Topological Twists in Nature

AlphaLasso-a web server to identify loop and lasso motifs in 3D structure of biopolymers

With the growing number of AI-predicted protein structures, automated methods of broad-scale analysis are required to parse this volume of data. The application of mathematically defined topologies to protein science enables such analysis. Building on the foundation of lasso peptides, complex lasso motifs are their macroscopic analogs in proteins, promising novel discoveries in drug design and the biopolymer industry. Here we present AlphaLasso, a web server designed to find and analyze lasso-type topologies in protein structures. It finds cysteine, amide, ester, and thioester or user-specified closing bridges. The modern visualization interface provides extensive capabilities to study lasso motifs, such as structure smoothing, creating topology maps, searching for similar proteins, in-depth model evaluation, and metadata annotation. This rich feature set makes AlphaLasso a powerful tool useful in biology, biophysics, chemistry, and mathematics. To enable large-scale analysis, we have precomputed the lasso topologies of high-quality models from the AlphaFold Database, finding >14 million proteins with lasso motifs closed by cysteine bridges, 2.2 million of which are complex lassos. Lasso motifs classified by complexity are available to users via an interactive website, supporting comparison with user-submitted structures. AlphaLasso is available at https://alphalasso.cent.uw.edu.pl/.

Lifetime of ground conformational state determines the activity of structured RNA

Biomolecules continually sample alternative conformations. Consequently, even the most energetically favored ground conformational state has a finite lifetime. Here, we show that, in addition to the three-dimensional (3D) structure, the lifetime of a ground conformational state determines its biological activity. Using hydrogen-deuterium exchange nuclear magnetic resonance spectroscopy, we found that Zika virus exoribonuclease-resistant RNA (xrRNA) encodes a ground conformational state with a lifetime that is ~105-107 longer than that of canonical base pairs. Mutations that shorten the apparent lifetime of the ground state without affecting its 3D structure decreased exoribonuclease resistance in vitro and impaired virus replication in cells. Additionally, we observed this exceptionally long-lived ground state in xrRNAs from diverse infectious mosquito-borne flaviviruses. These results demonstrate the biological importance of the lifetime of a preorganized ground state and further suggest that elucidating the lifetimes of dominant 3D structures of biomolecules may be crucial for understanding their behaviors and functions.

Exploring the folding landscape of leptin: Insights into threading pathways

The discovery of new protein topologies with entanglements and loop-crossings have shown the impact of local amino acid arrangement and global three-dimensional structures. This phenomenon plays a crucial role in understanding how protein structure relates to folding and function, affecting the global stability, and biological activity. Protein entanglements encompassing knots and non-trivial topologies add complexity to their folding free energy landscapes. However, the initial native contacts driving the threading event for entangled proteins remains elusive. The Pierced Lasso Topology (PLT) represents an entangled topology where a covalent linker creates a loop in which the polypeptide backbone is threaded through. Compared to true knotted topologies, PLTs are simpler topologies where the covalent-loop persists in all conformations. In this work, the PLT protein leptin, is used to visualize and differentiate the preference for slipknotting over plugging transition pathways along the folding route. We utilize the Energy Landscape Visualization Method (ELViM), a multidimensional projection technique, to visualize and distinguish early threaded conformations that cannot be observed in an in vitro experiment. Critical contacts for the leptin threading mechanisms were identified where the competing pathways are determined by the formation of a hairpin loop in the unfolded basin. Thus, prohibiting the dominant slipknotting pathway. Furthermore, ELViM offers insights into distinct folding pathways associated with slipknotting and plugging providing a novel tool for de novo design and in vitro experiments with residue specific information of threading events in silico.

Topological Reaction Coordinate Captures the Folding Transition State Ensemble in a Pierced Lasso Protein

Proteins with a pierced lasso topology (PLT) have a covalent loop created by a disulfide bond, and the backbone circles back to thread the loop. This threaded topology has unique features compared to knotted topologies; notably, the topology is controlled by the chemical environment and the covalent loop remains intact even when denatured. In this work, we use the hormone leptin as our model PLT system and study its folding using molecular dynamics simulations that employ a structure-based (Go̅-like) model. We find that the reduced protein has a two-state folding mechanism with a transition state ensemble (TSE) that can be characterized by the reaction coordinate Q, the fraction of native contacts formed. In contrast, the oxidized protein, which must thread part of the polypeptide chain through a covalent loop, has a folding process that is poorly characterized by Q. Instead, we find that a topological coordinate that monitors the residue crossing the loop can identify the TSE of oxidized leptin. By precisely identifying the predicted TSE, one may now reliably calculate theoretical phi-values for the PLT protein, thereby enabling a comparison with experimental measurements. We find the loop-threading constraint leads to noncanonical phi-values that are uniformly small because this PLT protein has a flat energy landscape through the TSE.

Protein self-entanglement modulates successful folding to the native state: A multi-scale modeling study

The computer-aided investigation of protein folding has greatly benefited from coarse-grained models, that is, simplified representations at a resolution level lower than atomistic, providing access to qualitative and quantitative details of the folding process that would be hardly attainable, via all-atom descriptions, for medium to long molecules. Nonetheless, the effectiveness of low-resolution models is itself hampered by the presence, in a small but significant number of proteins, of nontrivial topological self-entanglements. Features such as native state knots or slipknots introduce conformational bottlenecks, affecting the probability to fold into the correct conformation; this limitation is particularly severe in the context of coarse-grained models. In this work, we tackle the relationship between folding probability, protein folding pathway, and protein topology in a set of proteins with a nontrivial degree of topological complexity. To avoid or mitigate the risk of incurring in kinetic traps, we make use of the elastic folder model, a coarse-grained model based on angular potentials optimized toward successful folding via a genetic procedure. This light-weight representation allows us to estimate in silico folding probabilities, which we find to anti-correlate with a measure of topological complexity as well as to correlate remarkably well with experimental measurements of the folding rate. These results strengthen the hypothesis that the topological complexity of the native state decreases the folding probability and that the force-field optimization mimics the evolutionary process these proteins have undergone to avoid kinetic traps.