Circuit Topology Analysis of Single-Cell HiC Data.

The 3D fold structure of the genome is intricately linked to its function. As a result, descriptors of 3D genome conformation are becoming increasingly important as markers for disease and therapeutic responses. Circuit topology, a theory of folds, formalizes the arrangement of contacts in an entangled chain. It is uniquely suited for the topological description of the cellular genome and changes to genomic architecture during physiological processes like cellular differentiation or pathological and therapeutic alterations. In this discussion, we will explore circuit topology and its ability to extract topological information from single-cell HiC data.

Cytosolic Interactome Protects Against Protein Unfolding in a Single Molecule Experiment.

Single molecule techniques are particularly well suited for investigating the processes of protein folding and chaperone assistance. However, current assays provide only a limited perspective on the various ways in which the cellular environment can influence the folding pathway of a protein. In this study, a single molecule mechanical interrogation assay is developed and used to monitor protein unfolding and refolding within a cytosolic solution. This allows to test the cumulative topological effect of the cytoplasmic interactome on the folding process. The results reveal a stabilization against forced unfolding for partial folds, which are attributed to the protective effect of the cytoplasmic environment against unfolding and aggregation. This research opens the possibility of conducting single molecule molecular folding experiments in quasi-biological environments.

Circuit Topology Approach for the Comparative Analysis of Intrinsically Disordered Proteins.

Intrinsically disordered proteins (IDPs) lack a stable native conformation, making it challenging to characterize their structure and dynamics. Key topological motifs with fundamental biological relevance are often hidden in the conformational noise, eluding detection. Here, we develop a circuit topology toolbox to extract conformational patterns, critical contacts, and timescales from simulated dynamics of intrinsically disordered proteins. We follow the dynamics of IDPs by providing a smart low-dimensionality representation of their three-dimensional (3D) configuration in the topology space. Such an approach allows us to quantify topological similarity in dynamic systems, therefore providing a pipeline for structural comparison of IDPs.

ProteinCT: An implementation of the protein circuit topology framework.

The ability to describe the topology of a folded protein conformation is critically important for functional analysis, protein engineering, and drug design. Circuit topology is a unique topological framework which is widely applicable to protein analysis, yet a state-of-the art implementation of this concept is lacking. Here, we present an open-source Python-implemented circuit topology tool called ProteinCT. The platform provides a method for acquiring, visualizing, analyzing, and quantifying circuit topology data from proteins of interest. We mapped the universe of human proteins to a circuit topology space using conventional hardware within a few hours, demonstrating the performance of ProteinCT. In brief,•A Python-implemented circuit topology tool is developed to extract global and local topological information from a protein structure file.•Modules are developed to combine topological information with geometric and energetic information.•It is demonstrated that the method can be efficiently applied to a large set of proteins, opening a wide range of possibilities for structural proteomics research.

Topological dynamics of an intrinsically disordered N-terminal domain of the human androgen receptor.

Human androgen receptor contains a large N-terminal domain (AR-NTD) that is highly dynamic and this poses a major challenge for experimental and computational analysis to decipher its conformation. Misfolding of the AR-NTD is implicated in prostate cancer and Kennedy's disease, yet our knowledge of its structure is limited to primary sequence information of the chain and a few functionally important secondary structure motifs. Here, we employed an innovative combination of molecular dynamics simulations and circuit topology (CT) analysis to identify the tertiary structure of AR-NTD. We found that the AR-NTD adopts highly dynamic loopy conformations with two identifiable regions with distinct topological make-up and dynamics. This consists of a N-terminal region (NR, residues 1-224) and a C-terminal region (CR, residues 225-538), which carries a dense core. Topological mapping of the dynamics reveals a traceable time-scale dependent topological evolution. NR adopts different positioning with respect to the CR and forms a cleft that can partly enclose the hormone-bound ligand-binding domain (LBD) of the androgen receptor. Furthermore, our data suggest a model in which dynamic NR and CR compete for binding to the DNA-binding domain of the receptor, thereby regulating the accessibility of its DNA-binding site. Our approach allowed for the identification of a previously unknown regulatory binding site within the CR core, revealing the structural mechanisms of action of AR inhibitor EPI-001, and paving the way for other drug discovery applications.

Circuit topology analysis of cellular genome reveals signature motifs, conformational heterogeneity, and scaling.

Reciprocal regulation of genome topology and function is a fundamental and enduring puzzle in biology. The wealth of data provided by Hi-C libraries offers the opportunity to unravel this relationship. However, there is a need for a comprehensive theoretical framework in order to extract topological information for genome characterization and comparison. Here, we develop a toolbox for topological analysis based on Circuit Topology, allowing for the quantification of inter- and intracellular genomic heterogeneity, at various levels of fold complexity: pairwise contact arrangement, higher-order contact arrangement, and topological fractal dimension. Single-cell Hi-C data were analyzed and characterized based on topological content, revealing not only a strong multiscale heterogeneity but also highly conserved features such as a characteristic topological length scale and topological signature motifs in the genome. We propose that these motifs inform on the topological state of the nucleus and indicate the presence of active loop extrusion.

Topological principles of protein folding.

What is the topology of a protein and what governs protein folding to a specific topology? This is a fundamental question in biology. The protein folding reaction is a critically important cellular process, which is failing in many prevalent diseases. Understanding protein folding is also key to the design of new proteins for applications. However, our ability to predict the folding of a protein chain is quite limited and much is still unknown about the topological principles of folding. Current predictors of folding kinetics, including the contact order and size, present a limited predictive power, suggesting that these models are fundamentally incomplete. Here, we use a newly developed mathematical framework to define and extract the topology of a native protein conformation beyond knot theory, and investigate the relationship between native topology and folding kinetics in experimentally characterized proteins. We show that not only the folding rate, but also the mechanistic insight into folding mechanisms can be inferred from topological parameters. We identify basic topological features that speed up or slow down the folding process. The approach enabled the decomposition of protein 3D conformation into topologically independent elementary folding units, called circuits. The number of circuits correlates significantly with the folding rate, offering not only an efficient kinetic predictor, but also a tool for a deeper understanding of theoretical folding models. This study contributes to recent work that reveals the critical relevance of topology to protein folding with a new, contact-based, mathematically rigorous perspective. We show that topology can predict folding kinetics when geometry-based predictors like contact order and size fail.