New method detects and compares folding pathways of knotted proteins.
problem Understanding the function of knots in protein folding.
method Topological analysis of protein knotoid distributions and entanglement.
result Reveals unique folding pathway for shallow knotted Carbonic Anhydrases.
Mathematical pipeline identifies structural homology of knotted proteins.
problem Quantification and classification of protein structures, especially knotted proteins, require noise-free and complete data.
method Developed a geometric framework using persistent homology to analyze protein structures.
result Persistent homology accurately represents structural homology of knotted proteins and identifies geometric features of protein entanglement.
Study shows protein folding rate linked to topological changes.
problem Understanding protein folding kinetics and topology.
method Gauss linking integral, torsion, and sequence-distant contacts.
result Protein topology shifts from right-handed to left-handed with decreasing folding rate, associated with more sequence-distant contacts.
Knoto-ID studies the entanglement of open protein chains without closing them.
problem Analyzing the entanglement of open protein chains without altering their geometry.
method Using knotoids, a generalization of knot theory for open curves, to evaluate entanglement without closing the curve.
result Knoto-ID can analyze both global and local topologies of protein chains, identifying non-trivial folds.
Knot theory applied to proteins, distinguishing folded linear chains.
problem Classifying proteins as unknots when intra-chain interactions are ignored.
method Developing knot theory for folded linear molecular chains, considering self-bonding, and using Gauss codes and quandles.
result Extended knot theory to distinguish topologies of proteins with intra-chain bonds.
Pipeline learns topological features for protein stability prediction.
problem Predicting protein stability using topological features.
method Data-driven method to learn topological features, comparing with expert features.
result Topological features achieve 92%-99% of SME-based models' performance.
Study optimizes sampling for protein topology analysis.
problem Optimizing the sampling of protein projections for accurate topology classification.
method Characterized forbidden moves between knotoids and applied topological properties.
result Proposed a numerical measure for deeply knotted proteins.
Study uses knotoids to analyze open protein chains, revealing new topological regions.
problem Characterizing the topology of open protein chains.
method Introduced knotoids as a generalization of knots for open curves, analyzing protein chains without closure.
result Identified new topological regions in protein chains, including pre-knotted regions.
New method identifies knots in protein chains using virtual knots.
problem Identifying knots in open protein chains.
method Introducing virtual knots to analyze open curves without closure.
result Recovering and extending previous knotting results in proteins.
Method optimizes knotting pathways in constrained polymers.
problem Understanding how geometric constraints affect knot formation in polymers.
method Topological steering using knotoid spectrum and mean unravelling number.
result Geometric constraints increase the frequency of twist knots in polymers.
We develop topological methods for analyzing difference topology experiments involving 3-string tangles. Difference topology is a novel technique used to unveil the structure of stable protein-DNA complexes involving two or more DNA segments. We analyze such experiments for the Mu protein-DNA complex. We characterize t…
Persistent homology provides a new, efficient molecular descriptor for protein dynamics.
problem Designing effective molecular descriptors for high-dimensional MD trajectories.
method Introduced masked Flood complex, a protein-tailored modification of simplicial complexes, for persistent homology.
result Persistent homology-based descriptors are competitive across protein dynamics tasks, including frame-level observable regression and MSM estimation.
We use a semisupervised learning algorithm based on a topological data analysis approach to assign functional categories to yeast proteins using similarity graphs. This new approach to analyzing biological networks yields results that are as good as or better than state of the art existing approaches.
This thesis improves protein contact prediction using unsupervised and supervised methods.
problem Improving accuracy of protein contact prediction.
method Unsupervised and supervised deep learning methods.
result A scoring system called diversity score for measuring contact novelty.
New lattice path method for statistical inference of persistent diagrams.
problem Statistical inference on persistent diagrams.
method Lattice path representation and combinatorial enumerations.
result Topological changes observed in spike proteins of COVID-19 virus.
Machine learning predicts signaling peptides from protein star graphs.
problem Predicting signaling activity of proteins from molecular structure.
method Protein star graphs, S2SNet topological indices, Machine Learning (SVM-RFE, Laplacian kernel).
result Best model predicts 98.0% signaling pathways with AUROC 0.961.
Classifies uncolored bonded knots with up to 7 singularity points.
problem Classifying uncolored bonded knots with up to 7 singularity points.
method Generation of planar graphs, conversion into bonded knot diagrams, use of Yamada polynomial, and brute-force Reidemeister moves.
result Systematic classification of uncolored bonded knots with singularity number at most seven.
Graphoids are topological invariants of virtual graph diagrams.
problem Understanding knotted graphs with open ends in proteins and simplifying virtual spatial graphs.
method Topological interpretations of graphoids using graph Reidemeister moves.
result Virtual graphoids are useful for studying knotted graphs and simplifying spatial graphs.
Enhanced coloring invariant distinguishes folded molecular chain topologies.
problem Apparent indistinguishability of folded chain topologies using current coloring invariants.
method Introduced Boltzmann weights to improve the resolving power of quandle colorings.
result Improved resolution in distinguishing folded chain topologies.
Method uses network biology to construct gene expression models for cancer.
problem Building models for cancer phenotypes using gene expression data.
method Unsupervised construction of computational graphs based on protein-protein networks.
result The method outperforms other models in cancer phenotype analysis.
Model proteins with bonds using Kauffman bracket skein module.
problem Modeling proteins with bonds for structural analysis.
method Extend Kauffman bracket polynomial to bonded knots.
result Infinite generation and torsion-freeness of the bonded skein module.
Deep learning model predicts protein-ligand binding modes from docking data.
problem Improving protein-ligand binding mode prediction accuracy.
method Dual-graph architecture with separate sub-networks for ligand topology and protein-ligand interactions.
result Deep learning model outperforms docking programs in binding mode prediction.
New method for manifold topological learning avoids remeshing issues.
problem Persistent homology on manifolds is numerically inconsistent.
method Persistent de Rham-Hodge Laplacians in Eulerian representation.
result Avoids numerical inconsistency over multiscale manifolds.
Polynomial invariants classify molecular chains based on their contact arrangements.
problem No established invariants for molecular chains with both hard and soft contacts.
method Developed polynomial invariants for circuit topology of molecular chains.
result Polynomial invariants efficiently classify chains with various contact types.
New method analyzes knots and links using multiscale Gauss link integral.
problem Lack of localization and quantization in knot theory applications.
method Integrates curve segmentation and multiscale analysis into the Gauss link integral.
result Significantly outperforms other methods in protein flexibility analysis.
Integrase proteins acting on circular double-stranded DNA often change its topology by transforming unknotted circles into torus knots and links. Two systems of tangle equations--corresponding to the two initial DNA sequences--arise when modelling this transformation: direct and inverted. With no a priori assumptions o…
Review of mathematical representations for biomolecular data.
problem Complexity and high dimensionality of biomolecular datasets hinder ML applications.
method Developed low-dimensional and scalable mathematical representations using algebraic topology, differential geometry, and graph theory.
result Mathematical representations improve protein-ligand binding predictions and other biomolecular applications.
Novel ligand-based method improves protein representation performance.
problem Improving protein representation for bioinformatics tasks.
method Proposes SMILESVec method to represent ligands and compute protein similarity.
result Ligand-based protein representation performs as well as sequence-based methods.
SL2MF predicts synthetic lethality using logistic matrix factorization.
problem Predicting synthetic lethality in human cancers from limited experimental data.
method Logistic matrix factorization incorporating biological knowledge.
result SL2MF effectively predicts known and unknown SL interactions.
A new framework uses text descriptions to improve protein design.
problem Lack of effective methods to incorporate textual descriptions in protein design.
method ProteinDT framework that combines text and protein structural information.
result ProteinDT significantly improves protein design accuracy and performance.
Link prediction is one of the fundamental problems in network analysis. In many applications, notably in genetics, a partially observed network may not contain any negative examples of absent edges, which creates a difficulty for many existing supervised learning approaches. We develop a new method which treats the obs…
Deep learning models optimize protein sequences.
problem Optimizing protein properties through sequence design.
method Deep generative models guided by machine learning.
result Improved protein sequence generation from prior knowledge.
New method classifies protein structures using network features.
problem Efficiently predicting protein function from structural data.
method Modelled protein structures as PSNs, used graphlets and deep learning for features.
result Proposed methods outperform existing PSC approaches in accuracy.
mGPfusion predicts protein stability changes using a novel Gaussian process method.
problem Limited experimental data for predicting protein stability changes.
method Bayesian data fusion model combining experimental and molecular simulation data.
result mGPfusion outperforms state-of-the-art methods in predicting protein stability.
Ensemble method ranks homologous proteins robustly across various similarity metrics.
problem Ranking homologous proteins in a candidate set with high accuracy and robustness.
method Ensemble of models and assessment metrics, phalanxes, and aggregation of diverse metrics.
result Ensemble of phalanxes identifies strong and diverse subsets of feature variables for robust ranking.
ProGen models protein sequences for synthetic biology.
problem Generating proteins without structural annotations.
method Trained a 1.2B-parameter language model on 280M protein sequences.
result ProGen generates proteins with fine-grained control and accuracy.
Paper proposes MLPCD for protein community detection in large PPI networks.
problem Identifying reliable protein communities from large-scale PPI networks.
method Integrates Gene Expression Data and uses Multi-source Learning with cloud computing.
result Demonstrates superior performance compared to existing methods.
Complex biological systems have been successfully modeled by biochemical and genetic interaction networks, typically gathered from high-throughput (HTP) data. These networks can be used to infer functional relationships between genes or proteins. Using the intuition that the topological role of a gene in a network rela…
New 3D protein analysis methods improve accuracy.
problem Lack of suitable learning algorithms for protein data.
method Intrinsic-Extrinsic Convolution and Pooling for 3D protein structures.
result Outperforms state-of-the-art methods on protein analysis tasks.
Improved protein structure classification using weighted graphlets and deep neural networks.
problem Protein structure classification for function prediction.
method Developed a weighted network and graphlet-based measure, combined with a deep neural network.
result Significantly improved performance on 36 real datasets compared to existing methods.
PANDA predicts protein binding affinity changes from sequences, outperforming existing methods.
problem Accurately predicting changes in protein binding affinity due to mutations.
method Sequence-based machine learning approach using protein sequence information.
result PANDA achieves higher Pearson correlation coefficients than existing methods.
An invariant for knots with colored bonds respects HOMFLYPT relation.
problem Modeling and distinguishing knots with colored bonds.
method Introducing a HOMFLYPT skein module for colored bonded knots.
result The non-rigid version of the module provides information about knottedness of bonds.
Sequence-based model predicts protein-protein interactions with high accuracy.
problem Predicting protein-protein interactions for alternative treatment options.
method Sequence clustering, discrete cosine transform, supervised machine learning, SVM with RBF.
result Mesh model achieved an average AUC of 0.84.
A new model explains protein interactions via electron delocalization.
problem Understanding how protein interactions affect each other.
method Quantized discrete differential geometry of n-simplices.
result Allosteric regulation follows from the model of interactions.
EBM predicts protein conformations at atomic scale using crystallized data.
problem Predicting the conformation of a side chain from its context within a protein structure.
method Energy-based model trained on crystallized protein data, evaluating performance on rotamer recovery task.
result EBM achieves performance close to state-of-the-art methods, including Rosetta energy function.
Mathematician summarizes protein geometry and mutation effects.
problem Understanding how proteins mutate and their structure-function relationship.
method Mathematical analysis of protein structures and functions, focusing on hydrogen bonds and secondary structure.
result Protein secondary structure regulates mutation by stabilizing or destabilizing regions.
New multitask algorithm separates rare from frequent protein functions.
problem Challenging automated protein function prediction with unbalanced data.
method Uses dissimilarity information to separate rare class labels, unlike similarity-based approaches.
result Multitask label propagation algorithm performs best with dissimilarity matrix.
Improved 3D generative models for drug design reduce bias and enhance data efficiency.
problem Data sparsity and bias in 3D molecular design models.
method Multi-level contrastive learning protocol for bias control and data efficiency.
result Hierarchical generative models that are topologically unbiased and explainable.