Pierced Lasso Topology Controls Function in Leptin

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.

A Small Contribution to a Large System: The Leptin Receptor Complex

Obesity is a classified epidemic, increasing the risk of secondary diseases such as diabetes, inflammation, cardiovascular disease, and cancer. The pleiotropic hormone leptin is the proposed link for the gut-brain axis controlling nutritional status and energy expenditure. Research into leptin signaling provides great promise toward discovering therapeutics for obesity and its related diseases targeting leptin and its cognate leptin receptor (LEP-R). The molecular basis underlying the human leptin receptor complex assembly remains obscure, due to the lack of structural information regarding the biologically active complex. In this work, we investigate the proposed receptor binding sites in human leptin utilizing designed antagonist proteins combined with AlphaFold predictions. Our results show that binding site I has a more intricate role in the active signaling complex than previously described. We hypothesize that the hydrophobic patch in this region engages a third receptor forming a higher-order complex, or a new LEP-R binding site inducing allosteric rearrangement.

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.

Lasso Proteins: Modular Design, Cellular Synthesis, and Topological Transformation

Entangled proteins have attracted significant research interest. Herein, we report the first rationally designed lasso proteins, or protein [1]rotaxanes, by using a p53dim-entwined dimer for intramolecular entanglement and a SpyTag-SpyCatcher reaction for side-chain ring closure. The lasso structures were confirmed by proteolytic digestion, mutation, NMR spectrometry, and controlled ligation. Their dynamic properties were probed by experiments such as end-capping, proteolytic digestion, and heating/cooling. As a versatile topological intermediate, a lasso protein could be converted to a rotaxane, a heterocatenane, and a "slide-ring" network. Being entirely genetically encoded, this robust and modular lasso-protein motif is a valuable addition to the topological protein repertoire and a promising candidate for protein-based biomaterials.

The Pierced Lasso Topology Leptin has a Bolt on Dynamic Domain Composed by the Disordered Loops I and III

Leptin is an important signaling hormone, mostly known for its role in energy expenditure and satiety. Furthermore, leptin plays a major role in other proteinopathies, such as cancer, marked hyperphagia, impaired immune function, and inflammation. In spite of its biological relevance in human health, there are no NMR resonance assignments of the human protein available, obscuring high-resolution characterization of the soluble protein and/or its conformational dynamics, suggested as being important for receptor interaction and biological activity. Here, we report the nearly complete backbone resonance assignments of human leptin. Chemical shift-based secondary structure prediction confirms that in solution leptin forms a four-helix bundle including a pierced lasso topology. The conformational dynamics, determined on several timescales, show that leptin is monomeric, has a rigid four-helix scaffold, and a dynamic domain, including a transiently formed helix. The dynamic domain is anchored to the helical scaffold by a secondary hydrophobic core, pinning down the long loops of leptin to the protein body, inducing motional restriction without a well-defined secondary or tertiary hydrogen bond stabilized structure. This dynamic region is well suited for and may be involved in functional allosteric dynamics upon receptor binding.

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.

Directional Immobilization of Proteins on Gold Nanoparticles Is Essential for Their Biological Activity: Leptin as a Case Study

Gold nanomaterials hold great potential for biomedical applications. While this field is evolving rapidly, little attention has been paid to precise nanoparticle design and functionalization. Here, we show that when using proteins as targeting moieties, it is fundamental to immobilize them directionally to preserve their biological activity. Using full-length leptin as a case study, we have developed two alternative conjugation strategies for protein immobilization based on either a site-selective or a nonselective derivatization approach. We show that only nanoparticles with leptin immobilized site-selectively fully retain the ability to interact with the cognate leptin receptor. These results demonstrate the importance of a specified molecular design when preparing nanoparticles labeled with proteins.

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.

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

The shape and properties of closed loops depend on various topological factors. One of them is loop-threading, which is present in complex lasso proteins. In this work, we analyze the probability of loop-threading by the tail and its influence on the shape of the loop measured by the radius of gyration, distention, asphericity, and prolateness. In particular, we show that the probability of a trivial lasso for phantom polymer is non-zero even for an infinite structure, as well as that the threading flattens the loop by restricting its motion in one dimension. These results are further used to show that there are fewer non-trivial protein lassos than expected and select potentially functional complex lasso proteins.

Uncovering the molecular mechanisms behind disease-associated leptin variants

The pleiotropic hormone leptin has a pivotal role in regulating energy balance by inhibiting hunger and increasing energy expenditure. Homozygous mutations found in the leptin gene are associated with extreme obesity, marked hyperphagia, and impaired immune function. Although these mutations have been characterized in vivo, a detailed understanding of how they affect leptin structure and function remains elusive. In the current work, we used NMR, differential scanning calorimetry, molecular dynamics simulations, and bioinformatics calculations to characterize the effects of these mutations on leptin structure and function and binding to its cognate receptor. We found that mutations identified in patients with congenital leptin deficiency not only cause leptin misfolding or aggregation, but also cause changes in the dynamics of leptin residues on the receptor-binding interface. Therefore, we infer that mutation-induced leptin deficiency may arise from several distinct mechanisms including (i) blockade of leptin receptor interface II, (ii) decreased affinity in the second step of leptin's interaction with its receptor, (iii) leptin destabilization, and (iv) unsuccessful threading through the covalent loop, leading to leptin misfolding/aggregation. We propose that this expanded framework for understanding the mechanisms underlying leptin deficiency arising from genetic mutations may be useful in designing therapeutics for leptin-associated disorders.

A random version of principal component analysis in data clustering

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance/correlation matrix of the analyzed data. However, to properly work with high-dimensional data sets, PCA poses severe mathematical constraints on the minimum number of different replicates, or samples, that must be included in the analysis. Generally, improper sampling is due to a small number of data respect to the number of the degrees of freedom that characterize the ensemble. In the field of life sciences it is often important to have an algorithm that can accept poorly dimensioned data sets, including degenerated ones. Here a new random projection algorithm is proposed, in which a random symmetric matrix surrogates the covariance/correlation matrix of PCA, while maintaining the data clustering capacity. We demonstrate that what is important for clustering efficiency of PCA is not the exact form of the covariance/correlation matrix, but simply its symmetry.

To Tie or Not to Tie? That Is the Question

In this review, we provide an overview of entangled proteins. Around 6% of protein structures deposited in the PBD are entangled, forming knots, slipknots, lassos and links. We present theoretical methods and tools that enabled discovering and classifying such structures. We discuss the advantages and disadvantages of the non-trivial topology in proteins, based on available data about folding, stability, biological properties and evolutionary conservation. We also formulate intriguing and challenging questions on the border of biophysics, bioinformatics, biology and mathematics, which arise from the discovery of an entanglement in proteins. Finally, we discuss possible applications of entangled proteins in medicine and nanotechnology, such as the chance to design super stable proteins, whose stability could be controlled by chemical potential.