Protein folding thermodynamics and dynamics: where physics, chemistry, and biology meet

Delayed Excitations Induce Polymer Looping and Coherent Motion

We consider inhomogeneous polymers driven by energy-consuming active processes which encode temporal patterns of athermal kicks. We find that such temporal excitation programs, propagated by tension along the polymer, can effectively couple distinct polymer loci. Consequently, distant loci exhibit correlated motions that fold the polymer into specific conformations, as set by the local actions of the active processes and their distribution along the polymer. Interestingly, active kicks that are canceled out by a time-delayed echo can induce strong compaction of the active polymer.

Sequence-dependent and -independent information in a combined random energy model for protein folding and coding

Random energy models (REMs) provide a simple description of the energy landscapes that guide protein folding and evolution. The requirement of a large energy gap between the native structure and unfolded conformations, considered necessary for cooperative, protein-like, folding behavior, indicates that proteins differ markedly from random heteropolymers. It has been suggested, therefore, that natural selection might have acted to choose nonrandom amino acid sequences satisfying this particular condition, implying that a large fraction of possible, unselected random sequences, would not fold to any structure. From an informational perspective, however, this scenario could indicate that protein structures, regarded as messages to be transmitted through a communication channel, would not be efficiently encoded in amino acid sequences, regarded as the communication channel for this transmission, since a large fraction of possible channel states would not be used. Here, we use a combined REM for conformations and sequences, with previously estimated parameters for natural proteins, to explore an alternative possibility in which the appropriate shape of the landscape results mainly from the deviation from randomness of possible native structures instead of sequences. We observe that this situation emerges naturally if the distribution of conformational energies happens to arise from two independent contributions corresponding to sequence-dependent and -independent terms. This construction is consistent with the hypothesis of a protein burial folding code, with native structures being determined by a modest amount of sequence-dependent atomic burial information with sequence-independent constraints imposed by unspecific hydrogen bond formation. More generally, an appropriate combination of sequence-dependent and -independent information accommodates the possibility of an efficient structural encoding with the main physical requirement for folding, providing possible insight not only on the folding process but also on several aspects sequence evolution such as neutral networks, conformational coverage, and de novo gene emergence.

Rapid evolutionary change in trait correlations of single proteins

Many organismal traits are genetically determined and covary in evolving populations. The resulting trait correlations can either help or hinder evolvability - the ability to bring forth new and adaptive phenotypes. The evolution of evolvability requires that trait correlations themselves must be able to evolve, but we know little about this ability. To learn more about it, we here study two evolvable systems, a yellow fluorescent protein and the antibiotic resistance protein VIM-2 metallo beta-lactamase. We consider two traits in the fluorescent protein, namely the ability to emit yellow and green light, and three traits in our enzyme, namely the resistance against ampicillin, cefotaxime, and meropenem. We show that correlations between these traits can evolve rapidly through both mutation and selection on short evolutionary time scales. In addition, we show that these correlations are driven by a protein's ability to fold, because single mutations that alter foldability can dramatically change trait correlations. Since foldability is important for most proteins and their traits, mutations affecting protein folding may alter trait correlations mediated by many other proteins. Thus, mutations that affect protein foldability may also help shape the correlations of complex traits that are affected by hundreds of proteins.

Living in trinity of extremes: Genomic and proteomic signatures of halophilic, thermophilic, and pH adaptation

Since nucleic acids and proteins of unicellular prokaryotes are directly exposed to extreme environmental conditions, it is possible to explore the genomic-proteomic compositional determinants of molecular mechanisms of adaptation developed by them in response to harsh environmental conditions. Using a wealth of currently available complete genomes/proteomes we were able to explore signatures of adaptation to three environmental factors, pH, salinity, and temperature, observing major trends in compositions of their nucleic acids and proteins. We derived predictors of thermostability, halophilic, and pH adaptations and complemented them by the principal components analysis. We observed a clear difference between thermophilic and salinity/pH adaptations, whereas latter invoke seemingly overlapping mechanisms. The genome-proteome compositional trade-off reveals an intricate balance between the work of base paring and base stacking in stabilization of coding DNA and r/tRNAs, and, at the same time, universal requirements for the stability and foldability of proteins regardless of the nucleotide biases. Nevertheless, we still found hidden fingerprints of ancient evolutionary connections between the nucleotide and amino acid compositions indicating their emergence, mutual evolution, and adjustment. The evolutionary perspective on the adaptation mechanisms is further studied here by means of the comparative analysis of genomic/proteomic traits of archaeal and bacterial species. The overall picture of genomic/proteomic signals of adaptation obtained here provides a foundation for future engineering and design of functional biomolecules resistant to harsh environments.

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.

A Study of a Protein-Folding Machine: Transient Rotation of the Polypeptide Backbone Facilitates Rapid Folding of Protein Domains in All-Atom Molecular Dynamics Simulations

Molecular dynamics simulations of protein folding typically consider the polypeptide chain at equilibrium and in isolation from the cellular components. We argue that in order to understand protein folding as it occurs in vivo, it should be modeled as an active, energy-dependent process, in which the cellular protein-folding machine directly manipulates the polypeptide. We conducted all-atom molecular dynamics simulations of four protein domains, whose folding from the extended state was augmented by the application of rotational force to the C-terminal amino acid, while the movement of the N-terminal amino acid was restrained. We have shown earlier that such a simple manipulation of peptide backbone facilitated the formation of native structures in diverse α-helical peptides. In this study, the simulation protocol was modified, to apply the backbone rotation and movement restriction only for a short time at the start of simulation. This transient application of a mechanical force to the peptide is sufficient to accelerate, by at least an order of magnitude, the folding of four protein domains from different structural classes to their native or native-like conformations. Our in silico experiments show that a compact stable fold may be attained more readily when the motions of the polypeptide are biased by external forces and constraints.

Anisotropic Friction in a Ligand-Protein Complex

The effect of an externally applied directional force on molecular friction is so far poorly understood. Here, we study the force-driven dissociation of the ligand-protein complex biotin-streptavidin and identify anisotropic friction as a not yet described type of molecular friction. Using AFM-based stereographic single molecule force spectroscopy and targeted molecular dynamics simulations, we find that the rupture force and friction for biotin-streptavidin vary with the pulling angle. This observation holds true for friction extracted from Kramers' rate expression and by dissipation-corrected targeted molecular dynamics simulations based on Jarzynski's identity. We rule out ligand solvation and protein-internal friction as sources of the angle-dependent friction. Instead, we observe a heterogeneity in free energy barriers along an experimentally uncontrolled orientation parameter, which increases the rupture force variance and therefore the overall friction. We anticipate that anisotropic friction needs to be accounted for in a complete understanding of friction in biomolecular dynamics and anisotropic mechanical environments.

Polymer folding through active processes recreates features of genome organization

From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.

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.

Using machine learning to predict the effects and consequences of mutations in proteins

Machine and deep learning approaches can leverage the increasingly available massive datasets of protein sequences, structures, and mutational effects to predict variants with improved fitness. Many different approaches are being developed, but systematic benchmarking studies indicate that even though the specifics of the machine learning algorithms matter, the more important constraint comes from the data availability and quality utilized during training. In cases where little experimental data are available, unsupervised and self-supervised pre-training with generic protein datasets can still perform well after subsequent refinement via hybrid or transfer learning approaches. Overall, recent progress in this field has been staggering, and machine learning approaches will likely play a major role in future breakthroughs in protein biochemistry and engineering.

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.

Association of two polyelectrolytes in salt solutions

The association of polyelectrolytes (PEs) in solution affects a wealth of structural and dynamic behaviors, and is also fundamentally important for an understanding of protein association and aggregation. Here, we theoretically study the association of two PE chains by addressing the stability and morphology of the non-spherical associates. Our theory predicts that an elongated pearl-necklace (PN) associate can be stable at high salt concentrations due to the screened electrostatic repulsion. This contradicts the implication of scaling theory. In addition, there is no one-to-one correspondence between the morphology of the associate and its constituting unimers, which is demonstrated by the existence of different association modes.

Constrained Layer Assignment for the Protein Burial Folding Code Accounting for Chain Connectivity

The connection between protein sequences and tertiary structures has intrigued investigators for decades. A plausible hypothesis for the coding scheme postulates that atomic burial information obtainable from the sequence could be sufficient for structural determination when combined to sequence-independent constraints. Accordingly, folding simulations using native burial information expressed by atomic central distances, discretized into a small number L of equiprobable burial layers, have indeed been successful in reaching and distinguishing the native structure of several globular proteins. Attempted predictions of layers from sequence, however, turned out to be insufficiently accurate for most proteins. Here we explore the possibility that a nonuniform assignment of layers, which is intended to account for constraints imposed by chain connectivity, might provide a more efficient burial encoding of tertiary structures. We consider the condition that adjacent C_α-atoms along the sequence cannot occupy nonadjacent layers, in which case the information required to specify sequences of burials would be smaller. It is shown that appropriate folding behavior can still be observed in this explicitly more constrained scenario with a structure-dependent assignment intended to produce the thinnest possible layers still compatible with the imposed burial constraint. This thinnest assignment turns out to be sufficiently restrictive for the observed examples and provides appropriately thinner layers or, equivalently, a larger number of layers, for examples previously observed to indeed require more restrictive constraints when compared to counterparts of similar size, as well as the appropriate increase in number of layers for larger proteins. Implications for the general understanding of the protein folding code are discussed.

Different Temperature- and Pressure-Effects on the Water-Mediated Interactions between Hydrophobic, Hydrophilic, and Hydrophobic-Hydrophilic Nanoscale Surfaces

Water-mediated interactions (WMI) are responsible for diverse processes in aqueous solutions, including protein folding and nanoparticle aggregation. WMI may be affected by changes in temperature and pressure and hence, they can alter chemical/physical processes that occur in aqueous environments. Traditionally, attention has been focused on hydrophobic interactions while, in comparison, the role of hydrophilic and hybrid (hydrophobic-hydrophilic) interactions have been mostly overlooked. Here we study the role of T and P of the WMI between nanoscale (i) hydrophobic-hydrophobic, (ii) hydrophilic-hydrophilic, and (iii) hydrophilic-hydrophobic pairs of (hydroxylated/non-hydroxylated) graphene-based surfaces. We find that hydrophobic, hydrophilic and hybrid interactions are all sensitive to P. However, while hydrophobic interactions [case (i)] are sensitive to T-variations, hydrophilic [case (ii)] and hybrid interactions [case (iii)] are practically T-independent. An analysis of the entropic and enthalpic contributions to the PMF for cases (i)-(iii) is also presented. Our results are important in understanding T- and P-induced protein denaturation, and the interactions of biomolecules in solution, including protein aggregation andphase separation processes. From the computational point of view, the results presented here are relevant in the design of implicit water models for the study of molecular and colloidal/nanoparticle systems at different thermodynamic conditions.

Folding and Evolution of a Repeat Protein on the Ribosome

Life on earth is the result of the work of proteins, the cellular nanomachines that fold into elaborated 3D structures to perform their functions. The ribosome synthesizes all the proteins of the biosphere, and many of them begin to fold during translation in a process known as cotranslational folding. In this work we discuss current advances of this field and provide computational and experimental data that highlight the role of ribosome in the evolution of protein structures. First, we used the sequence of the Ankyrin domain from the Drosophila Notch receptor to launch a deep sequence-based search. With this strategy, we found a conserved 33-residue motif shared by different protein folds. Then, to see how the vectorial addition of the motif would generate a full structure we measured the folding on the ribosome of the Ankyrin repeat protein. Not only the on-ribosome folding data is in full agreement with classical in vitro biophysical measurements but also it provides experimental evidence on how folded proteins could have evolved by duplication and fusion of smaller fragments in the RNA world. Overall, we discuss how the ribosomal exit tunnel could be conceptualized as an active site that is under evolutionary pressure to influence protein folding.

De novo protein folding on computers. Benefits and challenges

There has been recent success in prediction of the three-dimensional folded native structures of proteins, most famously by the AlphaFold Algorithm running on Google's/Alphabet's DeepMind computer. However, this largely involves machine learning of protein structures and is not a de novo protein structure prediction method for predicting three-dimensional structures from amino acid residue sequences. A de novo approach would be based almost entirely on general principles of energy and entropy that govern protein folding energetics, and importantly do so without the use of the amino acid sequences and structural features of other proteins. Most consider that problem as still unsolved even though it has occupied leading scientists for decades. Many consider that it remains one of the major outstanding issues in modern science. There is crucial continuing help from experimental findings on protein unfolding and refolding in the laboratory, but only to a limited extent because many researchers consider that the speed by which real proteins folds themselves, often from milliseconds to minutes, is itself still not fully understood. This is unfortunate, because a practical solution to the problem would probably have a major effect on personalized medicine, the pharmaceutical industry, biotechnology, and nanotechnology, including for example "smaller" tasks such as better modeling of flexible "unfolded" regions of the SARS-COV-2 spike glycoprotein when interacting with its cell receptor, antibodies, and therapeutic agents. Some important ideas from earlier studies are given before moving on to lessons from periodic and aperiodic crystals, and a possible role for quantum phenomena. The conclusion is that better computation of entropy should be the priority, though that is presented guardedly.

Unifying coarse-grained force fields for folded and disordered proteins

Liquid-liquid phase separation drives the formation of biological condensates that play essential roles in transcriptional regulation and signal sensing. Computational modeling could provide high-resolution structural characterizations of these condensates and help uncover physicochemical interactions that dictate their stability. However, many protein molecules involved in phase separation often contain multiple ordered domains connected with flexible, structureless linkers. Simulating such proteins necessitates force fields with consistent accuracy for both folded and disordered proteins. We provide a critical review of existing coarse-grained force fields for disordered proteins and highlight the challenges in their application to folded proteins. After discussing existing algorithms for force field parameterization, we propose an optimization strategy that should lead to computer models with improved transferability across protein types.

Inferring the distribution of fitness effects in patient-sampled and experimental virus populations: two case studies

We here propose an analysis pipeline for inferring the distribution of fitness effects (DFE) from either patient-sampled or experimentally-evolved viral populations, that explicitly accounts for non-Wright-Fisher and non-equilibrium population dynamics inherent to pathogens. We examine the performance of this approach via extensive power and performance analyses, and highlight two illustrative applications - one from an experimentally-passaged RNA virus, and the other from a clinically-sampled DNA virus. Finally, we discuss how such DFE inference may shed light on major research questions in virus evolution, ranging from a quantification of the population genetic processes governing genome size, to the role of Hill-Robertson interference in dictating adaptive outcomes, to the potential design of novel therapeutic approaches to eradicate within-patient viral populations via induced mutational meltdown.

Is Protein Folding a Thermodynamically Unfavorable, Active, Energy-Dependent Process?

The prevailing current view of protein folding is the thermodynamic hypothesis, under which the native folded conformation of a protein corresponds to the global minimum of Gibbs free energy G. We question this concept and show that the empirical evidence behind the thermodynamic hypothesis of folding is far from strong. Furthermore, physical theory-based approaches to the prediction of protein folds and their folding pathways so far have invariably failed except for some very small proteins, despite decades of intensive theory development and the enormous increase of computer power. The recent spectacular successes in protein structure prediction owe to evolutionary modeling of amino acid sequence substitutions enhanced by deep learning methods, but even these breakthroughs provide no information on the protein folding mechanisms and pathways. We discuss an alternative view of protein folding, under which the native state of most proteins does not occupy the global free energy minimum, but rather, a local minimum on a fluctuating free energy landscape. We further argue that ΔG of folding is likely to be positive for the majority of proteins, which therefore fold into their native conformations only through interactions with the energy-dependent molecular machinery of living cells, in particular, the translation system and chaperones. Accordingly, protein folding should be modeled as it occurs in vivo, that is, as a non-equilibrium, active, energy-dependent process.

Folding Intermediates, Heterogeneous Native Ensembles and Protein Function

Single domain proteins fold via diverse mechanisms emphasizing the intricate relationship between energetics and structure, which is a direct consequence of functional constraints and demands imposed at the level of sequence. On the other hand, elucidating the interplay between folding mechanisms and function is challenging in large proteins, given the inherent shortcomings in identifying metastable states experimentally and the sampling limitations associated with computational methods. Here, we show that free energy profiles and surfaces of large systems (>150 residues), as predicted by a statistical mechanical model, display a wide array of folding mechanisms with ubiquitous folding intermediates and heterogeneous native ensembles. Importantly, residues around the ligand binding or enzyme active site display a larger tendency to partially unfold and this manifests as intermediates or excited states along the folding coordinate in ligand binding domains, transcription repressors, and representative enzymes from all the six classes, including the SARS-CoV-2 receptor binding domain (RBD) of the spike protein and the protease M^pro. It thus appears that it is relatively easier to distill the imprints of function on the folding landscape of larger proteins as opposed to smaller systems. We discuss how an understanding of energetic-entropic features in ordered proteins can pinpoint specific avenues through which folding mechanisms, populations of partially structured states and function can be engineered.

Energy landscapes and dynamics of ion translocation through membrane transporters: a meeting ground for physics, chemistry, and biology

The dynamics of ion translocation through membrane transporters is visualized from a comprehensive point of view by a Gibbs energy landscape approach. The ΔG calculations have been performed with the Kirkwood-Tanford-Warshel (KTW) electrostatic theory that properly takes into account the self-energies of the ions. The Gibbs energy landscapes for translocation of a single charge and an ion pair are calculated, compared, and contrasted as a function of the order parameter, and the characteristics of the frustrated system with bistability for the ion pair are described and quantified in considerable detail. These calculations have been compared with experimental data on the ΔG of ion pairs in proteins. It is shown that, under suitable conditions, the adverse Gibbs energy barrier can be almost completely compensated by the sum of the electrostatic energy of the charge-charge interactions and the solvation energy of the ion pair. The maxima in ΔG_KTW with interionic distance in the bound H⁺ - A^- charge pair on the enzyme is interpreted in thermodynamic and molecular mechanistic terms, and biological implications for molecular mechanisms of ATP synthesis are discussed. The timescale at which the order parameter moves between two stable states has been estimated by solving the dynamical equations of motion, and a wealth of novel insights into energy transduction during ATP synthesis by the membrane-bound F_OF₁-ATP synthase transporter is offered. In summary, a unifying analytical framework that integrates physics, chemistry, and biology has been developed for ion translocation by membrane transporters for the first time by means of a Gibbs energy landscape approach.

Temperature and Guanidine Hydrochloride Effects on the Folding Thermodynamics of WW Domain and Variants

We used simulations based on an all-atom Go model to calculate the folding temperatures (T_fs) and free energies (ΔGs) of two variants of the WW domain, which is a small all-β-sheet protein. The results, without adjusting any parameter, are in good agreement with experiments, thus validating the simulations. We then used the molecular transfer model to predict the changes in the ΔGs and T_fs as the guanidine hydrochloride concentration is varied. The predictions can be readily tested in experiments.

Using a Coarse-Grained Modeling Framework to Identify Oligomeric Motifs with Tunable Secondary Structure

Coarse-grained modeling can be used to explore general theories that are independent of specific chemical detail. In this paper, we present cg_openmm, a Python-based simulation framework for modeling coarse-grained hetero-oligomers and screening them for structural and thermodynamic characteristics of cooperative secondary structures. cg_openmm facilitates the building of coarse-grained topology and random starting configurations, setup of GPU-accelerated replica exchange molecular dynamics simulations with the OpenMM software package, and features a suite of postprocessing thermodynamic and structural analysis tools. In particular, native contact analysis, heat capacity calculations, and free energy of folding calculations are used to identify and characterize cooperative folding transitions and stable secondary structures. In this work, we demonstrate the capabilities of cg_openmm on a simple 1-1 Lennard-Jones coarse-grained model, in which each residue contains 1 backbone and 1 side-chain bead. By scanning both nonbonded and bonded force-field parameter spaces at the coarse-grained level, we identify and characterize sets of parameters which result in the formation of stable helices through cooperative folding transitions. Moreover, we show that the geometries and stabilities of these helices can be tuned by manipulating the force-field parameters.

Site-Specific Backbone and Side-Chain Contributions to Thermodynamic Stabilizing Forces of the WW Domain

The native structure of a protein is stabilized by a number of interactions such as main-chain hydrogen bonds and side-chain hydrophobic contacts. However, it has been challenging to determine how these interactions contribute to protein stability at single amino acid resolution. Here, we quantified site-specific thermodynamic stability at the molecular level to extend our understanding of the stabilizing forces in protein folding. We derived the free energy components of individual amino acid residues separately for the folding of the human Pin WW domain based on simulated structures. A further decomposition of the thermodynamic properties into contributions from backbone and side-chain groups enabled us to identify the critical residues in the secondary structure and hydrophobic core formation, without introducing physical modifications to the system as in site-directed mutagenesis methods. By relating the structural and thermodynamic changes upon folding for each residue, we find that the simultaneous formation of the backbone hydrogen bonds and side-chain contacts cooperatively stabilizes the folded structure. The identification of stabilizing interactions in a folding protein at atomic resolution will provide molecular insights into understanding the origin of the protein structure and into engineering a more stable protein.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Deriving and Using Descriptors of Elementary Functions in Rational Protein Design

The rational design of proteins with desired functions requires a comprehensive description of the functional building blocks. The evolutionary conserved functional units constitute nature's toolbox; however, they are not readily available to protein designers. This study focuses on protein units of subdomain size that possess structural properties and amino acid residues sufficient to carry out elementary reactions in the catalytic mechanisms. The interactions within such elementary functional loops (ELFs) and the interactions with the surrounding protein scaffolds constitute the descriptor of elementary function. The computational approach to deriving descriptors directly from protein sequences and structures and applying them in rational design was implemented in a proof-of-concept DEFINED-PROTEINS software package. Once the descriptor is obtained, the ELF can be fitted into existing or novel scaffolds to obtain the desired function. For instance, the descriptor may be used to determine the necessary spatial restraints in a fragment-based grafting protocol. We illustrated the approach by applying it to well-known cases of ELFs, including phosphate-binding P-loop, diphosphate-binding glycine-rich motif, and calcium-binding EF-hand motif, which could be used to jumpstart templates for user applications. The DEFINED-PROTEINS package is available for free at https://github.com/MelvinYin/Defined_Proteins.

Subcompartmentalization of polyampholyte species in organelle-like condensates is promoted by charge-pattern mismatch and strong excluded-volume interaction

Polyampholyte field theory and explicit-chain molecular dynamics models of sequence-specific phase separation of a system with two intrinsically disordered protein (IDP) species indicate consistently that a substantial polymer excluded volume and a significant mismatch of the IDP sequence charge patterns can act in concert, but not in isolation, to demix the two IDP species upon condensation. This finding reveals an energetic-geometric interplay in a stochastic, "fuzzy" molecular recognition mechanism that may facilitate subcompartmentalization of membraneless organelles.

Insights into colloidal nanoparticle-protein corona interactions for nanomedicine applications

Colloidal nanoparticles (NPs) have attracted significant attention due to their unique physicochemical properties suitable for diagnosing and treating different human diseases. Nevertheless, the successful implementation of NPs in medicine demands a proper understanding of their interactions with the different proteins found in biological fluids. Once introduced into the body, NPs are covered by a protein corona (PC) that determines the biological behavior of the NPs. The formation of the PC can eventually favor the rapid clearance of the NPs from the body before fulfilling the desired objective or lead to increased cytotoxicity. The PC nature varies as a function of the different repulsive and attractive forces that govern the NP-protein interaction and their colloidal stability. This review focuses on the phenomenon of PC formation on NPs from a physicochemical perspective, aiming to provide a general overview of this critical process. Main issues related to NP toxicity and clearance from the body as a result of protein adsorption are covered, including the most promising strategies to control PC formation and, thereby, ensure the successful application of NPs in nanomedicine.

Accelerating atomistic simulations of proteins using multiscale enhanced sampling with independent tempering

Efficient sampling of the conformational space is essential for quantitative simulations of proteins. The multiscale enhanced sampling (MSES) method accelerates atomistic sampling by coupling it to a coarse-grained (CG) simulation. Bias from coupling to the CG model is removed using Hamiltonian replica exchange, such that one could benefit simultaneously from the high accuracy of atomistic models and fast dynamics of CG ones. Here, we extend MSES to allow independent control of the effective temperatures of atomistic and CG simulations, by directly scaling the atomistic and CG Hamiltonians. The new algorithm, named MSES with independent tempering (MSES-IT), supports more sophisticated Hamiltonian and temperature replica exchange protocols to further improve the sampling efficiency. Using a small but nontrivial β-hairpin, we show that setting the effective temperature of CG model in all conditions to its melting temperature maximizes structural transition rates at the CG level and promotes more efficient replica exchange and diffusion in the condition space. As the result, MSES-IT drive faster reversible transitions at the atomic level and leads to significant improvement in generating converged conformational ensembles compared to the original MSES scheme.

Salt-bridges in the microenvironment of stable protein structures

Salt-bridges (sb) play an important role in the folding and stability of proteins. This is deduced from the evaluation of net energy in the microenvironments (ME, residues that are 4 Å away from positive and negative partners of salt-bridge and interact with them). MEs act as a determinant of net-energy due to the intrinsic features in the sequence. The stability of extremophilic proteins is due to the presence of favorable residues at the ME without any unfavorable residues. We studied a dataset of four structures from the protein data bank (PDB) and a homology model (1HM5) to gain insights on this issue. Data shows that the presence of isolated charges and polar residues in the core of extremophilic proteins helps in the formation of stable salt-bridges with reduced desolvation. Thus, site-specific mutations with favorable residues at the ME will help to develop thermo stable proteins with strong salt bridges.

Towards kinetic control of coordination self-assembly: a case study of a Pd3L6 double-walled triangle to predict the outcomes by a reaction network model

Numerical analysis of self-assembly process (NASAP) was performed for a [Pd3L6]6+ double-walled triangle (DWT) complex. With a chemical reaction network and a parameter set of the reaction rate constants obtained from a numerical search in an eighteen-dimensional parameter space to obtain a good fit to the data from the experimental counterpart (quantitative analysis of self-assembly process, QASAP), a refined calculation resulted in a detailed time evolution of each molecular species. Analysis based on those clues revealed dominant self-assembly pathways and a balance between inter- and intramolecular reactions, and enabled prediction of the reaction outcomes depending on the initial stoichiometric ratio under kinetic control.

Purification, physicochemical properties, and statistical optimization of fibrinolytic enzymes especially from fermented foods: A comprehensive review

Fibrinolytic enzymes are proteases responsible for cleavage of fibrin mesh in thrombus clots, which are the primary causative agents in cardiovascular diseases. Developing safe, effective and cheap thrombolytic agents are important for prevention and cure of thrombosis. Although a wide variety of sources have been discovered for fibrinolytic enzymes, only few of them have been employed in clinical and therapeutic applications due to the drawbacks such as high cost of production, low stability of enzyme or therapeutic side effects. However, the discovery of new fibrinolytic enzymes requires complex purification stages and characterization, which gives an insight into their diverse modes of action. Post-discovery, approaches such as a) statistical optimization for fermentative bioprocessing and b) genetic engineering are advantageous in providing economic viability by finding simple and cost-effective medium, strain development with sufficient nutrient supplements for stable and high-level production of recombinant enzyme. This review provides a comprehensive understanding of different sources, purification techniques, production through genetic engineering approaches and statistical optimization of fermentation parameters as proteases have a wide variety of industrial and biotechnological applications making 60% of total enzyme market worldwide. New strategies targeting increased enzyme yields, non-denaturing environments, improved stability, enzyme activity and strain improvement have been discussed.

Dramatic Shape Changes Occur as Cytochrome c Folds

Extensive experimental studies on the folding of cytochrome c (Cyt c) make this small protein an ideal target for atomic detailed simulations for the purposes of quantitatively characterizing the structural transitions and the associated time scales for folding to the native state from an ensemble of unfolded states. We use previously generated atomically detailed folding trajectories by the stochastic difference equation in length to calculate the time-dependent changes in the small-angle X-ray scattering (SAXS) profiles. Excellent agreement is obtained between experiments and simulations for the time-dependent SAXS spectra, allowing us to identify the structures of the folding intermediates, which shows that Cyt c reaches the native state by a sequential folding mechanism. Using the ensembles of structures along the folding pathways, we show that compaction and the sphericity of Cyt c change dramatically from the prolate ellipsoid shape in the unfolded state to the spherical native state. Our data, which are in unprecedented quantitative agreement with all aspects of time-resolved SAXS experiments, show that hydrophobic collapse and amide group protection coincide on the 100 microseconds time scale, which is in accordance with ultrafast hydrogen/deuterium exchange studies. Based on these results, we propose that compaction of polypeptide chains, accompanied by dramatic shape changes, is a universal characteristic of globular proteins, regardless of the underlying folding mechanism.

Potential energy landscape and thermodynamic transitions of coarse-grained protein models revealed by the multicanonical generalized hybrid Monte Carlo method

In the present study, thermodynamic properties of coarse-grained protein models have been studied by an extended ensemble method. Two types of protein model were analyzed; one is categorized into a fast folder and the other into a slow folder. Both models exhibit the following thermodynamic transitions: the collapse transition between random coil states and spatially compact, but non-native states and the folding transition between the collapsed states and the folded native states. Caloric curve for the fast folder shows strong statistical ensemble dependence, while almost no ensemble dependence is found for the slow folder. Microcanonical caloric curve for the fast folder exhibits S-shaped temperature dependence on the internal energy around the collapse transition which is reminiscent of the van der Waals loop observed for the first order transition; at the transition temperature, the collapsed and random coil states coexist dynamically. The corresponding microcanonical heat capacity is found to have negative region around the transition. This kind of exotic behaviors could be utilized to distinguish fast folding proteins.

Disorder-Order Transitions in Conformational Selection of a Peptide by Ebola Virus Nucleoprotein

This study presents parallel-tempering lattice Monte Carlo simulations based on the side-chain-only (SICHO) model for calculating the conformational landscape of a 28-residue intrinsically disordered peptide extracted from the Ebola virus protein VP35. The central issue is the applicability of the SICHO potential energy function and in general coarse-grained (CG) representations of intermediate resolution for modeling large-scale conformational heterogeneity that includes both folded and unstructured peptide states. Crystallographic data shows that the peptide folds in a 4₁₀-helix-turn-3₁₀-helix topology upon complex formation with the Ebola virus nucleoprotein, whereas in isolation, the peptide transitions to a disordered conformational ensemble as observed in circular dichroism experiments. The simulation reveals a potential of mean force that displays conformational diversity along the helix-forming reaction coordinate consistent with disorder-order transitions, yet unexpectedly the bound topology is poorly sampled, and a population shift to an unstructured state incurs a significant free-energy penalty. Applying an elastic network interpolation model suggests a hybrid binding mechanism through conformational selection of the 4₁₀-helix followed by an induced fit of the 3₁₀-helix. A comparison of the CG model with previously reported all-atom CHARMM-based simulations highlights a lattice-based approach that is computationally fast and with the correct parameterization yields good resolution to modeling conformational plasticity.

Self-organized emergence of folded protein-like network structures from geometric constraints

The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino acids, the biochemical environment and the temporal sequence of distinct interactions yield a complex folding process that cannot yet be easily tracked for all proteins. To gain qualitative insights into the fundamental mechanisms behind the folding dynamics and generic features of the folded structure, we propose a simple model of structure formation that takes into account only fundamental geometric constraints and otherwise assumes randomly paired connections. We find that despite its simplicity, the model results in a network ensemble consistent with key overall features of the ensemble of Protein Residue Networks we obtained from more than 1000 biological protein geometries as available through the Protein Data Base. Specifically, the distribution of the number of interaction neighbors a unit (amino acid) has, the scaling of the structure’s spatial extent with chain length, the eigenvalue spectrum and the scaling of the smallest relaxation time with chain length are all consistent between model and real proteins. These results indicate that geometric constraints alone may already account for a number of generic features of protein tertiary structures.

Comment on "Osmotic pressure of compressed lattice knots"

In a recent paper, E. J. Janse van Rensburg has presented computational data enumerating the conformations of closed circular self-avoiding lattice polymers with knots confined in a cubic box, and claimed to have observed a negative osmotic pressure in the system. The purpose of this comment is to state that osmotic pressure by a self-avoiding polymer, knotted or otherwise, is positive, which means a polymer pushes confining walls outwards, and the statement of the opposite is a mistake.

Solution of Levinthal's Paradox and a Physical Theory of Protein Folding Times

“How do proteins fold?” Researchers have been studying different aspects of this question for more than 50 years. The most conceptual aspect of the problem is how protein can find the global free energy minimum in a biologically reasonable time, without exhaustive enumeration of all possible conformations, the so-called “Levinthal’s paradox.” Less conceptual but still critical are aspects about factors defining folding times of particular proteins and about perspectives of machine learning for their prediction. We will discuss in this review the key ideas and discoveries leading to the current understanding of folding kinetics, including the solution of Levinthal’s paradox, as well as the current state of the art in the prediction of protein folding times.

A molecular simulation approach towards the development of universal nanocarriers by studying the pH- and electrostatic-driven changes in the dynamic structure of albumin

To explore the intramolecular interactions of protein, and its folding and unfolding mechanisms, we performed a simulation-based comparative study on albumin at different ionic strengths and pH. In this study, we performed molecular dynamics (MD) simulation for bovine serum albumin (BSA) at five different concentrations of NaCl (10, 20, 30, 40 and 50 mM), and five different pH values (2.0, 3.5, 4.3, 7.4, and 9.0). Herein, our aim was to unravel the effects of both pH and ionic strength on the conformations of the serum albumin structure. Our results indicate the effects of physicochemical factors in promoting conformational changes in the albumin structure, unlocking the hydrophobic sequences for hydrophobic drug binding. The BSA structure showed similarity to its native state in the pH range of 4.5 to 7.4 and at various ionic concentrations of NaCl. In the pH range of 3.5 to 4.5, the BSA structure showed denaturation in a controlled manner, which caused significant conformational changes in the molecular position of its hydrophobic amino acid residues. The resultant 3D structure gives insight into the amino acid trajectories. High denaturation and unstable behavior in the structural and conformational changes of the protein structure were observed at pH 2.0 and pH 9.0. We believe that these results and conditions will be helpful in the development of protein-based universal nanocarriers for the encapsulation of both hydrophilic and hydrophobic drugs.

Role of pH and electrostatic charges on the conformations and dynamics of albumin structure by molecular dynamic study.

Probing Structure and Reaction Dynamics of Proteins Using Time-Resolved Resonance Raman Spectroscopy

The mechanistic understanding of protein functions requires insight into the structural and reaction dynamics. To elucidate these processes, a variety of experimental approaches are employed. Among them, time-resolved (TR) resonance Raman (RR) is a particularly versatile tool to probe processes of proteins harboring cofactors with electronic transitions in the visible range, such as retinal or heme proteins. TR RR spectroscopy offers the advantage of simultaneously providing molecular structure and kinetic information. The various TR RR spectroscopic methods can cover a wide dynamic range down to the femtosecond time regime and have been employed in monitoring photoinduced reaction cascades, ligand binding and dissociation, electron transfer, enzymatic reactions, and protein un- and refolding. In this account, we review the achievements of TR RR spectroscopy of nearly 50 years of research in this field, which also illustrates how the role of TR RR spectroscopy in molecular life science has changed from the beginning until now. We outline the various methodological approaches and developments and point out current limitations and potential perspectives.

Tensor Algebra-based Geometrical (3D) Biomacro-Molecular Descriptors for Protein Research: Theory, Applications and Comparison with other Methods

In this report, a new type of tridimensional (3D) biomacro-molecular descriptors for proteins are proposed. These descriptors make use of multi-linear algebra concepts based on the application of 3-linear forms (i.e., Canonical Trilinear (Tr), Trilinear Cubic (TrC), Trilinear-Quadratic-Bilinear (TrQB) and so on) as a specific case of the N-linear algebraic forms. The definition of the kth 3-tuple similarity-dissimilarity spatial matrices (Tensor's Form) are used for the transformation and for the representation of the existing chemical information available in the relationships between three amino acids of a protein. Several metrics (Minkowski-type, wave-edge, etc) and multi-metrics (Triangle area, Bond-angle, etc) are proposed for the interaction information extraction, as well as probabilistic transformations (e.g., simple stochastic and mutual probability) to achieve matrix normalization. A generalized procedure considering amino acid level-based indices that can be fused together by using aggregator operators for descriptors calculations is proposed. The obtained results demonstrated that the new proposed 3D biomacro-molecular indices perform better than other approaches in the SCOP-based discrimination and the prediction of folding rate of proteins by using simple linear parametrical models. It can be concluded that the proposed method allows the definition of 3D biomacro-molecular descriptors that contain orthogonal information capable of providing better models for applications in protein science.

ProSNEx: a web-based application for exploration and analysis of protein structures using network formalism

ProSNEx (Protein Structure Network Explorer) is a web service for construction and analysis of Protein Structure Networks (PSNs) alongside amino acid flexibility, sequence conservation and annotation features. ProSNEx constructs a PSN by adding nodes to represent residues and edges between these nodes using user-specified interaction distance cutoffs for either carbon-alpha, carbon-beta or atom-pair contact networks. Different types of weighted networks can also be constructed by using either (i) the residue-residue interaction energies in the format returned by gRINN, resulting in a Protein Energy Network (PEN); (ii) the dynamical cross correlations from a coarse-grained Normal Mode Analysis (NMA) of the protein structure; (iii) interaction strength. Upon construction of the network, common network metrics (such as node centralities) as well as shortest paths between nodes and k-cliques are calculated. Moreover, additional features of each residue in the form of conservation scores and mutation/natural variant information are included in the analysis. By this way, tool offers an enhanced and direct comparison of network-based residue metrics with other types of biological information. ProSNEx is free and open to all users without login requirement at http://prosnex-tool.com.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.