranging from "static" models of network topology to dynamical and stochastic simulations.

Detection of genomic islands via segmental genome heterogeneity.

While the recognition of genomic islands can be a powerful mechanism for identifying genes that distinguish related bacteria, few methods have been developed to identify them specifically. Rather, identification of islands often begins with cataloging individual genes likely to have been recently introduced into the genome; regions with many putative alien genes are then examined for other features suggestive of recent acquisition of a large genomic region. When few phylogenetic relatives are available, the identification of alien genes relies on their atypical features relative to the bulk of the genes in the genome. The weakness of these 'bottom-up' approaches lies in the difficulty in identifying robustly those genes which are atypical, or phylogenetically restricted, due to recent foreign ancestry. Herein, we apply an alternative 'top-down' approach where bacterial genomes are recursively divided into progressively smaller regions, each with uniform composition. In this way, large chromosomal regions with atypical features are identified with high confidence due to the simultaneous analysis of multiple genes. This approach is based on a generalized divergence measure to quantify the compositional difference between segments in a hypothesis-testing framework. We tested the proposed genome island prediction algorithm on both artificial chimeric genomes and genuine bacterial genomes.

Identifying hubs in protein interaction networks.

BACKGROUND: In spite of the scale-free degree distribution that characterizes most protein interaction networks (PINs), it is common to define an ad hoc degree scale that defines "hub" proteins having special topological and functional significance. This raises the concern that some conclusions on the functional significance of proteins based on network properties may not be robust. METHODOLOGY: In this paper we present three objective methods to define hub proteins in PINs: one is a purely topological method and two others are based on gene expression and function. By applying these methods to four distinct PINs, we examine the extent of agreement among these methods and implications of these results on network construction. CONCLUSIONS: We find that the methods agree well for networks that contain a balance between error-free and unbiased interactions, indicating that the hub concept is meaningful for such networks.

Proteome profiling of aging in mouse models: differential expression of proteins involved in metabolism, transport, and stress response in kidney.

Aging is a time-dependent complex biological phenomenon observed in various organs and organelles of all living organisms. To understand the molecular mechanism of age-associated functional loss in aging kidneys, we have analyzed the expression of proteins in the kidneys of young (19-22 wk) and old (24 months) C57/BL6 male mice using 2-DE followed by LC-MS/MS. We found that expression levels of 49 proteins were upregulated (p < or = 0.05), while that of only ten proteins were downregulated (p < or = 0.05) due to aging. The proteins identified belong to three broad functional categories: (i) metabolism (e.g., aldehyde dehydrogenase family, ATP synthase beta-subunit, malate dehydrogenase, NADH dehydrogenase (ubiquinone), hydroxy acid oxidase 2), (ii) transport (e.g., transferrin), and (iii) chaperone/stress response (e.g., Ig-binding protein, low density lipoprotein receptor-related protein associated protein 1, selenium-binding proteins (SBPs)). Some proteins with unknown functions were also identified as being differentially expressed. ATP synthase beta subunit, transferrin, fumarate hydratase, SBPs, and albumin are present in multiple forms, possibly arising due to proteolysis or PTMs. The above functional categories suggest specific mechanisms and pathways for age-related kidney degeneration.

Mining protein networks for synthetic genetic interactions.

BACKGROUND: The local connectivity and global position of a protein in a protein interaction network are known to correlate with some of its functional properties, including its essentiality or dispensability. It is therefore of interest to extend this observation and examine whether network properties of two proteins considered simultaneously can determine their joint dispensability, i.e., their propensity for synthetic sick/lethal interaction. Accordingly, we examine the predictive power of protein interaction networks for synthetic genetic interaction in Saccharomyces cerevisiae, an organism in which high confidence protein interaction networks are available and synthetic sick/lethal gene pairs have been extensively identified. RESULTS: We design a support vector machine system that uses graph-theoretic properties of two proteins in a protein interaction network as input features for prediction of synthetic sick/lethal interactions. The system is trained on interacting and non-interacting gene pairs culled from large scale genetic screens as well as literature-curated data. We find that the method is capable of predicting synthetic genetic interactions with sensitivity and specificity both exceeding 85%. We further find that the prediction performance is reasonably robust with respect to errors in the protein interaction network and with respect to changes in the features of test datasets. Using the prediction system, we carried out novel predictions of synthetic sick/lethal gene pairs at a genome-wide scale. These pairs appear to have functional properties that are similar to those that characterize the known synthetic lethal gene pairs. CONCLUSION: Our analysis shows that protein interaction networks can be used to predict synthetic lethal interactions with accuracies on par with or exceeding that of other computational methods that use a variety of input features, including functional annotations. This indicates that protein interaction networks could plausibly be rich sources of information about epistatic effects among genes.

A highly uniform UV transillumination imaging system for quantitative analysis of nucleic acids and proteins.

The digital fluorescent imaging for documentation and analysis of gel electrophoretic separations of nucleic acids and proteins is widely used in quantitative biology. Most fluorescent stains used in postelectrophoretic analysis of proteins and nucleic acids have significant excitation peaks with UV light (300-365 nm), making midrange UV (UV-B) as the excitation source of choice. However, coupling quantitative CCD imaging with UV is difficult due to lack of uniformity found in typical UV transilluminators. The apparent amount of those macromolecules depends on the position of the gel band on the imaging surface of the transilluminator. Here, we report the development and validation of a highly uniform UV transillumination system. Using a novel high density lighting system containing a single lamp formed into a high density grid, an electronic ballast, a phosphor coating, and a bandpass filter to convert 254 nm light produced to 300-340 nm, uniformity of 80% CV observed in typical UV transilluminators. This system has been used for the quantitative analysis of electrophoretically separated nucleic acids and proteins (CV

Proteomic profiling of aging in the mouse heart: Altered expression of mitochondrial proteins.

Using two-dimensional gel electrophoresis and liquid chromatography-tandem mass spectrometry, we have used a systems biology approach to study the molecular basis of aging of the mouse heart. We have identified 8 protein spots whose expression is up-regulated due to aging and 36 protein spots whose expression is down-regulated due to aging (p0.05 as judged by Wilcoxon Rank Sum test). Among the up-regulated proteins, we have characterized 5 protein spots and 2 of them, containing 3 different enzymes, are mitochondrial proteins. Among the down-regulated proteins, we have characterized 27 protein spots and 16 of them are mitochondrial proteins. Mitochondrial damage is believed to be a key factor in the aging process. Our current study provides molecular evidence at the level of the proteome for the alteration of structural and functional parameters of the mitochondria that contribute to impaired activity of the mouse heart due to aging.

Molecular clock on a neutral network.

The number of fixed mutations accumulated in an evolving population often displays a variance that is significantly larger than the mean (the overdispersed molecular clock). By examining a generic evolutionary process on a neutral network of high-fitness genotypes, we establish a formalism for computing all cumulants of the full probability distribution of accumulated mutations in terms of graph properties of the neutral network, and use the formalism to prove overdispersion of the molecular clock. We further show that significant overdispersion arises naturally in evolution when the neutral network is highly sparse, exhibits large global fluctuations in neutrality, and small local fluctuations in neutrality. The results are also relevant for elucidating aspects of neutral network topology from empirical measurements of the substitution process.

Evolution favors protein mutational robustness in sufficiently large populations.

BACKGROUND: An important question is whether evolution favors properties such as mutational robustness or evolvability that do not directly benefit any individual but can influence the course of future evolution. Functionally similar proteins can differ substantially in their robustness to mutations and capacity to evolve new functions, but it has remained unclear whether any of these differences might be due to evolutionary selection for these properties. RESULTS: Here, we use laboratory experiments to demonstrate that evolution favors protein mutational robustness if the evolving population is sufficiently large. We neutrally evolve cytochrome P450 proteins under identical selection pressures and mutation rates in populations of different sizes, and show that proteins from the larger and thus more polymorphic population tend towards higher mutational robustness. Proteins from the larger population also evolve greater stability, a biophysical property that is known to enhance both mutational robustness and evolvability. The excess mutational robustness and stability is well described by mathematical theory, and can be quantitatively related to the way that the proteins occupy their neutral network. CONCLUSION: Our work is the first experimental demonstration of the general tendency of evolution to favor mutational robustness and protein stability in highly polymorphic populations. We suggest that this phenomenon could contribute to the mutational robustness and evolvability of viruses and bacteria that exist in large populations.

Thermodynamics of neutral protein evolution.

Naturally evolving proteins gradually accumulate mutations while continuing to fold to stable structures. This process of neutral evolution is an important mode of genetic change and forms the basis for the molecular clock. We present a mathematical theory that predicts the number of accumulated mutations, the index of dispersion, and the distribution of stabilities in an evolving protein population from knowledge of the stability effects (delta deltaG values) for single mutations. Our theory quantitatively describes how neutral evolution leads to marginally stable proteins and provides formulas for calculating how fluctuations in stability can overdisperse the molecular clock. It also shows that the structural influences on the rate of sequence evolution observed in earlier simulations can be calculated using just the single-mutation delta deltaG values. We consider both the case when the product of the population size and mutation rate is small and the case when this product is large, and show that in the latter case the proteins evolve excess mutational robustness that is manifested by extra stability and an increase in the rate of sequence evolution. All our theoretical predictions are confirmed by simulations with lattice proteins. Our work provides a mathematical foundation for understanding how protein biophysics shapes the process of evolution.

PathSys: integrating molecular interaction graphs for systems biology.

BACKGROUND: The goal of information integration in systems biology is to combine information from a number of databases and data sets, which are obtained from both high and low throughput experiments, under one data management scheme such that the cumulative information provides greater biological insight than is possible with individual information sources considered separately. RESULTS: Here we present PathSys, a graph-based system for creating a combined database of networks of interaction for generating integrated view of biological mechanisms. We used PathSys to integrate over 14 curated and publicly contributed data sources for the budding yeast (S. cerevisiae) and Gene Ontology. A number of exploratory questions were formulated as a combination of relational and graph-based queries to the integrated database. Thus, PathSys is a general-purpose, scalable, graph-data warehouse of biological information, complete with a graph manipulation and a query language, a storage mechanism and a generic data-importing mechanism through schema-mapping. CONCLUSION: Results from several test studies demonstrate the effectiveness of the approach in retrieving biologically interesting relations between genes and proteins, the networks connecting them, and of the utility of PathSys as a scalable graph-based warehouse for interaction-network integration and a hypothesis generator system. The PathSys's client software, named BiologicalNetworks, developed for navigation and analyses of molecular networks, is available as a Java Web Start application at http://brak.sdsc.edu/pub/BiologicalNetworks.

A single determinant dominates the rate of yeast protein evolution.

A gene's rate of sequence evolution is among the most fundamental evolutionary quantities in common use, but what determines evolutionary rates has remained unclear. Here, we carry out the first combined analysis of seven predictors (gene expression level, dispensability, protein abundance, codon adaptation index, gene length, number of protein-protein interactions, and the gene's centrality in the interaction network) previously reported to have independent influences on protein evolutionary rates. Strikingly, our analysis reveals a single dominant variable linked to the number of translation events which explains 40-fold more variation in evolutionary rate than any other, suggesting that protein evolutionary rate has a single major determinant among the seven predictors. The dominant variable explains nearly half the variation in the rate of synonymous and protein evolution. We show that the two most commonly used methods to disentangle the determinants of evolutionary rate, partial correlation analysis and ordinary multivariate regression, produce misleading or spurious results when applied to noisy biological data. We overcome these difficulties by employing principal component regression, a multivariate regression of evolutionary rate against the principal components of the predictor variables. Our results support the hypothesis that translational selection governs the rate of synonymous and protein sequence evolution in yeast.

Predicting the tolerance of proteins to random amino acid substitution.

We have recently proposed a thermodynamic model that predicts the tolerance of proteins to random amino acid substitutions. Here we test this model against extensive simulations with compact lattice proteins, and find that the overall performance of the model is very good. We also derive an approximate analytic expression for the fraction of mutant proteins that fold stably to the native structure, Pf(m), as a function of the number of amino acid substitutions m, and present several methods to estimate the asymptotic behavior of Pf(m) for large m. We test the accuracy of all approximations against our simulation results, and find good overall agreement between the approximations and the simulation measurements.

Some asymptotic properties of duplication graphs.

Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are studied: pure duplication growth, and two two-parameter models in which duplication forms one element of the growth dynamics. A power-law degree distribution is found to emerge in all three models. However, the parameter space of the latter two models is characterized by a range of parameter values for which duplication is the predominant mechanism of graph growth. For parameter values that lie in this "duplication-dominated" regime, it is shown that the degree distribution either approaches zero asymptotically, or approaches a nonzero power-law degree distribution very slowly. In either case, the approach to the true asymptotic degree distribution is characterized by a dependence of the scaling exponent on properties of the initial degree distribution. It is therefore conjectured that duplication-dominated, scale-free networks may contain identifiable remnants of their early structure. This feature is inherited from the idealized model of pure duplication growth, for which the exact finite-size degree distribution is found and its asymptotic properties studied.