Stability of structurally entangled protein dimers

Non-covalent Lasso Entanglements in Folded Proteins: Prevalence, Functional Implications, and Evolutionary Significance

One-third of protein domains in the CATH database contain a recently discovered tertiary topological motif: non-covalent lasso entanglements, in which a segment of the protein backbone forms a loop closed by non-covalent interactions between residues and is threaded one or more times by the N- or C-terminal backbone segment. Unknown is how frequently this structural motif appears across the proteomes of organisms. And the correlation of these motifs with various classes of protein function and biological processes have not been quantified. Here, using a combination of protein crystal structures, AlphaFold2 predictions, and Gene Ontology terms we show that in E. coli, S. cerevisiae and H. sapiens that 71%, 52% and 49% of globular proteins contain one-or-more non-covalent lasso entanglements in their native fold, and that some of these are highly complex with multiple threading events. Further, proteins containing these tertiary motifs are consistently enriched in certain functions and biological processes across these organisms and depleted in others, strongly indicating an influence of evolutionary selection pressures acting positively and negatively on the distribution of these motifs. Together, these results demonstrate that non-covalent lasso entanglements are widespread and indicate they may be extensively utilized for protein function and subcellular processes, thus impacting phenotype.

Folding kinetics of an entangled protein

The possibility of the protein backbone adopting lasso-like entangled motifs has attracted increasing attention. After discovering the surprising abundance of natively entangled protein domain structures, it was shown that misfolded entangled subpopulations might become thermosensitive or escape the homeostasis network just after translation. To investigate the role of entanglement in shaping folding kinetics, we introduce a novel indicator and analyze simulations of a coarse-grained, structure-based model for two small single-domain proteins. The model recapitulates the well-known two-state folding mechanism of a non-entangled SH3 domain. However, despite its small size, a natively entangled antifreeze RD1 protein displays a rich refolding behavior, populating two distinct kinetic intermediates: a short-lived, entangled, near-unfolded state and a longer-lived, non-entangled, near-native state. The former directs refolding along a fast pathway, whereas the latter is a kinetic trap, consistently with known experimental evidence of two different characteristic times. Upon trapping, the natively entangled loop folds without being threaded by the N-terminal residues. After trapping, the native entangled structure emerges by either backtracking to the unfolded state or threading through the already formed but not yet entangled loop. Along the fast pathway, trapping does not occur because the native contacts at the closure of the lasso-like loop fold after those involved in the N-terminal thread, confirming previous predictions. Despite this, entanglement may appear already in unfolded configurations. Remarkably, a longer-lived, near-native intermediate, with non-native entanglement properties, recalls what was observed in cotranslational folding.

Entangled Motifs in Membrane Protein Structures

Entangled motifs are found in one-third of protein domain structures, a reference set that contains mostly globular proteins. Their properties suggest a connection with co-translational folding. Here, we wish to investigate the presence and properties of entangled motifs in membrane protein structures. From existing databases, we build a non-redundant data set of membrane protein domains, annotated with the monotopic/transmembrane and peripheral/integral labels. We evaluate the presence of entangled motifs using the Gaussian entanglement indicator. We find that entangled motifs appear in one-fifth of transmembrane and one-fourth of monotopic proteins. Surprisingly, the main features of the distribution of the values of the entanglement indicator are similar to the reference case of general proteins. The distribution is conserved across different organisms. Differences with respect to the reference set emerge when considering the chirality of entangled motifs. Although the same chirality bias is found for single-winding motifs in both membrane and reference proteins, the bias is reversed, strikingly, for double-winding motifs only in the reference set. We speculate that these observations can be rationalized in terms of the constraints exerted on the nascent chain by the co-translational bio-genesis machinery, which is different for membrane and globular proteins.

Exploring whole-genome duplicate gene retention with complex genetic interaction analysis

Whole-genome duplication has played a central role in the genome evolution of many organisms, including the human genome. Most duplicated genes are eliminated, and factors that influence the retention of persisting duplicates remain poorly understood. We describe a systematic complex genetic interaction analysis with yeast paralogs derived from the whole-genome duplication event. Mapping of digenic interactions for a deletion mutant of each paralog, and of trigenic interactions for the double mutant, provides insight into their roles and a quantitative measure of their functional redundancy. Trigenic interaction analysis distinguishes two classes of paralogs: a more functionally divergent subset and another that retained more functional overlap. Gene feature analysis and modeling suggest that evolutionary trajectories of duplicated genes are dictated by combined functional and structural entanglement factors.

Transient knots in intrinsically disordered proteins and neurodegeneration

We provide a brief overview of the topological features found in structured proteins and of the dynamical processes that involve knots. We then discuss the knotted states that arise in the intrinsically disordered polyglutamine and α-synuclein. We argue that the existence of the knotted conformations stalls degradation by proteases and thus enhances aggregation. This mechanism works if the length of a peptide chain exceeds a threshold, as in the Huntington disease. We also study the cavities that form within the conformations of the disordered proteins. The volume of the cavities varies in time in a way that is different than that of the radius of gyration or the end-to-end distance. In addition, we study the traffic between the conformational basins and identify patterns associated with the deep and shallow knots. The results are obtained by molecular dynamics simulations that use coarse-grained and all-atom models (with and without the explicit solvent).

Folding Rate Optimization Promotes Frustrated Interactions in Entangled Protein Structures

Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in structural biology. Recently, the hypothesis that energetic frustration might be a mechanism to avoid topological frustration has been put forward based on the empirical observation that loops involved in entanglements are stabilized by weak interactions between amino-acids at their extrema. To verify this idea, we use a toy lattice model for the folding of proteins into two almost identical structures, one entangled and one not. As expected, the folding time is longer when random sequences folds into the entangled structure. This holds also under an evolutionary pressure simulated by optimizing the folding time. It turns out that optmized protein sequences in the entangled structure are in fact characterized by frustrated interactions at the closures of entangled loops. This phenomenon is much less enhanced in the control case where the entanglement is not present. Our findings, which are in agreement with experimental observations, corroborate the idea that an evolutionary pressure shapes the folding funnel to avoid topological and kinetic traps.

Computational methods in the study of self-entangled proteins: a critical appraisal

The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.

Searching the Optimal Folding Routes of a Complex Lasso Protein

Understanding how polypeptides can efficiently and reproducibly attain a self-entangled conformation is a compelling biophysical challenge that might shed new light on our general knowledge of protein folding. Complex lassos, namely self-entangled protein structures characterized by a covalent loop sealed by a cysteine bridge, represent an ideal test system in the framework of entangled folding. Indeed, because cysteine bridges form in oxidizing conditions, they can be used as on/off switches of the structure topology to investigate the role played by the backbone entanglement in the process. In this work, we have used molecular dynamics to simulate the folding of a complex lasso glycoprotein, granulocyte-macrophage colony-stimulating factor, modeling both reducing and oxidizing conditions. Together with a well-established Gō-like description, we have employed the elastic folder model, a coarse-grained, minimalistic representation of the polypeptide chain driven by a structure-based angular potential. The purpose of this study is to assess the kinetically optimal pathways in relation to the formation of the native topology. To this end, we have implemented an evolutionary strategy that tunes the elastic folder model potentials to maximize the folding probability within the early stages of the dynamics. The resulting protein model is capable of folding with high success rate, avoiding the kinetic traps that hamper the efficient folding in the other tested models. Employing specifically designed topological descriptors, we could observe that the selected folding routes avoid the topological bottleneck by locking the cysteine bridge after the topology is formed. These results provide valuable insights on the selection of mechanisms in self-entangled protein folding while, at the same time, the proposed methodology can complement the usage of established minimalistic models and draw useful guidelines for more detailed simulations.