Are current atomistic force fields accurate enough to study proteins in crowded environments?

Tips and Tricks in the Modeling of Supramolecular Peptide Assemblies

Supramolecular peptide assemblies (SPAs) hold promise as materials for nanotechnology and biomedicine. Although their investigation often entails adapting experimental techniques from their protein counterparts, SPAs are fundamentally distinct from proteins, posing unique challenges for their study. Computational methods have emerged as indispensable tools for gaining deeper insights into SPA structures at the molecular level, surpassing the limitations of experimental techniques, and as screening tools to reduce the experimental search space. However, computational studies have grappled with issues stemming from the absence of standardized procedures and relevant crystal structures. Fundamental disparities between SPAs and protein simulations, such as the absence of experimentally validated initial structures and the importance of the simulation size, number of molecules, and concentration, have compounded these challenges. Understanding the roles of various parameters and the capabilities of different models and simulation setups remains an ongoing endeavor. In this review, we aim to provide readers with guidance on the parameters to consider when conducting SPA simulations, elucidating their potential impact on outcomes and validity.

How arginine inhibits substrate-binding domain 2 elucidated using molecular dynamics simulations

The substrate-binding domain 2 (SBD2) is an important part of the bacterial glutamine (GLN) transporter and mediates binding and delivery of GLN to the transporter translocation subunit. The SBD2 consists of two domains, D1 and D2, that bind GLN in the space between domains in a closed structure. In the absence of ligand, the SBD2 adopts an open conformation with larger space between domains. The GLN binding and closing are essential for the subsequent transport into the cell. Arginine (ARG) can also bind to SBD2 but does not induce closing and inhibits GLN transport. We use atomistic molecular dynamics (MD) simulations in explicit solvent to study ARG binding in the presence of the open SBD2 structure and observed reversible binding to the native GLN binding site with similar contacts but no transition to a closed SBD2 state. Absolute binding free energy simulations predict a considerable binding affinity of ARG and GLN to the binding site on the D1 domain. Free energy simulations to induce subsequent closing revealed a strong free energy penalty in case of ARG binding in contrast to GLN binding that favors the closed SBD2 state but still retains a free energy barrier for closing. The simulations allowed the identification of the molecular origin of the closing penalty in case of bound ARG and suggested a mutation of lysine at position 373 to alanine that strongly reduced the penalty and allowed closing even in the presence of bound ARG. The study offers an explanation of the molecular mechanism of how ARG competitively inhibits GLN from binding to SBD2 and from triggering the transition to a closed conformation. The proposed Lys373Ala mutation shows promise as a potential tool to validate whether a conformational mismatch between open SBD2 and the translocator is responsible for preventing ARG uptake to the cell.

Intrinsic Conformational Dynamics of Glycine and Alanine in Polarizable Molecular Dynamics Force Fields: Comparison to Spectroscopic Data

Molecular dynamics (MD) is a great tool for elucidating conformational dynamics of proteins and peptides in water at the atomistic level that often surpasses the level of detail available experimentally. Structure predictions, however, are limited by the accuracy of the underlying MD force field. This limitation is particularly stark in the case of intrinsically disordered peptides and proteins, which are characterized by solvent-accessible and disordered peptide regions and domains. Recent studies show that most additive MD force fields, including CHARMM36m, do not reproduce the intrinsic conformational distributions of guest amino acid residues x in cationic GxG peptides in water in line with experimental data. Positing that a lack of polarizability in additive MD force fields may be the culprit for the reported discrepancies, we here examine the conformational dynamics of guest glycine and alanine residues in cationic GxG peptides in water using two polarizable MD force fields, CHARMM Drude and AMOEBA. Our results indicate that while AMOEBA captures the experimental data better than CHARMM Drude, neither of the two polarizable force fields offers an improvement of the Ramachandran distributions of glycine and alanine residues in cationic GGG and GAG peptides, respectively, over CHARMM36m.

PACSAB Server: A Web-Based Tool for the Study of Aggregation and the Conformational Ensemble of Disordered and Folded Proteins

We present in this article the PACSAB server, which is designed to provide information about the structural ensemble and interactions of both stable and disordered proteins to researchers in the field of molecular biology. The use of this tool does not require any computational skills as the user just needs to upload the structure of the protein to be studied; the server runs a simulation with the PACSAB model, a highly accurate coarse-grained model that is much more efficient than standard molecular dynamics for the exploration of the conformational space of multiprotein systems. The trajectories generated by the simulations based on this model reveal the propensity of the protein under study for aggregation, identify the residues playing a central role in the aggregation process, and reproduce the whole conformational space of disordered proteins. All of this information is shown and can be downloaded from the web page.

Computational Approaches to Predict Protein-Protein Interactions in Crowded Cellular Environments

Investigating protein-protein interactions is crucial for understanding cellular biological processes because proteins often function within molecular complexes rather than in isolation. While experimental and computational methods have provided valuable insights into these interactions, they often overlook a critical factor: the crowded cellular environment. This environment significantly impacts protein behavior, including structural stability, diffusion, and ultimately the nature of binding. In this review, we discuss theoretical and computational approaches that allow the modeling of biological systems to guide and complement experiments and can thus significantly advance the investigation, and possibly the predictions, of protein-protein interactions in the crowded environment of cell cytoplasm. We explore topics such as statistical mechanics for lattice simulations, hydrodynamic interactions, diffusion processes in high-viscosity environments, and several methods based on molecular dynamics simulations. By synergistically leveraging methods from biophysics and computational biology, we review the state of the art of computational methods to study the impact of molecular crowding on protein-protein interactions and discuss its potential revolutionizing effects on the characterization of the human interactome.

Hexagonal Lattices of HIV Capsid Proteins Explored by Simulations Based on a Thermodynamically Consistent Model

HIV capsid proteins (CAs) may self-assemble into a variety of shapes under in vivo and in vitro conditions. Here, we employed simulations based on a residue-level coarse-grained (CG) model with full conformational flexibility to investigate hexagonal lattices, which are the underlying structural pattern for CA aggregations. Facilitated by enhanced sampling simulations to rigorously calculate CA dimerization and polymerization affinities, we calibrated our model to reproduce the experimentally measured affinities. Using the calibrated model, we performed unbiased simulations on several large systems consisting of 1512 CA subunits, allowing reversible binding and unbinding of the CAs in a thermodynamically consistent manner. In one simulation, a preassembled hexagonal CA sheet developed spontaneous curvatures reminiscent of those observed in experiments, and the edges of the sheet exhibited local curvatures larger than those of the interior. In other simulations starting with randomly distributed CAs at different concentrations, existing CA assemblies grew by binding free capsomeres to the edges and by merging with other assemblies. At high CA concentrations, rapid establishment of predominant aggregates was followed by much slower adjustments toward more regular hexagonal lattices, with increasing numbers of intact CA hexamers and pentamers being formed. Our approach of adapting a general CG model to specific systems by using experimental binding data represents a practical and effective strategy for simulating and elucidating intricate protein aggregations.

Insights from the molecular mechanism of pyrazinamide to mutated pyrazinamidase linked to the pncA gene in clinical isolates of Mycobacterium tuberculosis

This study aims to conduct a comprehensive molecular dynamics strategy to evaluate whether mutations found in pyrazinamide monoresistant (PZAMR) strains of Mycobacterium tuberculosis (MTB) can potentially reduce the effectiveness of pyrazinamide (PZA) for tuberculosis (TB) treatment. Five single point mutations of pyrazinamidase (PZAse), an enzyme which is responsible for the activation of prodrug PZA into pyrazinoic acid, found in MTB clinical isolates, namely His82Arg, Thr87Met, Ser66Pro, Ala171Val, and Pro62Leu, were analyzed by the dynamics simulations both in the apo state (unbound state) and in the PZA bound state. The results showed that the mutation of His82 to Arg, Thr87 to Met, and Ser66 to Pro in PZAse affects the coordination state of the Fe2+ ion, which is a cofactor required for enzyme activity. These mutations change the flexibility, stability, and fluctuation of His51, His57, and ASP49 amino acid residues around the Fe2+ ion, culminating in an unstable complex and dissociation of PZA from the PZAse binding site. However, mutations of Ala171 to Val and Pro62 to Leu were found to have no effect on the complex's stability. Based on the results, PZAse mutations of His82Arg, Thr87Met, and Ser66Pro culminated in weak binding affinity for PZA and caused significant structural deformations that led to PZA resistance. Future structural and functional studies, as well as investigations into other aspects of drug resistance in PZAse, will require experimental clarification.Communicated by Ramaswamy H. Sarma.

Scrutinizing the protein hydration shell from molecular dynamics simulations against consensus small-angle scattering data

Biological macromolecules in solution are surrounded by a hydration shell, whose structure differs from the structure of bulk solvent. While the importance of the hydration shell for numerous biological functions is widely acknowledged, it remains unknown how the hydration shell is regulated by macromolecular shape and surface composition, mainly because a quantitative probe of the hydration shell structure has been missing. We show that small-angle scattering in solution using X-rays (SAXS) or neutrons (SANS) provide a protein-specific probe of the protein hydration shell that enables quantitative comparison with molecular simulations. Using explicit-solvent SAXS/SANS predictions, we derived the effect of the hydration shell on the radii of gyration Rg of five proteins using 18 combinations of protein force field and water model. By comparing computed Rg values from SAXS relative to SANS in D2O with consensus SAXS/SANS data from a recent worldwide community effort, we found that several but not all force fields yield a hydration shell contrast in remarkable agreement with experiments. The hydration shell contrast captured by Rg values depends strongly on protein charge and geometric shape, thus providing a protein-specific footprint of protein-water interactions and a novel observable for scrutinizing atomistic hydration shell models against experimental data.

QMrebind: incorporating quantum mechanical force field reparameterization at the ligand binding site for improved drug-target kinetics through milestoning simulations

Understanding the interaction of ligands with biomolecules is an integral component of drug discovery and development. Challenges for computing thermodynamic and kinetic quantities for pharmaceutically relevant receptor-ligand complexes include the size and flexibility of the ligands, large-scale conformational rearrangements of the receptor, accurate force field parameters, simulation efficiency, and sufficient sampling associated with rare events. Our recently developed multiscale milestoning simulation approach, SEEKR2 (Simulation Enabled Estimation of Kinetic Rates v.2), has demonstrated success in predicting unbinding (koff) kinetics by employing molecular dynamics (MD) simulations in regions closer to the binding site. The MD region is further subdivided into smaller Voronoi tessellations to improve the simulation efficiency and parallelization. To date, all MD simulations are run using general molecular mechanics (MM) force fields. The accuracy of calculations can be further improved by incorporating quantum mechanical (QM) methods into generating system-specific force fields through reparameterizing ligand partial charges in the bound state. The force field reparameterization process modifies the potential energy landscape of the bimolecular complex, enabling a more accurate representation of the intermolecular interactions and polarization effects at the bound state. We present QMrebind (Quantum Mechanical force field reparameterization at the receptor-ligand binding site), an ORCA-based software that facilitates reparameterizing the potential energy function within the phase space representing the bound state in a receptor-ligand complex. With SEEKR2 koff estimates and experimentally determined kinetic rates, we compare and interpret the receptor-ligand unbinding kinetics obtained using the newly reparameterized force fields for model host-guest systems and HSP90-inhibitor complexes. This method provides an opportunity to achieve higher accuracy in predicting receptor-ligand koff rate constants.

Viscosity Prediction of High-Concentration Antibody Solutions with Atomistic Simulations

The computational prediction of the viscosity of dense protein solutions is highly desirable, for example, in the early development phase of high-concentration biopharmaceutical formulations where the material needed for experimental determination is typically limited. Here, we use large-scale atomistic molecular dynamics (MD) simulations with explicit solvation to de novo predict the dynamic viscosities of solutions of a monoclonal IgG1 antibody (mAb) from the pressure fluctuations using a Green-Kubo approach. The viscosities at simulated mAb concentrations of 200 and 250 mg/mL are compared to the experimental values, which we measured with rotational rheometry. The computational viscosity of 24 mPa·s at the mAb concentration of 250 mg/mL matches the experimental value of 23 mPa·s obtained at a concentration of 213 mg/mL, indicating slightly different effective concentrations (or activities) in the MD simulations and in the experiments. This difference is assigned to a slight underestimation of the effective mAb-mAb interactions in the simulations, leading to a too loose dynamic mAb network that governs the viscosity. Taken together, this study demonstrates the feasibility of all-atom MD simulations for predicting the properties of dense mAb solutions and provides detailed microscopic insights into the underlying molecular interactions. At the same time, it also shows that there is room for further improvements and highlights challenges, such as the massive sampling required for computing collective properties of dense biomolecular solutions in the high-viscosity regime with reasonable statistical precision.

Antibacterial Potency of an Active Compound from Sansevieria trifasciata Prain: An Integrated In Vitro and In Silico Study

Sansevieria trifasciata Prain holds great potential as a valuable asset in pharmaceutical development. In this study, our focus is to explore and assess the antibacterial activity of various components derived from this plant, including extracts, fractions, subfractions, and isolates, explicitly targeting two common bacteria: Escherichia coli and Streptococcus aureus. The isolated compound, identified as a derivative pyridone alkaloid (5-methyl-11-(2-oxopyridin-1(2H)-yl)undecaneperoxoicacid), demonstrates notable antibacterial effects. The extracts, fractions, subfractions, and isolates reveal significant bacterial growth reductions (p < 0.05). The minimum inhibitory concentration (MIC) values for Escherichia coli were 1.95 ppm, 3.9 ppm, 15.62 ppm, and 7.81 ppm, respectively, while the MIC values for Streptococcus aureus were 1.95 ppm, 1.95 ppm, 15.62 ppm, and 7.81 ppm, respectively. Computational analysis showed the isolates' interaction with key residues on the active site of β-ketoacyl-ACP synthase from Escherichia coli and TyrRS from Streptococcus aureus. The findings indicate that the isolates exhibit a strong affinity for specific residues, including His333, Cys163, and Phe392 in β-ketoacyl-ACP synthase, as well as Arg88, His117, Glu160, and Gln213 in TyrRS. Comparative energy calculations using MMPBSA demonstrate the isolates' favorable binding energy (-104,101 kJ/mol for β-ketoacyl-ACP synthase and -81,060 kJ/mol for TyrRS) compared to ciprofloxacin. The elucidated antibacterial activity and molecular interactions of the isolates present valuable knowledge for future in vitro studies, facilitating the development of novel antibacterial agents targeting diverse bacterial strains.

Structure and interaction of therapeutic proteins in solution: a combined simulation and experimental study

The aggregation of therapeutic proteins in solution has attracted significant interest, driving efforts to understand the relationship between microscopic structural changes and protein-protein interactions determining aggregation processes in solution. Additionally, there is substantial interest in being able to predict aggregation based on protein structure as part of molecular developability assessments. Molecular Dynamics provides theoretical tools to complement experimental studies and to interrogate and identify the microscopic mechanisms determining aggregation. Here we perform all-atom MD simulations to study the structure and inter-protein interaction of the Fab and Fc fragments of the monoclonal antibody (mAb) COE3. We unravel the role of ion-protein interactions in building the ionic double layer and determining effective inter-protein interaction. Further, we demonstrate, using various state-of-the-art force fields (charmm, gromos, amber, opls/aa), that the protein solvation, ionic structure and protein-protein interaction depend significantly on the force field parameters. We perform SANS and Static Light Scattering experiments to assess the accuracy of the different forcefields. Comparison of the simulated and experimental results reveal significant differences in the forcefields' performance, particularly in their ability to predict the protein size in solution and inter-protein interactions quantified through the second virial coefficients. In addition, the performance of the forcefields is correlated with the protein hydration structure.

Structure, energetics and dynamics in crowded amino acid solutions: a molecular dynamics study

A comprehensive understanding of crowding effects on biomolecular processes necessitates investigating the bulk thermodynamic and kinetic properties of the solutions with an accurate molecular representation of the crowded milieu. Recent studies have reparameterized the non-bonded dispersion interaction of solutes to precisely model intermolecular interactions, which would circumvent artificial aggregation as shown by the original force-fields. However, the performance of this reparameterization is yet to be assessed for concentrated crowded solutions in terms of investigating the hydration shell structure, energetics and dynamics. In this study, we perform molecular dynamics simulations of crowded aqueous solutions of five zwitterionic neutral amino acids (Gly, Ala, Thr, Pro, and Ser), mimicking the molecular crowding environment, using a modified AMBER ff99SB-ILDN force-field. We systematically examine and show that the reproducibility of the osmotic coefficients, density, viscosity and self-diffusivity of amino acids improves using the modified force-field in crowded concentrations. The modified force-field also improves the structuring of the solute solvation shells, solute interaction energy and convergence of tails of radial distribution functions, indicating reduction in the artificial aggregation. Our results also indicate that the hydrogen bonding network of water weakens and water molecules anomalously diffuse at small time scales in the crowded solutions. These results underscore the significance of examining the solution properties and anomalous hydration behaviour of water in crowded solutions, which have implications in shaping the structure and dynamics of biomolecules. The findings also illustrate the improvement in predicting bulk solution properties using the modified force-field, thereby providing an approach towards accurate modeling of crowded molecular solutions.

In silico engineering a CD80 variant with increased affinity to CTLA-4 and decreased affinity to CD28 for optimized cancer immunotherapy

CD80 or cluster of differentiation 80, also known as B7-1, is a member of the immunoglobulin super family, which binds to CTLA-4 and CD28 T cell receptors and induces inhibitory and inductive signals respectively. Although CTLA-4 and CD28 receptors belong to the same protein family, slight differences in their structures leads to CD80 having a higher binding affinity to CTLA-4 (-14.55 kcal/mol) compared with CD28(-12.51 kcal/mol). In this study, we constructed a variant of CD80 protein with increased binding affinity to CTLA-4 and decreased binding affinity to CD28. This variant has no signaling capability, and can act as a cap for these receptors to protect them from natural CD80 proteins existing in the body. The first step was the evolutionary and alanine scanning analysis of CD80 protein to determine conserved regions in this protein. Next, complex alanine scanning technique was employed to determine CD80 protein hotspots in CD80-CTLA-4 and CD80-CD28 protein complexes. This information was fed into a computational model developed in R for in silico mutagenesis and CD80 variant library construction. The 3D structures of variants were modeled using the Swiss model webserver. After modeling the 3D structures, HADDOCK server was employed to build all protein-protein complexes, which contain CTLA-4-CD80 variant complexes, Wild type CD80-CD28 complexes and CD28-CD80 variant complexes. Protein-protein binding free energy was determined using FoldX and the variant number 316 with mutations at 29, 31, 33 positions showed increased binding affinity to CTLA-4 (-21.43 kcal/mol) and decreased binding affinity to CD28 (- 9.54 kcal/mol). Finally, molecular dynamics (MD) simulations confirmed the stability of variant 316. In conclusion, we designed a new CD80 protein variant with potential immunotherapeutic applications.

Predicting molecular properties of α-synuclein using force fields for intrinsically disordered proteins

Independent force field validation is an essential practice to keep track of developments and for performing meaningful Molecular Dynamics simulations. In this work, atomistic force fields for intrinsically disordered proteins (IDP) are tested by simulating the archetypical IDP α-synuclein in solution for 2.5 μs. Four combinations of protein and water force fields were tested: ff19SB/OPC, ff19SB/TIP4P-D, ff03CMAP/TIP4P-D, and a99SB-disp/TIP4P-disp, with four independent repeat simulations for each combination. We compare our simulations to the results of a 73 μs simulation using the a99SB-disp/TIP4P-disp combination, provided by D. E. Shaw Research. From the trajectories, we predict a range of experimental observations of α-synuclein and compare them to literature data. This includes protein radius of gyration and hydration, intramolecular distances, NMR chemical shifts, and ³ J-couplings. Both ff19SB/TIP4P-D and a99SB-disp/TIP4P-disp produce extended conformational ensembles of α-synuclein that agree well with experimental radius of gyration and intramolecular distances while a99SB-disp/TIP4P-disp reproduces a balanced α-synuclein secondary structure content. It was found that ff19SB/OPC and ff03CMAP/TIP4P-D produce overly compact conformational ensembles and show discrepancies in the secondary structure content compared to the experimental data.

Towards rational computational peptide design

Peptides are prevalent in biology, mediating as many as 40% of protein-protein interactions, and involved in other cellular functions such as transport and signaling. Their ability to bind with high specificity make them promising therapeutical agents with intermediate properties between small molecules and large biologics. Beyond their biological role, peptides can be programmed to self-assembly, and they are already being used for functions as diverse as oligonuclotide delivery, tissue regeneration or as drugs. However, the transient nature of their interactions has limited the number of structures and knowledge of binding affinities available-and their flexible nature has limited the success of computational pipelines that predict the structures and affinities of these molecules. Fortunately, recent advances in experimental and computational pipelines are creating new opportunities for this field. We are starting to see promising predictions of complex structures, thermodynamic and kinetic properties. We believe in the following years this will lead to robust rational peptide design pipelines with success similar to those applied for small molecule drug discovery.

Simulating Polyproline II-Helix-Rich Peptides with the Latest Kirkwood-Buff Force Field: A Direct Comparison with AMBER and CHARMM

We simulated the dynamics of a set of peptides characterized by ensembles rich in PPII-helical content, to assess the ability of the most recent Kirkwood-Buff force field (KBFF20) to sample this conformational peculiarity. KBFF has been previously shown to capably reproduce experimental dimensions of disordered proteins, while being limited in confidently sampling structured proteins. Further development of the force field bridged this gap. It is however still unknown what are the main differences between KBFF and AMBER/CHARMM force fields. A direct comparison is now possible as both AMBER/CHARMM force fields have been used to sample peptides rich in PPII-helical content. We found that KBFF20 samples' PPII-helical content qualitatively matches both AMBER and CHARMM force fields, with the main difference being the KBFF ability to populate the α_R region of the Ramachandran plot in the set of simulated peptides. Overall, KBFF20 is a well-balanced force field, able to sample the dynamics of both structured and unstructured proteins.

Applications of Molecular Dynamics Simulation in Protein Study

Molecular Dynamics (MD) Simulations is increasingly used as a powerful tool to study protein structure-related questions. Starting from the early simulation study on the photoisomerization in rhodopsin in 1976, MD Simulations has been used to study protein function, protein stability, protein-protein interaction, enzymatic reactions and drug-protein interactions, and membrane proteins. In this review, we provide a brief review for the history of MD Simulations application and the current status of MD Simulations applications in protein studies.

Unrevealing the Potential of Sansevieria trifasciata Prain Fraction for the Treatment of Androgenetic Alopecia by Inhibiting Androgen Receptors Based on LC-MS/MS Analysis, and In-Silico Studies

Androgenetic Alopecia (AGA) occurs due to over-response to androgens causing severe hair loss on the scalp, and requires the development of new and efficient drugs to treat this condition. This study explores and identifies secondary metabolites from Sansevieriatrifasciata Prain using the LC-MS/MS and in-silico method. The inhibitory activity of bioactive compounds from S. trifasciata Prain against androgen receptors (PDB ID: 4K7A) was evaluated molecularly using docking and dynamics studies by comparing their binding energies, interactions, and stability with minoxidil. The results of the LC-MS/MS analysis identified Methyl pyrophaeophorbide A (1), Oliveramine (2), (2S)-3′, 4′-Methylenedioxy-5, 7-dimethoxyflavane (3), 1-Acetyl-β-carboline (4), Digiprolactone (5), Trichosanic acid (6) and Methyl gallate (7) from the leaves subfraction of this plant. Three alkaloid compounds (compounds 1, 3, and 4), and one flavonoid (compound 2), had lower docking scores of −7.0, −5.8, −5.2, and −6.3 kcal/mol, respectively. The prediction of binding energy using the MM-PBSA approach ensured that the potency of the four compounds was better than minoxidil, with energies of −66.13, −59.36, −40.39, and −40.25 kJ/mol for compounds 1, 3, 2, and 4, respectively. The dynamics simulation shows the stability of compound 1 based on the trajectory analysis for the 100 ns simulation. This research succeeded in identifying the compound and assessing the anti-alopecia activity of Sansevieria trifasciata Prain. Seven compounds were identified as new compounds never reported in Sansevieria trifasciata Prain. Four compounds were predicted to have better anti-alopecia activity than minoxidil in inhibiting androgen receptors through an in silico approach.

Atomistic Simulation of Lysozyme in Solutions Crowded by Tetraethylene Glycol: Force Field Dependence

The behavior of biomolecules in crowded environments remains largely unknown due to the accuracy of simulation models and the limited experimental data for comparison. Here we chose a small crowder of tetraethylene glycol (PEG-4) to investigate the self-crowding of PEG-4 solutions and molecular crowding effects on the structure and diffusion of lysozyme at varied concentrations from dilute water to pure PEG-4 liquid. Two Amber-like force fields of Amber14SB and a99SB-disp were examined with TIP3P (fast diffusivity and low viscosity) and a99SB-disp (slow diffusivity and high viscosity) water models, respectively. Compared to the Amber14SB protein simulations, the a99SB-disp model yields more coordinated water and less PEG-4 molecules, less intramolecular hydrogen bonds (HBs), more protein-water HBs, and less protein-PEG HBs as well as stronger interactions and more hydrophilic and less hydrophobic contacts with solvent molecules. The a99SB-disp model offers comparable protein-solvent interactions in concentrated PEG-4 solutions to that in pure water. The PEG-4 crowding leads to a slow-down in the diffusivity of water, PEG-4, and protein, and the decline in the diffusion from atomistic simulations is close to or faster than the hard sphere model that neglects attractive interactions. Despite these differences, the overall structure of lysozyme appears to be maintained well at different PEG-4 concentrations for both force fields, except a slightly large deviation at 370 K at low concentrations with the a99SB-disp model. This is mainly attributed to the strong intramolecular interactions of the protein in the Amber14SB force field and to the large viscosity of the a99SB-disp water model. The results indicate that the protein force fields and the viscosity of crowder solutions affect the simulation of biomolecules under crowding conditions.

Computational models for studying physical instabilities in high concentration biotherapeutic formulations

Computational prediction of the behavior of concentrated protein solutions is particularly advantageous in early development stages of biotherapeutics when material availability is limited and a large set of formulation conditions needs to be explored. This review provides an overview of the different computational paradigms that have been successfully used in modeling undesirable physical behaviors of protein solutions with a particular emphasis on high-concentration drug formulations. This includes models ranging from all-atom simulations, coarse-grained representations to macro-scale mathematical descriptions used to study physical instability phenomena of protein solutions such as aggregation, elevated viscosity, and phase separation. These models are compared and summarized in the context of the physical processes and their underlying assumptions and limitations. A detailed analysis is also given for identifying protein interaction processes that are explicitly or implicitly considered in the different modeling approaches and particularly their relations to various formulation parameters. Lastly, many of the shortcomings of existing computational models are discussed, providing perspectives and possible directions toward an efficient computational framework for designing effective protein formulations.

Protein assembly and crowding simulations

Proteins encounter frequent molecular interactions in biological environments. Computer simulations have become an increasingly important tool in providing mechanistic insights into how such interactions in vivo relate to their biological function. The review here focuses on simulations describing protein assembly and molecular crowding effects as two important aspects that are distinguished mainly by how specific and long-lived protein contacts are. On the topic of crowding, recent simulations have provided new insights into how crowding affects protein folding and stability, modulates enzyme activity, and affects diffusive properties. Recent studies of assembly processes focus on assembly pathways, especially for virus capsids, amyloid aggregation pathways, and the role of multivalent interactions leading to phase separation. Also, discussed are technical challenges in achieving increasingly realistic simulations of interactions in cellular environments.

Do molecular dynamics force fields accurately model Ramachandran distributions of amino acid residues in water?

Molecular dynamics (MD) is a powerful tool for studying intrinsically disordered proteins, however, its reliability depends on the accuracy of the force field. We assess Amber ff19SB, Amber ff14SB, OPLS-AA/M, and CHARMM36m with respect to their capacity to capture intrinsic conformational dynamics of 14 guest residues x (=G, A, L, V, I, F, Y, D^P, E^P, R, C, N, S, T) in GxG peptides in water. The MD-derived Ramachandran distribution of each guest residue is used to calculate 5 J-coupling constants and amide I' band profiles to facilitate a comparison to spectroscopic data through reduced χ² functions. We show that the Gaussian model, optimized to best fit the experimental data, outperforms all MD force fields by an order of magnitude. The weaknesses of the MD force fields are: (i) insufficient variability of the polyproline II (pPII) population among the guest residues; (ii) oversampling of antiparallel at the expense of transitional β-strand region; (iii) inadequate sampling of turn-forming conformations for ionizable and polar residues; and (iv) insufficient guest residue-specificity of the Ramachandran distributions. Whereas Amber ff19SB performs worse than the other three force fields with respect to χ² values, it accounts for residue-specific pPII content better than the other three force fields. Additional testing of residue-specific RSFF1 and Amber ff14SB combined with TIP4P/2005 on six guest residues x (=A, I, F, D^P, R, S) reveals that residue specificity derived from protein coil libraries or an improved water model alone do not result in significantly lower χ² values.

Physics of biomolecular recognition and conformational dynamics

Biomolecular recognition usually leads to the formation of binding complexes, often accompanied by large-scale conformational changes. This process is fundamental to biological functions at the molecular and cellular levels. Uncovering the physical mechanisms of biomolecular recognition and quantifying the key biomolecular interactions are vital to understand these functions. The recently developed energy landscape theory has been successful in quantifying recognition processes and revealing the underlying mechanisms. Recent studies have shown that in addition to affinity, specificity is also crucial for biomolecular recognition. The proposed physical concept of intrinsic specificity based on the underlying energy landscape theory provides a practical way to quantify the specificity. Optimization of affinity and specificity can be adopted as a principle to guide the evolution and design of molecular recognition. This approach can also be used in practice for drug discovery using multidimensional screening to identify lead compounds. The energy landscape topography of molecular recognition is important for revealing the underlying flexible binding or binding-folding mechanisms. In this review, we first introduce the energy landscape theory for molecular recognition and then address four critical issues related to biomolecular recognition and conformational dynamics: (1) specificity quantification of molecular recognition; (2) evolution and design in molecular recognition; (3) flexible molecular recognition; (4) chromosome structural dynamics. The results described here and the discussions of the insights gained from the energy landscape topography can provide valuable guidance for further computational and experimental investigations of biomolecular recognition and conformational dynamics.

Crowding affects structural dynamics and contributes to membrane association of the NS3/4A complex

Using molecular dynamics simulations, we describe how crowded environments affect the internal dynamics and diffusion of the hepatitis C virus proteases NS3/4A. This protease plays a key role in viral replication and is successfully used as a target for antiviral treatment. The NS3 enzyme requires a peptide cofactor, called NS4A, with its central part interacting with the NS3 β-sheet, and flexible, protruding terminal tails that are unstructured in water solution. The simulations describe the enzyme and water molecules at atomistic resolution, whereas crowders are modeled via either all-atom or coarse-grained models to emphasize different aspects of crowding. Crowders reflect the polyethylene glycol (PEG) molecules used in the experiments to mimic the crowded surrounding. A bead-shell model of folded coarse-grained PEG molecules considers mainly the excluded volume effect, whereas all-atom PEG models afford more protein-like crowder interactions. Circular dichroism spectroscopy experiments of the NS4A N-terminal tail show that a helical structure is formed in the presence of PEG crowders. The simulations suggest that crowding may assist in the formation of an NS4A helical fragment, positioned exactly where a transmembrane helix would fold upon the NS4A contact with the membrane. In addition, partially interactive PEGs help the NS4A N-tail to detach from the protease surface, thus enabling the process of helix insertion and potentially helping the virus establish a replication machinery needed to produce new viruses. Results point to an active role of crowding in assisting structural changes in disordered protein fragments that are necessary for their biological function.

Soluble State of Villin Headpiece Protein as a Tool in the Assessment of MD Force Fields

Protein self-assembly plays an important role in cellular processes. Whereas molecular dynamics (MD) represents a powerful tool in studying assembly mechanisms, its predictions depend on the accuracy of underlying force fields, which are known to overly promote protein assembly. We here examine villin headpiece domain, HP36, which remains soluble at concentrations amenable to MD studies. The experimental characterization of soluble HP36 at concentrations of 0.05 to 1 mM reveals concentration-independent 90% monomeric and 10% dimeric populations. Extensive all-atom MD simulations at two protein concentrations, 0.9 and 8.5 mM, probe the HP36 dimer population, stability, and kinetics of dimer formation within two MD force fields, Amber ff14SB and CHARMM36m. MD results demonstrate that whereas CHARMM36m captures experimental HP36 monomer populations at the lower concentration, both force fields overly promote HP36 association at the higher concentration. Moreover, contacts stabilizing HP36 dimers are force-field-dependent. CHARMM36m produces consistently higher HP36 monomer populations, lower association rates, and weaker dependence of these quantities on the protein concentration than Amber ff14SB. Nonetheless, the highest monomer populations and dissociation constants are observed when the TIP3P water model in Amber ff14SB is replaced by TIP4P/2005, showcasing the critical role of the water model in addressing the protein solubility problem in MD.

Force Field Benchmark of Amino Acids. 3. Hydration with Scaled Lennard-Jones Interactions

Classical protein force fields were reported with too weak protein-water interactions relative to protein-protein interactions, leading to more compact structures and artificial protein aggregation. Here we investigated the impacts of scaled Lennard-Jones (LJ) interactions on the hydration of amino acids and the simulation of folded and intrinsically disordered proteins (IDPs). The obtained optimal scaling parameters reproduce accurately hydration free energies of neutral amino acid side chain analogues and do not affect the compactness and structural stability of folded proteins significantly. The scaling leads to less compact IDPs and varies from case to case. Strengthening the interactions between protein and water oxygen or hydrogen atoms by increasing the interacting LJ well depth (ε) appears more effective than weakening protein-protein interactions by reducing the interacting dispersion coefficients (C₆). We demonstrate that weakening water-water interactions is a solution as well to obtaining more favorable protein-water interactions in an indirect way, although modern force fields like Amber ff19SB and a99SB-disp tend to use water models with strong water-water interactions. This is likely a compromise between strong protein-protein interactions and strong water-water interactions. Independent optimization of protein force fields and water models is therefore needed to make both interactions more close to reality, leading to good accuracy without bias or scaling.

Molecular Dynamics of Cobalt Protoporphyrin Antagonism of the Cancer Suppressor REV-ERBβ

Nuclear receptor REV-ERBβ is an overexpressed oncoprotein that has been used as a target for cancer treatment. The metal-complex nature of its ligand, iron protoporphyrin IX (Heme), enables the REV-ERBβ to be used for multiple therapeutic modalities as a photonuclease, a photosensitizer, or a fluorescence imaging agent. The replacement of iron with cobalt as the metal center of protoporphyrin IX changes the ligand from an agonist to an antagonist of REV-ERBβ. The mechanism behind that phenomenon is still unclear, despite the availability of crystal structures of REV-ERBβ in complex with Heme and cobalt protoporphyrin IX (CoPP). This study used molecular dynamic simulations to compare the effects of REV-ERBβ binding to Heme and CoPP, respectively. The initial poses of Heme and CoPP in complex with agonist and antagonist forms of REV-ERBβ were predicted using molecular docking. The binding energies of each ligand were calculated using the MM/PBSA method. The computed binding affinity of Heme to REV-ERBβ was stronger than that of CoPP, in agreement with experimental results. CoPP altered the conformation of the ligand-binding site of REV-ERBβ, disrupting the binding site for nuclear receptor corepressor, which is required for REV-ERBβ to regulate the transcription of downstream target genes. Those results suggest that a subtle change in the metal center of porphyrin can change the behavior of porphyrin in cancer cell signaling. Therefore, modification of porphyrin-based agents for cancer therapy should be conducted carefully to avoid triggering unfavorable effects.

Docking-Based Virtual Screening and Molecular Dynamics Simulations of Quercetin Analogs as Enoyl-Acyl Carrier Protein Reductase (InhA) Inhibitors of Mycobacterium tuberculosis

The emergence of multidrug-resistant Mycobacterium tuberculosis (MTB) has become a major problem in treating tuberculosis (TB) and shows the need to develop new and efficient drugs for better TB control. This study aimed to use in silico techniques to discover potential inhibitors to the Enoyl-[acyl-carrier-protein] reductase (InhA), which controls mycobacterial cell wall construction. Initially, 391 quercetin analogs present in the KNApSAck_3D database were selected, filters were sequentially applied by docking-based virtual screening. After recategorizing the variables (bond energy prediction and molecular interaction, including hydrogen bond and hydrophobic bond), compounds C00013874, C00006532, and C00013887 were selected as hit ligands. These compounds showed great hydrophobic contributions, and for each hit ligand, 100 ns of molecular dynamic simulations were performed, and the binding free energy was calculated. C00013874 demonstrated the greatest capacity for the InhA enzyme inhibition with ΔGbind = −148.651 kcal/mol compare to NAD (native ligand) presented a ΔGbind = −87.570 kcal/mol. These data are preliminary studies and might be a suitable candidate for further experimental analysis.

Assessment of transferable forcefields for protein simulations attests improved description of disordered states and secondary structure propensities, and hints at multi-protein systems as the next challenge for optimization

Continuous assessment of transferable forcefields for molecular simulations is essential to identify their weaknesses and direct improvement efforts. The latest efforts focused on better describing disordered proteins while retaining proper description of folded domains, important because forcefields of the previous generations produce overly compact disordered states. Such improvements should additionally alleviate the related problem of over-stabilized protein–protein interactions, which has been largely overlooked. Here we evaluated three state-of-the-art forcefields, current flagships of their respective developers, optimized for ordered and disordered proteins: CHARMM36m with its recommended corrected TIP3P* water, ff19SB with the recommended OPC water, and the 2019 a99SBdisp forcefield by D. E. Shaw Research with its modified TIP4P water; plus ff14SB with TIP3P as an example of the former generation of forcefields. Our evaluation entailed simulations of (i) multiple copies of a protein that is highly soluble yet undergoes weak dimerization, (ii) a disordered peptide with low, well-characterized alpha helical propensity, and (iii) a peptide known to form insoluble β-aggregates. Our results recapitulate ff14SB-TIP3P over-stabilizing aggregates and secondary structures and place a99SBdisp-TIP4PD at the other end i.e. predicting overly weak intermolecular interactions despite reasonably predicting secondary structure propensities. In-between, CHARMM36m-TIP3P* still over-stabilizes aggregates but predicts residue-wise alpha helical propensities in solution slightly better than ff19SB-OPC, while ff19SB-OPC poses the best prediction of weak dimerization of the soluble protein still predicting aggregation of the β-peptides. This independent assessment shows that the claimed forcefield improvements are real, but also that a right balance between noncovalent attraction and repulsion has not yet been reached. We thus propose developers to consider systems like those tested here in their forcefield tuning protocols. Last, the good performance of CHARMM36m-TIP3P* further shows that tuning 3-point water models might still be an alternative to the more costly 4-point models like OPC and TIP4PD.

Martini 3: a general purpose force field for coarse-grained molecular dynamics

The coarse-grained Martini force field is widely used in biomolecular simulations. Here we present the refined model, Martini 3 ( http://cgmartini.nl ), with an improved interaction balance, new bead types and expanded ability to include specific interactions representing, for example, hydrogen bonding and electronic polarizability. The updated model allows more accurate predictions of molecular packing and interactions in general, which is exemplified with a vast and diverse set of applications, ranging from oil/water partitioning and miscibility data to complex molecular systems, involving protein-protein and protein-lipid interactions and material science applications as ionic liquids and aedamers.

Quantitative Analysis of Protein Unfolded State Energetics: Experimental and Computational Studies Demonstrate That Non-Native Side-Chain Interactions Stabilize Local Native Backbone Structure

Proteins fold on relatively smooth free energy landscapes which are biased toward the native state, but even simple topologies which fold rapidly can experience roughness on their free energy landscape. The details of these interactions are difficult to elucidate experimentally. Closely related to the problem of deciphering the details of the free energy landscape is the problem of defining the interactions in the denatured state ensemble (DSE) which is populated under native conditions, that is, under conditions where the native state is stable. The DSE of many proteins deviates from random coil models, but quantifying and defining the energetics of the transiently populated interactions in this ensemble is extremely challenging. Characterization of the DSE of proteins which fold to compact structures is also relevant to studies of intrinsically disordered proteins (IDPs) since interactions in the dynamic ensemble populated by IDPs can modulate their behavior. Here we show how experimental thermodynamic and pK_a measurements can be combined with computational thermodynamic integration to quantify interactions in the DSE. We show that non-native side chain interactions can stabilize native backbone structure in the DSE and demonstrate that that even rapidly folding proteins can form energetically significant non-native interactions in their DSE. As an example, we characterize a non-native salt bridge that stabilizes local native backbone structure in the DSE of a widely studied fast-folding protein, the villin headpiece helical domain. The combined computational experimental approach is applicable to other protein unfolded states and provides insight that is impossible to obtain with either method alone.

Exploring the structure and dynamics of proteins in soil organic matter

Alongside inorganic materials, water, and air, soil organic matter (SOM) is one of the major components of soil and has tremendous influence on the environment given its vital role in the carbon cycle. Many soil dwelling organisms like plants, fungi and bacteria excrete proteins, whose interaction with SOM is poorly understood on an atomistic level. In this study, molecular dynamics simulations were used to investigate selected proteins in soil models of different complexity from simple co-solvent molecules to Leonardite humic acids (LHA). We analyzed the proteins in terms of their structural stability, the nature and strength of the interactions with their surroundings, as well as their aggregation behavior. Upon insertion of proteins in complex SOM models, their structural stability decreased, although no unfolding or disruption of secondary structure was observed. The interactions of proteins and SOM were primarily governed by electrostatic forces, often in form of hydrogen bonds. However, also weaker van der Waals forces made a significant contribution to the total interaction energies. Moreover, we showed that even though the molecular structure and size of SOM molecules varied, the functional groups of SOM ordered around the protein in a similar pattern. Finally, the number of aggregates formed by proteins and SOM molecules was shown to be primarily proportional to the size of the latter. Strikingly, for varying protein net charges no changes in the formation of aggregates with the strongly negatively charged LHA were observed.

The hitchhiker's guide to the periplasm: Unexpected molecular interactions of polymyxin B1 in E. coli

The periplasm of Gram-negative bacteria is a complex, highly crowded molecular environment. Little is known about how antibiotics move across the periplasm and the interactions they experience. Here, atomistic molecular dynamics simulations are used to study the antibiotic polymyxin B1 within models of the periplasm, which are crowded to different extents. We show that PMB1 is likely to be able to "hitchhike" within the periplasm by binding to lipoprotein carriers-a previously unreported passive transport route. The simulations reveal that PMB1 forms both transient and long-lived interactions with proteins, osmolytes, lipids of the outer membrane, and the cell wall, and is rarely uncomplexed when in the periplasm. Furthermore, it can interfere in the conformational dynamics of native proteins. These are important considerations for interpreting its mechanism of action and are likely to also hold for other antibiotics that rely on diffusion to cross the periplasm.

Effect of the Water Model in Simulations of Protein-Protein Recognition and Association

We study self-association of ubiquitin and the disordered protein ACTR using the most commonly used water models. We find that dissociation events are found only with TIP4P-EW and TIP4P/2005, while the widely used TIP3P water model produces straightforward aggregation of the molecules due to the absence of dissociation events. We also find that TIP4P/2005 is the only water model that reproduces the fast association/dissociation dynamics of ubiquitin and best identifies its binding surface. Our results show the critical role of the water model in the description of protein–protein interactions and binding.

In-cell protein landscapes: making the match between theory, simulation and experiment

Theory, computation and experiment have matched up for the folding of small proteins in vitro, a difficult feat because folding energy landscapes are fairly smooth and free energy differences between states are small. Smoothness means that protein structure and folding are susceptible to the local environment inside living cells. Theory, computation and experiment are now exploring cellular modulation of energy landscapes. Interesting concepts have emerged, such as co-evolution of protein surfaces with their cellular environment to reduce detrimental interactions. Here we look at very recent work beginning to bring together theory, simulations and experiments in the area of protein landscape modulation, to see what problems might be solved in the near future by combining these approaches.

Coarse-Grained Molecular Model for the Glycosylphosphatidylinositol Anchor with and without Protein

Glycosylphosphatidylinositol (GPI) anchors are a unique class of complex glycolipids that anchor a great variety of proteins to the extracellular leaflet of plasma membranes of eukaryotic cells. These anchors can exist either with or without an attached protein called GPI-anchored protein (GPI-AP) both in vitro and in vivo. Although GPIs are known to participate in a broad range of cellular functions, it is to a large extent unknown how these are related to GPI structure and composition. Their conformational flexibility and microheterogeneity make it difficult to study them experimentally. Simplified atomistic models are amenable to all-atom computer simulations in small lipid bilayer patches but not suitable for studying their partitioning and trafficking in complex and heterogeneous membranes. Here, we present a coarse-grained model of the GPI anchor constructed with a modified version of the MARTINI force field that is suited for modeling carbohydrates, proteins, and lipids in an aqueous environment using MARTINI's polarizable water. The nonbonded interactions for sugars were reparametrized by calculating their partitioning free energies between polar and apolar phases. In addition, sugar-sugar interactions were optimized by adjusting the second virial coefficients of osmotic pressures for solutions of glucose, sucrose, and trehalose to match with experimental data. With respect to the conformational dynamics of GPI-anchored green fluorescent protein, the accessible time scales are now at least an order of magnitude larger than for the all-atom system. This is particularly important for fine-tuning the mutual interactions of lipids, carbohydrates, and amino acids when comparing to experimental results. We discuss the prospective use of the coarse-grained GPI model for studying protein-sorting and trafficking in membrane models.

Protein thermal stability

Proteins, in general, fold to a well-organized three-dimensional structure in order to function. The stability of this functional shape can be perturbed by external environmental conditions, such as temperature. Understanding the molecular factors underlying the resistance of proteins to the thermal stress has important consequences. First of all, it can aid the design of thermostable enzymes able to perform efficient catalysis in the high-temperature regime. Second, it is an essential brick of knowledge required to decipher the evolutionary pathways of life adaptation on Earth. Thanks to the development of atomistic simulations and ad hoc enhanced sampling techniques, it is now possible to investigate this problem in silico, and therefore provide support to experiments. After having described the methodological aspects, the chapter proposes an extended discussion on two problems. First, we focus on thermophilic proteins, a perfect model to address the issue of thermal stability and molecular evolution. Second, we discuss the issue of how protein thermal stability is affected by crowded in vivo-like conditions.

The nuclear Overhauser Effect (NOE) as a tool to study macromolecular confinement: Elucidation and disentangling of crowding and encapsulation effects

We propose a methodology to capture short-lived but biophysically important contacts of biomacromolecules using the biomolecule-water nuclear Overhauser effect as an indirect microscope. Thus, instead of probing the direct correlation with the foreign biomolecule, we detect its presence by the disturbance it causes in the surrounding water. In addition, this information obtained is spatially resolved and can thus be attributed to specific sites. We extend this approach to the influence of more than one change in chemical environment and show a methodological way of resolution. This is achieved by taking double differences of corresponding σ_NOE/σ_ROE ratios of the systems studied and separating specific, unspecific, and intermediate influence. While applied to crowding and encapsulation in this study, this method is generally suitable for any combination of changes in chemical environment.

The protein-water nuclear Overhauser effect (NOE) as an indirect microscope for molecular surface mapping of interaction patterns

In this computational study, the intermolecular solute-solvent Nuclear Overhauser Effect (NOE) of the model protein ubiquitin in different chemical environments (free, bound to a partner protein and encapsulated) is investigated. Short-ranged NOE observables such as the NOE/ROE ratio reveal hydration phenomena on absolute timescales such as fast hydration sites and slow water clefts. We demonstrate the ability of solute-solvent NOE differences measured of the same protein in different chemical environments to reveal hydration changes on the relative timescale. The resulting NOE/ROE-surface maps are shown to be a central key for analyzing biologically relevant chemical influences such as complexation and confinement: the presence of a complexing macromolecule or a confining surface wall modulates the water mobility in the vicinity of the probe protein, hence revealing which residues of said protein are proximate to the foreign interface and which are chemically unaffected. This way, hydration phenomena can serve to indirectly map the precise influence (position) of other molecules or interfaces onto the protein surface. This proposed one-protein many-solvents approach may offer experimental benefits over classical one-protein other-protein pseudo-intermolecular transient NOEs. Furthermore, combined influences such as complexation and confinement may exert non-additive influences on the protein compared to a reference state. We offer a mathematical method to disentangle the influence of these two different chemical environments.

Combining Molecular and Spin Dynamics Simulations with Solid-State NMR: A Case Study of Amphiphilic Lysine-Leucine Repeat Peptide Aggregates

Interpreting dynamics in solid-state molecular systems requires characterization of the potentially heterogeneous environmental contexts of molecules. In particular, the analysis of solid-state nuclear magnetic resonance (ssNMR) data to elucidate molecular dynamics (MD) involves modeling the restriction to overall tumbling by neighbors, as well as the concentrations of water and buffer. In this exploration of the factors that influence motion, we utilize atomistic MD trajectories of peptide aggregates with varying hydration to mimic an amorphous solid-state environment and predict ssNMR relaxation rates. We also account for spin diffusion in multiply spin-labeled (up to 19 nuclei) residues, with several models of dipolar-coupling networks. The framework serves as a general approach to determine essential spin couplings affecting relaxation, benchmark MD force fields, and reveal the hydration dependence of dynamics in a crowded environment. We demonstrate the methodology on a previously characterized amphiphilic 14-residue lysine-leucine repeat peptide, LKα14 (Ac-LKKLLKLLKKLLKL-c), which has an α-helical secondary structure and putatively forms leucine-burying tetramers in the solid state. We measure the R₁ relaxation rates of uniformly ¹³C-labeled and site-specific ²H-labeled leucines in the hydrophobic core of LKα14 at multiple hydration levels. Studies of 9 and 18 tetramer bundles reveal the following: (a) for the incoherent component of ¹³C relaxation, the nearest-neighbor spin interactions dominate, while the ¹H-¹H interactions have minimal impact; (b) the AMBER ff14SB dihedral barriers for the leucine C_γ-C_δ bond ("methyl rotation barriers") must be lowered by a factor of 0.7 to better match the ²H data; (c) proton-driven spin diffusion explains some of the discrepancy between experimental and simulated rates for the C_β and C_α nuclei; and (d) ¹³C relaxation rates are mostly underestimated in the MD simulations at all hydrations, and the discrepancies identify likely motions missing in the 50 ns MD trajectories.

Rotational and Translational Diffusion of Proteins as a Function of Concentration

Atomistic simulations of three different proteins at different concentrations are performed to obtain insight into protein mobility as a function of protein concentration. We report on simulations of proteins from diluted to the physiological water concentration (about 70% of the mass). First, the viscosity was computed and found to increase by a factor of 7-9 going from pure water to the highest protein concentration, in excellent agreement with in vivo nuclear magnetic resonance results. At a physiological concentration of proteins, the translational diffusion is found to be slowed down to about 30% of the in vitro values. The slow-down of diffusion found here using atomistic models is slightly more than that of a hard sphere model that neglects the electrostatic interactions. Interestingly, rotational diffusion of proteins is slowed down somewhat more (by about 80-95% compared to in vitro values) than translational diffusion, in line with experimental findings and consistent with the increased viscosity. The finding that rotation is retarded more than translation is attributed to solvent-separated clustering. No direct interactions between the proteins are found, and the clustering can likely be attributed to dispersion interactions that are stronger between proteins than between protein and water. Based on these simulations, we can also conclude that the internal dynamics of the proteins in our study are affected only marginally under crowding conditions, and the proteins become somewhat more stable at higher concentrations. Simulations were performed using a force field that was tuned for dealing with crowding conditions by strengthening the protein-water interactions. This force field seems to lead to a reproducible partial unfolding of an α-helix in one of the proteins, an effect that was not observed in the unmodified force field.

ff19SB: Amino-Acid-Specific Protein Backbone Parameters Trained against Quantum Mechanics Energy Surfaces in Solution

Molecular dynamics (MD) simulations have become increasingly popular in studying the motions and functions of biomolecules. The accuracy of the simulation, however, is highly determined by the molecular mechanics (MM) force field (FF), a set of functions with adjustable parameters to compute the potential energies from atomic positions. However, the overall quality of the FF, such as our previously published ff99SB and ff14SB, can be limited by assumptions that were made years ago. In the updated model presented here (ff19SB), we have significantly improved the backbone profiles for all 20 amino acids. We fit coupled φ/ψ parameters using 2D φ/ψ conformational scans for multiple amino acids, using as reference data the entire 2D quantum mechanics (QM) energy surface. We address the polarization inconsistency during dihedral parameter fitting by using both QM and MM in aqueous solution. Finally, we examine possible dependency of the backbone fitting on side chain rotamer. To extensively validate ff19SB parameters, and to compare to results using other Amber models, we have performed a total of ∼5 ms MD simulations in explicit solvent. Our results show that after amino-acid-specific training against QM data with solvent polarization, ff19SB not only reproduces the differences in amino-acid-specific Protein Data Bank (PDB) Ramachandran maps better but also shows significantly improved capability to differentiate amino-acid-dependent properties such as helical propensities. We also conclude that an inherent underestimation of helicity is present in ff14SB, which is (inexactly) compensated for by an increase in helical content driven by the TIP3P bias toward overly compact structures. In summary, ff19SB, when combined with a more accurate water model such as OPC, should have better predictive power for modeling sequence-specific behavior, protein mutations, and also rational protein design. Of the explicit water models tested here, we recommend use of OPC with ff19SB.

Pitfalls of the Martini Model

The computational and conceptual simplifications realized by coarse-grain (CG) models make them a ubiquitous tool in the current computational modeling landscape. Building block based CG models, such as the Martini model, possess the key advantage of allowing for a broad range of applications without the need to reparametrize the force field each time. However, there are certain inherent limitations to this approach, which we investigate in detail in this work. We first study the consequences of the absence of specific cross Lennard-Jones parameters between different particle sizes. We show that this lack may lead to artificially high free energy barriers in dimerization profiles. We then look at the effect of deviating too far from the standard bonded parameters, both in terms of solute partitioning behavior and solvent properties. Moreover, we show that too weak bonded force constants entail the risk of artificially inducing clustering, which has to be taken into account when designing elastic network models for proteins. These results have implications for the current use of the Martini CG model and provide clear directions for the reparametrization of the Martini model. Moreover, our findings are generally relevant for the parametrization of any other building block based force field.

In-Cell Protein-Protein Contacts: Transient Interactions in the Crowd

Proteins in vivo are immersed in a crowded environment of water, ions, metabolites, and macromolecules. In-cell experiments highlight how transient weak protein-protein interactions promote (via functional "quinary structure") or hinder (via competitive binding or "sticking") complex formation. Computational models of the cytoplasm are expensive. We tackle this challenge with an all-atom model of a small volume of the E. coli cytoplasm to simulate protein-protein contacts up to the 5 μs time scale on the special-purpose supercomputer Anton 2. We use three CHARMM-derived force fields: C22*, C36m, and C36mCU (with CUFIX corrections). We find that both C36m and C36mCU form smaller contact surfaces than C22*. Although CUFIX was developed to reduce protein-protein sticking, larger contacts are observed with C36mCU than C36m. We show that the lifespan Δt of protein-protein contacts obeys a power law distribution between 0.03 and 3 μs, with ∼90% of all contacts lasting <1 μs (similar to the time scale for downhill folding).

Modeling Crowded Environment in Molecular Simulations

Biomolecules perform their various functions in living cells, namely in an environment that is crowded by many macromolecules. Thus, simulating the dynamics and interactions of biomolecules should take into account not only water and ions but also other binding partners, metabolites, lipids and macromolecules found in cells. In the last decade, research on how to model macromolecular crowders around proteins in order to simulate their dynamics in models of cellular environments has gained a lot of attention. In this mini-review we focus on the models of crowding agents that have been used in computer modeling studies of proteins and peptides, especially via molecular dynamics simulations.