Rapid near-atomic resolution single-particle 3D reconstruction with SIMPLE.

Cryogenic electron microscopy (cryo-EM) and single-particle analysis enables determination of near-atomic resolution structures of biological molecules. However, large computational requirements limit throughput and rapid testing of new image processing tools. We developed PRIME, an algorithm part of the SIMPLE software suite, for determination of the relative 3D orientations of single-particle projection images. PRIME has primarily found use for generation of an initial ab initio 3D reconstruction. Here we show that the strategy behind PRIME, iterative estimation of per-particle orientation distributions with stochastic hill climbing, provides a competitive approach to near-atomic resolution single-particle 3D reconstruction. A number of mathematical techniques for accelerating the convergence rate are introduced, leading to a speedup of nearly two orders of magnitude. We benchmarked our developments on numerous publicly available data sets and conclude that near-atomic resolution ab initio 3D reconstructions can be obtained with SIMPLE in a matter of hours, using standard over-the-counter CPU workstations.

The influence of societal individualism on a century of tobacco use: modelling the prevalence of smoking.

BACKGROUND: Smoking of tobacco is estimated to have caused approximately six million deaths worldwide in 2014. Responding effectively to this epidemic requires a thorough understanding of how smoking behaviour is transmitted and modified. METHODS: We present a new mathematical model of the social dynamics that cause cigarette smoking to spread in a population, incorporating aspects of individual and social utility. Model predictions are tested against two independent data sets spanning 25 countries: a newly compiled century-long composite data set on smoking prevalence, and Hofstede's individualism/collectivism measure (IDV). RESULTS: The general model prediction that more individualistic societies will show faster adoption and cessation of smoking is supported by the full 25 country smoking prevalence data set. Calibration of the model to the available smoking prevalence data is possible in a subset of 7 countries. Consistency of fitted model parameters with an additional, independent, data set further supports our model: the fitted value of the country-specific model parameter that determines the relative importance of social and individual factors in the decision of whether or not to smoke, is found to be significantly correlated with Hofstede's IDV for the 25 countries in our data set. CONCLUSIONS: Our model in conjunction with extensive data on smoking prevalence provides evidence for the hypothesis that individualism/collectivism may have an important influence on the dynamics of smoking prevalence at the aggregate, population level. Significant implications for public health interventions are discussed.

Multilevel Monte Carlo Methods for Stochastic Convection-Diffusion Eigenvalue Problems.

We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element (FE) discretizations of the eigenvalue problem on a hierarchy of increasingly finer meshes. For the discretized, algebraic eigenproblems we use both the Rayleigh quotient (RQ) iteration and implicitly restarted Arnoldi (IRA), providing an analysis of the cost in each case. By studying the variance on each level and adapting classical FE error bounds to the stochastic setting, we are able to bound the total error of our MLMC estimator and provide a complexity analysis. As expected, the complexity bound for our MLMC estimator is superior to plain Monte Carlo. To improve the efficiency of the MLMC further, we exploit the hierarchy of meshes and use coarser approximations as starting values for the eigensolvers on finer ones. To improve the stability of the MLMC method for convection-dominated problems, we employ two additional strategies. First, we consider the streamline upwind Petrov-Galerkin formulation of the discrete eigenvalue problem, which allows us to start the MLMC method on coarser meshes than is possible with standard FEs. Second, we apply a homotopy method to add stability to the eigensolver for each sample. Finally, we present a multilevel quasi-Monte Carlo method that replaces Monte Carlo with a quasi-Monte Carlo (QMC) rule on each level. Due to the faster convergence of QMC, this improves the overall complexity. We provide detailed numerical results comparing our different strategies to demonstrate the practical feasibility of the MLMC method in different use cases. The results support our complexity analysis and further demonstrate the superiority over plain Monte Carlo in all cases.

Natural and artificial RNAs occupy the same restricted region of sequence space.

Different chemical and mutational processes within genomes give rise to sequences with different compositions and perhaps different capacities for evolution. The evolution of functional RNAs may occur on a "neutral network" in which sequences with any given function can easily mutate to sequences with any other. This neutral network hypothesis is more likely if there is a particular region of composition that contains sequences that are functional in general, and if many different functions are possible within this preferred region of composition. We show that sequence preferences in active sites recovered by in vitro selection combine with biophysical folding rules to support the neutral network hypothesis. These simple active-site specifications and folding preferences obtained by artificial selection experiments recapture the previously observed purine bias and specific spread along the GC axis of naturally occurring aptamers and ribozymes isolated from organisms, although other types of RNAs, such as miRNA precursors and spliceosomal RNAs, that act primarily through complementarity to other amino acids do not share these preferences. These universal evolved sequence features are therefore intrinsic in RNA molecules that bind small-molecule targets or catalyze reactions.

Monte Carlo study of degenerate ground states and residual entropy in a frustrated honeycomb lattice Ising model.

We study a classical fully frustrated honeycomb lattice Ising model using Markov-chain Monte Carlo methods and exact calculations. The Hamiltonian realizes a degenerate ground-state manifold of equal-energy states, where each hexagonal plaquette of the lattice has one and only one unsatisfied bond, with an extensive residual entropy that grows as the number of spins N. Traditional single-spin-flip Monte Carlo methods fail to sample all possible spin configurations in this ground state efficiently, due to their separation by large energy barriers. We develop a nonlocal "chain-flip" algorithm that solves this problem, and demonstrate its effectiveness on the Ising Hamiltonian with and without perturbative interactions. The two perturbations considered are a slightly weakened bond and an external magnetic field h. For some cases, the chain-flip move is necessary for the simulation to find an ordered ground state. In the case of the magnetic field, two magnetized ground states with nonextensive entropy are found, and two special values of h exist where the residual entropy again becomes extensive, scaling proportionally to N ln phi, where phi is the golden ratio.

Abundance of correctly folded RNA motifs in sequence space, calculated on computational grids.

Although functional RNA molecules are known to be biased in overall composition, the effects of background composition on the probability of finding a particular active site by chance has received little attention. The probability of finding a particular motif has important implications both for understanding the distribution of functional RNAs in ancient and modern organisms with varying genome compositions and for tuning SELEX pools to optimize the chance of finding specific functions. Here we develop a new method for calculating the probability of finding a modular motif containing base-paired regions, and use a computational grid to fold several hundred million random RNA sequences containing the core elements of the isoleucine aptamer and the hammerhead ribozyme to estimate the probability that a sequence containing these structural elements will fold correctly when isolated from background sequences of different compositions. We find that the two motifs are most likely to be found in distinct regions of compositional space, and that the regions of greatest abundance are influenced by the probability of finding the conserved bases, finding the flanking helices, and folding, in that order of importance. Additionally, we can refine our estimates of the number of random sequences required for a 50% probability of finding an example of each site in unbiased random pools of length 100 to 4.1 x 10(9) for the isoleucine aptamer and 1.6 x 10(10) for the hammerhead ribozyme. These figures are consistent with the facile recovery of these motifs from SELEX experiments.

The statistical mechanics of human weight change.

Over the past 35 years there has been a near doubling in the worldwide prevalence of obesity. Body Mass Index (BMI) distributions in high-income societies have increasingly shifted rightwards, corresponding to increases in average BMI that are due to well-studied changes in the socioeconomic environment. However, in addition to this shift, BMI distributions have also shown marked changes in their particular shape over time, exhibiting an ongoing right-skewed broadening that is not well understood. Here, we compile and analyze the largest data set so far of year-over-year BMI changes. The data confirm that, on average, heavy individuals become lighter while light individuals become heavier year-over-year, and also show that year-over-year BMI evolution is characterized by fluctuations with a magnitude that is linearly proportional to BMI. We find that the distribution of human BMIs is intrinsically dynamic-due to the short-term variability of human weight-and its shape is determined by a balance between deterministic drift towards a natural set point and diffusion resulting from random fluctuations in, e.g., diet and physical activity. We formulate a stochastic mathematical model for BMI dynamics, deriving a theoretical shape for the BMI distribution and offering a mechanism that may explain the right-skewed broadening of BMI distributions over time. An extension of the base model investigates the hypothesis that peer-to-peer social influence plays a role in BMI dynamics. While including this effect improves the fit with the data, indicating that correlations in the behavior of individuals with similar BMI may be important for BMI dynamics, testing social transmission against other plausible unmodeled effects and interpretations remains the subject of future work. Implications of our findings on the dynamics of BMI distributions for public health interventions are discussed.

Generalized Monte Carlo loop algorithm for two-dimensional frustrated Ising models.

We introduce a generalized loop move (GLM) update for Monte Carlo simulations of frustrated Ising models on two-dimensional lattices with bond-sharing plaquettes. The GLM updates are designed to enhance Monte Carlo sampling efficiency when the system's low-energy states consist of an extensive number of degenerate or near-degenerate spin configurations, separated by large energy barriers to single spin flips. Through implementation on several frustrated Ising models, we demonstrate the effectiveness of the GLM updates in cases where both degenerate and near-degenerate sets of configurations are favored at low temperatures. The GLM update's potential to be straightforwardly extended to different lattices and spin interactions allows it to be readily adopted on many other frustrated Ising models of physical relevance.

Multilevel space-time aggregation for bright field cell microscopy segmentation and tracking.

A multilevel aggregation method is applied to the problem of segmenting live cell bright field microscope images. The method employed is a variant of the so-called "Segmentation by Weighted Aggregation" technique, which itself is based on Algebraic Multigrid methods. The variant of the method used is described in detail, and it is explained how it is tailored to the application at hand. In particular, a new scale-invariant "saliency measure" is proposed for deciding when aggregates of pixels constitute salient segments that should not be grouped further. It is shown how segmentation based on multilevel intensity similarity alone does not lead to satisfactory results for bright field cells. However, the addition of multilevel intensity variance (as a measure of texture) to the feature vector of each aggregate leads to correct cell segmentation. Preliminary results are presented for applying the multilevel aggregation algorithm in space time to temporal sequences of microscope images, with the goal of obtaining space-time segments ("object tunnels") that track individual cells. The advantages and drawbacks of the space-time aggregation approach for segmentation and tracking of live cells in sequences of bright field microscope images are presented, along with a discussion on how this approach may be used in the future work as a building block in a complete and robust segmentation and tracking system.