From Levinthal to pathways to funnels

Membrane lateral organization from potential energy disconnectivity graph

Understanding the thermodynamic and kinetic properties of biomolecules requires elucidation of their complex energy landscape. A disconnectivity graph analysis of the energy landscape provides a framework for mapping the multi-dimensional landscape onto a two-dimensional representation while preserving the key features of the energy landscape. Several studies show that the structure or shape of the disconnectity graph is directly associated with the function of protein and nucleic acid molecules. In this review, we discuss how disconnectivity analysis of the potential energy surface can be extended to lipid molecules to glean important information about membrane organization. The shape of the disconnectivity graphs can be used to predict the lateral organization of multi-component lipid bilayer. We hope that this review encourages the use of disconnectivity graphs routinely by membrane biophysicists to predict the lateral organization of lipids.

Altered assembly paths mitigate interference among paralogous complexes

Protein complexes are fundamental to all cellular processes, so understanding their evolutionary history and assembly processes is important. Gene duplication followed by divergence is considered a primary mechanism for diversifying protein complexes. Nonetheless, to what extent assembly of present-day paralogous complexes has been constrained by their long evolutionary pathways and how cross-complex interference is avoided remain unanswered questions. Subunits of protein complexes are often stabilized upon complex formation, whereas unincorporated subunits are degraded. How such cooperative stability influences protein complex assembly also remains unclear. Here, we demonstrate that subcomplexes determined by cooperative stabilization interactions serve as building blocks for protein complex assembly. We further develop a protein stability-guided method to compare the assembly processes of paralogous complexes in cellulo. Our findings support that oligomeric state and the structural organization of paralogous complexes can be maintained even if their assembly processes are rearranged. Our results indicate that divergent assembly processes by paralogous complexes not only enable the complexes to evolve new functions, but also reinforce their segregation by establishing incompatibility against deleterious hybrid assemblies.

Protein superfolds are characterised as frustration-free topologies: A case study of pure parallel β-sheet topologies

A protein superfold is a type of protein fold that is observed in at least three distinct, non-homologous protein families. Structural classification studies have revealed a limited number of prevalent superfolds alongside several infrequent occurring folds, and in α/β type superfolds, the C-terminal β-strand tends to favor the edge of the β-sheet, while the N-terminal β-strand is often found in the middle. The reasons behind these observations, whether they are due to evolutionary sampling bias or physical interactions, remain unclear. This article offers a physics-based explanation for these observations, specifically for pure parallel β-sheet topologies. Our investigation is grounded in several established structural rules that are based on physical interactions. We have identified "frustration-free topologies" which are topologies that can satisfy all the rules simultaneously. In contrast, topologies that cannot are termed "frustrated topologies." Our findings reveal that frustration-free topologies represent only a fraction of all theoretically possible patterns, these topologies strongly favor positioning the C-terminal β-strand at the edge of the β-sheet and the N-terminal β-strand in the middle, and there is significant overlap between frustration-free topologies and superfolds. We also used a lattice protein model to thoroughly investigate sequence-structure relationships. Our results show that frustration-free structures are highly designable, while frustrated structures are poorly designable. These findings suggest that superfolds are highly designable due to their lack of frustration, and the preference for positioning C-terminal β-strands at the edge of the β-sheet is a direct result of frustration-free topologies. These insights not only enhance our understanding of sequence-structure relationships but also have significant implications for de novo protein design.

Stabilization of Non-Native Folds and Programmable Protein Gelation in Compositionally Designed Deep Eutectic Solvents

Proteins are adjustable units from which biomaterials with designed properties can be developed. However, non-native folded states with controlled topologies are hardly accessible in aqueous environments, limiting their prospects as building blocks. Here, we demonstrate the ability of a series of anhydrous deep eutectic solvents (DESs) to precisely control the conformational landscape of proteins. We reveal that systematic variations in the chemical composition of binary and ternary DESs dictate the stabilization of a wide range of conformations, that is, compact globular folds, intermediate folding states, or unfolded chains, as well as controlling their collective behavior. Besides, different conformational states can be visited by simply adjusting the composition of ternary DESs, allowing for the refolding of unfolded states and vice versa. Notably, we show that these intermediates can trigger the formation of supramolecular gels, also known as eutectogels, where their mechanical properties correlate to the folding state of the protein. Given the inherent vulnerability of proteins outside the native fold in aqueous environments, our findings highlight DESs as tailorable solvents capable of stabilizing various non-native conformations on demand through solvent design.

Amino-Acid Characteristics in Protein Native State Structures

The molecular machines of life, proteins, are made up of twenty kinds of amino acids, each with distinctive side chains. We present a geometrical analysis of the protrusion statistics of side chains in more than 4000 high-resolution protein structures. We employ a coarse-grained representation of the protein backbone viewed as a linear chain of Cα atoms and consider just the heavy atoms of the side chains. We study the large variety of behaviors of the amino acids based on both rudimentary structural chemistry as well as geometry. Our geometrical analysis uses a backbone Frenet coordinate system for the common study of all amino acids. Our analysis underscores the richness of the repertoire of amino acids that is available to nature to design protein sequences that fit within the putative native state folds.

From Nucleosomes to Compartments: Physicochemical Interactions Underlying Chromatin Organization

Chromatin organization plays a critical role in cellular function by regulating access to genetic information. However, understanding chromatin folding is challenging due to its complex, multiscale nature. Significant progress has been made in studying in vitro systems, uncovering the structure of individual nucleosomes and their arrays, and elucidating the role of physicochemical forces in stabilizing these structures. Additionally, remarkable advancements have been achieved in characterizing chromatin organization in vivo, particularly at the whole-chromosome level, revealing important features such as chromatin loops, topologically associating domains, and nuclear compartments. However, bridging the gap between in vitro and in vivo studies remains challenging. The resemblance between in vitro and in vivo chromatin conformations and the relevance of internucleosomal interactions for chromatin folding in vivo are subjects of debate. This article reviews experimental and computational studies conducted at various length scales, highlighting the significance of intrinsic interactions between nucleosomes and their roles in chromatin folding in vivo.

A Perspective on Protein Structure Prediction Using Quantum Computers

Despite the recent advancements by deep learning methods such as AlphaFold2, in silico protein structure prediction remains a challenging problem in biomedical research. With the rapid evolution of quantum computing, it is natural to ask whether quantum computers can offer some meaningful benefits for approaching this problem. Yet, identifying specific problem instances amenable to quantum advantage and estimating the quantum resources required are equally challenging tasks. Here, we share our perspective on how to create a framework for systematically selecting protein structure prediction problems that are amenable for quantum advantage, and estimate quantum resources for such problems on a utility-scale quantum computer. As a proof-of-concept, we validate our problem selection framework by accurately predicting the structure of a catalytic loop of the Zika Virus NS3 Helicase, on quantum hardware.

A Water-Stable Boronate Ester Cage

The reversible condensation of catechols and boronic acids to boronate esters is a paradigm reaction in dynamic covalent chemistry. However, facile backward hydrolysis is detrimental for stability and has so far prevented applications for boronate-based materials. Here, we introduce cubic boronate ester cages 6 derived from hexahydroxy tribenzotriquinacenes and phenylene diboronic acids with ortho-t-butyl substituents. Due to steric shielding, dynamic exchange at the Lewis acidic boron sites is feasible only under acid or base catalysis but fully prevented at neutral conditions. For the first time, boronate ester cages 6 tolerate substantial amounts of water or alcohols both in solution and solid state. The unprecedented applicability of these materials under ambient and aqueous conditions is showcased by efficient encapsulation and on-demand release of β-carotene dyes and heterogeneous water oxidation catalysis after the encapsulation of ruthenium catalysts.

Protein-folding chaperones predict structure-function relationships and cancer risk in BRCA1 mutation carriers

Predicting the risk of cancer mutations is critical for early detection and prevention, but differences in allelic severity of human carriers confound risk predictions. Here, we elucidate protein folding as a cellular mechanism driving differences in mutation severity of tumor suppressor BRCA1. Using a high-throughput protein-protein interaction assay, we show that protein-folding chaperone binding patterns predict the pathogenicity of variants in the BRCA1 C-terminal (BRCT) domain. HSP70 selectively binds 94% of pathogenic BRCA1-BRCT variants, most of which engage HSP70 more than HSP90. Remarkably, the magnitude of HSP70 binding linearly correlates with loss of folding and function. We identify a prevalent class of human hypomorphic BRCA1 variants that bind moderately to chaperones and retain partial folding and function. Furthermore, chaperone binding signifies greater mutation penetrance and earlier cancer onset in the clinic. Our findings demonstrate the utility of chaperones as quantitative cellular biosensors of variant folding, phenotypic severity, and cancer risk.

Log-periodic oscillations as real-time signatures of hierarchical dynamics in proteins

The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. D. Sornette [Phys. Rep. 297, 239 (1998)] showed that this behavior can be explained by a discrete scale invariance of the system, which is associated with discrete and equidistant timescales on a logarithmic scale. Examples include such diverse fields as financial crashes, random diffusion, and quantum topological materials. Recent time-resolved experiments and molecular dynamics simulations suggest that discrete scale invariance may also apply to hierarchical dynamics in proteins, where several fast local conformational changes are a prerequisite for a slow global transition to occur. Employing entropy-based timescale analysis and Markov state modeling to a simple one-dimensional hierarchical model and biomolecular simulation data, it is found that hierarchical systems quite generally give rise to logarithmically spaced discrete timescales. By introducing a one-dimensional reaction coordinate that collectively accounts for the hierarchically coupled degrees of freedom, the free energy landscape exhibits a characteristic staircase shape with two metastable end states, which causes the log-periodic time evolution of the system. The period of the log-oscillations reflects the effective roughness of the energy landscape and can, in simple cases, be interpreted in terms of the barriers of the staircase landscape.

Protein dynamics underlying allosteric regulation

Allostery is the mechanism by which information and control are propagated in biomolecules. It regulates ligand binding, chemical reactions, and conformational changes. An increasing level of experimental resolution and control over allosteric mechanisms promises a deeper understanding of the molecular basis for life and powerful new therapeutics. In this review, we survey the literature for an up-to-date biological and theoretical understanding of protein allostery. By delineating five ways in which the energy landscape or the kinetics of a system may change to give rise to allostery, we aim to help the reader grasp its physical origins. To illustrate this framework, we examine three systems that display these forms of allostery: allosteric inhibitors of beta-lactamases, thermosensation of TRP channels, and the role of kinetic allostery in the function of kinases. Finally, we summarize the growing power of computational tools available to investigate the different forms of allostery presented in this review.

Base Pairing Promoted the Self-Organization of Genetic Coding, Catalysis, and Free-Energy Transduction

How Nature discovered genetic coding is a largely ignored question, yet the answer is key to explaining the transition from biochemical building blocks to life. Other, related puzzles also fall inside the aegis enclosing the codes themselves. The peptide bond is unstable with respect to hydrolysis. So, it requires some form of chemical free energy to drive it. Amino acid activation and acyl transfer are also slow and must be catalyzed. All living things must thus also convert free energy and synchronize cellular chemistry. Most importantly, functional proteins occupy only small, isolated regions of sequence space. Nature evolved heritable symbolic data processing to seek out and use those sequences. That system has three parts: a memory of how amino acids behave in solution and inside proteins, a set of code keys to access that memory, and a scoring function. The code keys themselves are the genes for cognate pairs of tRNA and aminoacyl-tRNA synthetases, AARSs. The scoring function is the enzymatic specificity constant, kcat/kM, which measures both catalysis and specificity. The work described here deepens the evidence for and understanding of an unexpected consequence of ancestral bidirectional coding. Secondary structures occur in approximately the same places within antiparallel alignments of their gene products. However, the polar amino acids that define the molecular surface of one are reflected into core-defining non-polar side chains on the other. Proteins translated from base-paired coding strands fold up inside out. Bidirectional genes thus project an inverted structural duality into the proteome. I review how experimental data root the scoring functions responsible for the origins of coding and catalyzed activation of unfavorable chemical reactions in that duality.

Identification of amentoflavone as a potent SARS-CoV-2 Mpro inhibitor: a combination of computational studies and in vitro biological evaluation

Small-molecule inhibitors of SARS-CoV-2 Mpro that block the active site pocket of the viral main protease have been considered potential therapeutics for the development of drugs against SARS-CoV-2. Here, we report the identification of amentoflavone (a biflavonoid) through docking-based virtual screening of a library comprised of 231 compounds consisting of flavonoids and isoflavonoids. The docking results were further substantiated through extensive analysis of the data obtained from all-atom 150 ns MD simulation. End-state effective free energy calculations using MM-PBSA calculations further suggested that (Ra)-amentoflavone (C3'-C8''-atropisomer) may show a greater binding affinity towards the Mpro than (Sa)-amentoflavone. In vitro cytotoxicity assay established that amentoflavone showed a high CC50 value indicating much lower toxicity. Further, potent inhibition of the Mpro by amentoflavone was established by studying the effect on HEK293T cells treated with SARS-CoV-2 Mpro expressing plasmid.Communicated by Ramaswamy H. Sarma.

Unfolding of protein using MoS2/SnS2heterostructure for nanopore-based sequencing

Protein sequencing is crucial for understanding the complex mechanisms driving biological functions. However, proteins are usually folded in their native state and the mechanism of fast protein conformation transitions still remains unclear, which make protein sequencing challenging. Molecular dynamics simulations with accurate force field are now able to observe the entire folding/unfolding process, providing valuable insights into protein folding mechanisms. Given that proteins can be unfolded, nanopore technology shows great potential for protein sequencing. In this study, we proposed to use MoS2/SnS2heterostructures to firstly unfold proteins and then detect them by a nanopore in the heterostructural membrane. All-atom molecular dynamics simulations performed in this work provided rich atomic-level information for a comprehensive understanding of protein unfolding process and mechanism on the MoS2/SnS2heterostructure, it was found that the strong binding of protein to SnS2nanostripe and hydrogen bond breaking were the main reasons for unfolding the protein on the heterostructure. After the protein was fully unfolded, it was restrained on the nanostripe because of the affinity of protein to the SnS2nanostripe. Thus by integrating the proposed unfolding technique with nanopore technology, detection of linear unfolded peptide was realized in this work, allowing for the identification of protein components, which is essential for sequencing proteins in the near future.

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables

The typically rugged nature of molecular free-energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free-energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for the data-driven discovery of CVs parametrizing the important large-scale motions of the system. A challenge to CV discovery is learning CVs invariant to the symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multimolecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate permutation invariant vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand the sampling of configurational phase space and obtain converged CVs and free-energy landscapes. We demonstrate the permutationally invariant network for enhanced sampling (PINES) approach in applications to the self-assembly of a 13-atom argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C45H92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

The PPP1R15 Family of eIF2-alpha Phosphatase Targeting Subunits (GADD34 and CReP)

The vertebrate PPP1R15 family consists of the proteins GADD34 (growth arrest and DNA damage-inducible protein 34, the product of the PPP1R15A gene) and CReP (constitutive repressor of eIF2α phosphorylation, the product of the PPP1R15B gene), both of which function as targeting/regulatory subunits for protein phosphatase 1 (PP1) by regulating subcellular localization, modulating substrate specificity and assembling complexes with target proteins. The primary cellular function of these proteins is to facilitate the dephosphorylation of eukaryotic initiation factor 2-alpha (eIF2α) by PP1 during cell stress. In this review, we will provide a comprehensive overview of the cellular function, biochemistry and pharmacology of GADD34 and CReP, starting with a brief introduction of eIF2α phosphorylation via the integrated protein response (ISR). We discuss the roles GADD34 and CReP play as feedback inhibitors of the unfolded protein response (UPR) and highlight the critical function they serve as inhibitors of the PERK-dependent branch, which is particularly important since it can mediate cell survival or cell death, depending on how long the stressful stimuli lasts, and GADD34 and CReP play key roles in fine-tuning this cellular decision. We briefly discuss the roles of GADD34 and CReP homologs in model systems and then focus on what we have learned about their function from knockout mice and human patients, followed by a brief review of several diseases in which GADD34 and CReP have been implicated, including cancer, diabetes and especially neurodegenerative disease. Because of the potential importance of GADD34 and CReP in aspects of human health and disease, we will discuss several pharmacological inhibitors of GADD34 and/or CReP that show promise as treatments and the controversies as to their mechanism of action. This review will finish with a discussion of the biochemical properties of GADD34 and CReP, their regulation and the additional interacting partners that may provide insight into the roles these proteins may play in other cellular pathways. We will conclude with a brief outline of critical areas for future study.

Intrinsically Disordered Regions Function as a Cervical Collar to Remotely Regulate the Nodding Dynamics of SARS-CoV-2 Prefusion Spike Heads

The SARS-CoV-2 prefusion spike heads (receptor binding domains, RBDs) frequently nod down and up to interact with host cell receptors. As the spike protein is a trimeric unit of significant size, to understand its large-scale structural dynamics associated with the nodding mechanism and the mutational impact on the same, we develop a topological symmetry-information-loaded coarse-grained structure-based model of a spike trimer using recent cryo-EM structural data. Our study reveals the control of two distant intrinsically disordered regions (IDRs), namely, 630 and FPPR loops, over the nodding dynamics of spike heads. We find that the order-disorder transition of IDRs becomes more evident in the variants of concern (VOCs) that are associated with the characteristic mutation, D614G, in the proximity of these IDRs. In some VOCs, the two other mutations A570D and S982A also show an integral effect. The driver mutation D614G instigates a salt-bridge disruption, altering the order-disorder dynamics of both 630 and FPPR loops and their interaction with the C-terminal domains (CTD1/CTD2). This altered connectivity in these mutants allows the two IDRs to act collectively as a "cervical collar" for the RBD, supporting various spike head postures, consistent with cryo-EM results available for specific cases. The IDRs' control over the spike structure and dynamics presents an exciting opportunity where they can be targeted as remote operational switches to artificially maneuver the nod for effective therapeutic interventions.

Protein Structure Prediction: Challenges, Advances, and the Shift of Research Paradigms

Protein structure prediction is an interdisciplinary research topic that has attracted researchers from multiple fields, including biochemistry, medicine, physics, mathematics, and computer science. These researchers adopt various research paradigms to attack the same structure prediction problem: biochemists and physicists attempt to reveal the principles governing protein folding; mathematicians, especially statisticians, usually start from assuming a probability distribution of protein structures given a target sequence and then find the most likely structure, while computer scientists formulate protein structure prediction as an optimization problem - finding the structural conformation with the lowest energy or minimizing the difference between predicted structure and native structure. These research paradigms fall into the two statistical modeling cultures proposed by Leo Breiman, namely, data modeling and algorithmic modeling. Recently, we have also witnessed the great success of deep learning in protein structure prediction. In this review, we present a survey of the efforts for protein structure prediction. We compare the research paradigms adopted by researchers from different fields, with an emphasis on the shift of research paradigms in the era of deep learning. In short, the algorithmic modeling techniques, especially deep neural networks, have considerably improved the accuracy of protein structure prediction; however, theories interpreting the neural networks and knowledge on protein folding are still highly desired.

Protein-Folding Chaperones Predict Structure-Function Relationships and Cancer Risk in BRCA1 Mutation Carriers

Identifying pathogenic mutations and predicting their impact on protein structure, function and phenotype remain major challenges in genome sciences. Protein-folding chaperones participate in structure-function relationships by facilitating the folding of protein variants encoded by mutant genes. Here, we utilize a high-throughput protein-protein interaction assay to test HSP70 and HSP90 chaperone interactions as predictors of pathogenicity for variants in the tumor suppressor BRCA1. Chaperones bind 77% of pathogenic BRCA1-BRCT variants, most of which engaged HSP70 more than HSP90. Remarkably, the magnitude of chaperone binding to variants is proportional to the degree of structural and phenotypic defect induced by BRCA1 mutation. Quantitative chaperone interactions identified BRCA1-BRCT separation-of-function variants and hypomorphic alleles missed by pathogenicity prediction algorithms. Furthermore, increased chaperone binding signified greater cancer risk in human BRCA1 carriers. Altogether, our study showcases the utility of chaperones as quantitative cellular biosensors of variant folding and phenotypic severity.

HIGHLIGHTS

Chaperones detect an abundance of pathogenic folding variants of BRCA1-BRCT.Degree of chaperone binding reflects severity of structural and phenotypic defect.Chaperones identify separation-of-function and hypomorphic variants. Chaperone interactions indicate penetrance and expressivity of BRCA1 alleles.

Dynamozones are the most obvious sign of the evolution of conformational dynamics in HIV-1 protease

Proteins are not static but are flexible molecules that can adopt many different conformations. The HIV-1 protease is an important target for the development of therapies to treat AIDS, due to its critical role in the viral life cycle. We investigated several dynamics studies on the HIV-1 protease families to illustrate the significance of examining the dynamic behaviors and molecular motions for an entire understanding of their dynamics-structure-function relationships. Using computer simulations and principal component analysis approaches, the dynamics data obtained revealed that: (i) The flap regions are the most obvious sign of the evolution of conformational dynamics in HIV-1 protease; (ii) There are dynamic structural regions in some proteins that contribute to the biological function and allostery of proteins via appropriate flexibility. These regions are a clear sign of the evolution of conformational dynamics of proteins, which we call dynamozones. The flap regions are one of the most important dynamozones members that are critical for HIV-1 protease function. Due to the existence of other members of dynamozones in different proteins, we propose to consider dynamozones as a footprint of the evolution of the conformational dynamics of proteins.

A geometrical framework for thinking about proteins

We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise attraction that assembles these building blocks, while respecting their individual symmetries. Instead of seeking to mimic the complexity of proteins, we look for a simple abstraction of reality that yet captures the essence of proteins. We employ analytic calculations and detailed Monte Carlo simulations to explore some consequences of our theory. The predictions of our approach are in accord with experimental data. Our framework provides a rationalization for understanding the common characteristics of proteins. Our results show that the free energy landscape of a globular protein is pre-sculpted at the backbone level, sequences and functionalities evolve in the fixed backdrop of the folds determined by geometry and symmetry, and that protein structures are unique in being simultaneously characterized by stability, diversity, and sensitivity.

RNA folding pathways from all-atom simulations with a variationally improved history-dependent bias

Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. As a step forward in tackling these issues, we extend to RNA an enhanced path-sampling method previously successfully applied to proteins. In this scheme, the information about the RNA's native structure is harnessed by a soft history-dependent biasing force promoting the generation of productive folding trajectories in an all-atom force field with explicit solvent. A rigorous variational principle is then applied to minimize the effect of the bias. Here, we report on an application of this method to RNA molecules from 20 to 47 nucleotides long and increasing topological complexity. By comparison with analog simulations performed on small proteins with similar size and architecture, we show that the RNA folding landscape is significantly more frustrated, even for relatively small chains with a simple topology. The predicted RNA folding mechanisms are found to be consistent with the available experiments and some of the existing coarse-grained models. Due to its computational performance, this scheme provides a promising platform to efficiently gather atomistic RNA folding trajectories, thus retain the information about the chemical composition of the sequence.

The Energetic Landscape of Catch Bonds in TCR Interfaces

Recognition of peptide/MHC complexes by αβ TCRs has traditionally been viewed through the lens of conventional receptor-ligand theory. Recent work, however, has shown that TCR recognition and T cell signaling can be profoundly influenced and tuned by mechanical forces. One outcome of applied force is the catch bond, where TCR dissociation rates decrease (half-lives increase) when limited force is applied. Although catch bond behavior is believed to be widespread in biology, its counterintuitive nature coupled with the difficulties of describing mechanisms at the structural level have resulted in considerable mystique. In this review, we demonstrate that viewing catch bonds through the lens of energy landscapes, barriers, and the ensuing reaction rates can help demystify catch bonding and provide a foundation on which atomic-level TCR catch bond mechanisms can be built.

Protein folding rate evolution upon mutations

Despite the spectacular success of cutting-edge protein fold prediction methods, many critical questions remain unanswered, including why proteins can reach their native state in a biologically reasonable time. A satisfactory answer to this simple question could shed light on the slowest folding rate of proteins as well as how mutations-amino-acid substitutions and/or post-translational modifications-might affect it. Preliminary results indicate that (i) Anfinsen's dogma validity ensures that proteins reach their native state on a reasonable timescale regardless of their sequence or length, and (ii) it is feasible to determine the evolution of protein folding rates without accounting for epistasis effects or the mutational trajectories between the starting and target sequences. These results have direct implications for evolutionary biology because they lay the groundwork for a better understanding of why, and to what extent, mutations-a crucial element of evolution and a factor influencing it-affect protein evolvability. Furthermore, they may spur significant progress in our efforts to solve crucial structural biology problems, such as how a sequence encodes its folding.

The "Beacon" Structural Model of Protein Folding: Application for Trp-Cage in Water

Protein folding is a process in which a polypeptide must undergo folding process to obtain its three-dimensional structure. Thermodynamically, it is a process of enthalpy to overcome the loss of conformational entropy in folding. Folding is primarily related to hydrophobic interactions and intramolecular hydrogen bondings. During folding, hydrophobic interactions are regarded to be the driving forces, especially in the initial structural collapse of a protein. Additionally, folding is guided by the strong interactions within proteins, such as intramolecular hydrogen bondings related to the α-helices and β-sheets of proteins. Therefore, a protein is divided into the folding key (FK) regions related to intramolecular hydrogen bondings and the non-folding key (non-FK) regions. Various conformations are expected for FK and non-FK regions. Different from non-FK regions, it is necessary for FK regions to form the specific conformations in folding, which are regarded as the necessary folding pathways (or "beacons"). Additionally, sequential folding is expected for the FK regions, and the intermediate state is found during folding. They are reflected on the local basins in the free energy landscape (FEL) of folding. To demonstrate the structural model, molecular dynamics (MD) simulations are conducted on the folding pathway of the TRP-cage in water.

Kinetic control in amyloid polymorphism: Different agitation and solution conditions promote distinct amyloid polymorphs of alpha-synuclein

Aggregation of neuronal protein α-synuclein is implicated in synucleinopathies, including Parkinson's disease. Despite abundant in vitro studies, the mechanism of α-synuclein assembly process remains ambiguous. In this work, α-synuclein aggregation was induced by its constant mixing in two separate modes, either by agitation in a 96-well microplate reader (MP) or in microcentrifuge tubes using a shaker incubator (SI). Aggregation in both modes occurred through a sigmoidal growth pattern with a well-defined lag, growth, and saturation phase. The end-stage MP- and SI-derived aggregates displayed distinct differences in morphological, biochemical, and spectral signatures as discerned through AFM, proteinase-K digestion, FTIR, Raman, and CD spectroscopy. The MP-derived aggregates showed irregular morphology with a significant random coil conformation, contrary to SI-derived aggregates, which showed typical β-sheet fibrillar structures. The end-stage MP aggregates convert to β-rich SI-like aggregates upon 1) seeding with SI-derived aggregates and 2) agitating in SI. We conclude that end-stage MP aggregates were in a kinetically trapped conformation, whose kinetic barrier was bypassed upon either seeding by SI-derived fibrils or shaking in SI. We further show that MP-derived aggregates that form in the presence of sorbitol, an osmolyte, displayed a β-rich signature, indicating that the preferential exclusion effect of osmolytes helped overcome the kinetic barrier. Our findings help in unravelling the kinetic origin of different α-synuclein aggregated polymorphs (strains) that encode diverse variants of synucleinopathies. We demonstrate that kinetic control shapes the polymorphic landscape of α-synuclein aggregates, both through de novo generation of polymorphs, and by their interconversion.

Effects of Hydrogen/Deuterium Exchange on Protein Stability in Solution and in the Gas Phase

Mass spectrometry (MS)-based techniques are widely used for probing protein structure and dynamics in solution. H/D exchange (HDX)-MS is one of the most common approaches in this context. HDX is often considered to be a "benign" labeling method, in that it does not perturb protein behavior in solution. However, several studies have reported that D₂O pushes unfolding equilibria toward the native state. The origin, and even the existence of this protein stabilization remain controversial. Here we conducted thermal unfolding assays in solution to confirm that deuterated proteins in D₂O are more stable, with 2-4 K higher melting temperatures than unlabeled proteins in H₂O. Previous studies tentatively attributed this phenomenon to strengthened H-bonds after deuteration, an effect that may arise from the lower zero-point vibrational energy of the deuterated species. Specifically, it was proposed that strengthened water-water bonds (W···W) in D₂O lower the solubility of nonpolar side chains. The current work takes a broader view by noting that protein stability in solution also depends on water-protein (W···P) and protein-protein (P···P) H-bonds. To help unravel these contributions, we performed collision-induced unfolding (CIU) experiments on gaseous proteins generated by native electrospray ionization. CIU profiles of deuterated and unlabeled proteins were indistinguishable, implying that P···P contacts are insensitive to deuteration. Thus, protein stabilization in D₂O is attributable to solvent effects, rather than alterations of intraprotein H-bonds. Strengthening of W···W contacts represents one possible explanation, but the stabilizing effect of D₂O can also originate from weakened W···P bonds. Future work will be required to elucidate which of these two scenarios is correct, or if both contribute to protein stabilization in D₂O. In any case, the often-repeated adage that "D-bonds are more stable than H-bonds" does not apply to intramolecular contacts in native proteins.

Globular Proteins and Where to Find Them within a Polymer Brush-A Case Study

Protein adsorption by polymerized surfaces is an interdisciplinary topic that has been approached in many ways, leading to a plethora of theoretical, numerical and experimental insight. There is a wide variety of models trying to accurately capture the essence of adsorption and its effect on the conformations of proteins and polymers. However, atomistic simulations are case-specific and computationally demanding. Here, we explore universal aspects of the dynamics of protein adsorption through a coarse-grained (CG) model, that allows us to explore the effects of various design parameters. To this end, we adopt the hydrophobic-polar (HP) model for proteins, place them uniformly at the upper bound of a CG polymer brush whose multibead-spring chains are tethered to a solid implicit wall. We find that the most crucial factor affecting the adsorption efficiency appears to be the polymer grafting density, while the size of the protein and its hydrophobicity ratio come also into play. We discuss the roles of ligands and attractive tethering surfaces to the primary adsorption as well as secondary and ternary adsorption in the presence of attractive (towards the hydrophilic part of the protein) beads along varying spots of the backbone of the polymer chains. The percentage and rate of adsorption, density profiles and the shapes of the proteins, alongside with the respective potential of mean force are recorded to compare the various scenarios during protein adsorption.

Rethinking the protein folding problem from a new perspective

One of the main concerns of Anfinsen was to reveal the connection between the amino-acid sequence and their biologically active conformation. This search gave rise to two crucial questions in structural biology, namely, why the proteins fold and how a sequence encodes its folding. As to the why, he proposes a plausible answer, namely, the thermodynamic hypothesis. As to the how, this remains an unsolved challenge. Consequently, the protein folding problem is examined here from a new perspective, namely, as an 'analytic whole'. Conceiving the protein folding in this way enabled us to (i) examine in detail why the force-field-based approaches have failed, among other purposes, in their ability to predict the three-dimensional structure of a protein accurately; (ii) propose how to redefine them to prevent these shortcomings, and (iii) conjecture on the origin of the state-of-the-art numerical-methods success to predict the tridimensional structure of proteins accurately.

Structural Dynamics of Amyloid-β Protofibrils and Actions of Anti-Amyloid-β Antibodies as Observed by High-Speed Atomic Force Microscopy

Amyloid-β (Aβ) aggregation intermediates, including oligomers and protofibrils (PFs), have attracted attention as neurotoxic aggregates in Alzheimer's disease. However, due to the complexity of the aggregation pathway, the structural dynamics of aggregation intermediates and how drugs act on them have not been clarified. Here we used high-speed atomic force microscopy to observe the structural dynamics of Aβ42 PF at the single-molecule level and the effect of lecanemab, an anti-Aβ PF antibody with the positive results from Phase 3 Clarity AD. PF was found to be a curved nodal structure with stable binding angle between individual nodes. PF was also a dynamic structure that associates with other PF molecules and undergoes intramolecular cleavage. Lecanemab remained stable in binding to PFs and to globular oligomers, inhibiting the formation of large aggregates. These results provide direct evidence for a mechanism by which antibody drugs interfere with the Aβ aggregation process.

Crystal Growth Rates from Molecular Liquids: The Kinetics of Entropy Loss

It has been established empirically that the rate of addition of molecules to the crystal during crystal growth from the melt is proportional to exp(-|ΔS_fus|/R), where ΔS_fus is the entropy of fusion. Here we show that this entropic slowdown arises directly from the separation of the entropy loss and energy loss processes associated with the freezing of the liquid. We present a theoretical treatment of the kinetics based on a model flat energy landscape and derive an explicit expression for the coupling magnitude in terms of the crystal-melt interfacial free energy. The implications of our work for nucleation kinetics are also discussed.

Evolutionary conservation of amino acids contributing to the protein folding transition state

The question of whether amino acids critical to protein folding kinetics are evolutionarily conserved has been investigated intensively in the past, but no consensus has yet been reached. Recently, we have demonstrated that the transition state, dictating folding kinetics, is characterized as the state of maximum dynamic cooperativity, i.e., the state of maximum correlations between amino acid contact formations. Here, we investigate the evolutionary conservation of those amino acids contributing significantly to the dynamic cooperativity. We find a strong indication of a new kind of relationship-necessary but not sufficient causality-between the evolutionary conservation and the dynamic cooperativity: larger contributions to the dynamic cooperativity arise from more conserved residues, but not vice versa. This holds for all the protein systems for which long folding simulation trajectories are available. To our knowledge, this is the first systematic demonstration of any kind of evolutionary conservation of amino acids relevant to folding kinetics.

Deep mining of the protein energy landscape

For over half a century, it has been known that protein molecules naturally undergo extensive structural fluctuations, and that these internal motions are intimately related to their functional properties. The energy landscape view has provided a powerful framework for describing the various physical states that proteins visit during their lifetimes. This Perspective focuses on the commonly neglected and often disparaged axis of the protein energy landscape: entropy. Initially seen largely as a barrier to functionally relevant states of protein molecules, it has recently become clear that proteins retain considerable conformational entropy in the "native" state, and that this entropy can and often does contribute significantly to the free energy of fundamental protein properties, processes, and functions. NMR spectroscopy, molecular dynamics simulations, and emerging crystallographic views have matured in parallel to illuminate dynamic disorder of the "ground state" of proteins and their importance in not only transiting between biologically interesting structures but also greatly influencing their stability, cooperativity, and contribution to critical properties such as allostery.

Enhanced statistical sampling reveals microscopic complexity in the talin mechanosensor folding energy landscape

Statistical mechanics can describe the major conformational ensembles determining the equilibrium free-energy landscape of a folding protein. The challenge is to capture the full repertoire of low-occurrence conformations separated by high kinetic barriers that define complex landscapes. Computationally, enhanced sampling methods accelerate the exploration of molecular rare events. However, accessing the entire protein's conformational space in equilibrium experiments requires technological developments to enable extended observation times. We developed single-molecule magnetic tweezers to capture over a million individual transitions as a single talin protein unfolds and refolds under force in equilibrium. When observed at classically-probed timescales, talin folds in an apparently uncomplicated two-state manner. As the sampling time extends from minutes to days, the underlying energy landscape exhibits gradually larger signatures of complexity, involving a finite number of well-defined rare conformations. A fluctuation analysis allows us to propose plausible structures of each low-probability conformational state. The physiological relevance of each distinct conformation can be connected to the binding of the cytoskeletal protein vinculin, suggesting an extra layer of complexity in talin-mediated mechanotransduction. More generally, our experiments directly test the fundamental notion that equilibrium dynamics depend on the observation timescale.

The residual structure of acid-denatured β2 -microglobulin is relevant to an ordered fibril morphology

β₂ -Microglobulin (β2m) forms amyloid fibrils in vitro under acidic conditions. Under these conditions, the residual structure of acid-denatured β2m is relevant to seeding and fibril extension processes. Disulfide (SS) bond-oxidized β2m has been shown to form rigid, ordered fibrils, whereas SS bond-reduced β2m forms curvy, less-ordered fibrils. These findings suggest that the presence of an SS bond affects the residual structure of the monomer, which subsequently influences the fibril morphology. To clarify this process, we herein performed NMR experiments. The results obtained revealed that oxidized β2m contained a residual structure throughout the molecule, including the N- and C-termini, whereas the residual structure of the reduced form was localized and other regions had a random coil structure. The range of the residual structure in the oxidized form was wider than that of the fibril core. These results indicate that acid-denatured β2m has variable conformations. Most conformations in the ensemble cannot participate in fibril formation because their core residues are hidden by residual structures. However, when hydrophobic residues are exposed, polypeptides competently form an ordered fibril. This conformational selection phase may be needed for the ordered assembly of amyloid fibrils.

Knotting Optimization and Folding Pathways of a Go-Model with a Deep Knot

Formation of protein knots is an intriguing offshoot of the protein folding problem. Since experimental resolution on knot formation is limited, theoretical methods currently provide the most detailed insights into the knotting process. While suitable for shallow knots, molecular dynamics simulations have faced challenges capturing the formation of deep knots in proteins such as the minimally tied trefoil α/β methyltransferase from Thermotoga maritima (MTTTM). To improve the efficiency of MTTTM knotting in Cα Go-model simulations, mutant variants of the MTTTM Go-model were investigated. Through a structure-based analysis of knotted and unknotted states, four residues (K71, R72, E75, V76) were identified to increase the knotting efficiency from 2% to 83% when their contact energies were doubled and dihedral strength around the knot loop increased. The key features of this model are (i) a C-terminal slipknot intermediate that threads the knot in a highly unstructured intermediate, (ii) the inability to knot in native-like intermediate states, and (iii) a minor population in a long-lived trap that cannot knot. Examination of residue 71-76 contacts provides a small set of potential mutants that can directly test the model's validity. In addition, the knotting optimization process developed here has broad applicability in generating knotting-efficient models of other knotted proteins.

Molecular Origin of Internal Friction in Intrinsically Disordered Proteins

Protein folding and dynamics are controlled by an interplay of thermal and viscosity effects. The effect of viscous drag through the solvent molecules is described by the classic Kramers theory in the high friction limit, which considers the dampening of the reactant molecules in the solution and quantifies the dependence of the reaction rate on the frictional drag. In addition to the external energy dissipation originating from the surrounding solvent molecules, there is an additional mode of internal energy dissipative force operative within the polypeptide chain reflecting the internal resistance of the chain to its conformational alterations. This dry, solvent-independent intrinsic frictional drag is termed internal friction. In the case of natively folded proteins, the physical origin of internal friction is primarily attributed to the intrachain interactions or other nonnative interactions in their compact states. However, the molecular origin of internal friction in intrinsically disordered proteins (IDPs) remains elusive.In this Account, we address this fundamental issue: what are the principal drivers of viscosity-independent (dry) friction in highly solvated, expanded, conformationally flexible, rapidly fluctuating IDPs that do not possess persistent intrachain interactions? IDPs exhibit diffusive conformational dynamics that is predominantly dominated by the segmental motion of the backbone arising due to the dihedral rotations in the Ramachandran Φ-Ψ space. The physical origin of friction in a complex biopolymeric system such as IDPs can be described by classic polymer models, namely, Rouse/Zimm models with internal friction. These one-dimensional models do not invoke torsional fluctuation components. Kuhn's classic description includes the connection between internal friction and microscopic dihedral hopping. Based on our time-resolved fluorescence anisotropy results, we describe that the sequence-dependent, collective, short-range backbone dihedral rotations govern localized internal friction in an archetypal IDP, namely, α-synuclein. The highly sensitive, residue-specific fluorescence depolarization kinetics offers a potent methodology to characterize and quantify the directional decorrelation engendered due to the short-range dihedral relaxation of the polypeptide backbone in the dihedral space. We utilized this characteristic relaxation time scale as our dynamic readout to quantify the site-specific frictional component. Our linear viscosity-dependent model of torsional relaxation time scale furnished a finite nonzero time constant at the zero solvent viscosity representing the solvent-independent internal friction. These results unveil the effect of the degree of dihedral restraining parameter on the internal friction component by showing that a restrained proline residue imparts higher torsional stiffness in the chain segments and, therefore, exhibits higher internal friction. This Account sheds light on the molecular underpinning of the sequence-specific internal friction in IDPs and will be of interest to unmask the role of internal friction in a diverse range of biomolecular processes involving binding-induced folding, allosteric interaction, protein misfolding and aggregation, and biomolecular condensation via phase separation.

Protein folding problem: enigma, paradox, solution

The ability of protein chains to spontaneously form their three-dimensional structures is a long-standing mystery in molecular biology. The most conceptual aspect of this mystery is how the protein chain can find its native, "working" spatial structure (which, for not too big protein chains, corresponds to the global free energy minimum) in a biologically reasonable time, without exhaustive enumeration of all possible conformations, which would take billions of years. This is the so-called "Levinthal's paradox." In this review, we discuss the key ideas and discoveries leading to the current understanding of protein folding kinetics, including folding landscapes and funnels, free energy barriers at the folding/unfolding pathways, and the solution of Levinthal's paradox. A special role here is played by the "all-or-none" phase transition occurring at protein folding and unfolding and by the point of thermodynamic (and kinetic) equilibrium between the "native" and the "unfolded" phases of the protein chain (where the theory obtains the simplest form). The modern theory provides an understanding of key features of protein folding and, in good agreement with experiments, it (i) outlines the chain length-dependent range of protein folding times, (ii) predicts the observed maximal size of "foldable" proteins and domains. Besides, it predicts the maximal size of proteins and domains that fold under solely thermodynamic (rather than kinetic) control. Complementarily, a theoretical analysis of the number of possible protein folding patterns, performed at the level of formation and assembly of secondary structures, correctly outlines the upper limit of protein folding times.

Slow dynamics measured by phosphorescence lifetime reveals global conformational changes in human adult hemoglobin induced by allosteric effectors

The mechanism underlying allostery in hemoglobin (Hb) is still not completely understood. Various models describing the action of allosteric effectors on Hb function have been published in the literature. It has also been reported that some allosteric effectors-such as chloride ions, inositol hexaphosphate, 2,3-diphospho-glycerate and bezafibrate-considerably lower the oxygen affinity of Hb. In this context, an important question is the extent to which these changes influence the conformational dynamics of the protein. Earlier, we elaborated a challenging method based on phosphorescence quenching, which makes characterizing protein-internal dynamics possible in the ms time range. The experimental technique involves phosphorescence lifetime measurements in thermal equilibrium at varied temperatures from 10 K up to 273 K, based on the signal of Zn-protoporphyrin substituted for the heme in the β-subunits of Hb. The thermal activation of protein dynamics was observed by the enhancement of phosphorescence quenching attributed to O2 diffusion. It was shown that the thermal activation of protein matrix dynamics was clearly distinguishable from the dynamic activation of the aqueous solvent, and was therefore highly specific for the protein. In the present work, the same method was used to study the changes in the parameters of the dynamic activation of human HbA induced by binding allosteric effectors. We interpreted the phenomenon as phase transition between two states. The fitting of this model to lifetime data yielded the change of energy and entropy in the activation process and the quenching rate in the dynamically activated state. The fitted parameters were particularly sensitive to the presence of allosteric effectors and could be interpreted in line with results from earlier experimental studies. The results suggest that allosteric effectors are tightly coupled to the dynamics of the whole protein, and thus underline the importance of global dynamics in the regulation of Hb function.

Transient On- and Off-Pathway Protein Folding Intermediate States Characterized with NMR Relaxation Dispersion

The earliest events in the folding of a protein are in general poorly understood. We used NMR R2 relaxation dispersion experiments to study transient local collapse events in the unfolded-state (U) conformational ensemble of apomyoglobin (apoMb). Local residual secondary structure (seen in regions corresponding to the A, D, E, and H helices of the folded protein) is largely unchanged over the pH range of 2.3-2.75, yet a significant pH-dependent increase in the conformational exchange contribution to the R2 relaxation rate (Rex) indicates that transient intramolecular contacts occur on a microsecond to millisecond time scale at pH 2.75. A comparison of 15N and 13CO relaxation dispersion data at pH 2.75 for residues in the A, B, G, and H regions, which participate in the earliest folding intermediates, indicates that chain collapse and secondary structure formation are rapid and concomitant. Increasingly stabilizing conditions (lower temperature, higher pH) result in the observation of a relaxation dispersion in the C, CD, and E regions of the protein, which are known to fold at later stages. Mutation of Trp14 in the A-helix region to Ala eliminates conformational exchange throughout the protein, and the mutation of hydrophobic residues in other regions results in the selective inhibition of conformational exchange in the B, G, or H regions. The R2 dispersion data for WT apoMb at pH 2.75 and 10 °C are best fit to a four-state model ABGH ⇆ AGH ⇆ U ⇆ ABCD that includes on-pathway (AGH and ABGH) and off-pathway (ABCD) transiently folded states, both of which are required to explain the behavior of the mutant proteins. The off-pathway intermediate is destabilized at higher temperatures. Our analysis provides insights into the earliest stages of apoMb folding where the collapsing polypeptide chain samples both productive and nonproductive states with stabilized secondary structure.

Analytical Formulation and Field-Theoretic Simulation of Sequence-Specific Phase Separation of Protein-Like Heteropolymers with Short- and Long-Spatial-Range Interactions

A theory for sequence-dependent liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) in the study of biomolecular condensates is formulated by extending the random phase approximation (RPA) and field-theoretic simulation (FTS) of heteropolymers with spatially long-range Coulomb interactions to include the fundamental effects of short-range, hydrophobic-like interactions between amino acid residues. To this end, short-range effects are modeled by Yukawa interactions between multiple nonelectrostatic charges derived from an eigenvalue decomposition of pairwise residue-residue contact energies. Chain excluded volume is afforded by incompressibility constraints. A mean-field approximation leads to an effective Flory-Huggins χ parameter, which, in conjunction with RPA, accounts for the contact-interaction effects of amino acid composition and the sequence-pattern effects of long-range electrostatics in IDP LLPS, whereas FTS based on the formulation provides full sequence dependence for both short- and long-range interactions. This general approach is illustrated here by applications to variants of a natural IDP in the context of several different amino-acid interaction schemes as well as a set of different model hydrophobic-polar sequences sharing the same composition. Effectiveness of the methodology is verified by coarse-grained explicit-chain molecular dynamics simulations.

Scanning pH-metry for Observing Reversibility in Protein Folding

One of the main factors affecting protein structure in solution is pH. Traditionally, to study pH-dependent conformational changes in proteins, the concentration of the H+ ions is adjusted manually, complicating real-time analyses, hampering dynamic pH regulation, and consequently leading to a limited number of tested pH levels. Here, we present a programmable device, a scanning pH-meter, that can automatically generate different types of pH ramps and waveforms in a solution. A feedback loop algorithm calculates the required flow rates of the acid/base titrants, allowing one, for example, to generate periodic pH sine waveforms to study the reversibility of protein folding by fluorescence spectroscopy. Interestingly, for some proteins, the fluorescence intensity profiles recorded in such a periodically oscillating pH environment display hysteretic behavior indicating an asymmetry in the sequence of the protein unfolding/refolding events, which can most likely be attributed to their distinct kinetics. Another useful application of the scanning pH-meter concerns coupling it with an electrospray ionization mass spectrometer to observe pH-induced structural changes in proteins as revealed by their varying charge-state distributions. We anticipate a broad range of applications of the scanning pH-meter developed here, including protein folding studies, determination of the optimum pH for achieving maximum fluorescence intensity, and characterization of fluorescent dyes and other synthetic materials.

Protein Design: From the Aspect of Water Solubility and Stability

Water solubility and structural stability are key merits for proteins defined by the primary sequence and 3D-conformation. Their manipulation represents important aspects of the protein design field that relies on the accurate placement of amino acids and molecular interactions, guided by underlying physiochemical principles. Emulated designer proteins with well-defined properties both fuel the knowledge-base for more precise computational design models and are used in various biomedical and nanotechnological applications. The continuous developments in protein science, increasing computing power, new algorithms, and characterization techniques provide sophisticated toolkits for solubility design beyond guess work. In this review, we summarize recent advances in the protein design field with respect to water solubility and structural stability. After introducing fundamental design rules, we discuss the transmembrane protein solubilization and de novo transmembrane protein design. Traditional strategies to enhance protein solubility and structural stability are introduced. The designs of stable protein complexes and high-order assemblies are covered. Computational methodologies behind these endeavors, including structure prediction programs, machine learning algorithms, and specialty software dedicated to the evaluation of protein solubility and aggregation, are discussed. The findings and opportunities for Cryo-EM are presented. This review provides an overview of significant progress and prospects in accurate protein design for solubility and stability.

Electronic properties of amino acids and nucleobases: similarity classes and pairing principles from chemical reactivity indices

We present a new classification scheme for amino acids and nucleobases based on the electronic properties of the individual molecules. Using chemical reactivity indices such as electronegativity, electrophilicity, and chemical hardness, we can identify similarities and differences between each class of amino acids and nucleobases. Notable differences emerge in particular with regard to high, neutral or low electronegativity as well as different combinations of chemical hardness. Our approach allows us to relate these insights to the properties of the side groups in terms of a unique reference scheme. We further show that hydrophobic differences between amino acids are rather negligible in the context of electronic properties. Our classification scheme also rationalizes the occurrence of distinct stable nucleobase pairs and clearly emphasizes certain differences between individual molecules. The stability and abundant occurrence of Watson-Crick nucleobase pairs is further discussed in the context of the minimum electrophilicity principle.

Volumetric Properties of the Transition State Ensemble for Protein Folding

Understanding how high hydrostatic pressure affects biomacromolecular interaction is important for deciphering the molecular mechanisms by which organisms adapt to live at the bottom of the ocean. The relative effect of hydrostatic pressure on the rates of folding/unfolding reactions is defined by the volumetric properties of the transition state ensemble relative to the folded and unfolded states. All-atom structure-based molecular dynamics simulations combined with quantitative computational protocol to compute volumes from three-dimensional coordinates allow volumetric mapping of protein folding landscape. This, is turn, provides qualitative understanding of the effects of hydrostatic pressure on energy landscape of proteins. The computational results for six different proteins are directly benchmark against experimental data and show an excellent agreement. Both experiments and computation show that the transition-state ensemble volume appears to be in-between the folded and unfolded state volumes, and thus the hydrostatic pressure accelerates protein unfolding.

Allostery: Allosteric Cancer Drivers and Innovative Allosteric Drugs

Here, we discuss the principles of allosteric activating mutations, propagation downstream of the signals that they prompt, and allosteric drugs, with examples from the Ras signaling network. We focus on Abl kinase where mutations shift the landscape toward the active, imatinib binding-incompetent conformation, likely resulting in the high affinity ATP outcompeting drug binding. Recent pharmacological innovation extends to allosteric inhibitor (GNF-5)-linked PROTAC, targeting Bcr-Abl1 myristoylation site, and broadly, allosteric heterobifunctional degraders that destroy targets, rather than inhibiting them. Designed chemical linkers in bifunctional degraders can connect the allosteric ligand that binds the target protein and the E3 ubiquitin ligase warhead anchor. The physical properties and favored conformational state of the engineered linker can precisely coordinate the distance and orientation between the target and the recruited E3. Allosteric PROTACs, noncompetitive molecular glues, and bitopic ligands, with covalent links of allosteric ligands and orthosteric warheads, increase the effective local concentration of productively oriented and placed ligands. Through covalent chemical or peptide linkers, allosteric drugs can collaborate with competitive drugs, degrader anchors, or other molecules of choice, driving innovative drug discovery.

Modeling protein structure as a stable static equilibrium

We present evidence that the protein structure can be modeled as a stable static equilibrium, determined mainly by compressive supports in the nonpolar interior. That is, protein structures derive their structural strength through the same mechanical principles as do conventional structures like bridges and buildings. This is based on the observation that the experimentally elucidated structural determinants, the interior nonpolar side chains, are engaged in strong compressions in static terms. At the same time, major substructures in proteins, helices and h-bonded strands, because of their geometry, inherently leave gaps in the space they occupy. Under the compressive force, nonpolar side chains from one substructure can protrude into the gaps of another neighboring substructure and block its motion. As a result, interlocking of substructures can form, which builds up the nonpolar core assembly. The native structure then is the one with the structurally most stable core assembly. While intuitively appealing, this is a radical departure from the prevailing thinking that protein native structure is determined by global energy minimum, which is founded on thermodynamic hypothesis. Furthermore, to develop an effective model for analyzing protein structure with conventional tools, a proper mechanical representation must be established. By proving that the stability of the equilibrium in compressive interactions is conditioned on a form of mechanical energy minimum, we show that our notion of native structure can be equally consistent with the thermodynamic hypothesis. By mathematically treating the blocking action, an interaction, as a bar, a physical object, we succeed in representing and analyzing the core assembly as truss, a conventional structure. In this paper we define and expound step-by-step increasingly integrated interlocking patterns. We then analyze the core assemblies of a large set of diverse protein database structures. A native structure can be distinguished from decoys by comparing the composition and strength of their core assemblies. We show the results for two sets of native structures vs decoys.

Protein folding in vitro and in the cell: From a solitary journey to a team effort

Correct protein folding is essential for the health and function of living organisms. Yet, it is not well understood how unfolded proteins reach their native state and avoid aggregation, especially within the cellular milieu. Some proteins, especially small, single-domain and apparent two-state folders, successfully attain their native state upon dilution from denaturant. Yet, many more proteins undergo misfolding and aggregation during this process, in a concentration-dependent fashion. Once formed, native and aggregated states are often kinetically trapped relative to each other. Hence, the early stages of protein life are absolutely critical for proper kinetic channeling to the folded state and for long-term solubility and function. This review summarizes current knowledge on protein folding/aggregation mechanisms in buffered solution and within the bacterial cell, highlighting early stages. Remarkably, teamwork between nascent chain, ribosome, trigger factor and Hsp70 molecular chaperones enables all proteins to overcome aggregation propensities and reach a long-lived bioactive state.