S. C. Kou

Nonspecifically bound proteins spin while diffusing along DNA

It is known that DNA-binding proteins can slide along the DNA helix while searching for specific binding sites, but their path of motion remains obscure. Do these proteins undergo simple one-dimensional (1D) translational diffusion, or do they rotate to maintain a specific orientation with respect to the DNA helix? We measured 1D diffusion constants as a function of protein size while maintaining the DNA-protein interface. Using bootstrap analysis of single-molecule diffusion data, we compared the results to theoretical predictions for pure translational motion and rotation-coupled sliding along the DNA. The data indicate that DNA-binding proteins undergo rotation-coupled sliding along the DNA helix and can be described by a model of diffusion along the DNA helix on a rugged free-energy landscape. A similar analysis including the 1D diffusion constants of eight proteins of varying size shows that rotation-coupled sliding is a general phenomenon. The average free-energy barrier for sliding along the DNA was 1.1 ± 0.2 kBT. Such small barriers facilitate rapid search for binding sites.

Equi-energy sampler with applications in statistical inference and statistical mechanics

We introduce a new sampling algorithm, the equi-energy sampler, for efficient statistical sampling and estimation. Complementary to the widely used temperature-domain methods, the equi-energy sampler, utilizing the temperature-energy duality, targets the energy directly. The focus on the energy function not only facilitates efficient sampling, but also provides a powerful means for statistical estimation, for example, the calculation of the density of states and microcanonical averages in statistical mechanics. The equi-energy sampler is applied to a variety of problems, including exponential regression in statistics, motif sampling in computational biology and protein folding in biophysics. We congratulate Samuel Kou, Qing Zhou and Wing Wong (referred to subsequently as KZW) for this beautifully written paper, which opens a new direction in Monte Carlo computation. This discussion has two parts. First, we describe a very closely related method, multicanonical sampling (MCS), and report a simulation example that compares the equi-energy (EE) sampler with MCS. Overall, we found the two algorithms to be of comparable efficiency for the simulation problem considered. In the second part, we develop some additional convergence results for the EE sampler. Novel sampling algorithms can significantly impact open questions in computational biology, most notably the in silico protein folding problem. By using computational methods, protein folding aims to find the three-dimensional structure of a protein chain given the sequence of its amino acid building blocks. The complexity of the problem strongly depends on the protein representation and its energy function. The more detailed the model, the more complex its corresponding energy function and the more challenge it sets for sampling algorithms. Kou, Zhou and Wong have introduced a novel sampling method, which could contribute significantly to the field of structural prediction.

Stochastic Modeling in Nanoscale Biophysics: Subdiffusion within Proteins

Advances in nanotechnology have allowed scientists to study biological processes on an unprecedented nanoscale molecule-by-molecule basis, opening the door to addressing many important biological problems. A phenomenon observed in recent nanoscale single-molecule biophysics experiments is subdiffusion, which largely departs from the classical Brownian diffusion theory. In this paper, by incorporating fractional Gaussian noise into the generalized Langevin equation, we formulate a model to describe subdiffusion. We conduct a detailed analysis of the model, including (i) a spectral analysis of the stochastic integro-differential equations introduced in the model and (ii) a microscopic derivation of the model from a system of interacting particles. In addition to its analytical tractability and clear physical underpinning, the model is capable of explaining data collected in fluorescence studies on single protein molecules. Excellent agreement between the model prediction and the single-molecule experimental data is seen.

Accurate estimation of influenza epidemics using Google search data via ARGO.

Accurate real-time tracking of influenza outbreaks helps public health ocials make timely and meaningful decisions that could save lives. We propose a new influenza tracking model, ARGO (AutoRegression with GOogle search data), that uses publicly available online search data. In addition to having a rigorous statistical foundation, ARGO outperforms all previously available tracking models, including the latest version of Google Flu Trends (GFT), even though it uses only low-quality search data as input from publicly available Google Trends and Google Correlate websites. ARGO not only incorporates the seasonality in influenza epidemics, but also captures changes in people’s online search behavior over time. ARGO is also flexible, self-correcting, robust and scalable, making it a potentially powerful tool that can be used for real-time tracking of other social events at multiple temporal and spatial resolutions.Significance Big data generated from the Internet have great potential in tracking and predicting massive social activities. In this article, we focus on tracking influenza epidemics. We propose a model that utilizes publicly available Google search data to estimate current influenza-like illness activity level. Our model outperforms all available Google-search–based real-time tracking models for influenza epidemics at the national level of the United States, including Google Flu Trends. Our model is flexible, self-correcting, robust, and scalable, making it a potentially powerful tool that can be used for estimation and prediction at multiple temporal and spatial resolutions for other social events. Accurate real-time tracking of influenza outbreaks helps public health officials make timely and meaningful decisions that could save lives. We propose an influenza tracking model, ARGO (AutoRegression with GOogle search data), that uses publicly available online search data. In addition to having a rigorous statistical foundation, ARGO outperforms all previously available Google-search–based tracking models, including the latest version of Google Flu Trends, even though it uses only low-quality search data as input from publicly available Google Trends and Google Correlate websites. ARGO not only incorporates the seasonality in influenza epidemics but also captures changes in people’s online search behavior over time. ARGO is also flexible, self-correcting, robust, and scalable, making it a potentially powerful tool that can be used for real-time tracking of other social events at multiple temporal and spatial resolutions.

Modeling growth stocks via birth-death processes

The inability to predict the future growth rates and earnings of growth stocks (such as biotechnology and internet stocks) leads to the high volatility of share prices and difficulty in applying the traditional valuation methods. This paper attempts to demonstrate that the high volatility of share prices can nevertheless be used in building a model that leads to a particular cross-sectional size distribution. The model focuses on both transient and steady-state behavior of the market capitalization of the stock, which in turn is modeled as a birth-death process. Numerical illustrations of the cross-sectional size distribution are also presented.

Biopolymer structure simulation and optimization via fragment regrowth Monte Carlo

An efficient exploration of the configuration space of a biopolymer is essential for its structure modeling and prediction. In this study, the authors propose a new Monte Carlo method, fragment regrowth via energy-guided sequential sampling (FRESS), which incorporates the idea of multigrid Monte Carlo into the framework of configurational-bias Monte Carlo and is suitable for chain polymer simulations. As a by-product, the authors also found a novel extension of the Metropolis Monte Carlo framework applicable to all Monte Carlo computations. They tested FRESS on hydrophobic-hydrophilic (HP) protein folding models in both two and three dimensions. For the benchmark sequences, FRESS not only found all the minimum energies obtained by previous studies with substantially less computation time but also found new lower energies for all the three-dimensional HP models with sequence length longer than 80 residues.

SURE Estimates for a Heteroscedastic Hierarchical Model

Hierarchical models are extensively studied and widely used in statistics and many other scientific areas. They provide an effective tool for combining information from similar resources and achieving partial pooling of inference. Since the seminal work by James and Stein (1961) and Stein (1962), shrinkage estimation has become one major focus for hierarchical models. For the homoscedastic normal model, it is well known that shrinkage estimators, especially the James-Stein estimator, have good risk properties. The heteroscedastic model, though more appropriate for practical applications, is less well studied, and it is unclear what types of shrinkage estimators are superior in terms of the risk. We propose in this article a class of shrinkage estimators based on Stein’s unbiased estimate of risk (SURE). We study asymptotic properties of various common estimators as the number of means to be estimated grows (p → ∞). We establish the asymptotic optimality property for the SURE estimators. We then extend our construction to create a class of semiparametric shrinkage estimators and establish corresponding asymptotic optimality results. We emphasize that though the form of our SURE estimators is partially obtained through a normal model at the sampling level, their optimality properties do not heavily depend on such distributional assumptions. We apply the methods to two real datasets and obtain encouraging results.

A study of density of states and ground states in hydrophobic-hydrophilic protein folding models by equi-energy sampling

We propose an equi-energy (EE) sampling approach to study protein folding in the two-dimensional hydrophobic-hydrophilic (HP) lattice model. This approach enables efficient exploration of the global energy landscape and provides accurate estimates of the density of states, which then allows us to conduct a detailed study of the thermodynamics of HP protein folding, in particular, on the temperature dependence of the transition from folding to unfolding and on how sequence composition affects this phenomenon. With no extra cost, this approach also provides estimates on global energy minima and ground states. Without using any prior structural information of the protein the EE sampler is able to find the ground states that match the best known results in most benchmark cases. The numerical results demonstrate it as a powerful method to study lattice protein folding models.

Smoothers and the Cp, generalized maximum likelihood, and extended exponential criteria: A geometric approach

Nonparametric regression, often called smoothing, is a widely used data analysis method. The use of a smoother requires the choice of a smoothing parameter that by balancing fidelity and roughness controls how much smoothing is done. Two popular selection criteria for choosing the smoothing parameter are Cp and generalized maximum likelihood (GML). Each of these has its own problems. ForCp, the problem is its high variability, whereas for GML, the problem is its potentially large bias. By studying the geometry of selection criteria, we give an intuitive explanation of the strength and weakness of Cp and GML. The geometry then motivates a new selection method, the extended exponential (EE) criterion, which combines the strength of Cp and GML but mitigates their weaknesses in terms of variability, bias, and undersmoothing.

Stepwise Signal Extraction via Marginal Likelihood

This article studies the estimation of a stepwise signal. To determine the number and locations of change-points of the stepwise signal, we formulate a maximum marginal likelihood estimator, which can be computed with a quadratic cost using dynamic programming. We carry out an extensive investigation on the choice of the prior distribution and study the asymptotic properties of the maximum marginal likelihood estimator. We propose to treat each possible set of change-points equally and adopt an empirical Bayes approach to specify the prior distribution of segment parameters. A detailed simulation study is performed to compare the effectiveness of this method with other existing methods. We demonstrate our method on single-molecule enzyme reaction data and on DNA array comparative genomic hybridization (CGH) data. Our study shows that this method is applicable to a wide range of models and offers appealing results in practice. Supplementary materials for this article are available online.