Statistical Properties of Lasso-Shape Polymers and Their Implications for Complex Lasso Proteins Function

Discovery of a trefoil knot in the RydC RNA: Challenging previous notions of RNA topology

Knots are very common in polymers, including DNA and protein molecules. Yet, no genuine knot has been identified in natural RNA molecules to date. Upon re-examining experimentally determined RNA 3D structures, we discovered a trefoil knot 31, the most basic non-trivial knot, in the RydC RNA. This knotted RNA is a member of a small family of short bacterial RNAs, whose secondary structure is characterized by an H-type pseudoknot. Molecular dynamics simulations suggest a folding pathway of the RydC RNA that starts with a native twisted loop. Based on sequence analyses and computational RNA 3D structure predictions, we postulate that this trefoil knot is a conserved feature of all RydC-related RNAs. The first discovery of a knot in a natural RNA molecule introduces a novel perspective on RNA 3D structure formation and on fundamental research on the relationship between function and spatial structure of biopolymers.

Lasso Proteins-Unifying Cysteine Knots and Miniproteins

Complex lasso proteins are a recently identified class of biological compounds that are present in considerable fraction of proteins with disulfide bridges. In this work, we look at complex lasso proteins as a generalization of well-known cysteine knots and miniproteins (lasso peptides). In particular, we show that complex lasso proteins with the same crucial topological features-cysteine knots and lasso peptides-are antimicrobial proteins, which suggests that they act as a molecular plug. Based on an analysis of the stability of the lasso piercing residue, we also introduce a method to determine which lasso motif is potentially functional. Using this method, we show that the lasso motif in antimicrobial proteins, as well in that in cytokines, is functionally relevant. We also study the evolution of lasso motifs, their conservation, and the usefulness of the lasso fingerprint, which extracts all topologically non-triviality concerning covalent loops. The work is completed by the presentation of extensive statistics on complex lasso proteins to analyze, in particular, the strange propensity for "negative" piercings. We also identify 21 previously unknown complex lasso proteins with an ester and a thioester bridge.

Topoly: Python package to analyze topology of polymers

The increasing role of topology in (bio)physical properties of matter creates a need for an efficient method of detecting the topology of a (bio)polymer. However, the existing tools allow one to classify only the simplest knots and cannot be used in automated sample analysis. To answer this need, we created the Topoly Python package. This package enables the distinguishing of knots, slipknots, links and spatial graphs through the calculation of different topological polynomial invariants. It also enables one to create the minimal spanning surface on a given loop, e.g. to detect a lasso motif or to generate random closed polymers. It is capable of reading various file formats, including PDB. The extensive documentation along with test cases and the simplicity of the Python programming language make it a very simple to use yet powerful tool, suitable even for inexperienced users. Topoly can be obtained from https://topoly.cent.uw.edu.pl.

Topological Twists in Nature

The first entangled protein was observed about 30 years ago, resulting in an increased interest for uncovering the biological functions and biophysical properties of these complex topologies. Recently, the Pierced Lasso Topology (PLT) was discovered in which a covalent bond forms an intramolecular loop, leaving one or both termini free to pierce the loop. This topology is related to knots and other entanglements. PLTs exist in many well-researched systems where the PLTs have previously been unnoticed. PLTs represents 18% of all disulfide containing proteins across all kingdoms of life. In this review, we investigate the biological implications of this specific topology in which the PLT-forming disulfide may act as a molecular switch for protein function and consequently human health.

GLN: a method to reveal unique properties of lasso type topology in proteins

Geometry and topology are the main factors that determine the functional properties of proteins. In this work, we show how to use the Gauss linking integral (GLN) in the form of a matrix diagram-for a pair of a loop and a tail-to study both the geometry and topology of proteins with closed loops e.g. lassos. We show that the GLN method is a significantly faster technique to detect entanglement in lasso proteins in comparison with other methods. Based on the GLN technique, we conduct comprehensive analysis of all proteins deposited in the PDB and compare it to the statistical properties of the polymers. We show how high and low GLN values correlate with the internal exibility of proteins, and how the GLN in the form of a matrix diagram can be used to study folding and unfolding routes. Finally, we discuss how the GLN method can be applied to study entanglement between two structures none of which are closed loops. Since this approach is much faster than other linking invariants, the next step will be evaluation of lassos in much longer molecules such as RNA or loops in a single chromosome.

On folding of entangled proteins: knots, lassos, links and θ-curves

Around 6% of protein structures deposited in the PDB are entangled, forming knots, slipknots, lassos, links, and θ-curves. In each of these cases, the protein backbone weaves through itself in a complex way, and at some point passes through a closed loop, formed by other regions of the protein structure. Such a passing can be interpreted as crossing a topological barrier. How proteins overcome such barriers, and therefore different degrees of frustration, challenged scientists and has shed new light on the field of protein folding. In this review, we summarize the current knowledge about the free energy landscape of proteins with non-trivial topology. We describe identified mechanisms which lead proteins to self-tying. We discuss the influence of excluded volume, such as crowding and chaperones, on tying, based on available data. We briefly discuss the diversity of topological complexity of proteins and their evolution. We also list available tools to investigate non-trivial topology. Finally, we formulate intriguing and challenging questions at the boundary of biophysics, bioinformatics, biology, and mathematics, which arise from the discovery of entangled proteins.