Insulin Dissociates by Diverse Mechanisms of Coupled Unfolding and Unbinding

Ligand Gaussian Accelerated Molecular Dynamics 3 (LiGaMD3): Improved Calculations of Binding Thermodynamics and Kinetics of Both Small Molecules and Flexible Peptides

Binding thermodynamics and kinetics play critical roles in drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics of small molecules and flexible peptides using conventional molecular dynamics (cMD), due to limited simulation time scales. Based on our previously developed ligand Gaussian accelerated molecular dynamics (LiGaMD) method, we present a new approach, termed "LiGaMD3″, in which we introduce triple boosts into three individual energy terms that play important roles in small-molecule/peptide dissociation, rebinding, and system conformational changes to improve the sampling efficiency of small-molecule/peptide interactions with target proteins. To validate the performance of LiGaMD3, MDM2 bound by a small molecule (Nutlin 3) and two highly flexible peptides (PMI and P53) were chosen as the model systems. LiGaMD3 could efficiently capture repetitive small-molecule/peptide dissociation and binding events within 2 μs simulations. The predicted binding kinetic constant rates and free energies from LiGaMD3 were in agreement with the available experimental values and previous simulation results. Therefore, LiGaMD3 provides a more general and efficient approach to capture dissociation and binding of both small-molecule ligands and flexible peptides, allowing for accurate prediction of their binding thermodynamics and kinetics.

Unnatural Amino Acids for Biological Spectroscopy and Microscopy

Due to advances in methods for site-specific incorporation of unnatural amino acids (UAAs) into proteins, a large number of UAAs with tailored chemical and/or physical properties have been developed and used in a wide array of biological applications. In particular, UAAs with specific spectroscopic characteristics can be used as external reporters to produce additional signals, hence increasing the information content obtainable in protein spectroscopic and/or imaging measurements. In this Review, we summarize the progress in the past two decades in the development of such UAAs and their applications in biological spectroscopy and microscopy, with a focus on UAAs that can be used as site-specific vibrational, fluorescence, electron paramagnetic resonance (EPR), or nuclear magnetic resonance (NMR) probes. Wherever applicable, we also discuss future directions.

Ligand Gaussian accelerated Molecular Dynamics 3 (LiGaMD3): Improved Calculations of Binding Thermodynamics and Kinetics of Both Small Molecules and Flexible Peptides

Binding thermodynamics and kinetics play critical roles in drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics of small molecules and flexible peptides using conventional Molecular Dynamics (cMD), due to limited simulation timescales. Based on our previously developed Ligand Gaussian accelerated Molecular Dynamics (LiGaMD) method, we present a new approach, termed "LiGaMD3", in which we introduce triple boosts into three individual energy terms that play important roles in small-molecule/peptide dissociation, rebinding and system conformational changes to improve the sampling efficiency of small-molecule/peptide interactions with target proteins. To validate the performance of LiGaMD3, MDM2 bound by a small molecule (Nutlin 3) and two highly flexible peptides (PMI and P53) were chosen as model systems. LiGaMD3 could efficiently capture repetitive small-molecule/peptide dissociation and binding events within 2 microsecond simulations. The predicted binding kinetic constant rates and free energies from LiGaMD3 agreed with available experimental values and previous simulation results. Therefore, LiGaMD3 provides a more general and efficient approach to capture dissociation and binding of both small-molecule ligand and flexible peptides, allowing for accurate prediction of their binding thermodynamics and kinetics.

Exploring Kinase Asp-Phe-Gly (DFG) Loop Conformational Stability with AlphaFold2-RAVE

Kinases compose one of the largest fractions of the human proteome, and their misfunction is implicated in many diseases, in particular, cancers. The ubiquitousness and structural similarities of kinases make specific and effective drug design difficult. In particular, conformational variability due to the evolutionarily conserved Asp-Phe-Gly (DFG) motif adopting in and out conformations and the relative stabilities thereof are key in structure-based drug design for ATP competitive drugs. These relative conformational stabilities are extremely sensitive to small changes in sequence and provide an important problem for sampling method development. Since the invention of AlphaFold2, the world of structure-based drug design has noticeably changed. In spite of it being limited to crystal-like structure prediction, several methods have also leveraged its underlying architecture to improve dynamics and enhanced sampling of conformational ensembles, including AlphaFold2-RAVE. Here, we extend AlphaFold2-RAVE and apply it to a set of kinases: the wild type DDR1 sequence and three mutants with single point mutations that are known to behave drastically differently. We show that AlphaFold2-RAVE is able to efficiently recover the changes in relative stability using transferable learned order parameters and potentials, thereby supplementing AlphaFold2 as a tool for exploration of Boltzmann-weighted protein conformations (Meller, A.; Bhakat, S.; Solieva, S.; Bowman, G. R. Accelerating Cryptic Pocket Discovery Using AlphaFold. J. Chem. Theory Comput. 2023, 19, 4355-4363).

Using 2D-IR Spectroscopy to Measure the Structure, Dynamics, and Intermolecular Interactions of Proteins in H2O

Infrared (IR) spectroscopy probes molecular structure at the level of the chemical bond or functional group. In the case of proteins, the most informative band in the IR spectrum is the amide I band, which arises predominantly from the C═O stretching vibration of the peptide link. The folding of proteins into secondary and tertiary structures leads to vibrational coupling between peptide units, generating specific amide I spectral signatures that provide a fingerprint of the macromolecular conformation. Ultrafast two-dimensional IR (2D-IR) spectroscopy allows the amide I band of a protein to be spread over a second frequency dimension in a way that mirrors 2D-NMR methods. This means that amide I 2D-IR spectroscopy produces a spectral map that is exquisitely sensitive to protein structure and dynamics and so provides detailed insights that cannot be matched by IR absorption spectroscopy. As a result, 2D-IR spectroscopy has emerged as a powerful tool for probing protein structure and dynamics over a broad range of time and length scales in the solution phase at room temperature. However, the protein amide I band coincides with an IR absorption from the bending vibration of water (δHOH), the natural biological solvent. To circumvent this problem, protein IR studies are routinely performed in D2O solutions because H/D substitution shifts the solvent bending mode (δDOD) to a lower frequency, revealing the amide I band. While effective, this method raises fundamental questions regarding the impact of the change in solvent mass on the structural or solvation dynamics of the protein and the removal of the energetic resonance between solvent and solute.In this Account, a series of studies applying 2D-IR to study the spectroscopy and dynamics of proteins in H2O-rich solvents is reviewed. A comparison of IR absorption spectroscopy and 2D-IR spectroscopy of protein-containing fluids is used to demonstrate the basis of the approach before a series of applications is presented. These range from measurements of fundamental protein biophysics to recent applications of machine learning to gain insight into protein-drug binding in complex mixtures. An outlook is presented, considering the potential for 2D-IR measurements to contribute to our understanding of protein behavior under near-physiological conditions, along with an evaluation of the obstacles that still need to be overcome.

Exploring kinase DFG loop conformational stability with AlphaFold2-RAVE

Kinases compose one of the largest fractions of the human proteome, and their misfunction is implicated in many diseases, in particular cancers. The ubiquitousness and structural similarities of kinases makes specific and effective drug design difficult. In particular, conformational variability due to the evolutionarily conserved DFG motif adopting in and out conformations and the relative stabilities thereof are key in structure-based drug design for ATP competitive drugs. These relative conformational stabilities are extremely sensitive to small changes in sequence, and provide an important problem for sampling method development. Since the invention of AlphaFold2, the world of structure-based drug design has noticably changed. In spite of it being limited to crystal-like structure prediction, several methods have also leveraged its underlying architecture to improve dynamics and enhanced sampling of conformational ensembles, including AlphaFold2-RAVE. Here, we extend AlphaFold2-RAVE and apply it to a set of kinases: the wild type DDR1 sequence and three mutants with single point mutations that are known to behave drastically differently. We show that AlphaFold2-RAVE is able to efficiently recover the changes in relative stability using transferable learnt order parameters and potentials, thereby supplementing AlphaFold2 as a tool for exploration of Boltzmann-weighted protein conformations.

Understanding the sources of error in MBAR through asymptotic analysis

Many sampling strategies commonly used in molecular dynamics, such as umbrella sampling and alchemical free energy methods, involve sampling from multiple states. The Multistate Bennett Acceptance Ratio (MBAR) formalism is a widely used way of recombining the resulting data. However, the error of the MBAR estimator is not well-understood: previous error analyses of MBAR assumed independent samples. In this work, we derive a central limit theorem for MBAR estimates in the presence of correlated data, further justifying the use of MBAR in practical applications. Moreover, our central limit theorem yields an estimate of the error that can be decomposed into contributions from the individual Markov chains used to sample the states. This gives additional insight into how sampling in each state affects the overall error. We demonstrate our error estimator on an umbrella sampling calculation of the free energy of isomerization of the alanine dipeptide and an alchemical calculation of the hydration free energy of methane. Our numerical results demonstrate that the time required for the Markov chain to decorrelate in individual states can contribute considerably to the total MBAR error, highlighting the importance of accurately addressing the effect of sample correlation.

Predicting Biomolecular Binding Kinetics: A Review

Biomolecular binding kinetics including the association (k_on) and dissociation (k_off) rates are critical parameters for therapeutic design of small-molecule drugs, peptides, and antibodies. Notably, the drug molecule residence time or dissociation rate has been shown to correlate with their efficacies better than binding affinities. A wide range of modeling approaches including quantitative structure-kinetic relationship models, Molecular Dynamics simulations, enhanced sampling, and Machine Learning has been developed to explore biomolecular binding and dissociation mechanisms and predict binding kinetic rates. Here, we review recent advances in computational modeling of biomolecular binding kinetics, with an outlook for future improvements.

Ligand Gaussian Accelerated Molecular Dynamics 2 (LiGaMD2): Improved Calculations of Ligand Binding Thermodynamics and Kinetics with Closed Protein Pocket

Ligand binding thermodynamics and kinetics are critical parameters for drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics from molecular simulations due to limited simulation timescales. Protein dynamics, especially in the ligand binding pocket, often plays an important role in ligand binding. Based on our previously developed Ligand Gaussian accelerated molecular dynamics (LiGaMD), here we present LiGaMD2 in which a selective boost potential was applied to both the ligand and protein residues in the binding pocket to improve sampling of ligand binding and dissociation. To validate the performance of LiGaMD2, the T4 lysozyme (T4L) mutants with open and closed pockets bound by different ligands were chosen as model systems. LiGaMD2 could efficiently capture repetitive ligand dissociation and binding within microsecond simulations of all T4L systems. The obtained ligand binding kinetic rates and free energies agreed well with available experimental values and previous modeling results. Therefore, LiGaMD2 provides an improved approach to sample opening of closed protein pockets for ligand dissociation and binding, thereby allowing for efficient calculations of ligand binding thermodynamics and kinetics.

Glycation restrains open-closed conformation of Insulin

In hyperglycemic conditions, the level of reactive dicarbonyl metabolites concentration is found to be high, which plays a significant role in protein glycation. Despite decades of research, the effect of methylglyoxal on the structure and function of insulin is still unknown. Through a shift in conformation at the B-chain C-terminal (BT-CT) hinge from an "open" to a "wide-open" conformation, insulin binds to the receptor and activates the signal cascade. Insulin resistance, which is the main sign of Type 2 Diabetes, can be caused by a lack of insulin signaling. Methylglyoxal site-specific glycation in residue R22 at B chain forms AGE product Methylglyoxal-hydroimidazolone (MGH1) in insulin. In this work, we present molecular dynamics study of this glycated insulin R22MGH1, which revealed new insights into the conformational and structural changes. We find the following key results: 1) B-chain in insulin undergoes a closed conformational change upon glycation. 2) Glycated insulin shows secondary structure alteration. 3) Glycated insulin retains its closed shape due to an unusually strong hydrophobic contact between B-chain residues. 4) Wide open native conformation of insulin allows the B chain helix to be surrounded by more water molecules compared to the closed conformation of glycated insulin. The closed conformation of glycated insulin impairs its binding to insulin receptor (IR).

Identifying signatures of proteolytic stability and monomeric propensity in O-glycosylated insulin using molecular simulation

Insulin has been commonly adopted as a peptide drug to treat diabetes as it facilitates the uptake of glucose from the blood. The development of oral insulin remains elusive over decades owing to its susceptibility to the enzymes in the gastrointestinal tract and poor permeability through the intestinal epithelium upon dimerization. Recent experimental studies have revealed that certain O-linked glycosylation patterns could enhance insulin's proteolytic stability and reduce its dimerization propensity, but understanding such phenomena at the molecular level is still difficult. To address this challenge, we proposed and tested several structural determinants that could potentially influence insulin's proteolytic stability and dimerization propensity. We used these metrics to assess the properties of interest from [Formula: see text] aggregate molecular dynamics of each of 12 targeted insulin glyco-variants from multiple wild-type crystal structures. We found that glycan-involved hydrogen bonds and glycan-dimer occlusion were useful metrics predicting the proteolytic stability and dimerization propensity of insulin, respectively, as was in part the solvent-accessible surface area of proteolytic sites. However, other plausible metrics were not generally predictive. This work helps better explain how O-linked glycosylation influences the proteolytic stability and monomeric propensity of insulin, illuminating a path towards rational molecular design of insulin glycoforms.

Non-Markovian rate theory on a multidimensional reaction surface: Complex interplay between enhanced configuration space and memory

A theory of barrier crossing rate on a multidimensional reaction energy surface is presented. The theory is a generalization of the earlier theoretical schemes to higher dimensions, with the inclusion of non-Markovian friction along both the reactive and the nonreactive coordinates. The theory additionally includes the bilinear coupling between the reactive and the nonreactive modes at the Hamiltonian level. Under suitable conditions, we recover the rate expressions of Langer and Hynes and establish a connection with the rate treatment of Pollak. Within the phenomenology of generalized Langevin equation description, our formulation provides an improvement over the existing ones because we explicitly include both the non-Markovian effects along the reaction coordinate and the bilinear coupling at the Hamiltonian level. At intermediate-to-large friction, an increase in dimensionality by itself tends to reduce the rate, while the inclusion of the memory effects increases the rate. The theory predicts an increase in rate when off-diagonal friction terms are included. We present a model calculation to study isomerization of a stilbene-like molecule using the prescription of Hochstrasser and co-workers on a two-dimensional reaction energy surface, employing Zwanzig–Bixon hydrodynamic theory of frequency-dependent friction. The calculated rate shows a departure from the predictions of Langer’s theory and also from the two-dimensional transition state theory.

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.

Protein-Protein Interaction-Gaussian Accelerated Molecular Dynamics (PPI-GaMD): Characterization of Protein Binding Thermodynamics and Kinetics

Protein-protein interactions (PPIs) play key roles in many fundamental biological processes such as cellular signaling and immune responses. However, it has proven challenging to simulate repetitive protein association and dissociation in order to calculate binding free energies and kinetics of PPIs due to long biological timescales and complex protein dynamics. To address this challenge, we have developed a new computational approach to all-atom simulations of PPIs based on a robust Gaussian accelerated molecular dynamics (GaMD) technique. The method, termed "PPI-GaMD", selectively boosts interaction potential energy between protein partners to facilitate their slow dissociation. Meanwhile, another boost potential is applied to the remaining potential energy of the entire system to effectively model the protein's flexibility and rebinding. PPI-GaMD has been demonstrated on a model system of the ribonuclease barnase interactions with its inhibitor barstar. Six independent 2 μs PPI-GaMD simulations have captured repetitive barstar dissociation and rebinding events, which enable calculations of the protein binding thermodynamics and kinetics simultaneously. The calculated binding free energies and kinetic rate constants agree well with the experimental data. Furthermore, PPI-GaMD simulations have provided mechanistic insights into barstar binding to barnase, which involves long-range electrostatic interactions and multiple binding pathways, being consistent with previous experimental and computational findings of this model system. In summary, PPI-GaMD provides a highly efficient and easy-to-use approach for binding free energy and kinetics calculations of PPIs.

Challenges and frontiers of computational modelling of biomolecular recognition

Biomolecular recognition including binding of small molecules, peptides and proteins to their target receptors plays a key role in cellular function and has been targeted for therapeutic drug design. However, the high flexibility of biomolecules and slow binding and dissociation processes have presented challenges for computational modelling. Here, we review the challenges and computational approaches developed to characterise biomolecular binding, including molecular docking, molecular dynamics simulations (especially enhanced sampling) and machine learning. Further improvements are still needed in order to accurately and efficiently characterise binding structures, mechanisms, thermodynamics and kinetics of biomolecules in the future.

Progress in Simulation Studies of Insulin Structure and Function

Insulin is a peptide hormone known for chiefly regulating glucose level in blood among several other metabolic processes. Insulin remains the most effective drug for treating diabetes mellitus. Insulin is synthesized in the pancreatic β-cells where it exists in a compact hexameric architecture although its biologically active form is monomeric. Insulin exhibits a sequence of conformational variations during the transition from the hexamer state to its biologically-active monomer state. The structural transitions and the mechanism of action of insulin have been investigated using several experimental and computational methods. This review primarily highlights the contributions of molecular dynamics (MD) simulations in elucidating the atomic-level details of conformational dynamics in insulin, where the structure of the hormone has been probed as a monomer, dimer, and hexamer. The effect of solvent, pH, temperature, and pressure have been probed at the microscopic scale. Given the focus of this review on the structure of the hormone, simulation studies involving interactions between the hormone and its receptor are only briefly highlighted, and studies on other related peptides (e.g., insulin-like growth factors) are not discussed. However, the review highlights conformational dynamics underlying the activities of reported insulin analogs and mimetics. The future prospects for computational methods in developing promising synthetic insulin analogs are also briefly highlighted.

Current State and Principles of Basal Insulin Therapy in Type 2 Diabetes

Treatment with basal insulins is a fundamental part of management in many patients with type 2 diabetes mellitus. Multiple management schemes may be indicated in these individuals, for example, the use of oral antihyperglycemic agents with basal insulins (basal-supported oral therapy) or the combinations of basal insulins with glucagon-like peptide-1 receptor agonists; each of these strategies makes it easier to achieve glycemic control goals. A basic knowledge of the physiology, pharmacodynamic and pharmacokinetic aspects of the different basal insulins is essential to achieve treatment goals and compliance. This review addresses the principles of management with basal insulins.

Resolving Dynamics in the Ensemble: Finding Paths through Intermediate States and Disordered Protein Structures

Proteins have been found to inhabit a diverse set of three-dimensional structures. The dynamics that govern protein interconversion between structures happen over a wide range of time scales─picoseconds to seconds. Our understanding of protein functions and dynamics is largely reliant upon our ability to elucidate physically populated structures. From an experimental structural characterization perspective, we are often limited to measuring the ensemble-averaged structure both in the steady-state and time-resolved regimes. Generating kinetic models and understanding protein structure-function relationships require atomistic knowledge of the populated states in the ensemble. In this Perspective, we present ensemble refinement methodologies that integrate time-resolved experimental signals with molecular dynamics models. We first discuss integration of experimental structural restraints to molecular models in disordered protein systems that adhere to the principle of maximum entropy for creating a complete set of ensemble structures. We then propose strategies to find kinetic pathways between the refined structures, using time-resolved inputs to guide molecular dynamics trajectories and the use of inference to generate tailored stimuli to prepare a desired ensemble of protein states.

Structural Stability of Insulin Oligomers and Protein Association-Dissociation Processes: Free Energy Landscape and Universal Role of Water

Association and dissociation of proteins are important biochemical events. In this Feature Article, we analyze the available studies of these processes for insulin oligomers in aqueous solution. We focus on the solvation of the insulin monomer in water, stability and dissociation of its dimer, and structural integrity of the hexamer. The intricate role of water in solvation of the dimer- and hexamer-forming surfaces, in long-range interactions between the monomers and the stability of the oligomers, is discussed. Ten water molecules inside the central cavity stabilize the structure of the insulin hexamer. We discuss how different order parameters can be used to understand the dissociation of the insulin dimer. The calculation of the rate using a recently computed multidimensional free energy provides considerable insight into the interplay between protein and water dynamics.

Kinetics of Phenol Escape from the Insulin R6 Hexamer

Therapeutic preparations of insulin often contain phenolic molecules, which can impact both pharmacokinetics and shelf life. Thus, understanding the interactions of insulin and phenolic molecules can aid in designing improved therapeutics. In this study, we use molecular dynamics to investigate phenol release from the insulin hexamer. Leveraging recent advances in methods for analyzing molecular dynamics data, we expand on existing simulation studies to identify and quantitatively characterize six phenol binding/unbinding pathways for wild-type and A10 Ile → Val and B13 Glu → Gln mutant insulins. A number of these pathways involve large-scale opening of the primary escape channel, suggesting that the hexamer is much more dynamic than previously appreciated. We show that phenol unbinding is a multipathway process, with no single pathway representing more than 50% of the reactive current and all pathways representing at least 10%. We use the mutant simulations to show how the contributions of specific pathways can be rationally manipulated. Predicting the net effects of mutations is more challenging because the kinetics depend on all of the pathways, demanding quantitatively accurate simulations and experiments.

Structural Ensemble of the Insulin Monomer

Experimental evidence suggests that monomeric insulin exhibits significant conformational heterogeneity, and modifications of apparently disordered regions affect both biological activity and the longevity of pharmaceutical formulations, presumably through receptor binding and fibrillation/degradation, respectively. However, a microscopic understanding of conformational heterogeneity has been lacking. Here, we integrate all-atom molecular dynamics simulations with an analysis pipeline to investigate the structural ensemble of human insulin monomers. We find that 60% of the structures present at least one of the following elements of disorder: melting of the A-chain N-terminal helix, detachment of the B-chain N-terminus, and detachment of the B-chain C-terminus. We also observe partial melting and extension of the B-chain helix and significant conformational heterogeneity in the region containing the B-chain β-turn. We then estimate hydrogen-exchange protection factors for the sampled ensemble and find them in line with experimental results for KP-insulin, although the simulations underestimate the importance of unfolded states. Our results help explain the ready exchange of specific amide sites that appear to be protected in crystal structures. Finally, we discuss the implications for insulin function and stability.

Rate of Insulin Dimer Dissociation: Interplay between Memory Effects and Higher Dimensionality

We calculate the rate of dissociation of an insulin dimer into two monomers in water. The rate of this complex reaction is determined by multiple factors that are elucidated. By employing advanced sampling techniques, we first obtain the reaction free energy surface for the dimer dissociation as a function of two order parameters, namely, the distance between the center-of-mass of two monomers (R) and the number of cross-contacts (Q) among the backbone C_α atoms of two monomers. We then construct an orthogonal 2D reaction energy surface by introducing the reaction coordinate X to denote the minimum energy pathway and a conjugate coordinate Y that spans the orthogonal direction. The free energy landscape is rugged with multiple maxima and minima. We calculate the rate by employing not only the non-Markovian multidimensional rate theory but also several other theoretical approaches. The necessary reaction frequencies and the frictions are calculated from the time correlation function formalism. Our best estimate of the rate is 0.4 μs^-1. Our study reveals interesting opposite influences of dimensionality and memory in determining the rate constant of the reaction. We gain interesting insights into the dimer dissociation process by looking directly at the trajectories obtained from molecular dynamics simulation.

Dissociation of hydrogen peroxide in water and methanol through a biased molecular dynamics investigation

The two dissociation channels of HOOH, namely, HOOH and HOOH, in water and methanol are investigated using umbrella-sampling ab initio molecular dynamics. Our potential of mean force calculations reveals the HOOH dissociation to be more favorable in methanol with a free energy barrier of 7.56 kcal/mol, while the HOOH dissociation possesses a free energy barrier of 11.46 kcal/mol. In water, the HOOH dissociation channel is more favorable (8.25 kcal/mol), while the HOOH dissociation process requires a higher free energy (11.28 kcal/mol). Such reaction favorability can be explained by inspecting the formation of secondary radical species during the course of multiple hydrogen donating-accepting processes in each reaction channel. The radical species, that is, H₃ O^• (observed in water) and CH₃ OH₂ ^• (observed in methanol), are the first subordinate species upon the HOOH dissociation. For the HOOH dissociation channel in methanol, the secondary species such as water and formaldehyde can be observed, while the re-generation of HOOH in water can be spotted.

Unfolding of Dynamical Events in the Early Stage of Insulin Dimer Dissociation

The dissociation of an insulin dimer is an important biochemical event that could also serve as a prototype of dissociations in similar biomolecular assemblies. We use a recently developed multidimensional free energy landscape for insulin dimer dissociation to unearth the microscopic and mechanistic aspects of the initial stages of the process that could hold the key to understanding the stability and the rate. The following sequence of events occurs in the initial stages: (i) The backbone hydrogen bonds break partially at the antiparallel β-sheet junction, (ii) the two α-helices (chain B) move away from each other while several residues (chain A) move closer, and (iii) a flow of adjacent water molecules occurs into the junction region. Interestingly, the intermonomeric center-to-center distance does not increase, but the number of native contacts exhibits a sharp decrease. Subsequent steps involve further disengagement of hydrophobic groups. This process is slow because of an entropic bottleneck created by the existence of the large configuration space available in the native state (NS), which is inhabited by low-frequency conformational fluctuations. We carry out a density-of-states analyses in the dimer NS to unearth distinctive features not present in the monomers. These low-frequency modes are also responsible for a large entropic stabilization of the NS. Hydrophobic disengagement in the early stage leads to the formation of a twisted intermediate state which itself is a metastable minimum (IS-1). The subsequent progress leads to another dimeric complex (IS-2), which is on the dissociative pathway and characterized by a further decrease in the native contacts. The dissociation process provides insights into the workings of a biomolecular assembly.

Computational IR Spectroscopy of Insulin Dimer Structure and Conformational Heterogeneity

We have investigated the structure and conformational dynamics of insulin dimer using a Markov state model (MSM) built from extensive unbiased atomistic molecular dynamics simulations and performed infrared spectral simulations of the insulin MSM to describe how structural variation within the dimer can be experimentally resolved. Our model reveals two significant conformations to the dimer: a dominant native state consistent with other experimental structures of the dimer and a twisted state with a structure that appears to reflect a ∼55° clockwise rotation of the native dimer interface. The twisted state primarily influences the contacts involving the C-terminus of insulin's B chain, shifting the registry of its intermolecular hydrogen bonds and reorganizing its side-chain packing. The MSM kinetics predict that these configurations exchange on a 14 μs time scale, largely passing through two Markov states with a solvated dimer interface. Computational amide I spectroscopy of site-specifically ¹³C¹⁸O labeled amides indicates that the native and twisted conformation can be distinguished through a series of single and dual labels involving the B24F, B25F, and B26Y residues. Additional structural heterogeneity and disorder is observed within the native and twisted states, and amide I spectroscopy can also be used to gain insight into this variation. This study will provide important interpretive tools for IR spectroscopic investigations of insulin structure and transient IR kinetics experiments studying the conformational dynamics of insulin dimer.

Site-selective dynamics of azidolysozyme

The spectroscopic response of and structural dynamics around all azido-modified alanine residues (AlaN₃) in lysozyme are characterized. It is found that AlaN₃ is a positionally sensitive probe for the local dynamics, covering a frequency range of ∼15 cm^-1 for the center frequency of the line shape. This is consistent with findings from selective replacements of amino acids in PDZ2, which reported a frequency span of ∼10 cm^-1 for replacements of Val, Ala, or Glu by azidohomoalanine. For the frequency fluctuation correlation functions, the long-time decay constants τ₂ range from ∼1 to ∼10 ps, which compares with experimentally measured correlation times of 3 ps. Attaching azide to alanine residues can yield dynamics that decays to zero on the few ps time scale (i.e., static component Δ₀ ∼ 0 ps^-1) or to a remaining, static contribution of ∼0.5 ps^-1 (corresponding to 2.5 cm^-1), depending on the local environment on the 10 ps time scale. The magnitude of the static component correlates qualitatively with the degree of hydration of the spectroscopic probe. Although attaching azide to alanine residues is found to be structurally minimally invasive with respect to the overall protein structure, analysis of the local hydrophobicity indicates that the hydration around the modification site differs for modified and unmodified alanine residues, respectively.

Long-Time-Scale Predictions from Short-Trajectory Data: A Benchmark Analysis of the Trp-Cage Miniprotein

Elucidating physical mechanisms with statistical confidence from molecular dynamics simulations can be challenging owing to the many degrees of freedom that contribute to collective motions. To address this issue, we recently introduced a dynamical Galerkin approximation (DGA) [Thiede, E. H. J. Chem. Phys., 150, 2019, 244111], in which chemical kinetic statistics that satisfy equations of dynamical operators are represented by a basis expansion. Here, we reformulate this approach, clarifying (and reducing) the dependence on the choice of lag time. We present a new projection of the reactive current onto collective variables and provide improved estimators for rates and committors. We also present simple procedures for constructing suitable smoothly varying basis functions from arbitrary molecular features. To evaluate estimators and basis sets numerically, we generate and carefully validate a data set of short trajectories for the unfolding and folding of the trp-cage miniprotein, a well-studied system. Our analysis demonstrates a comprehensive strategy for characterizing reaction pathways quantitatively.

Shedding Light on the Inhibitory Mechanisms of SARS-CoV-1/CoV-2 Spike Proteins by ACE2-Designed Peptides

Angiotensin-converting enzyme 2 (ACE2) is the host cellular receptor that locks onto the surface spike protein of the 2002 SARS coronavirus (SARS-CoV-1) and of the novel, highly transmissible and deadly 2019 SARS-CoV-2, responsible for the COVID-19 pandemic. One strategy to avoid the virus infection is to design peptides by extracting the human ACE2 peptidase domain α1-helix, which would bind to the coronavirus surface protein, preventing the virus entry into the host cells. The natural α1-helix peptide has a stronger affinity to SARS-CoV-2 than to SARS-CoV-1. Another peptide was designed by joining α1 with the second portion of ACE2 that is far in the peptidase sequence yet grafted in the spike protein interface with ACE2. Previous studies have shown that, among several α1-based peptides, the hybrid peptidic scaffold is the one with the highest/strongest affinity for SARS-CoV-1, which is comparable to the full-length ACE2 affinity. In this work, binding and folding dynamics of the natural and designed ACE2-based peptides were simulated by the well-known coarse-grained structure-based model, with the computed thermodynamic quantities correlating with the experimental binding affinity data. Furthermore, theoretical kinetic analysis of native contact formation revealed the distinction between these processes in the presence of the different binding partners SARS-CoV-1 and SARS-CoV-2 spike domains. Additionally, our results indicate the existence of a two-state folding mechanism for the designed peptide en route to bind to the spike proteins, in contrast to a downhill mechanism for the natural α1-helix peptides. The presented low-cost simulation protocol demonstrated its efficiency in evaluating binding affinities and identifying the mechanisms involved in the neutralization of spike-ACE2 interaction by designed peptides. Finally, the protocol can be used as a computer-based screening of more potent designed peptides by experimentalists searching for new therapeutics against COVID-19.

Dynamics and Infrared Spectrocopy of Monomeric and Dimeric Wild Type and Mutant Insulin

The infrared spectroscopy and dynamics of -CO labels in wild type and mutant insulin monomer and dimer are characterized from molecular dynamics simulations using validated force fields. It is found that the spectroscopy of monomeric and dimeric forms in the region of the amide-I vibration differs for residues B24-B26 and D24-D26, which are involved in dimerization of the hormone. Also, the spectroscopic signatures change for mutations at position B24 from phenylalanine, which is conserved in many organisms and is known to play a central role in insulin aggregation, to alanine or glycine. Using three different methods to determine the frequency trajectories (solving the nuclear Schrödinger equation on an effective 1-dimensional potential energy curve, using instantaneous normal modes, and using parametrized frequency maps) leads to the same overall conclusions. The spectroscopic response of monomeric WT and mutant insulin differs from that of their respective dimers, and the spectroscopy of the two monomers in the dimer is also not identical. For the WT and F24A and F24G monomers, spectroscopic shifts are found to be ∼20 cm^-1 for residues (B24-B26) located at the dimerization interface. Although the crystal structure of the dimer is that of a symmetric homodimer, dynamically the two monomers are not equivalent on the nanosecond time scale. Together with earlier work on the thermodynamic stability of the WT and the same mutants, it is concluded that combining computational and experimental infrared spectroscopy provides a potentially powerful way to characterize the aggregation state and dimerization energy of modified insulins.