Polymer principles and protein folding

Opportunities and challenges in design and optimization of protein function

The field of protein design has made remarkable progress over the past decade. Historically, the low reliability of purely structure-based design methods limited their application, but recent strategies that combine structure-based and sequence-based calculations, as well as machine learning tools, have dramatically improved protein engineering and design. In this Review, we discuss how these methods have enabled the design of increasingly complex structures and therapeutically relevant activities. Additionally, protein optimization methods have improved the stability and activity of complex eukaryotic proteins. Thanks to their increased reliability, computational design methods have been applied to improve therapeutics and enzymes for green chemistry and have generated vaccine antigens, antivirals and drug-delivery nano-vehicles. Moreover, the high success of design methods reflects an increased understanding of basic rules that govern the relationships among protein sequence, structure and function. However, de novo design is still limited mostly to α-helix bundles, restricting its potential to generate sophisticated enzymes and diverse protein and small-molecule binders. Designing complex protein structures is a challenging but necessary next step if we are to realize our objective of generating new-to-nature activities.

Resolving Hidden Solution Conformations of Hemoglobin Using IMS-IMS on a Cyclic Instrument

Ion mobility spectrometry-mass spectrometry (IMS-MS) experiments on a cyclic IMS instrument were used to examine heterogeneous distributions of structures found in the 15+ to 18+ charge states of the hemoglobin tetramer (Hb). The resolving power of IMS measurements is known to increase with increasing drift-region length. This effect is not significant for Hb charge states as peaks were shown to broaden with increasing drift-region length. This observation suggests that multiple structures with similar cross sections may be present. To examine this hypothesis, selections of drift time distributions were isolated and subsequently reinjected into the mobility region for additional separation. These IMS-IMS experiments demonstrate that selected regions separate further upon additional passes around the drift cell, consistent with the idea that initial resolving power was limited due to the presence of many closely related conformations. Additional variable temperature electrospray ionization (vT-ESI) experiments were conducted to study how changing the solution temperature affects solution conformations. Some features in these IMS-IMS studies were observed to change similarly with solution temperature compared to features in the single IMS distribution. Other features changed differently in the selected mobility data, indicating that solution structures that were obscured upon IMS analysis because of the complex heterogeneity of the original distribution are discernible after reducing the number of conformers that are analyzed by further IMS analysis. These results illustrate that the combination of vT-ESI with IMS-IMS is useful for resolving and exploring conformer distributions and stabilities in systems that exhibit a large degree of structural heterogeneity.

Protein-Inspired Control over Synthetic Polymer Folding for Structured Functional Nanoparticles in Water

The folding of proteins into functional nanoparticles with defined 3D structures has inspired chemists to create simple synthetic systems mimicking protein properties. The folding of polymers into nanoparticles in water proceeds via different strategies, resulting in the global compaction of the polymer chain. Herein, we review the different methods available to control the conformation of synthetic polymers and collapse/fold them into structured, functional nanoparticles, such as hydrophobic collapse, supramolecular self-assembly, and covalent cross-linking. A comparison is made between the design principles of protein folding to synthetic polymer folding and the formation of structured nanocompartments in water, highlighting similarities and differences in design and function. We also focus on the importance of structure for functional stability and diverse applications in complex media and cellular environments.

Predicting non-equilibrium folding behavior of polymer chains using the steepest-entropy-ascent quantum thermodynamic framework

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is used to explore the influence of heating and cooling on polymer chain folding kinetics. The framework predicts how a chain moves from an initial non-equilibrium state to stable equilibrium along a unique thermodynamic path. The thermodynamic state is expressed by occupation probabilities corresponding to the levels of a discrete energy landscape. The landscape is generated using the Replica Exchange Wang-Landau method applied to a polymer chain represented by a sequence of hydrophobic and polar monomers with a simple hydrophobic-polar amino acid model. The chain conformation evolves as energy shifts among the levels of the energy landscape according to the principle of steepest entropy ascent. This principle is implemented via the SEAQT equation of motion. The SEAQT framework has the benefit of providing insight into structural properties under non-equilibrium conditions. Chain conformations during heating and cooling change continuously without sharp transitions in morphology. The changes are more drastic along non-equilibrium paths than along quasi-equilibrium paths. The SEAQT-predicted kinetics are fitted to rates associated with the experimental intensity profiles of cytochrome c protein folding with Rouse dynamics.

Dissecting the energetic architecture within an RNA tertiary structural motif via high-throughput thermodynamic measurements

Structured RNAs and RNA/protein complexes perform critical cellular functions. They often contain structurally conserved tertiary contact "motifs," whose occurrence simplifies the RNA folding landscape. Prior studies have focused on the conformational and energetic modularity of intact motifs. Here, we turn to the dissection of one common motif, the 11nt receptor (11ntR), using quantitative analysis of RNA on a massively parallel array to measure the binding of all single and double 11ntR mutants to GAAA and GUAA tetraloops, thereby probing the energetic architecture of the motif. While the 11ntR behaves as a motif, its cooperativity is not absolute. Instead, we uncovered a gradient from high cooperativity amongst base-paired and neighboring residues to additivity between distant residues. As expected, substitutions at residues in direct contact with the GAAA tetraloop resulted in the largest decreases to binding, and energetic penalties of mutations were substantially smaller for binding to the alternate GUAA tetraloop, which lacks tertiary contacts present with the canonical GAAA tetraloop. However, we found that the energetic consequences of base partner substitutions are not, in general, simply described by base pair type or isostericity. We also found exceptions to the previously established stability-abundance relationship for 11ntR sequence variants. These findings of "exceptions to the rule" highlight the power of systematic high-throughput approaches to uncover novel variants for future study in addition to providing an energetic map of a functional RNA.

Evolutionary adaptation of the protein folding pathway for secretability

Secretory preproteins of the Sec pathway are targeted post-translationally and cross cellular membranes through translocases. During cytoplasmic transit, mature domains remain non-folded for translocase recognition/translocation. After translocation and signal peptide cleavage, mature domains fold to native states in the bacterial periplasm or traffic further. We sought the structural basis for delayed mature domain folding and how signal peptides regulate it. We compared how evolution diversified a periplasmic peptidyl-prolyl isomerase PpiA mature domain from its structural cytoplasmic PpiB twin. Global and local hydrogen-deuterium exchange mass spectrometry showed that PpiA is a slower folder. We defined at near-residue resolution hierarchical folding initiated by similar foldons in the twins, at different order and rates. PpiA folding is delayed by less hydrophobic native contacts, frustrated residues and a β-turn in the earliest foldon and by signal peptide-mediated disruption of foldon hierarchy. When selected PpiA residues and/or its signal peptide were grafted onto PpiB, they converted it into a slow folder with enhanced in vivo secretion. These structural adaptations in a secretory protein facilitate trafficking.

Size of the protein-protein energy funnel in crowded environment

Association of proteins to a significant extent is determined by their geometric complementarity. Large-scale recognition factors, which directly relate to the funnel-like intermolecular energy landscape, provide important insights into the basic rules of protein recognition. Previously, we showed that simple energy functions and coarse-grained models reveal major characteristics of the energy landscape. As new computational approaches increasingly address structural modeling of a whole cell at the molecular level, it becomes important to account for the crowded environment inside the cell. The crowded environment drastically changes protein recognition properties, and thus significantly alters the underlying energy landscape. In this study, we addressed the effect of crowding on the protein binding funnel, focusing on the size of the funnel. As crowders occupy the funnel volume, they make it less accessible to the ligands. Thus, the funnel size, which can be defined by ligand occupancy, is generally reduced with the increase of the crowders concentration. This study quantifies this reduction for different concentration of crowders and correlates this dependence with the structural details of the interacting proteins. The results provide a better understanding of the rules of protein association in the crowded environment.

Assessing the Experimental Hydrogen Bonding Energy of the Cyclic Water Dimer Transition State with a Cyclooctatetraene-Based Molecular Balance

We have conducted an experimental and computational study of cyclooctatetraene-1,4/1,6-dimethanol (1,4 and 1,6) as a molecular balance with the goal in mind to determine the otherwise inaccessible hydrogen bonding energy (HBE) of the cyclic water dimer, which constitutes a transition state. The 1,4/1,6 folding equilibrium is governed by an intramolecular hydrogen bond in the folded 1,6-isomer, in which the OH groups adopt a cyclic planar geometry, akin to the structure of the cyclic water dimer transition state. We characterized hydrogen bonding in 1,6 and reference complexes utilizing SAPT2 + (3)δMP2/aug-cc-pVTZ and selected quantum theory of atoms in molecule descriptors at M06-2XD3(0)/ma-def2-TZVPP. Additionally, we computed HBEs at the DLPNO-CCSD(T)/aug-cc-pVQZ level of theory. We find that hydrogen bonding in 1,6 is very similar to the interaction in the C_i symmetric cyclic water dimer TS, both in magnitude and character. We experimentally determined the Gibbs free energy of the folding process (ΔG_eq) in a variety of organic solvents via nuclear magnetic resonance spectroscopy measurements at room temperature. By combining experimentally obtained ΔG_eq values with corrections derived from accurate computational methods, we provide estimates for the HBE of cyclic water dimers and the cyclic water dimer TS, as the most stable cyclic water dimer.

Quantitative Agreement between Conformational Substates of Holo Calcium-Loaded Calmodulin Detected by Double Electron-Electron Resonance EPR and Predicted by Molecular Dynamics Simulations

Calcium-loaded calmodulin (CaM/4Ca²⁺) comprises two domains that undergo rigid body reorientation from a predominantly extended conformation to a compact one upon binding target peptides. A recent replica-exchange molecular dynamics (MD) simulation on holo CaM/4Ca²⁺ suggested the existence of distinct structural clusters (substates) along the path from extended to compact conformers in the absence of substrates. Here, we experimentally demonstrate the existence of CaM/4Ca²⁺ substates trapped in local minima by three freezing/annealing regimes (slow, 40 s; intermediate, 1.5 s; fast, 0.5 ms) using pulsed Q-band double electron-electron resonance (DEER) EPR spectroscopy to measure interdomain distances between nitroxide spin-labels positioned at A17C and A128C in the N- and C-terminal domains, respectively. The DEER echo curves were directly fit to population-optimized P(r) pairwise distance distributions calculated from the coordinates of the MD clusters and compact crystal structure. DEER data on fully deuterated CaM/4Ca²⁺ were acquired at multiple values of the second echo period (10-35 μs) and analyzed globally to eliminate instrumental and overfitting artifacts and ensure accurate populations, peak positions, and widths. The DEER data for all three freezing regimes are quantitatively accounted for within experimental error by 5-6 distinct conformers comprising a predominantly populated extended form (60-75%) and progressively more compact states whose populations decrease as the degree of compactness increases. The shortest interdomain separation is found in the compact crystal structure, which has an occupancy of 4-6%. Thus, CaM/4Ca²⁺ samples high energy local minima comprising a few discrete substates of increasing compactness in a rugged energy landscape.

What Have We Learned from Design of Function in Large Proteins?

The overarching goal of computational protein design is to gain complete control over protein structure and function. The majority of sophisticated binders and enzymes, however, are large and exhibit diverse and complex folds that defy atomistic design calculations. Encouragingly, recent strategies that combine evolutionary constraints from natural homologs with atomistic calculations have significantly improved design accuracy. In these approaches, evolutionary constraints mitigate the risk from misfolding and aggregation, focusing atomistic design calculations on a small but highly enriched sequence subspace. Such methods have dramatically optimized diverse proteins, including vaccine immunogens, enzymes for sustainable chemistry, and proteins with therapeutic potential. The new generation of deep learning-based ab initio structure predictors can be combined with these methods to extend the scope of protein design, in principle, to any natural protein of known sequence. We envision that protein engineering will come to rely on completely computational methods to efficiently discover and optimize biomolecular activities.

Vibrational circular dichroism of D-amino acid-containing peptide NdWFamide in the crystal form

Microcrystals of l-Asn-d-Trp-l-Phe-NH₂ (NdWFamide), a tripeptide derived from Aplysia kurodai that exhibits invertebrate cardiac activity, were evaluated by vibrational circular dichroism (VCD). The chirality of the tryptophan residue at the second position in NdWFamide was associated with the conformation and biological characteristics. The VCD spectrum of NdWFamide was a mirror image of its enantiomer; however, it was significantly different from that of its diastereomer, NWFamide, which is its precursor. The obtained VCD signals of NdWFamide were in good agreement with the VCD signals that were calculated based on the optimized aggregates of NdWFamide, which formed a helical-like backbone conformation. The evaluation of the VCD results revealed the conformation of NdWFamide in the crystalline state and succeeded in distinguishing its stereoisomers. Therefore, this study demonstrates VCD as a useful method for the structural analysis of naturally occurring d-amino acid-containing peptides.

Integrative Structural Biology in the Era of Accurate Structure Prediction

Characterizing the three-dimensional structure of macromolecules is central to understanding their function. Traditionally, structures of proteins and their complexes have been determined using experimental techniques such as X-ray crystallography, NMR, or cryo-electron microscopy-applied individually or in an integrative manner. Meanwhile, however, computational methods for protein structure prediction have been improving their accuracy, gradually, then suddenly, with the breakthrough advance by AlphaFold2, whose models of monomeric proteins are often as accurate as experimental structures. This breakthrough foreshadows a new era of computational methods that can build accurate models for most monomeric proteins. Here, we envision how such accurate modeling methods can combine with experimental structural biology techniques, enhancing integrative structural biology. We highlight the challenges that arise when considering multiple structural conformations, protein complexes, and polymorphic assemblies. These challenges will motivate further developments, both in modeling programs and in methods to solve experimental structures, towards better and quicker investigation of structure-function relationships.

The breakthrough in protein structure prediction

Proteins are the essential agents of all living systems. Even though they are synthesized as linear chains of amino acids, they must assume specific three-dimensional structures in order to manifest their biological activity. These structures are fully specified in their amino acid sequences - and therefore in the nucleotide sequences of their genes. However, the relationship between sequence and structure, known as the protein folding problem, has remained elusive for half a century, despite sustained efforts. To measure progress on this problem, a series of doubly blind, biennial experiments called CASP (critical assessment of structure prediction) were established in 1994. We were part of the assessment team for the most recent CASP experiment, CASP14, where we witnessed an astonishing breakthrough by DeepMind, the leading artificial intelligence laboratory of Alphabet Inc. The models filed by DeepMind's structure prediction team using the program AlphaFold2 were often essentially indistinguishable from experimental structures, leading to a consensus in the community that the structure prediction problem for single protein chains has been solved. Here, we will review the path to CASP14, outline the method employed by AlphaFold2 to the extent revealed, and discuss the implications of this breakthrough for the life sciences.

Cotranscriptional Kinetic Folding of RNA Secondary Structures Including Pseudoknots

Computational prediction of ribonucleic acid (RNA) structures is an important problem in computational structural biology. Studies of RNA structure formation often assume that the process starts from a fully synthesized sequence. Experimental evidence, however, has shown that RNA folds concurrently with its elongation. We investigate RNA secondary structure formation, including pseudoknots, that takes into account the cotranscriptional effects. We propose a single-nucleotide resolution kinetic model of the folding process of RNA molecules, where the polymerase-driven elongation of an RNA strand by a new nucleotide is included as a primitive operation, together with a stochastic simulation method that implements this folding concurrently with the transcriptional synthesis. Numerical case studies show that our cotranscriptional RNA folding model can predict the formation of conformations that are favored in actual biological systems. Our new computational tool can thus provide quantitative predictions and offer useful insights into the kinetics of RNA folding.

Effects of lattice constraints in coarse-grained protein models

We compare and contrast folding behavior in several coarse-grained protein models, both on- and off-lattice, in an attempt to uncover the effect of lattice constraints in these kinds of models. Using modern, extended ensemble Monte Carlo methods-Wang-Landau sampling, multicanonical sampling, replica-exchange Wang-Landau sampling, and replica-exchange multicanonical sampling, we investigate the thermodynamic and structural behavior of the protein Crambin within the context of the hydrophobic-polar, hydrophobic-"neutral"-polar (H0P), and semi-flexible H0P model frameworks. We uncover the folding process in all cases; all models undergo, at least, the two major structural transitions observed in nature-the coil-globule collapse and the folding transition. As the complexity of the model increases, these two major transitions begin to split into multi-step processes, wherein the lattice coarse-graining has a significant impact on the details of these processes. The results show that the level of structural coarse-graining is coupled to the level of interaction coarse-graining.

The concept of protein folding/unfolding and its impacts on human health

Proteins have evolved in specific 3D structures and play different functions in cells and determine various reactions and pathways. The newly synthesized amino acid chains once depart ribosome must crumple into three-dimensional structures so can be biologically active. This process of protein that makes a functional molecule is called protein folding. The protein folding is both a biological and a physicochemical process that depends on the sequence of it. In fact, this process occurs more complicated and in some cases and in exposure to some molecules like glucose (glycation), mistaken folding leads to amyloid structures and fatal disorders called conformational diseases. Such conditions are detected by the quality control system of the cell and these abnormal proteins undergo renovation or degradation. This scenario takes place by the chaperones, chaperonins, and Ubiquitin-proteasome complex. Understanding of protein folding mechanisms from different views including experimental and computational approaches has revealed some intermediate ensembles such as molten globule and has been subjected to biophysical and molecular biology attempts to know more about prevalent conformational diseases.

The Cold-Unfolded State Is Expanded but Contains Long- and Medium-Range Contacts and Is Poorly Described by Homopolymer Models

Cold unfolding of proteins is predicted by the Gibbs-Helmholtz equation and is thought to be driven by a strongly temperature-dependent interaction of protein nonpolar groups with water. Studies of the cold-unfolded state provide insight into protein energetics, partially structured states, and folding cooperativity and are of practical interest in biotechnology. However, structural characterization of the cold-unfolded state is much less extensive than studies of thermally or chemically denatured unfolded states, in large part because the midpoint of the cold unfolding transition is usually below freezing. We exploit a rationally designed point mutation (I98A) in the hydrophobic core of the C-terminal domain of the ribosomal protein L9 that allows the cold denatured state ensemble to be observed above 0 °C at near neutral pH and ambient pressure in the absence of added denaturants. A combined approach consisting of paramagnetic relaxation enhancement measurements, analysis of small-angle X-ray scattering data, all-atom simulations, and polymer theory provides a detailed description of the cold-unfolded state. Despite a globally expanded ensemble, as determined by small-angle X-ray scattering, sequence-specific medium- and long-range interactions in the cold-unfolded state give rise to deviations from homopolymer-like behavior. Our results reveal that the cold-denatured state is heterogeneous with local and long-range intramolecular interactions that may prime the folded state and also demonstrate that significant long-range interactions are compatible with expanded unfolded ensembles. The work also highlights the limitations of homopolymer-based descriptions of unfolded states of proteins.

Protein structure optimization using improved simulated annealing algorithm on a three-dimensional AB off-lattice model

This paper proposed an improved simulated annealing (ISA) algorithm for protein structure optimization based on a three-dimensional AB off-lattice model. In the algorithm, we provided a general formula used for producing initial solution, and designed a multivariable disturbance term, relating to the parameters of simulated annealing and a tuned constant, to generate neighborhood solution. To avoid missing optimal solution, storage operation was performed in searching process. We applied the algorithm to test artificial protein sequences from literature and constructed a benchmark dataset consisting of 10 real protein sequences from the Protein Data Bank (PDB). Otherwise, we generated C_α space-filling model to represent protein folding conformation. The results indicate our algorithm outperforms the five methods before in searching lower energies of artificial protein sequences. In the testing on real proteins, our method can achieve the energy conformations with C_α-RMSD less than 3.0 Å from the PDB structures. Moreover, C_α space-filling model may simulate dynamic change of protein folding conformation at atomic level.

The Amyloid as a Ribbon-Like Micelle in Contrast to Spherical Micelles Represented by Globular Proteins

Selected amyloid structures available in the Protein Data Bank have been subjected to a comparative analysis. Classification is based on the distribution of hydrophobicity in amyloids that differ with respect to sequence, chain length, the distribution of beta folds, protofibril structure, and the arrangement of protofibrils in each superfibril. The study set includes the following amyloids: Aβ (1-42), which is listed as Aβ (15-40) and carries the D23N mutation, and Aβ (11-42) and Aβ (1-40), both of which carry the E22Δ mutation, tau amyloid, and α-synuclein. Based on the fuzzy oil drop model (FOD), we determined that, despite their conformational diversity, all presented amyloids adopt a similar structural pattern that can be described as a ribbon-like micelle. The same model, when applied to globular proteins, results in structures referred to as "globular micelles," emerging as a result of interactions between the proteins' constituent residues and the aqueous solvent. Due to their composition, amyloids are unable to attain entropically favorable globular forms and instead attempt to limit contact between hydrophobic residues and water by producing elongated structures. Such structures typically contain quasi hydrophobic cores that stretch along the fibril's long axis. Similar properties are commonly found in ribbon-like micelles, with alternating bands of high and low hydrophobicity emerging as the fibrils increase in length. Thus, while globular proteins are generally consistent with a 3D Gaussian distribution of hydrophobicity, the distribution instead conforms to a 2D Gaussian distribution in amyloid fibrils.

Turncoat Polypeptides: We Adapt to Our Environment

A common interpretation of Anfinsen's hypothesis states that one amino acid sequence should fold into a single, native, ordered state, or a highly similar set thereof, coinciding with the global minimum in the folding-energy landscape, which, in turn, is responsible for the function of the protein. However, this classical view is challenged by many proteins and peptide sequences, which can adopt exchangeable, significantly dissimilar conformations that even fulfill different biological roles. The similarities and differences of concepts related to these proteins, mainly chameleon sequences, metamorphic proteins, and switch peptides, which are all denoted herein "turncoat" polypeptides, are reviewed. As well as adding a twist to the conventional view of protein folding, the lack of structural definition adds clear versatility to the activity of proteins and can be used as a tool for protein design and further application in biotechnology and biomedicine.

PET-RAFT and SAXS: High Throughput Tools to Study Compactness and Flexibility of Single-Chain Polymer Nanoparticles

From protein science, it is well understood that ordered folding and 3D structure mainly arises from balanced and noncovalent polar and nonpolar interactions, such as hydrogen bonding. Similarly, it is understood that single-chain polymer nanoparticles (SCNPs) will also compact and become more rigid with greater hydrophobicity and intrachain hydrogen bonding. Here, we couple high throughput photoinduced electron/energy transfer reversible addition-fragmentation chain-transfer (PET-RAFT) polymerization with high throughput small-angle X-ray scattering (SAXS) to characterize a large combinatorial library (>450) of several homopolymers, random heteropolymers, block copolymers, PEG-conjugated polymers, and other polymer-functionalized polymers. Coupling these two high throughput tools enables us to study the major influence(s) for compactness and flexibility in higher breadth than ever before possible. Not surprisingly, we found that many were either highly disordered in solution, in the case of a highly hydrophilic polymer, or insoluble if too hydrophobic. Remarkably, we also found a small group (9/457) of PEG-functionalized random heteropolymers and block copolymers that exhibited compactness and flexibility similar to that of bovine serum albumin (BSA) by dynamic light scattering (DLS), NMR, and SAXS. In general, we found that describing a rough association between compactness and flexibility parameters (R g /R h and Porod Exponent, respectively) with logP, a quantity that describes hydrophobicity, helps to demonstrate and predict material parameters that lead to SCNPs with greater compactness, rigidity, and stability. Future implementation of this combinatorial and high throughput approach for characterizing SCNPs will allow for the creation of detailed design parameters for well-defined macromolecular chemistry.

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.

Periodic Operation of a Dynamic DNA Origami Structure Utilizing the Hydrophilic-Hydrophobic Phase-Transition of Stimulus-Sensitive Polypeptides

Dynamic DNA nanodevices are designed to perform structure-encoded motion actuated by a variety of different physicochemical stimuli. In this context, hybrid devices utilizing other components than DNA have the potential to considerably expand the library of functionalities. Here, the reversible reconfiguration of a DNA origami structure using the stimulus sensitivity of elastin-like polypeptides is reported. To this end, a rectangular sheet made using the DNA origami technique is functionalized with these peptides and by applying changes in salt concentration the hydrophilic-hydrophobic phase transition of these peptides actuate the folding of the structure. The on-demand and reversible switching of the rectangle is driven by externally imposed temperature oscillations and appears at specific transition temperatures. Using transmission electron microscopy, it is shown that the structure exhibits distinct conformational states with different occupation probabilities, which are dependent on structure-intrinsic parameters such as the local number and the arrangement of the peptides on the rectangle. It is also shown through ensemble fluorescence resonance energy transfer spectroscopy that the transition temperature and thus the thermodynamics of the rectangle-peptide system depends on the stimuli salt concentration and temperature, as well as on the intrinsic parameters.

Dihedral Angle Calculations To Elucidate the Folding of Peptides through Its Main Mechanical Forces

This study reports a general method to calculate dihedral angles (φ and ψ) of a given amino acid sequence, focusing on potential energy and torque moment concepts. By defining these physical measures in relation to the chemical interactions that occur on each single amino acid residue within a peptide, we analyze the folding process as the result of main mechanical forces (MMFs) exerted in the specific amino acid chain of interest. As a proof of concept, Leu-enkephalin was initially used as a model peptide to carry out the theoretical study. Our data show agreement between calculated Leu-enkephalin backbone dihedral angles and the corresponding experimentally determined X-ray values. Hence, we used calcitonin to validate our MMF-based method on a larger peptide, i.e., 32 amino acid residues forming an α-helix. Through a similar approach (although simplified with regard to electrostatic interactions), the calculations for calcitonin also demonstrate a good agreement with experimental values. This study offers new opportunities to analyze peptides' amino acid sequences and to help in the prediction of how they must fold, assisting in the development of new computational techniques in the field.

Lectin engineering: the possible and the actual

Lectins are a widespread group of sugar-binding proteins occurring in all types of organisms including animals, plants, bacteria, fungi and even viruses. According to a recent report, there are more than 50 lectin scaffolds (∼Pfam), for which three-dimensional structures are known and sugar-binding functions have been confirmed in the literature, which far exceeds our view in the twentieth century (Fujimoto et al. 2014 Methods Mol. Biol. 1200, 579-606 (doi:10.1007/978-1-4939-1292-6_46)). This fact suggests that new lectins will be discovered either by a conventional screening approach or just by chance. It is also expected that new lectin domains including those found in enzymes as carbohydrate-binding modules will be generated in the future through evolution, although this has never been attempted on an experimental level. Based on the current state of the art, various methods of lectin engineering are available, by which lectin specificity and/or stability of a known lectin scaffold can be improved. However, the above observation implies that any protein scaffold, including those that have never been described as lectins, may be modified to acquire a sugar-binding function. In this review, possible approaches to confer sugar-binding properties on synthetic proteins and peptides are described.

Elucidating thermal behavior, native contacts, and folding funnels of simple lattice proteins using replica exchange Wang-Landau sampling

We studied the folding behavior of two coarse-grained, lattice models, the HP (hydrophobic-polar) model and the semi-flexible H0P model, whose 124 monomer long sequences were derived from the protein Ribonuclease A. Taking advantage of advanced parallel computing techniques, we applied replica exchange Wang-Landau sampling and calculated the density of states over the models entire energy ranges to high accuracy. We then determined both energetic and structural quantities in order to elucidate the folding behavior of each model completely. As a result of sufficiently long sequences and model complexity, yet computational accessibility, we were able to depict distinct free energy folding funnels for both models. In particular, we found that the HP model folds in a single-step process with a very highly degenerate native state and relatively flat low temperature folding funnel minimum. By contrast, the semi-flexible H0P model folds via a multi-step process and the native state is almost four orders of magnitude less degenerate than that for the HP model. In addition, for the H0P model, the bottom of the free energy folding funnel remains rough, even at low temperatures.

The role of chain-stiffness in lattice protein models: A replica-exchange Wang-Landau study

Using Monte Carlo simulations, we investigate simple, physically motivated extensions to the hydrophobic-polar lattice protein model for the small (46 amino acid) protein Crambin. We use two-dimensional replica-exchange Wang-Landau sampling to study the effects of a bond angle stiffness parameter on the folding and uncover a new step in the collapse process for particular values of this stiffness parameter. A physical interpretation of the folding is developed by analysis of changes in structural quantities, and the free energy landscape is explored. For these special values of stiffness, we find non-degenerate ground states, a property that is consistent with behavior of real proteins, and we use these unique ground states to elucidate the formation of native contacts during the folding process. Through this analysis, we conclude that chain-stiffness is particularly influential in the low energy, low temperature regime of the folding process once the lattice protein has partially collapsed.

Protein docking refinement by convex underestimation in the low-dimensional subspace of encounter complexes

We propose a novel stochastic global optimization algorithm with applications to the refinement stage of protein docking prediction methods. Our approach can process conformations sampled from multiple clusters, each roughly corresponding to a different binding energy funnel. These clusters are obtained using a density-based clustering method. In each cluster, we identify a smooth “permissive” subspace which avoids high-energy barriers and then underestimate the binding energy function using general convex polynomials in this subspace. We use the underestimator to bias sampling towards its global minimum. Sampling and subspace underestimation are repeated several times and the conformations sampled at the last iteration form a refined ensemble. We report computational results on a comprehensive benchmark of 224 protein complexes, establishing that our refined ensemble significantly improves the quality of the conformations of the original set given to the algorithm. We also devise a method to enhance the ensemble from which near-native models are selected.

Foldamer hypothesis for the growth and sequence differentiation of prebiotic polymers

It is not known how life originated. It is thought that prebiotic processes were able to synthesize short random polymers. However, then, how do short-chain molecules spontaneously grow longer? Also, how would random chains grow more informational and become autocatalytic (i.e., increasing their own concentrations)? We study the folding and binding of random sequences of hydrophobic ([Formula: see text]) and polar ([Formula: see text]) monomers in a computational model. We find that even short hydrophobic polar (HP) chains can collapse into relatively compact structures, exposing hydrophobic surfaces. In this way, they act as primitive versions of today's protein catalysts, elongating other such HP polymers as ribosomes would now do. Such foldamer catalysts are shown to form an autocatalytic set, through which short chains grow into longer chains that have particular sequences. An attractive feature of this model is that it does not overconverge to a single solution; it gives ensembles that could further evolve under selection. This mechanism describes how specific sequences and conformations could contribute to the chemistry-to-biology (CTB) transition.

Folding Cooperativity of Synthetic Polypeptides with or without "Tertiary" Interactions

Model-based studies on helix-coil transition and folding cooperativity of synthetic polypeptides have contributed to the understanding of protein folding and stability and to the development of polypeptide-based functional materials. Polypeptide-containing macromolecules with complex architectures, however, remain a challenge in the model-based analysis. Herein, a modified Schellman-Zimm-Bragg model has been utilized to quantitatively analyze the folding cooperativity of polypeptide-containing macromolecules. While the helix-coil transition of homopolypeptides (e.g., poly(ε-benzyloxycarbonyl-l-lysine) (PZLL)) can be described by the classic model, the folding of grafted polypeptide chains in the comb macromolecules (e.g., polynorbornene-g-poly(ε-benzyloxycarbonyl-l-lysine) (PN-g-PZLL)) cannot be accurately predicted by the existing theories, due to the side-chain interactions between grafted polypeptides in the comb macromolecules. Incorporating nonlocal interaction explicability into the statistical mechanics treatment is found to be instructive to account for the possible "tertiary" interactions of polypeptides in the macromolecules with complex architectures.

Revisiting the Helical Cooperativity of Synthetic Polypeptides in Solution

Using synthetic polypeptides as a model system, the theories of helix-coil transition were developed into one of the most beautiful and fruitful subjects in macromolecular science. The classic models proposed by Schellman and Zimm-Bragg more than 50 years ago, differ in the assumption on whether the configuration of multiple helical sequences separated by random coil sections is allowed in a longer polypeptide chain. Zimm also calculated the critical chain lengths that facilitate such interrupted helices in different solvent conditions. The experimental validation of Zimm's prediction, however, was not carefully examined at that time. Herein, we synthesize a series of homopolypeptide samples with different lengths, to systematically examine their helix-coil transition and folding cooperativity in solution. We find that for longer chains, polypeptides do exist as interrupted helices with scattered coil sections even in helicogenic solvent conditions, as predicted in the Zimm-Bragg model. The critical chain lengths that facilitate such interrupted helices, however, are substantially smaller than Zimm's original estimation. The inaccuracy is in part due to an approximation that Zimm made in simplifying the calculation. But more importantly, we find there exist intramolecular interactions between different structural segments in the longer polypeptides, which are not considered in the classic helix-coil theories. As such, even the Zimm-Bragg model in its exact form cannot fully describe the transition behavior and folding cooperativity of longer polypeptides. The results suggest that long "all-helix" chains may be much less prevalent in solution than previously imagined, and a revised theory is required to accurately account for the helix-coil transition of the longer chains with potential "non-local" intramolecular interactions.

Molecular simulations and Markov state modeling reveal the structural diversity and dynamics of a theophylline-binding RNA aptamer in its unbound state

RNA aptamers are oligonucleotides that bind with high specificity and affinity to target ligands. In the absence of bound ligand, secondary structures of RNA aptamers are generally stable, but single-stranded and loop regions, including ligand binding sites, lack defined structures and exist as ensembles of conformations. For example, the well-characterized theophylline-binding aptamer forms a highly stable binding site when bound to theophylline, but the binding site is unstable and disordered when theophylline is absent. Experimental methods have not revealed at atomic resolution the conformations that the theophylline aptamer explores in its unbound state. Consequently, in the present study we applied 21 microseconds of molecular dynamics simulations to structurally characterize the ensemble of conformations that the aptamer adopts in the absence of theophylline. Moreover, we apply Markov state modeling to predict the kinetics of transitions between unbound conformational states. Our simulation results agree with experimental observations that the theophylline binding site is found in many distinct binding-incompetent states and show that these states lack a binding pocket that can accommodate theophylline. The binding-incompetent states interconvert with binding-competent states through structural rearrangement of the binding site on the nanosecond to microsecond timescale. Moreover, we have simulated the complete theophylline binding pathway. Our binding simulations supplement prior experimental observations of slow theophylline binding kinetics by showing that the binding site must undergo a large conformational rearrangement after the aptamer and theophylline form an initial complex, most notably, a major rearrangement of the C27 base from a buried to solvent-exposed orientation. Theophylline appears to bind by a combination of conformational selection and induced fit mechanisms. Finally, our modeling indicates that when Mg²⁺ ions are present the population of binding-competent aptamer states increases more than twofold. This population change, rather than direct interactions between Mg²⁺ and theophylline, accounts for altered theophylline binding kinetics.

Structural Interface Forms and Their Involvement in Stabilization of Multidomain Proteins or Protein Complexes

The presented analysis concerns the inter-domain and inter-protein interface in protein complexes. We propose extending the traditional understanding of the protein domain as a function of local compactness with an additional criterion which refers to the presence of a well-defined hydrophobic core. Interface areas in selected homodimers vary with respect to their contribution to share as well as individual (domain-specific) hydrophobic cores. The basic definition of a protein domain, i.e., a structural unit characterized by tighter packing than its immediate environment, is extended in order to acknowledge the role of a structured hydrophobic core, which includes the interface area. The hydrophobic properties of interfaces vary depending on the status of interacting domains—In this context we can distinguish: (1) Shared hydrophobic cores (spanning the whole dimer); (2) Individual hydrophobic cores present in each monomer irrespective of whether the dimer contains a shared core. Analysis of interfaces in dystrophin and utrophin indicates the presence of an additional quasi-domain with a prominent hydrophobic core, consisting of fragments contributed by both monomers. In addition, we have also attempted to determine the relationship between the type of interface (as categorized above) and the biological function of each complex. This analysis is entirely based on the fuzzy oil drop model.

Contingency, convergence and hyper-astronomical numbers in biological evolution

Counterfactual questions such as "what would happen if you re-run the tape of life?" turn on the nature of the landscape of biological possibilities. Since the number of potential sequences that store genetic information grows exponentially with length, genetic possibility spaces can be so unimaginably vast that commentators frequently reach of hyper-astronomical metaphors that compare their size to that of the universe. Re-run the tape of life and the likelihood of encountering the same sequences in such hyper-astronomically large spaces is infinitesimally small, suggesting that evolutionary outcomes are highly contingent. On the other hand, the wide-spread occurrence of evolutionary convergence implies that similar phenotypes can be found again with relative ease. How can this be? Part of the solution to this conundrum must lie in the manner that genotypes map to phenotypes. By studying simple genotype-phenotype maps, where the counterfactual space of all possible phenotypes can be enumerated, it is shown that strong bias in the arrival of variation may explain why certain phenotypes are (repeatedly) observed in nature, while others never appear. This biased variation provides a non-selective cause for certain types of convergence. It illustrates how the role of randomness and contingency may differ significantly between genetic and phenotype spaces.

Control globular structure formation of a copolymer chain through inverse design

A copolymer chain in dilute solution can exhibit various globular structures with characteristic morphologies, which makes it a potentially useful candidate for artificial materials design. However, the chain has a huge conformation space and may not naturally form the globular structure we desire. An ideal way to control globular structure formation should be inverse design, i.e., starting from the target structure and finding out what kind of polymers can effectively generate it. To accomplish this, we propose an inverse design procedure, which is combined with Wang-Landau Monte Carlo to fully and precisely explore the huge conformation space of the chain. Starting from a desired target structure, all the geometrically possible sequences are exactly enumerated. Interestingly, reasonable interaction strengths are obtained and found to be not specified for only one sequence. Instead, they can be combined with many other sequences and also achieve a relatively high yield for target structure, although these sequences may be rather different. These results confirm the possibility of controlling globular structure formation of a copolymer chain through inverse design and pave the way for targeted materials design.

Hybrid Approaches to Structural Characterization of Conformational Ensembles of Complex Macromolecular Systems Combining NMR Residual Dipolar Couplings and Solution X-ray Scattering

Solving structures or structural ensembles of large macromolecular systems in solution poses a challenging problem. While NMR provides structural information at atomic resolution, increased spectral complexity, chemical shift overlap, and short transverse relaxation times (associated with slow tumbling) render application of the usual techniques that have been so successful for medium sized systems (<50 kDa) difficult. Solution X-ray scattering, on the other hand, is not limited by molecular weight but only provides low resolution structural information related to the overall shape and size of the system under investigation. Here we review how combining atomic resolution structures of smaller domains with sparse experimental data afforded by NMR residual dipolar couplings (which yield both orientational and shape information) and solution X-ray scattering data in rigid-body simulated annealing calculations provides a powerful approach for investigating the structural aspects of conformational dynamics in large multidomain proteins. The application of this hybrid methodology is illustrated for the 128 kDa dimer of bacterial Enzyme I which exists in a variety of open and closed states that are sampled at various points in the catalytic cycles, and for the capsid protein of the human immunodeficiency virus.

Relative Cosolute Size Influences the Kinetics of Protein-Protein Interactions

Protein signaling occurs in crowded intracellular environments, and while high concentrations of macromolecules are postulated to modulate protein-protein interactions, analysis of their impact at each step of the reaction pathway has not been systematically addressed. Potential cosolute-induced alterations in target association are particularly important for a signaling molecule like calmodulin (CaM), where competition among >300 targets governs which pathways are selectively activated. To explore how high concentrations of cosolutes influence CaM-target affinity and kinetics, we methodically investigated each step of the CaM-target binding mechanism under crowded or osmolyte-rich environments mimicked by ficoll-70, dextran-10, and sucrose. All cosolutes stabilized compact conformers of CaM and modulated association kinetics by affecting diffusion and rates of conformational change; however, the results showed that differently sized molecules had variable effects to enhance or impede unique steps of the association pathway. On- and off-rates were modulated by all cosolutes in a compensatory fashion, producing little change in steady-state affinity. From this work insights were gained on how high concentrations of inert crowding agents and osmolytes fit into a kinetic framework to describe protein-protein interactions relevant for cellular signaling.

Predicting Designability of Small Proteins from Graph Features of Contact Maps

Highly designable structures can be distinguished based on certain geometric graphical features of the interactions, confirming the fact that the topology of a protein structure and its residue-residue interaction network are important determinants of its designability. The most designable structures and least designable structures obtained for sets of proteins having the same number of residues are compared. It is shown that the most designable structures predicted by the graph features of the contact diagrams are more densely packed, whereas the poorly designable structures are more open structures or structures that are loosely packed. Interestingly enough, it can also be seen that the highly designable identified are also common structural motifs found in nature.

Dynamic Protein Interaction Networks and New Structural Paradigms in Signaling

Understanding signaling and other complex biological processes requires elucidating the critical roles of intrinsically disordered proteins (IDPs) and regions (IDRs), which represent ∼30% of the proteome and enable unique regulatory mechanisms. In this review, we describe the structural heterogeneity of disordered proteins that underpins these mechanisms and the latest progress in obtaining structural descriptions of conformational ensembles of disordered proteins that are needed for linking structure and dynamics to function. We describe the diverse interactions of IDPs that can have unusual characteristics such as "ultrasensitivity" and "regulated folding and unfolding". We also summarize the mounting data showing that large-scale assembly and protein phase separation occurs within a variety of signaling complexes and cellular structures. In addition, we discuss efforts to therapeutically target disordered proteins with small molecules. Overall, we interpret the remodeling of disordered state ensembles due to binding and post-translational modifications within an expanded framework for allostery that provides significant insights into how disordered proteins transmit biological information.

Accurate Prediction of Contact Numbers for Multi-Spanning Helical Membrane Proteins

Prediction of the three-dimensional (3D) structures of proteins by computational methods is acknowledged as an unsolved problem. Accurate prediction of important structural characteristics such as contact number is expected to accelerate the otherwise slow progress being made in the prediction of 3D structure of proteins. Here, we present a dropout neural network-based method, TMH-Expo, for predicting the contact number of transmembrane helix (TMH) residues from sequence. Neuronal dropout is a strategy where certain neurons of the network are excluded from back-propagation to prevent co-adaptation of hidden-layer neurons. By using neuronal dropout, overfitting was significantly reduced and performance was noticeably improved. For multi-spanning helical membrane proteins, TMH-Expo achieved a remarkable Pearson correlation coefficient of 0.69 between predicted and experimental values and a mean absolute error of only 1.68. In addition, among those membrane protein-membrane protein interface residues, 76.8% were correctly predicted. Mapping of predicted contact numbers onto structures indicates that contact numbers predicted by TMH-Expo reflect the exposure patterns of TMHs and reveal membrane protein-membrane protein interfaces, reinforcing the potential of predicted contact numbers to be used as restraints for 3D structure prediction and protein-protein docking. TMH-Expo can be accessed via a Web server at www.meilerlab.org .

Effect of the Solvent Temperatures on Dynamics of Serine Protease Proteinase K

To obtain detailed information about the effect of the solvent temperatures on protein dynamics, multiple long molecular dynamics (MD) simulations of serine protease proteinase K with the solute and solvent coupled to different temperatures (either 300 or 180 K) have been performed. Comparative analyses demonstrate that the internal flexibility and mobility of proteinase K are strongly dependent on the solvent temperatures but weakly on the protein temperatures. The constructed free energy landscapes (FELs) at the high solvent temperatures exhibit a more rugged surface, broader spanning range, and higher minimum free energy level than do those at the low solvent temperatures. Comparison between the dynamic hydrogen bond (HB) numbers reveals that the high solvent temperatures intensify the competitive HB interactions between water molecules and protein surface atoms, and this in turn exacerbates the competitive HB interactions between protein internal atoms, thus enhancing the conformational flexibility and facilitating the collective motions of the protein. A refined FEL model was proposed to explain the role of the solvent mobility in facilitating the cascade amplification of microscopic motions of atoms and atomic groups into the global collective motions of the protein.

Paradoxes and wonders of intrinsic disorder: Complexity of simplicity

At first glance it may seem that intrinsically disordered proteins (IDPs) and IDP regions (IDPRs) are simpler than ordered proteins and domains on multiple levels. However, such multilevel simplicity equips these proteins with the ability to have very complex behavior.

Soft matter food physics--the physics of food and cooking

This review discusses the (soft matter) physics of food. Although food is generally not considered as a typical model system for fundamental (soft matter) physics, a number of basic principles can be found in the interplay between the basic components of foods, water, oil/fat, proteins and carbohydrates. The review starts with the introduction and behavior of food-relevant molecules and discusses food-relevant properties and applications from their fundamental (multiscale) behavior. Typical food aspects from 'hard matter systems', such as chocolates or crystalline fats, to 'soft matter' in emulsions, dough, pasta and meat are covered and can be explained on a molecular basis. An important conclusion is the point that the macroscopic properties and the perception are defined by the molecular interplay on all length and time scales.

Critical examination of the colloidal particle model of globular proteins

Recent studies of globular protein solutions have uniformly adopted a colloidal view of proteins as particles, a perspective that neglects the polymeric primary structure of these biological macromolecules, their intrinsic flexibility, and their ability to sample a large configurational space. While the colloidal perspective often serves as a useful idealization in many cases, the macromolecular identity of proteins must reveal itself under thermodynamic conditions in which the native state is no longer stable, such as denaturing solvents and high protein concentrations where macromolecules tend to have screened excluded volume, charge, and hydrodynamic interactions. Under extreme pH conditions, charge repulsion interactions within the protein chain can overcome the attractive hydrogen-bonding interactions, holding it in its native globular state. Conformational changes can therefore be expected to have great significance on the shear viscosity and other rheological properties of protein solutions. These changes are not envisioned in conventional colloidal protein models and we have initiated an investigation of the scattering and rheological properties of model proteins. We initiate this effort by considering bovine serum albumin because it is a globular protein whose solution properties have also been extensively investigated as a function of pH, temperature, ionic strength, and concentration. As we anticipated, near-ultraviolet circular dichroism measurements and intrinsic viscosity measurements clearly indicate that the bovine serum albumin tertiary structure changes as protein concentration and pH are varied. Our findings point to limited validity of the colloidal protein model and to the need for further consideration and quantification of the effects of conformational changes on protein solution viscosity, protein association, and the phase behavior. Small-angle Neutron Scattering measurements have allowed us to assess how these conformational changes influence protein size, shape, and interprotein interaction strength.

Lessons in Protein Design from Combined Evolution and Conformational Dynamics

Protein-protein interactions play important roles in the control of every cellular process. How natural selection has optimized protein design to produce molecules capable of binding to many partner proteins is a fascinating problem but not well understood. Here, we performed a combinatorial analysis of protein sequence evolution and conformational dynamics to study how calmodulin (CaM), which plays essential roles in calcium signaling pathways, has adapted to bind to a large number of partner proteins. We discovered that amino acid residues in CaM can be partitioned into unique classes according to their degree of evolutionary conservation and local stability. Holistically, categorization of CaM residues into these classes reveals enriched physico-chemical interactions required for binding to diverse targets, balanced against the need to maintain the folding and structural modularity of CaM to achieve its overall function. The sequence-structure-function relationship of CaM provides a concrete example of the general principle of protein design. We have demonstrated the synergy between the fields of molecular evolution and protein biophysics and created a generalizable framework broadly applicable to the study of protein-protein interactions.