MOTIVATION: Bottom-up mass spectrometry-based proteomics studies changes in protein abundance and structure across conditions. Since the currency of these experiments are peptides, i.e. subsets of protein sequences that carry the quantitative information, conclusions at a different level must be computationally inferred. The inference is particularly challenging in situations where the peptides are shared by multiple proteins or post-translational modifications. While many approaches infer the underlying abundances from unique peptides, there is a need to distinguish the quantitative patterns when peptides are shared. RESULTS: We propose a statistical approach for estimating protein abundances, as well as site occupancies of post-translational modifications, based on quantitative information from shared peptides. The approach treats the quantitative patterns of shared peptides as convex combinations of abundances of individual proteins or modification sites, and estimates the abundance of each source in a sample together with the weights of the combination. In simulation-based evaluations, the proposed approach improved the precision of estimated fold changes between conditions. We further demonstrated the practical utility of the approach in experiments with diverse biological objectives, ranging from protein degradation and thermal proteome stability, to changes in protein post-translational modifications. AVAILABILITY AND IMPLEMENTATION: The approach is implemented in an open-source R package MSstatsWeightedSummary. The package is currently available at https://github.com/Vitek-Lab/MSstatsWeightedSummary (doi: 10.5281/zenodo.14662989). Code required to reproduce the results presented in this article can be found in a repository https://github.com/mstaniak/MWS_reproduction (doi: 10.5281/zenodo.14656053).

Extracting relevant features from data sets where the number of observations (n) is much smaller then the number of predictors (p) is a major challenge in modern statistics. Sorted L-One Penalized Estimation (SLOPE)—a generalization of the lasso—is a promising method within this setting. Current numerical procedures for SLOPE, however, lack the efficiency that respective tools for the lasso enjoy, particularly in the context of estimating a complete regularization path. A key component in the efficiency of the lasso is predictor screening rules: rules that allow predictors to be discarded before estimating the model. This is the first paper to establish such a rule for SLOPE. We develop a screening rule for SLOPE by examining its subdifferential and show that this rule is a generalization of the strong rule for the lasso. Our rule is heuristic, which means that it may discard predictors erroneously. In our paper, however, we show that such situations are rare and easily safeguarded against by a simple check of the optimality conditions. Our numerical experiments show that the rule performs well in practice, leading to improvements by orders of magnitude for data in the (p >> n) domain, as well as incurring no additional computational overhead when (n > p).

In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible to adopt recent developments in saddle-point optimization, to achieve the optimal O(1/k) rate of convergence. Compared to the optimal non-SP algorithms, ours do not require specification of sensitive parameters that affect algorithm performance or solution quality. We also provide a new analysis showing a possibility of local acceleration to achieve the rate of O(1/k^2) in special cases even without strong convexity or strong smoothness. As an application, we propose a GDS equipped with the ordered \ell_1-norm, showing its false discovery rate control properties in variable selection. Algorithm performance is compared between ours and other alternatives, including the linearized ADMM, Nesterov’s smoothing, Nemirovski’s mirror-prox, and the accelerated hybrid proximal extragradient techniques.

MOTIVATION: Pairwise local sequence alignment is commonly used to search data bases for sequences related to some query sequence. Alignments are obtained using a scoring matrix that takes into account the different frequencies of occurrence of the various types of amino acid substitutions. Software like BLAST provides the user with a set of scoring matrices available to choose from, and in the literature it is sometimes recommended to try several scoring matrices on the sequences of interest. The significance of an alignment is usually assessed by looking at E-values and p-values. While sequence lengths and data base sizes enter the standard calculations of significance, it is much less common to take the use of several scoring matrices on the same sequences into account. Altschul proposed corrections of the p-value that account for the simultaneous use of an infinite number of PAM matrices. Here we consider the more realistic situation where the user may choose from a finite set of popular PAM and BLOSUM matrices, in particular the ones available in BLAST. It turns out that the significance of a result can be considerably overestimated, if a set of substitution matrices is used in an alignment problem and the most significant alignment is then quoted. RESULTS: Based on extensive simulations, we study the multiple testing problem that occurs when several scoring matrices for local sequence alignment are used. We consider a simple Bonferroni correction of the p-values and investigate its accuracy. Finally, we propose a more accurate correction based on extreme value distributions fitted to the maximum of the normalized scores obtained from different scoring matrices. For various sets of matrices we provide correction factors which can be easily applied to adjust p- and E-values reported by software packages.