We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in the limit of infinite data), followed by results that apply to updates based on a finite set of samples. First, we characterize the domain of attraction of any global maximizer of the population likelihood. This characterization is based on a novel view of the EM updates as a perturbed form of likelihood ascent, or in parallel, of the gradient EM updates as a perturbed form of standard gradient ascent. Leveraging this characterization, we then provide non-asymptotic guarantees on the EM and gradient EM algorithms when applied to a finite set of samples. We develop consequences of our general theory for three canonical examples of incompletedata problems: mixture of Gaussians, mixture of regressions, and linear regression with covariates missing completely at random. In each case, our theory guarantees that with a suitable initialization, a relatively small number of EM (or gradient EM) steps will yield (with high probability) an estimate that is within statistical error of the MLE. We provide simulations to confirm this theoretically predicted behavior.

Statistical models of the amino acid composition of the proteins within a fold family are widely used in science and engineering. Existing techniques for learning probabilistic graphical models from multiple sequence alignments either make strong assumptions about the conditional independencies within the model (e.g., HMMs), or else use sub-optimal algorithms to learn the structure and parameters of the model. We introduce an approach to learning the topological structure and parameters of an undirected probabilistic graphical model. The learning algorithm uses block-L 1 regularization and solves a convex optimization problem, thus guaranteeing a globally optimal solution at convergence. The resulting model encodes both the position-specific conservation statistics and the correlated mutation statistics between sequential and long-range pairs of residues. Our model is generative, allowing for the design of new proteins that have corresponding statistical properties to those seen in nature. We apply our approach to two widely studied protein families: the WW and the PDZ folds. We demonstrate that our model is able to capture interactions that are important in folding and allostery. Our results additionally indicate that while the network of interactions within a protein is sparse, it is richer than previously believed.

While platelet adhesion to biomaterial surfaces is widely recognized to be related to adsorbed fibrinogen (Fg), it has remained controversial whether platelet adhesion is in response to the adsorbed amount or the adsorbed conformation of this protein. To address this issue, we designed a series of platelet adhesion studies to clearly separate these two factors, thus enabling us to definitively determine whether it is the amount or the conformation of adsorbed Fg that mediates platelet response. Fg was adsorbed to a broad range of surface chemistries from a wide range of solution concentrations, with the amount and conformation of adsorbed Fg determined by absorbance and circular dichroism (CD) spectropolarimetry, respectively. Platelet adhesion response was determined by lactate dehydrogenase (LDH) assay and scanning electron microscopy (SEM). Our results show that platelet adhesion is strongly correlated with the degree of adsorption-induced unfolding of Fg (r 2 = 0.96) with essentially no correlation with the amount of Fg adsorbed (r 2 = 0.04). Platelet receptor inhibitor studies using an RGDS peptide reduced platelet adhesion by only about 50%, and SEM results show that adherent platelets after RGDS blocking were much more rounded with minimal extended filopodia compared with the unblocked platelets. These results provide definitive proof that the conformation of adsorbed Fg is the critical determinant of platelet adhesion, not the amount of Fg adsorbed, with adsorption-induced unfolding potentially exposing two distinctly different types of platelet binding sites in Fg; one that induces platelet adhesion alone and one that induces both platelet adhesion and activation.

Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short lifetimes are informally considered to be "topological noise," and those with a long lifetime are considered to be "topological signal." In this paper, we bring some statistical ideas to persistent homology. In particular, we derive confidence sets that allow us to separate topological signal from topological noise.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1252 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

In this paper we present the development of methods using circular dichroism spectropolarimetry with a custom-designed cuvette to increase the signal-to-noise ratio for the measurement of the secondary structure of adsorbed proteins, thus providing enhanced sensitivity and reproducibility. These methods were then applied to investigate how surface chemistry and solution concentration influence both the amount of adsorbed proteins and their secondary structure. Human fibrinogen and albumin were adsorbed onto alkanethiol self-assembled monolayers (SAMs) on gold with CH 3 , OCH 2 -CF 3 , NH 2 , COOH, and OH terminal groups from both dilute (0.1 mg/mL) and moderately concentrated (1.0 mg/mL) solutions. An increase in surface hydrophobicity was found to cause an increase in both the amount of the protein adsorbed and the degree of structural change that was caused by the adsorption process, while an increase in solution concentration caused an increase in the amount of protein adsorbed but a decrease in the degree of conformational change, with these effects being more pronounced on the more hydrophobic surfaces. The combined use of these two parameters (i.e., surface chemistry and solution concentration) thus provides a means of independently varying the degree of structural change following adsorption from the amount of adsorbed protein. Further studies are underway to examine which of these factors most strongly influences platelet response, with the overall goal of developing a better understanding of the fundamental factors governing the hemocompatibility of biomaterial surfaces.

Although albumin (Alb) is the most abundant plasma protein, it is considered to be non-adhesive to platelets, as it lacks any known amino acid sequences for binding platelet receptors. Recent studies have suggested that platelets adhere to adsorbed Alb by mechanisms linked to its conformational state. To definitively address this issue we used circular dichroism (CD) spectropolarimetry to characterize the conformation of Alb adsorbed on a broad range of surface chemistries from a wide range of Alb solution concentrations, with platelet adhesion examined using a lactate dehydrogenase (LDH) assay and scanning electron microscopy (SEM). Our results prove that platelets bind to adsorbed Alb through receptor-mediated processes, with binding sites in Alb exposed and/or formed by adsorption-induced protein unfolding. Most importantly, beyond a critical degree of unfolding, the platelet adhesion levels correlated strongly with the adsorption-induced unfolding in Alb. The blockage of Arg-Gly-Asp (RGD) specific platelet receptors using an Arg-Gly-Asp-Ser (RGDS) peptide led to significant inhibition of platelet adhesion to adsorbed Alb, with the extent of inhibition and morphology of adherent platelets being similar for both Alb and Fg. Chemical neutralization of arginine (Arg) residues in the adsorbed Alb layer inhibited platelet-Alb interactions significantly, indicating that Arg residues play a prominent role in mediating platelet adhesion to Alb. These results provide deeper insight into the molecular mechanisms that mediate the interactions of platelets with adsorbed proteins, and how to control these interactions to improve the blood compatibility of biomaterials for cardiovascular applications.

Abdominal aortic aneurysms (AAAs) are abnormal expansions of the aortic wall, typically characterized by chronic upregulation of matrix metalloproteases (MMPs) -2 and -9. These MMPs degrade elastin and elastic matrix within the aortic wall, leading to a progressive loss of elasticity of the abdominal aorta as the condition progresses. Doxycycline (DOX) is tetracycline-based antibiotic which has shown significant promise in delaying and slowing the growth of AAAs in clinical studies and in animal models. However, it has been found to inhibit elastic matrix deposition by vascular cells at dosages in the µg/mL range which is typically observed in the circulation, in addition to systemic side effects, following oral dosage. In this paper, we describe the development of DOX-loaded poly(lactic-co-glycolic acid) (PLGA) nanoparticles for localized, controlled and sustained DOX delivery towards AAA therapy. Further, we demonstrate that surface-functionalization of these nanoparticles with cationic amphiphiles, not only impart them with a positive charge for potentially enhanced aortic uptake, but also enabled enhanced elastin binding via hydrophobic interactions, as well as upregulating activity of the elastin crosslinking enzyme lysyl oxidase (LOX). In addition to the DOX released from the nanoparticles being effective in inhibiting MMP-2 production and activity, we also demonstrate that surface-functionalization of the nanoparticles cationic amphiphiles may also play a role in MMP-2 inhibition via (i) electrostatic interactions with negatively-charged residues in the active-site of MMP-2, or (ii) steric blockade of the active site on account of the presence of two dodecyl chains in the DMAB molecule. Thus, in addition to enhanced aortic uptake and retention illustrated in studies by other groups, we have demonstrated that cationic functionalization of PLGA nanoparticles enhances elastogenic outcomes, by targeted binding to elastin, as well as their potential to inhibit elastolysis. These results establish their multifunctionality as a localized delivery system for AAA therapy. Overall, this delivery system has potential in enhancing regenerative outcomes at sites of proteolytic matrix disruption/degradation by enabling targeted, controlled, and long-term release of therapeutic agents.

We propose a general method for constructing confidence sets and hypothesis tests that have finite-sample guarantees without regularity conditions. We refer to such procedures as “universal.” The method is very simple and is based on a modified version of the usual likelihood-ratio statistic that we call “the split likelihood-ratio test” (split LRT) statistic. The (limiting) null distribution of the classical likelihood-ratio statistic is often intractable when used to test composite null hypotheses in irregular statistical models. Our method is especially appealing for statistical inference in these complex setups. The method we suggest works for any parametric model and also for some nonparametric models, as long as computing a maximum-likelihood estimator (MLE) is feasible under the null. Canonical examples arise in mixture modeling and shape-constrained inference, for which constructing tests and confidence sets has been notoriously difficult. We also develop various extensions of our basic methods. We show that in settings when computing the MLE is hard, for the purpose of constructing valid tests and intervals, it is sufficient to upper bound the maximum likelihood. We investigate some conditions under which our methods yield valid inferences under model misspecification. Further, the split LRT can be used with profile likelihoods to deal with nuisance parameters, and it can also be run sequentially to yield anytime-valid P values and confidence sequences. Finally, when combined with the method of sieves, it can be used to perform model selection with nested model classes.