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We model the evolution of eukaryotic protein-protein interaction (PPI) networks. In our model, PPI networks evolve by two known biological mechanisms: (1) Gene duplication, which is followed by rapid diversification of duplicate…
Recently described stochastic models of protein evolution have demonstrated that the inclusion of structural information in addition to amino acid sequences leads to a more reliable estimation of evolutionary parameters. We present a…
Accurately assigning folds for divergent protein sequences is a major obstacle to structural studies and underlies the inverse protein folding problem. Herein, we outline our theories for fold-recognition in the "twilight-zone" of sequence…
The structure of molecular networks derives from dynamical processes on evolutionary time scales. For protein interaction networks, global statistical features of their structure can now be inferred consistently from several…
Non-native conformations drive protein misfolding diseases, complicate bioengineering efforts, and fuel molecular evolution. No current experimental technique is well-suited for elucidating them and their phenotypic effects. Especially…
Proteins exist as a dynamic ensemble of multiple conformations, and these motions are often crucial for their functions. However, current structure prediction methods predominantly yield a single conformation, overlooking the conformational…
Background. Non-specific Lipid Transfer Proteins (nsLTPs) are widely distributed in the plant kingdom and constitute a superfamily of related proteins. More than 800 different sequences have been characterized so far, but their biological…
Determining the structure of a protein has been a decades-long open question. A protein's three-dimensional structure often poses nontrivial computation costs, when classical simulation algorithms are utilized. Advances in the transformer…
Predicting protein structure from the amino acid sequence has been a challenge with theoretical and practical significance in biophysics. Despite the recent progresses elicited by improved residue-residue contact prediction, contact-based…
The ability to computationally generate novel yet physically foldable protein structures could lead to new biological discoveries and new treatments targeting yet incurable diseases. Despite recent advances in protein structure prediction,…
This chapter gives a graceful introduction to problem of protein three- dimensional structure prediction, and focuses on how to make structural sense out of a single input sequence with unknown structure, the 'query' or 'target' sequence.…
Motivation: Drug discovery demands rapid quantification of compound-protein interaction (CPI). However, there is a lack of methods that can predict compound-protein affinity from sequences alone with high applicability, accuracy, and…
Understanding how proteins structurally interact is crucial to modern biology, with applications in drug discovery and protein design. Recent machine learning methods have formulated protein-small molecule docking as a generative problem…
When biological foundation models such as scGPT and Geneformer process single-cell gene expression, what geometric and topological structure forms in their internal representations? Is that structure biologically meaningful or a training…
Protein structure prediction and folding are fundamental to understanding biology, with recent deep learning advances reshaping the field. Diffusion-based generative models have revolutionized protein design, enabling the creation of novel…
Despite substantial efforts, deep learning has not yet delivered a transformative impact on elucidating regulatory biology, particularly in the realm of predicting gene expression profiles. Here, we argue that genuine "foundation models" of…
Penalized linear regression is of fundamental importance in high-dimensional statistics and has been routinely used to regress a response on a high-dimensional set of predictors. In many scientific applications, there exists external…
Protein-protein interactions (PPIs) are fundamental to numerous cellular processes, and their characterization is vital for understanding disease mechanisms and guiding drug discovery. While protein language models (PLMs) have demonstrated…
A new theoretical survey of proteins' resistance to constant speed stretching is performed for a set of 17 134 proteins as described by a structure-based model. The proteins selected have no gaps in their structure determination and consist…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…