Loss of conformational entropy in protein folding calculated using realistic ensembles and its implications for NMR-based calculations

Advances in uncovering the mechanisms of macromolecular conformational entropy

During protein folding, proteins transition from a disordered polymer into a globular structure, markedly decreasing their conformational degrees of freedom, leading to a substantial reduction in entropy. Nonetheless, folded proteins retain substantial entropy as they fluctuate between the conformations that make up their native state. This residual entropy contributes to crucial functions like binding and catalysis, supported by growing evidence primarily from NMR and simulation studies. Here, we propose three major ways that macromolecules use conformational entropy to perform their functions; first, prepaying entropic cost through ordering of the ground state; second, spatially redistributing entropy, in which a decrease in entropy in one area is reciprocated by an increase in entropy elsewhere; third, populating catalytically competent ensembles, in which conformational entropy within the enzymatic scaffold aids in lowering transition state barriers. We also provide our perspective on how solving the current challenge of structurally defining the ensembles encoding conformational entropy will lead to new possibilities for controlling binding, catalysis and allostery.

Collapse and Protein Folding: Should We Be Surprised That Biothermodynamics Works So Well?

A complete understanding of protein function and dynamics requires the characterization of the multiple thermodynamic states, including the denatured state ensemble (DSE). Whereas residual structure in the DSE (as well as in partially folded states) is pertinent in many biological contexts, here we are interested in how such structure affects protein thermodynamics. We examine issues related to chain collapse in light of new developments, focusing on potential complications arising from differences in the DSE's properties under various conditions. Despite some variability in the degree of collapse and structure in the DSE, stability measurements are remarkably consistent between two standard methods, calorimetry and chemical denaturation, as well as with hydrogen-deuterium exchange. This robustness is due in part to the DSEs obtained with different perturbations being thermodynamically equivalent and hence able to serve as a common reference state. An examination of the properties of the DSE points to it as being a highly expanded ensemble with minimal amounts of stable hydrogen bonded structure. These two features are likely to be critical in the broad and successful application of thermodynamics to protein folding. Our review concludes with a discussion of the impact of these findings on folding mechanisms and pathways.

Designing mimosine-containing peptides as efficient metal chelators: Insights from molecular dynamics and quantum calculations

Mimosine, a non-essential amino acid derived from plants, has a strong affinity for binding divalent and trivalent metal cations, including Zn2+, Ni2+, Fe2+/3+, and Al3+. This ability endows mimosine with significant antimicrobial and anti-cancer properties, making it a promising candidate for therapeutic applications. Previous research has demonstrated the effectiveness of mimosine-containing peptides as metal chelators, offering a safer alternative to conventional chelation agents. However, optimizing the design of these peptides necessitates a thorough understanding of their conformational ensembles in both free and metal-bound states. Here, we perform an in-depth analysis of mimosine-containing peptides using long-time MD simulations and quantum calculations to identify key factors critical for peptide design. Our results show that these peptides can achieve metal-binding affinities comparable to established aluminum chelators like deferiprone and citrate. Additionally, we underscore the crucial role of the peptide backbone in reducing the entropic penalty associated with metal binding. We propose strategies to modulate this entropic penalty-a challenging thermodynamic property to evaluate but essential in complexes between short peptides and metals-by incorporating proline residues and optimizing sequence length. These approaches offer promising pathways for developing efficient peptide chelators.

AMARO: All Heavy-Atom Transferable Neural Network Potentials of Protein Thermodynamics

All-atom molecular simulations offer detailed insights into macromolecular phenomena, but their substantial computational cost hinders the exploration of complex biological processes. We introduce Advanced Machine-learning Atomic Representation Omni-force-field (AMARO), a new neural network potential (NNP) that combines an O(3)-equivariant message-passing neural network architecture, TensorNet, with a coarse-graining map that excludes hydrogen atoms. AMARO demonstrates the feasibility of training coarser NNP, without prior energy terms, to run stable protein dynamics with scalability and generalization capabilities.

The ribosome lowers the entropic penalty of protein folding

Most proteins fold during biosynthesis on the ribosome1, and co-translational folding energetics, pathways and outcomes of many proteins have been found to differ considerably from those in refolding studies2-10. The origin of this folding modulation by the ribosome has remained unknown. Here we have determined atomistic structures of the unfolded state of a model protein on and off the ribosome, which reveal that the ribosome structurally expands the unfolded nascent chain and increases its solvation, resulting in its entropic destabilization relative to the peptide chain in isolation. Quantitative 19F NMR experiments confirm that this destabilization reduces the entropic penalty of folding by up to 30 kcal mol-1 and promotes formation of partially folded intermediates on the ribosome, an observation that extends to other protein domains and is obligate for some proteins to acquire their active conformation. The thermodynamic effects also contribute to the ribosome protecting the nascent chain from mutation-induced unfolding, which suggests a crucial role of the ribosome in supporting protein evolution. By correlating nascent chain structure and dynamics to their folding energetics and post-translational outcomes, our findings establish the physical basis of the distinct thermodynamics of co-translational protein folding.

On the Stabilizing Effect of Aspartate and Glutamate and Its Counteraction by Common Denaturants

By performing differential scanning calorimetry(DSC) measurements on RNase A, we studied the stabilization provided by the addition of potassium aspartate(KAsp) or potassium glutamate (KGlu) and found that it leads to a significant increase in the denaturation temperature of the protein. The stabilization proves to be mainly entropic in origin. A counteraction of the stabilization provided by KAsp or KGlu is obtained by adding common denaturants such as urea, guanidinium chloride, or guanidinium thiocyanate. A rationalization of the experimental data is devised on the basis of a theoretical approach developed by one of the authors. The main contribution to the conformational stability of globular proteins comes from the gain in translational entropy of water and co-solute ions and/or molecules for the decrease in solvent-excluded volume associated with polypeptide folding (i.e., there is a large decrease in solvent-accessible surface area). The magnitude of this entropic contribution increases with the number density and volume packing density of the solution. The two destabilizing contributions come from the conformational entropy of the chain, which should not depend significantly on the presence of co-solutes, and from the direct energetic interactions between co-solutes and the protein surface in both the native and denatured states. It is the magnitude of the latter that discriminates between stabilizing and destabilizing agents.

The experimental approach for the interleaved joint modulation of PHIP and NMR

Nuclear spin hyperpolarization derived from parahydrogen is a technique for enhancing nuclear magnetic resonance (NMR) sensitivity. The key to hyperpolarization experiments is to achieve rapid transfer and detection to minimize relaxation losses, while also avoiding bubbles or turbulence to guarantee high spectral resolution. In this article, we describe an experimental approach for the interleaved joint modulation of parahydrogen-induced polarization and NMR. We provide schematic diagrams of parahydrogen-based polarizer with in situ high-pressure detection capability and low-field polarization transfer. This approach can help to control the experimental process and acquire experimental information, one example of which is the attainment of the highest hyperpolarization signal intensity at 3.6 s after closing the valve. The polarizer demonstrates in situ detection capability, allowing sample to be restabilized within 0.3 ± 0.1 s and high-resolution NMR sampling under a pressure of 3 bars. Moreover, it can transfer polarized samples from the polarization transfer field to the detection region of NMR within 1 ± 0.3 s for completing signal amplification by reversible exchange experiments.

Top-Down Machine Learning of Coarse-Grained Protein Force Fields

Developing accurate and efficient coarse-grained representations of proteins is crucial for understanding their folding, function, and interactions over extended time scales. Our methodology involves simulating proteins with molecular dynamics and utilizing the resulting trajectories to train a neural network potential through differentiable trajectory reweighting. Remarkably, this method requires only the native conformation of proteins, eliminating the need for labeled data derived from extensive simulations or memory-intensive end-to-end differentiable simulations. Once trained, the model can be employed to run parallel molecular dynamics simulations and sample folding events for proteins both within and beyond the training distribution, showcasing its extrapolation capabilities. By applying Markov state models, native-like conformations of the simulated proteins can be predicted from the coarse-grained simulations. Owing to its theoretical transferability and ability to use solely experimental static structures as training data, we anticipate that this approach will prove advantageous for developing new protein force fields and further advancing the study of protein dynamics, folding, and interactions.

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

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

The relevance of short peptides for an understanding of unfolded and intrinsically disordered proteins

Over the last thirty years the unfolded state of proteins has attracted considerable interest owing to the discovery of intrinsically disordered proteins which perform a plethora of functions despite resembling unfolded proteins to a significant extent. Research on both, unfolded and disordered proteins has revealed that their conformational properties can deviate locally from random coil behavior. In this context results from work on short oligopeptides suggest that individual amino acid residues sample the sterically allowed fraction of the Ramachandran plot to a different extent. Alanine has been found to exhibit a peculiarity in that it has a very high propensity for adopting polyproline II like conformations. This Perspectives article reviews work on short peptides aimed at exploring the Ramachandran distributions of amino acid residues in different contexts with experimental and computational means. Based on the thus provided overview the article discussed to what extent short peptides can serve as tools for exploring unfolded and disordered proteins and as benchmarks for the development of a molecular dynamics force field.

Molecular Information Theory Meets Protein Folding

We propose an application of molecular information theory to analyze the folding of single domain proteins. We analyze results from various areas of protein science, such as sequence-based potentials, reduced amino acid alphabets, backbone configurational entropy, secondary structure content, residue burial layers, and mutational studies of protein stability changes. We found that the average information contained in the sequences of evolved proteins is very close to the average information needed to specify a fold ∼2.2 ± 0.3 bits/(site·operation). The effective alphabet size in evolved proteins equals the effective number of conformations of a residue in the compact unfolded state at around 5. We calculated an energy-to-information conversion efficiency upon folding of around 50%, lower than the theoretical limit of 70%, but much higher than human-built macroscopic machines. We propose a simple mapping between molecular information theory and energy landscape theory and explore the connections between sequence evolution, configurational entropy, and the energetics of protein folding.

Deep mutational scanning and machine learning reveal structural and molecular rules governing allosteric hotspots in homologous proteins

A fundamental question in protein science is where allosteric hotspots - residues critical for allosteric signaling - are located, and what properties differentiate them. We carried out deep mutational scanning (DMS) of four homologous bacterial allosteric transcription factors (aTFs) to identify hotspots and built a machine learning model with this data to glean the structural and molecular properties of allosteric hotspots. We found hotspots to be distributed protein-wide rather than being restricted to 'pathways' linking allosteric and active sites as is commonly assumed. Despite structural homology, the location of hotspots was not superimposable across the aTFs. However, common signatures emerged when comparing hotspots coincident with long-range interactions, suggesting that the allosteric mechanism is conserved among the homologs despite differences in molecular details. Machine learning with our large DMS datasets revealed global structural and dynamic properties to be a strong predictor of whether a residue is a hotspot than local and physicochemical properties. Furthermore, a model trained on one protein can predict hotspots in a homolog. In summary, the overall allosteric mechanism is embedded in the structural fold of the aTF family, but the finer, molecular details are sequence-specific.

Evolution and folding of repeat proteins

Repeat proteins are made with tandem copies of similar amino acid stretches that fold into elongated architectures. These proteins constitute excellent model systems to investigate how evolution relates to structure, folding, and function. Here, we propose a scheme to map evolutionary information at the sequence level to a coarse-grained model for repeat-protein folding and use it to investigate the folding of thousands of repeat proteins. We model the energetics by a combination of an inverse Potts-model scheme with an explicit mechanistic model of duplications and deletions of repeats to calculate the evolutionary parameters of the system at the single-residue level. These parameters are used to inform an Ising-like model that allows for the generation of folding curves, apparent domain emergence, and occupation of intermediate states that are highly compatible with experimental data in specific case studies. We analyzed the folding of thousands of natural Ankyrin repeat proteins and found that a multiplicity of folding mechanisms are possible. Fully cooperative all-or-none transitions are obtained for arrays with enough sequence-similar elements and strong interactions between them, while noncooperative element-by-element intermittent folding arose if the elements are dissimilar and the interactions between them are energetically weak. Additionally, we characterized nucleation-propagation and multidomain folding mechanisms. We show that the global stability and cooperativity of the repeating arrays can be predicted from simple sequence scores.

Effect of Ion and Binding Site on the Conformation of Chosen Glycosaminoglycans at the Albumin Surface

Albumin is one of the major components of synovial fluid. Due to its negative surface charge, it plays an essential role in many physiological processes, including the ability to form molecular complexes. In addition, glycosaminoglycans such as hyaluronic acid and chondroitin sulfate are crucial components of synovial fluid involved in the boundary lubrication regime. This study presents the influence of Na+, Mg2+ and Ca2+ ions on human serum albumin–hyaluronan/chondroitin-6-sulfate interactions examined using molecular docking followed by molecular dynamics simulations. We analyze chosen glycosaminoglycans binding by employing a conformational entropy approach. In addition, several protein–polymer complexes have been studied to check how the binding site and presence of ions influence affinity. The presence of divalent cations contributes to the decrease of conformational entropy near carboxyl and sulfate groups. This observation can indicate the higher affinity between glycosaminoglycans and albumin. Moreover, domains IIIA and IIIB of albumin have the highest affinity as those are two domains that show a positive net charge that allows for binding with negatively charged glycosaminoglycans. Finally, in discussion, we suggest some research path to find particular features that would carry information about the dynamics of the particular type of polymers or ions.

Some Clues about Enzymes from Psychrophilic Microorganisms

Enzymes purified from psychrophilic microorganisms prove to be efficient catalysts at low temperatures and possess a great potential for biotechnological applications. The low-temperature catalytic activity has to come from specific structural fluctuations involving the active site region, however, the relationship between protein conformational stability and enzymatic activity is subtle. We provide a survey of the thermodynamic stability of globular proteins and their rationalization grounded in a theoretical approach devised by one of us. Furthermore, we provide a link between marginal conformational stability and protein flexibility grounded in the harmonic approximation of the vibrational degrees of freedom, emphasizing the occurrence of long-wavelength and excited vibrations in all globular proteins. Finally, we offer a close view of three enzymes: chloride-dependent α-amylase, citrate synthase, and β-galactosidase.

Arrow of Time, Entropy, and Protein Folding: Holistic View on Biochirality

Chirality is a universal phenomenon, embracing the space–time domains of non-organic and organic nature. The biological time arrow, evident in the aging of proteins and organisms, should be linked to the prevalent biomolecular chirality. This hypothesis drives our exploration of protein aging, in relation to the biological aging of an organism. Recent advances in the chirality discrimination methods and theoretical considerations of the non-equilibrium thermodynamics clarify the fundamental issues, concerning the biphasic, alternative, and stepwise changes in the conformational entropy associated with protein folding. Living cells represent open, non-equilibrium, self-organizing, and dissipative systems. The non-equilibrium thermodynamics of cell biology are determined by utilizing the energy stored, transferred, and released, via adenosine triphosphate (ATP). At the protein level, the synthesis of a homochiral polypeptide chain of L-amino acids (L-AAs) represents the first state in the evolution of the dynamic non-equilibrium state of the system. At the next step the non-equilibrium state of a protein-centric system is supported and amended by a broad set of posttranslational modifications (PTMs). The enzymatic phosphorylation, being the most abundant and ATP-driven form of PTMs, illustrates the principal significance of the energy-coupling, in maintaining and reshaping the system. However, the physiological functions of phosphorylation are under the permanent risk of being compromised by spontaneous racemization. Therefore, the major distinct steps in protein-centric aging include the biosynthesis of a polypeptide chain, protein folding assisted by the system of PTMs, and age-dependent spontaneous protein racemization and degradation. To the best of our knowledge, we are the first to pay attention to the biphasic, alternative, and stepwise changes in the conformational entropy of protein folding. The broader view on protein folding, including the impact of spontaneous racemization, will help in the goal-oriented experimental design in the field of chiral proteomics.

Protein Dynamics to Define and Refine Disordered Protein Ensembles

Intrinsically disordered proteins and unfolded proteins have fluctuating conformational ensembles that are fundamental to their biological function and impact protein folding, stability, and misfolding. Despite the importance of protein dynamics and conformational sampling, time-dependent data types are not fully exploited when defining and refining disordered protein ensembles. Here we introduce a computational framework using an elastic network model and normal-mode displacements to generate a dynamic disordered ensemble consistent with NMR-derived dynamics parameters, including transverse R₂ relaxation rates and Lipari-Szabo order parameters (S² values). We illustrate our approach using the unfolded state of the drkN SH3 domain to show that the dynamical ensembles give better agreement than a static ensemble for a wide range of experimental validation data including NMR chemical shifts, J-couplings, nuclear Overhauser effects, paramagnetic relaxation enhancements, residual dipolar couplings, hydrodynamic radii, single-molecule fluorescence Förster resonance energy transfer, and small-angle X-ray scattering.

How physical forces drive the process of helical membrane protein folding

Protein folding is a fundamental process of life with important implications throughout biology. Indeed, tens of thousands of mutations have been associated with diseases, and most of these mutations are believed to affect protein folding rather than function. Correct folding is also a key element of design. These factors have motivated decades of research on protein folding. Unfortunately, knowledge of membrane protein folding lags that of soluble proteins. This gap is partly caused by the greater technical challenges associated with membrane protein studies, but also because of additional complexities. While soluble proteins fold in a homogenous water environment, membrane proteins fold in a setting that ranges from bulk water to highly charged to apolar. Thus, the forces that drive folding vary in different regions of the protein, and this complexity needs to be incorporated into our understanding of the folding process. Here, we review our understanding of membrane protein folding biophysics. Despite the greater challenge, better model systems and new experimental techniques are starting to unravel the forces and pathways in membrane protein folding.

A Rationalization of the Effect That TMAO, Glycine, and Betaine Exert on the Collapse of Elastin-like Polypeptides

Elastin-like polypeptides (ELPs) are soluble in water at low temperature, but, on increasing the temperature, they undergo a reversible and cooperative, coil-to-globule collapse transition. It has been shown that the addition to water of either trimethylamine N-oxide (TMAO), glycine, or betaine causes a significant decrease of T(collapse) in the case of a specific ELP. Traditional rationalizations of these phenomena do not work in the present case. We show that an alternative approach, grounded in the magnitude of the solvent-excluded volume effect and its temperature dependence (strictly linked to the translational entropy of solvent and co-solute molecules), is able to rationalize the occurrence of ELP collapse in water on raising the temperature, as well as the T(collapse) lowering caused by the addition to water of either TMAO, glycine, or betaine.

Fundamental Clock of Biological Aging: Convergence of Molecular, Neurodegenerative, Cognitive and Psychiatric Pathways: Non-Equilibrium Thermodynamics Meet Psychology

In humans, age-associated degrading changes, widely observed in molecular and cellular processes underly the time-dependent decline in spatial navigation, time perception, cognitive and psychological abilities, and memory. Cross-talk of biological, cognitive, and psychological clocks provides an integrative contribution to healthy and advanced aging. At the molecular level, genome, proteome, and lipidome instability are widely recognized as the primary causal factors in aging. We narrow attention to the roles of protein aging linked to prevalent amino acids chirality, enzymatic and spontaneous (non-enzymatic) post-translational modifications (PTMs ^SP), and non-equilibrium phase transitions. The homochirality of protein synthesis, resulting in the steady-state non-equilibrium condition of protein structure, makes them prone to multiple types of enzymatic and spontaneous PTMs, including racemization and isomerization. Spontaneous racemization leads to the loss of the balanced prevalent chirality. Advanced biological aging related to irreversible PTMs ^SP has been associated with the nontrivial interplay between somatic (molecular aging) and mental (psychological aging) health conditions. Through stress response systems (SRS), the environmental and psychological stressors contribute to the age-associated “collapse” of protein homochirality. The role of prevalent protein chirality and entropy of protein folding in biological aging is mainly overlooked. In a more generalized context, the time-dependent shift from enzymatic to the non-enzymatic transformation of biochirality might represent an important and yet underappreciated hallmark of aging. We provide the experimental arguments in support of the racemization theory of aging.

Dynamics in natural and designed elastins and their relation to elastic fiber structure and recoil

Elastin fibers assemble in the extracellular matrix from the precursor protein tropoelastin and provide the flexibility and spontaneous recoil required for arterial function. Unlike many proteins, a structure-function mechanism for elastin has been elusive. We have performed detailed NMR relaxation studies of the dynamics of the minielastins 24x' and 20x' using solution NMR, and of purified bovine elastin fibers in the presence and absence of mechanical stress using solid state NMR. The low sequence complexity of the minielastins enables us to determine average dynamical timescales and degrees of local ordering in the cross-link and hydrophobic modules separately using NMR relaxation by taking advantage of their residue-specific resolution. We find an extremely high degree of disorder, with order parameters for the entirety of the hydrophobic domains near zero, resembling that of simple chemical polymers and less than the order parameters that have been observed in other intrinsically disordered proteins. We find that average backbone order parameters in natural, purified elastin fibers are comparable to those found in 24x' and 20x' in solution. The difference in dynamics, compared with the minielastins, is that backbone correlation times are significantly slowed in purified elastin. Moreover, when elastin is mechanically stretched, the high chain disorder in purified elastin is retained, showing that any change in local ordering is below that detectable in our experiment. Combined with our previous finding of a 10-fold increase in the ordering of water when fully hydrated elastin fibers are stretched by 50%, these results support the hypothesis that stretch induced solvent ordering, i.e., the hydrophobic effect, is a key player in the elastic recoil of elastin as opposed to configurational entropy loss.

Entropic singularities give rise to quantum transmission

When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity- a fundamental synergy which allows quantum devices (aka quantum channels) to send more information than expected. Previously, non-additivity was known to occur in very noisy channels with coherent information much smaller than that of a perfect channel; but, our work shows non-additivity in a simple low-noise channel. Our results extend even further. We prove a general theorem concerning positivity of a channel's coherent information. A corollary of this theorem gives a simple dimensional test for a channel's capacity. Applying this corollary solves an open problem by characterizing all qubit channels whose complement has non-zero capacity. Another application shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information. These results arise from introducing and linking logarithmic singularities in the von-Neumann entropy with quantum transmission: changes in entropy caused by this singularity are a mechanism responsible for both positivity and non-additivity of the coherent information. Analysis of such singularities may be useful in other physics problems.

Mobile Protons Limit the Stability of Salt Bridges in the Gas Phase: Implications for the Structures of Electrosprayed Protein Ions

Electrosprayed protein ions can retain native-like conformations. The intramolecular contacts that stabilize these compact gas-phase structures remain poorly understood. Recent work has uncovered abundant salt bridges in electrosprayed proteins. Salt bridges are zwitterionic BH⁺/A^- contacts. The low dielectric constant in the vacuum strengthens electrostatic interactions, suggesting that salt bridges could be a key contributor to the retention of compact protein structures. A problem with this assertion is that H⁺ are mobile, such that H⁺ transfer can convert salt bridges into neutral B⁰/HA⁰ contacts. This possible salt bridge annihilation puts into question the role of zwitterionic motifs in the gas phase, and it calls for a detailed analysis of BH⁺/A^- versus B⁰/HA⁰ interactions. Here, we investigate this issue using molecular dynamics (MD) simulations and electrospray experiments. MD data for short model peptides revealed that salt bridges with static H⁺ have dissociation energies around 700 kJ mol^-1. The corresponding B⁰/HA⁰ contacts are 1 order of magnitude weaker. When considering the effects of mobile H⁺, BH⁺/A^- bond energies were found to be between these two extremes, confirming that H⁺ migration can significantly weaken salt bridges. Next, we examined the protein ubiquitin under collision-induced unfolding (CIU) conditions. CIU simulations were conducted using three different MD models: (i) Positive-only runs with static H⁺ did not allow for salt bridge formation and produced highly expanded CIU structures. (ii) Zwitterionic runs with static H⁺ resulted in abundant salt bridges, culminating in much more compact CIU structures. (iii) Mobile H⁺ simulations allowed for the dynamic formation/annihilation of salt bridges, generating CIU structures intermediate between scenarios (i) and (ii). Our results uncover that mobile H⁺ limit the stabilizing effects of salt bridges in the gas phase. Failure to consider the effects of mobile H⁺ in MD simulations will result in unrealistic outcomes under CIU conditions.

Differential Stabilities of Mefloquine-Bound Human and Plasmodium falciparum Acyl-CoA-Binding Proteins

Toxic effects of pharmacological drugs restrict their robust application against human diseases. Although used as a drug in the combinatorial therapy to treat malaria, the use of mefloquine is not highly recommended because of its adverse effects in humans. Mefloquine inhibits the binding of acyl-CoAs to acyl-CoA-binding proteins of Plasmodium falciparum (PfACBPs) and human (hACBP). In this study, we have used molecular dynamics simulation and other computational approaches to investigate the differences of stabilities of mefloquine-PfACBP749 and mefloquine-hACBP complexes. The stability of mefloquine in the binding cavity of PfACBP749 is less than its stability in the binding pocket of hACBP. Although the essential tyrosine residues (tyrosine-30 and tyrosine-33 of PfACBP749 and tyrosine-29 and tyrosine-32 of hACBP) mediate the initial binding of mefloquine to the proteins by π-stacking interactions, additional temporally longer interactions between mefloquine and aspartate-22 and methionine-25 of hACBP result in stronger binding of mefloquine to hACBP. The higher fluctuation of mefloquine-binding residues of PfACBP749 contributes to the instability of mefloquine in the binding cavity of the protein. On the contrary, in the mefloquine-bound state, the stability of hACBP protein is less than the stability of PfACBP749. The helix-to-coil transition of the N-terminal hydrophobic region of hACBP has a destabilizing effect upon the protein's structure. This causes the induction of aggregation properties in the hACBP in the mefloquine-bound state. Taken together, we describe the mechanistic features that affect the differential dynamic stabilities of mefloquine-bound PfACBP749 and hACBP proteins.

On the Role of Entropy in the Stabilization of α-Helices

Protein folding evolves by exploring the conformational space with a subtle balance between enthalpy and entropy changes which eventually leads to a decrease of free energy upon reaching the folded structure. A complete understanding of this process requires, therefore, a deep insight into both contributions to free energy. In this work, we clarify the role of entropy in favoring the stabilization of folded structures in polyalanine peptides with up to 12 residues. We use a novel method referred to as K2V that allows us to obtain the potential-energy landscapes in terms of residue conformations extracted from molecular dynamics simulations at conformational equilibrium and yields folding thermodynamic magnitudes, which are in agreement with the experimental data available. Our results demonstrate that the folded structures of the larger polyalanine chains are stabilized with respect to the folded structures of the shorter chains by both an energetic contribution coming from the formation of the intramolecular hydrogen bonds and an entropic contribution coming from an increase of the entropy of the solvent with approximate weights of 60 and 40%, respectively, thus unveiling a key piece in the puzzle of protein folding. In addition, the ability of the K2V method to provide the enthalpic and entropic contributions for individual residues along the peptide chain makes it clear that the energetic and entropic stabilizations are basically governed by the nearest neighbor residue conformations, with the folding propensity being rationalized in terms of triads of residues.

Machine-learning iterative calculation of entropy for physical systems

Characterizing the entropy of a system is a crucial, and often computationally costly, step in understanding its thermodynamics. It plays a key role in the study of phase transitions, pattern formation, protein folding, and more. Current methods for entropy estimation suffer from a high computational cost, lack of generality, or inaccuracy and inability to treat complex, strongly interacting systems. In this paper, we present a method, termed machine-learning iterative calculation of entropy (MICE), for calculating the entropy by iteratively dividing the system into smaller subsystems and estimating the mutual information between each pair of halves. The estimation is performed with a recently proposed machine-learning algorithm which works with arbitrary network architectures that can be chosen to fit the structure and symmetries of the system at hand. We show that our method can calculate the entropy of various systems, both thermal and athermal, with state-of-the-art accuracy. Specifically, we study various classical spin systems and identify the jamming point of a bidisperse mixture of soft disks. Finally, we suggest that besides its role in estimating the entropy, the mutual information itself can provide an insightful diagnostic tool in the study of physical systems.

Conformational editing of intrinsically disordered protein by α-methylation

Intrinsically disordered proteins (IDPs) constitute a large portion of “Dark Proteome” – difficult to characterize or yet to be discovered protein structures. Here we used conformationally constrained α-methylated amino acids to bias the conformational ensemble in the free unstructured activation domain of transcriptional coactivator ACTR. Different sites and patterns of substitutions were enabled by chemical protein synthesis and led to distinct populations of α-helices. A specific substitution pattern resulted in a substantially higher binding affinity to nuclear coactivator binding domain (NCBD) of CREB-binding protein, a natural binding partner of ACTR. The first X-ray structure of the modified ACTR domain - NCBD complex visualized a unique conformation of ACTR and confirmed that the key α-methylated amino acids are localized within α-helices in the bound state. This study demonstrates a strategy for characterization of individual conformational states of IDPs.

Control of protein conformation was achieved for intrinsically disordered protein by incorporation of α-methylated amino acids.

Disulfide Reduction Allosterically Destabilizes the β-Ladder Subdomain Assembly within the NS1 Dimer of ZIKV

The Zika virus (ZIKV) was responsible for a recent debilitating epidemic that till date has no cure. A potential way to reduce ZIKV virulence is to limit the action of the nonstructural proteins involved in its viral replication. One such protein, NS1, encoded as a monomer by the viral genome, plays a major role via symmetric oligomerization. We examine the homodimeric structure of the dominant β-ladder segment of NS1 with extensive all atom molecular dynamics. We find it stably bounded by two spatially separated interaction clusters (C1 and C2) with significant differences in the nature of their interactions. Four pairs of distal, intramonomeric disulfide bonds are found to be coupled to the stability, local structure, and wettability of the interfacial region. Symmetric reduction of the intramonomeric disulfides triggers marked dynamical heterogeneity, interfacial wettability, and asymmetric salt-bridging propensity. Harnessing the model-free Lipari-Szabo based formalism for estimation of conformational entropy (S_conf), we find clear signatures of heterogeneity in the monomeric conformational entropies. The observed asymmetry, very small in the unperturbed state, expands significantly in the reduced states. This allosteric effect is most noticeable in the electrostatically bound C2 cluster that underlies the greatest stability in the unperturbed state. Allosteric induction of conformational and thermodynamic asymmetry is expected to affect the pathways leading to symmetric higher-ordered oligomerization, and thereby affect crucial replication pathways.

Why small proteins tend to have high denaturation temperatures

Data indicate that small globular proteins (consisting of less than about 70 residues) tend to have high denaturation temperatures. This finding is analysed by comparing experimental denaturation enthalpy and entropy changes of a selected set of small proteins with values calculated on the basis of average and common properties of globular proteins. The conclusion is that the denaturation entropy change is smaller than expected, leading to an increase in denaturation temperature. The proposed molecular rationalization considers the existence of long-wavelength, low-frequency vibrational modes in the native state of small proteins due to their large surface-to-interior ratio. The effect of decreasing the conformational entropy gain associated with denaturation on thermal stability is directly verified by means of an already devised theoretical model [G. Graziano, Phys. Chem. Chem. Phys. 2010, 12, 14245-14252; 2014, 16, 21755-21767].

Physical Chemistry of the Protein Backbone: Enabling the Mechanisms of Intrinsic Protein Disorder

Over the last two decades it has become clear that well-defined structure is not a requisite for proteins to properly function. Rather, spectra of functionally competent, structurally disordered states have been uncovered requiring canonical paradigms in molecular biology to be revisited or reimagined. It is enticing and oftentimes practical to divide the proteome into structured and unstructured, or disordered, proteins. While function, composition, and structural properties largely differ, these two classes of protein are built upon the same scaffold, namely, the protein backbone. The versatile physicochemical properties of the protein backbone must accommodate structural disorder, order, and transitions between these states. In this review, we survey these properties through the conceptual lenses of solubility and conformational populations and in the context of protein-disorder mediated phenomena (e.g., phase separation, order-disorder transitions, allostery). Particular attention is paid to the results of computational studies, which, through thermodynamic decomposition and dissection of molecular interactions, can provide valuable mechanistic insight and testable hypotheses to guide further solution experiments. Lastly, we discuss changes in the dynamics of side chains and order-disorder transitions of the protein backbone as two modes or realizations of "entropic reservoirs" capable of tuning coupled thermodynamic processes.

Interplay between Conformational Strain and Intramolecular Interaction in Protein Structures: Which of Them Is Evolutionarily Conserved?

By computing strain energies of peptide fragments within protein structures and their intramolecular interaction energies, we attempt to reveal general biophysical trends behind the secondary structure formation in the context of protein evolution. Our "protein basis set" consisted of 1143 representatives of different folds obtained from curated SCOPe database, and for each member of the set, the strain and intramolecular energy was calculated on the "rolling tripeptide" basis, employing the DFT-D3/COSMO-RS method for the former and the QM-calibrated force field method (MM) for the latter. The calculated data, strain and interactions, were correlated with the conservation of amino acid residues in secondary structure elements and also with the level of the residue burial within the protein three-dimensional structure. It allowed us to formulate several observations concerning fundamental differences between two main secondary structure motifs: α-helices and β-strands. We have shown that a strong interaction is one of the determining characteristics of the β-sheet formation, at least at the level of tripeptides (and likely penta- or heptapeptides, too), and that the β-strand is a prevailing secondary structure in the strongly-interacting regions of the protein folds conserved by evolution. On the other hand, low strain was neither proven to be an important physicochemical property conserved by evolution nor does it correlate with the propensity for the α-helix and β-strand. Finally, it has been demonstrated that the strong interaction has a certain level of connection with residue burial; however, we demonstrate that these two characteristics should be rather regarded as two complementary factors. These findings represent an important contribution to understanding protein folding from first principles, which is a complementary approach to ongoing efforts to solve the protein folding problem by knowledge-based approaches and machine-learning.

Entropy Hotspots for the Binding of Intrinsically Disordered Ligands to a Receptor Domain

Proline-rich motifs (PRMs) are widely used for mediating protein-protein interactions with weak binding affinities. Because they are intrinsically disordered when unbound, conformational entropy plays a significant role for the binding. However, residue-level differences of the entropic contribution in the binding of different ligands remain not well understood. We use all-atom molecular dynamics simulation and the maximal information spanning tree formalism to analyze conformational entropy associated with the binding of two PRMs, one from the Abl kinase and the other from the nonstructural protein 1 of the 1918 Spanish influenza A virus, to the N-terminal SH3 (nSH3) domain of the CrkII protein. Side chains of the stably folded nSH3 experience more entropy change upon ligand binding than the backbone, whereas PRMs involve comparable but heterogeneous entropy changes among the backbone and side chains. In nSH3, two conserved nonpolar residues forming contacts with the PRM experience the largest side-chain entropy loss. In contrast, the C-terminal charged residues of PRMs that form polar contacts with nSH3 experience the greatest side-chain entropy loss, although their "fuzzy" nature is attributable to the backbone that remains relatively flexible. Thus, residues that form high-occupancy contacts between nSH3 and PRM do not reciprocally contribute to entropy loss. Furthermore, certain surface residues of nSH3 distal to the interface with PRMs gain entropy, indicating a nonlocal effect of ligand binding. Comparing between the PRMs from cAbl and nonstructural protein 1, the latter involves a larger side-chain entropy loss and forms more contacts with nSH3. Consistent with experiments, this indicates stronger binding of the viral ligand at the expense of losing the flexibility of side chains, whereas the backbone experiences less entropy loss. The entropy "hotspots" as identified in this study will be important for tuning the binding affinity of various ligands to a receptor.

Changes of Conformation in Albumin with Temperature by Molecular Dynamics Simulations

This work presents the analysis of the conformation of albumin in the temperature range of 300K–312K, i.e., in the physiological range. Using molecular dynamics simulations, we calculate values of the backbone and dihedral angles for this molecule. We analyze the global dynamic properties of albumin treated as a chain. In this range of temperature, we study parameters of the molecule and the conformational entropy derived from two angles that reflect global dynamics in the conformational space. A thorough rationalization, based on the scaling theory, for the subdiffusion Flory–De Gennes type exponent of 0.4 unfolds in conjunction with picking up the most appreciable fluctuations of the corresponding statistical-test parameter. These fluctuations coincide adequately with entropy fluctuations, namely the oscillations out of thermodynamic equilibrium. Using Fisher’s test, we investigate the conformational entropy over time and suggest its oscillatory properties in the corresponding time domain. Using the Kruscal–Wallis test, we also analyze differences between the root mean square displacement of a molecule at various temperatures. Here we show that its values in the range of 306K–309K are different than in another temperature. Using the Kullback–Leibler theory, we investigate differences between the distribution of the root mean square displacement for each temperature and time window.

Role of Chemical Dynamics Simulations in Mass Spectrometry Studies of Collision-Induced Dissociation and Collisions of Biological Ions with Organic Surfaces

In this article, a perspective is given of chemical dynamics simulations of collisions of biological ions with surfaces and of collision-induced dissociation (CID) of ions. The simulations provide an atomic-level understanding of the collisions and, overall, are in quite good agreement with experiment. An integral component of ion/surface collisions is energy transfer to the internal degrees of freedom of both the ion and the surface. The simulations reveal how this energy transfer depends on the collision energy, incident angle, biological ion, and surface. With energy transfer to the ion's vibration fragmentation may occur, i.e. surface-induced dissociation (SID), and the simulations discovered a new fragmentation mechanism, called shattering, for which the ion fragments as it collides with the surface. The simulations also provide insight into the atomistic dynamics of soft-landing and reactive-landing of ions on surfaces. The CID simulations compared activation by multiple "soft" collisions, resulting in random excitation, versus high energy single collisions and nonrandom excitation. These two activation methods may result in different fragment ions. Simulations provide fragmentation products in agreement with experiments and, hence, can provide additional information regarding the reaction mechanisms taking place in experiment. Such studies paved the way on using simulations as an independent and predictive tool in increasing fundamental understanding of CID and related processes.

T54R mutation destabilizes the dimer of superoxide dismutase 1T54R by inducing steric clashes at the dimer interface

Mutations cause abnormalities in protein structure, function and oligomerization. Different mutations in the superoxide dismutase 1 (SOD1) protein cause its misfolding, loss of dimerization and aggravate its aggregation in the amyotrophic lateral sclerosis disease. In this study, we report the mechanistic details of how a threonine-to-arginine mutation at the 54^th position (T54R) of SOD1 results in destabilization of the dimer interface of SOD1^T54R. Using computational and experimental methods, we show that the T54R mutation increases fluctuation of the mutation-harboring loop (R54-loop) of SOD1^T54R. Fluctuation of this loop causes steric clashes that involve arginine-54 (R54) and other residues of SOD1^T54R, resulting in loss of inter-subunit contacts at the dimer interface. Since the T54 residue-containing loop is necessary for the dimerization of wild-type SOD1, fluctuation of the R54-loop, steric clashes involving R54 and loss of inter-subunit contacts give rise to the loss of SOD1^T54R dimer stability. This correlates to energetically unfavorable tethering of the monomers of SOD1^T54R. The outcome is gradual splitting of SOD1^T54R dimers into monomers, thereby exposing the previously buried hydrophobic interface residues to the aqueous environment. This event finally leads to aggregation of SOD1^T54R. T54R mutation has no effect in altering the relative positions of copper and zinc ion binding residues of SOD1^T54R. The native SOD1 structure is stable, and there is no destabilizing effect at its dimer interface. Overall, our study reveals the intricate mechanism of T54R mutation-associated destabilization of the dimer of the SOD1^T54R protein.

T54R mutation destabilizes the dimer of SOD1^T54R.

Protein tolerance to random circular permutation correlates with thermostability and local energetics of residue-residue contacts

Adenylate kinase (AK) orthologs with a range of thermostabilities were subjected to random circular permutation, and deep mutational scanning was used to evaluate where new protein termini were nondisruptive to activity. The fraction of circularly permuted variants that retained function in each library correlated with AK thermostability. In addition, analysis of the positional tolerance to new termini, which increase local conformational flexibility, showed that bonds were either functionally sensitive to cleavage across all homologs, differentially sensitive, or uniformly tolerant. The mobile AMP-binding domain, which displays the highest calculated contact energies, presented the greatest tolerance to new termini across all AKs. In contrast, retention of function in the lid and core domains was more dependent upon AK melting temperature. These results show that family permutation profiling identifies primary structure that has been selected by evolution for dynamics that are critical to activity within an enzyme family. These findings also illustrate how deep mutational scanning can be applied to protein homologs in parallel to differentiate how topology, stability, and local energetics govern mutational tolerance.

Surprising Non-Additivity of Methyl Groups in Drug-Kinase Interaction

Drug optimization is guided by biophysical methods with increasing popularity. In the context of lead structure modifications, the introduction of methyl groups is a simple but potentially powerful approach. Hence, it is crucial to systematically investigate the influence of ligand methylation on biophysical characteristics such as thermodynamics. Here, we investigate the influence of ligand methylation in different positions and combinations on the drug-kinase interaction. Binding modes and complex structures were analyzed using protein crystallography. Thermodynamic signatures were measured via isothermal titration calorimetry (ITC). An extensive computational analysis supported the understanding of the underlying mechanisms. We found that not only position but also stereochemistry of the methyl group has an influence on binding potency as well as the thermodynamic signature of ligand binding to the protein. Strikingly, the combination of single methyl groups does not lead to additive effects. In our case, the merger of two methyl groups in one ligand leads to an entirely new alternative ligand binding mode in the protein ligand complex. Moreover, the combination of the two methyl groups also resulted in a nonadditive thermodynamic profile of ligand binding. Molecular dynamics (MD) simulations revealed distinguished characteristic motions of the ligands in solution explaining the pronounced thermodynamic changes. The unexpected drastic change in protein ligand interaction highlights the importance of crystallographic control even for minor modifications such as the introduction of a methyl group. For an in-depth understanding of ligand binding behavior, MD simulations have shown to be a powerful tool.

Effect of sodium thiocyanate and sodium perchlorate on poly(N-isopropylacrylamide) collapse

The T(collapse) of poly(N-isopropylacrylamide), PNIPAM, shows a nonlinear dependence on the concentration of NaSCN or NaClO4; in the case of NaClO4, for example, at very low concentrations of the salt, T(collapse) increases with the concentration, while it has an opposite trend at higher NaClO4 concentrations [J. Am. Chem. Soc., 2005, 127, 14505]. These puzzling experimental data can be rationalized by considering that low charge density and poorly hydrated ions, such as thiocyanate and perchlorate, interact preferentially with the surface of the polymer, and cause an increase of the magnitude of the energetic term that stabilizes swollen conformations at low salt concentrations. However, as both swollen and collapsed PNIPAM conformations are accessible to such ions in view of their large conformational freedom, the difference in the number of ions bound to PNIPAM surface upon collapse changes little on increasing the salt concentration. Thus, the energetic term that favors swollen conformations increases with salt concentration to a lesser extent than the solvent-excluded volume term (linked to the density increase caused by salt addition to water), that favors collapsed conformations, leading to a nonlinear trend of T(collapse).

The Ambivalent Role of Proline Residues in an Intrinsically Disordered Protein: From Disorder Promoters to Compaction Facilitators

Intrinsically disordered proteins (IDPs) carry out many biological functions. They lack a stable three-dimensional structure, but rather adopt many different conformations in dynamic equilibrium. The interplay between local dynamics and global rearrangements is key for their function. In IDPs, proline residues are significantly enriched. Given their unique physicochemical and structural properties, a more detailed understanding of their potential role in stabilizing partially folded states in IDPs is highly desirable. Nuclear magnetic resonance (NMR) spectroscopy, and in particular ¹³C-detected NMR, is especially suitable to address these questions. We applied a ¹³C-detected strategy to study Osteopontin, a largely disordered IDP with a central compact region. By using the exquisite sensitivity and spectral resolution of these novel techniques, we gained unprecedented insight into cis-Pro populations, their local structural dynamics, and their role in mediating long-range contacts. Our findings clearly call for a reassessment of the structural and functional role of proline residues in IDPs. The emerging picture shows that proline residues have ambivalent structural roles. They are not simply disorder promoters but rather can, depending on the primary sequence context, act as nucleation sites for structural compaction in IDPs. These unexpected features provide a versatile mechanistic toolbox to enrich the conformational ensembles of IDPs with specific features for adapting to changing molecular and cellular environments.

Polarity of the ATP binding site of the Na+,K+-ATPase, gastric H+,K+-ATPase and sarcoplasmic reticulum Ca2+-ATPase

A fluorescence ratiometric method utilizing the probe eosin Y is presented for estimating the ATP binding site polarity of P-type ATPases in different conformational states. The method has been calibrated by measurements in a series of alcohols and tested using complexation of eosin Y with methyl-β-cyclodextrin. The results obtained with the Na⁺,K⁺-, H⁺,K⁺- and sarcoplasmic reticulum Ca²⁺-ATPases indicate that the ATP binding site, to which eosin is known to bind, is significantly more polar in the case of the Na⁺,K⁺- and H⁺,K⁺-ATPases compared to the Ca²⁺-ATPase. This result was found to be consistent with docking calculations of eosin with the E2 conformational state of the Na⁺,K⁺-ATPase and the Ca²⁺-ATPase. Fluorescence experiments showed that eosin binds significantly more strongly to the E1 conformation of the Na⁺,K⁺-ATPase than the E2 conformation, but in the case of the Ca²⁺-ATPase both fluorescence experiments and docking calculations showed no significant difference in binding affinity between the two conformations. This result could be due to the fact that, in contrast to the Na⁺,K⁺- and H⁺,K⁺-ATPases, the E2-E1 transition of the Ca²⁺-ATPase does not involve the movement of a lysine-rich N-terminal tail which may affect the overall enzyme conformation. Consistent with this hypothesis, the eosin affinity of the E1 conformation of the Na⁺,K⁺-ATPase was significantly reduced after N-terminal truncation. It is suggested that changes in conformational entropy of the N-terminal tail of the Na⁺, K⁺- and the H⁺,K⁺-ATPases during the E2-E1 transition could affect the thermodynamic stability of the E1 conformation and hence its ATP binding affinity.

Thermodynamics of Conformational Transitions in a Disordered Protein Backbone Model

Conformational entropy is expected to contribute significantly to the thermodynamics of structural transitions in intrinsically disordered proteins or regions in response to protein/ligand binding, posttranslational modifications, and environmental changes. We calculated the backbone (dihedral) conformational entropy of oligoglycine (Gly_N), a protein backbone mimic and model intrinsically disordered region, as a function of chain length (N=3, 4, 5, 10, and 15) from simulations using three different approaches. The backbone conformational entropy scales linearly with chain length with a slope consistent with the entropy of folding of well-structured proteins. The entropic contributions of second-order dihedral correlations are predominantly through intraresidue ϕ-ψ pairs, suggesting that oligoglycine may be thermodynamically modeled as a system of independent glycine residues. We find the backbone conformational entropy to be largely independent of global structural parameters, like the end-to-end distance and radius of gyration. We introduce a framework referred to herein as "ensemble confinement" to estimate the loss (gain) of conformational free energy and its entropic component when individual residues are constrained to (released from) particular regions of the ϕ-ψ map. Quantitatively, we show that our protein backbone model resists ordering/folding with a significant, unfavorable ensemble confinement free energy because of the loss of a substantial portion of the absolute backbone entropy. Proteins can couple this free-energy reservoir to distal binding events as a regulatory mechanism to promote or suppress binding.

Switchable and Obedient Interfacial Properties That Grant New Biomedical Applications

Toward imitating the natural smartness and responsivity of biological systems, surface interfacial properties are considered to be responsive and tunable if they show a reactive behavior to an environmental stimulus. This is still quite different from many contemporary biomaterials that lack responsiveness to interact with blood and different body tissues in a physiological manner. Meanwhile it is possible to even go one step further from responsiveness to dual-mode switchability and explore "switchable" or "reversible" responses of synthetic materials. We understand "switchable biomaterials" as materials undergoing a stepwise, structural transformation coupled with considerable changes of interfacial and other surface properties as a response to a stimulus. Therewith, a survey on stimuli-induced dynamic changes of charge, wettability, stiffness, topography, porosity, and thickness/swelling is presented here, as potentially powerful new technologies especially for future biomaterial development. Since living cells constantly sense their environment through a variety of surface receptors and other mechanisms, these obedient interfacial properties were particularly discussed regarding their advantageous multifunctionality for protein adsorption and cell adhesion signaling, which may alter in time and with environmental conditions.

Factors Stabilizing β-Sheets in Protein Structures from a Quantum-Chemical Perspective

Protein folds are determined by the interplay between various (de)stabilizing forces, which can be broadly divided into a local strain of the protein chain and intramolecular interactions. In contrast to the α-helix, the β-sheet secondary protein structure is significantly stabilized by long-range interactions between the individual β-strands. It has been observed that quite diverse amino acid sequences can form a very similar small β-sheet fold, such as in the three-β-strand WW domain. Employing "calibrated" quantum-chemical methods, we show herein on two sequentially diverse examples of the WW domain that the internal strain energy is higher in the β-strands and lower in the loops, while the interaction energy has an opposite trend. Low strain energy computed for peptide sequences in the loop 1 correlates with its postulated early formation in the folding process. The relatively high strain energy within the β-strands (up to 8 kcal mol^-1 per amino acid residue) is compensated by even higher intramolecular interaction energy (up to 15 kcal mol^-1 per residue). It is shown in a quantitative way that the most conserved residues across the structural family of WW domains have the highest contributions to the intramolecular interaction energy. On the other hand, the residues in the regions with the lowest strain are not conserved. We conclude that the internal interaction energy is the physical quantity tuned by evolution to define the β-sheet protein fold.

GTP Hydrolysis Without an Active Site Base: A Unifying Mechanism for Ras and Related GTPases

GTP hydrolysis is a biologically crucial reaction, being involved in regulating almost all cellular processes. As a result, the enzymes that catalyze this reaction are among the most important drug targets. Despite their vital importance and decades of substantial research effort, the fundamental mechanism of enzyme-catalyzed GTP hydrolysis by GTPases remains highly controversial. Specifically, how do these regulatory proteins hydrolyze GTP without an obvious general base in the active site to activate the water molecule for nucleophilic attack? To answer this question, we perform empirical valence bond simulations of GTPase-catalyzed GTP hydrolysis, comparing solvent- and substrate-assisted pathways in three distinct GTPases, Ras, Rab, and the G_αi subunit of a heterotrimeric G-protein, both in the presence and in the absence of the corresponding GTPase activating proteins. Our results demonstrate that a general base is not needed in the active site, as the preferred mechanism for GTP hydrolysis is a conserved solvent-assisted pathway. This pathway involves the rate-limiting nucleophilic attack of a water molecule, leading to a short-lived intermediate that tautomerizes to form H₂PO₄^- and GDP as the final products. Our fundamental biochemical insight into the enzymatic regulation of GTP hydrolysis not only resolves a decades-old mechanistic controversy but also has high relevance for drug discovery efforts. That is, revisiting the role of oncogenic mutants with respect to our mechanistic findings would pave the way for a new starting point to discover drugs for (so far) "undruggable" GTPases like Ras.

A protein interaction free energy model based on amino acid residue contributions: Assessment of point mutation stability of T4 lysozyme

Here we present a model to estimate the interaction free energy contribution of each amino acid residue of a given protein. Protein interaction energy is described in terms of per-residue interaction factors, μ. Multibody interactions are implicitly captured in μ through the combination of amino acid terms (γ) guided by local conformation indices (σ). The model enables construction of an interaction factor heat map for a protein in a given fold, allows prima facie assessment of the degree of residue-residue interaction, and facilitates a qualitative and quantitative evaluation of protein association properties. The model was used to compute thermal stability of T4 bacteriophage lysozyme mutants across seven sites. Qualitative assessment of mutational effects provides a straightforward rationale regarding whether a particular site primarily perturbs native or non-native states, or both. The presented model was found to be in good agreement with experimental mutational data (R 2 = 0.73) and suggests an approach by which to convert structure space into energy space.

Mechanism of protein-RNA recognition: analysis based on the statistical mechanics of hydration

We investigate the RBD1-r(GUAGU) binding as a case study using all-atom models for the biomolecules, molecular models for water, and the currently most reliable statistical-mechanical method. RBD1 is one of the RNA-binding domains of mammalian Musashi1 (Msi1), and r(GUAGU) contains the minimum recognition sequence for Msi1, r(GUAG). We show that the binding is driven by a large gain of configurational entropy of water in the entire system. It is larger than the sum of conformational-entropy losses for RBD1 and r(GUAGU). The decrease in RBD1-r(GUAGU) interaction energy upon binding is largely cancelled out by the increase in the sum of RBD1-water, r(GUAGU)-water, and water-water interaction energies. We refer to this increase as "energetic dehydration". The decrease is larger than the increase for the van der Waals component, whereas the opposite is true for the electrostatic component. We give a novel reason for the empirically known fact that protein residues possessing side chains with positive charges and with flat moieties frequently appear within protein-RNA binding interfaces. A physical picture of the general protein-RNA binding mechanism is then presented. To achieve a sufficiently large water-entropy gain, shape complementarity at the atomic level needs to be constructed by utilizing the stacking and sandwiching of flat moieties (aromatic rings of the protein and nucleobases of RNA) as fundamental motifs. To compensate for electrostatic energetic dehydration, charge complementarity becomes crucial within the binding interface. We argue the reason why the RNA recognition motif (RRM) is the most ubiquitous RNA binding domain.