Protein folding classes -- High-dimensional geometry of amino acid composition space revisited

Boryeu Mao

Home/Archive/arXiv

arXiv · 2506.01857

Protein folding classes -- High-dimensional geometry of amino acid composition space revisited

Boryeu Mao

View original source ↗Read source document ↗Export metadata ↓

Abstract

In this study, the distributions of protein structure classes (or folding types) of experimentally determined structures from a legacy dataset and a comprehensive database (SCOP) are modeled precisely with geometric constructs such as convex polytopes in high-dimensional amino acid composition space. This is a follow-up of a previous non-statistical, geometry-motivated modeling of protein classes with ellipsoidal models, which is superseded presently in three important respects: (1) as a paradigm shift a descriptive 'distribution model' of experimental data is de-coupled from, and serves as the basis for, a possible future predictive 'domain model' generalizable to proteins in the same class for which 3D structures have yet to be determined experimentally, (2) the geometric and analytic characteristics of class distributions are obtained via exact computational geometry calculations, and (3) the full data from a comprehensive database are included in such calculations, eschewing training set selection and biases. In contrast to statistical and machine-learning approaches, the analytical, non-statistical geometry models of protein class distributions demonstrated in this study furnish complete and precise information on their size and relative disposition in the high-dimensional space (vis-à-vis any overlaps leading to ambiguity and classification limits). Intended primarily as an accurate and summary description of the complex relationships between amino acid composition and protein classes, and suitably as a basis for predictive modeling where possible, the results suggest that pen-ultimately they may be useful adjuncts for validating sequence-based protein structure predictions and contribute to theoretical and fundamental understanding of secondary structure formation and protein folding, demonstrating the role of high dimensional amino acid composition space in protein studies.

Explore related subjects

q-bio.BM q-bio.QM

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Boryeu Mao. 2025-10-20. Protein folding classes -- High-dimensional geometry of amino acid composition space revisited. https://arxiv.org/abs/2506.01857

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

In Vivo Length Distributions as Mechanistic Fingerprints of Pathological Protein Aggregation

Modern imaging techniques can resolve individual pathological protein aggregates in postmortem human samples, providing detailed measurements of aggregate size distributions that are inaccessible with conventional bulk approaches. These distributions represent mechanistic fingerprints of the microscopic processes that generated the observed pathology, but extracting this mechanistic information requires a quantitative theoretical framework. Here, we develop the mathematical tools needed to interpret aggregate length distributions in living systems, where aggregate growth competes with active removal. We show that, across a class of models, the length distribution of sufficiently large aggregates approaches a geometric decay. Crucially, the decay rate is determined by the balance between aggregate elongation and removal, providing a direct quantitative readout of these competing processes from a single time point measurement. This enables mechanistic comparisons between healthy and diseased human samples without requiring longitudinal measurements of aggregate dynamics. We further analyse how additional aggregation and removal processes modify the observed length distributions. Together, these results establish the mathematical foundations and tools to use aggregate length distributions as an experimentally accessible route for inferring microscopic aggregation dynamics directly from human tissue.

q-bio.BM↗

arXiv2026

Decoding enzyme-substrate interaction topology reveals principles underlying catalytic efficiency and mutational outcomes

The enzyme turnover number (kcat) defines catalytic efficiency and constrains quantitative models of metabolism, yet the molecular determinants governing kcat and its response to mutation remain poorly understood. Measurements are sparse and labor-intensive, and most computational approaches provide numerical predictions without explaining how enzyme-substrate interactions shape catalytic outcomes. A central challenge is therefore to identify the topological principles that determine where mutations act and how their functional outcomes are encoded within the enzyme-substrate interaction network. Here, we show that catalytic efficiency and mutational effects can be interpreted through enzyme-substrate interaction topology. We developed Interkcat, an interpretable bidirectional cross-attention framework that captures reciprocal coordination between protein residues and substrate atoms. Optimized on a unified benchmark, Interkcat achieves state-of-the-art predictive performance (R2 = 0.701). From its learned representations, we derive an Interaction Topology Score (ITS) that identifies sequence regions statistically enriched for mutation-sensitive sites without explicit structural inputs. We further demonstrate that higher-order topological features distinguish opposing mutational outcomes: lethal mutations disrupt coordinated networks, whereas activity-preserving or enhancing mutations retain sparse, globally organized coupling. These findings establish interaction topology as a unifying principle linking enzyme sequence, catalytic efficiency, and evolutionary perturbation.

q-bio.BM↗

arXiv2026

Adapting Boltz-2 with limited experimental activity data improves early enrichment in virtual screening

Virtual screening aims to prioritize active compounds from large chemical libraries within a limited experimental budget. When applying Boltz-2 to virtual screening, a key challenge is how to use limited experimental data from the target assay to improve the prioritization of active compounds. We investigated whether fine-tuning the Boltz-2 affinity heads with a small number of binary activity labels could improve early enrichment of active compounds in hit discovery. We compared fine-tuning with 40-300 labels in a retrospective evaluation on eight MF-PCBA targets. With 300 activity measurements, fine-tuning increased the number of actives in the top 1% by a geometric mean of 1.77-fold across the eight targets and improved average precision (AP) by 2.14-fold relative to the control without fine-tuning. We also investigated whether rescoring a subset of candidates could retain the improvement in hit recovery by reranking only the top-ranked Boltz-2 candidates with the fine-tuned head. Restricting rescoring to approximately 10% of the evaluation set retained hit recovery comparable to full rescoring. These findings show that affinity-head fine-tuning with limited activity labels improves early enrichment with Boltz-2 and that this benefit can be retained when rescoring a restricted set of candidates.

q-bio.BM↗