Introducing an Implicit Membrane in Generalized Born/Solvent Accessibility Continuum Solvent Models

Challenges of Protein-Protein Docking of the Membrane Proteins

Despite the recent advances in the determination of high-resolution membrane protein (MP) structures, the structural and functional characterization of MPs remains extremely challenging, mainly due to the hydrophobic nature, low abundance, poor expression, purification, and crystallization difficulties associated with MPs. Whereby the major challenges/hurdles for MP structure determination are associated with the expression, purification, and crystallization procedures. Although there have been significant advances in the experimental determination of MP structures, only a limited number of MP structures (approximately less than 1% of all) are available in the Protein Data Bank (PDB). Therefore, the structures of a large number of MPs still remain unresolved, which leads to the availability of widely unplumbed structural and functional information related to MPs. As a result, recent developments in the drug discovery realm and the significant biological contemplation have led to the development of several novel, low-cost, and time-efficient computational methods that overcome the limitations of experimental approaches, supplement experiments, and provide alternatives for the characterization of MPs. Whereby the fine tuning and optimizations of these computational approaches remains an ongoing endeavor.Computational methods offer a potential way for the elucidation of structural features and the augmentation of currently available MP information. However, the use of computational modeling can be extremely challenging for MPs mainly due to insufficient knowledge of (or gaps in) atomic structures of MPs. Despite the availability of numerous in silico methods for 3D structure determination the applicability of these methods to MPs remains relatively low since all methods are not well-suited or adequate for MPs. However, sophisticated methods for MP structure predictions are constantly being developed and updated to integrate the modifications required for MPs. Currently, different computational methods for (1) MP structure prediction, (2) stability analysis of MPs through molecular dynamics simulations, (3) modeling of MP complexes through docking, (4) prediction of interactions between MPs, and (5) MP interactions with its soluble partner are extensively used. Towards this end, MP docking is widely used. It is notable that the MP docking methods yet few in number might show greater potential in terms of filling the knowledge gap. In this chapter, MP docking methods and associated challenges have been reviewed to improve the applicability, accuracy, and the ability to model macromolecular complexes.

Discovery of antiviral SARS-CoV-2 main protease inhibitors by structure-guided hit-to-lead optimization of carmofur

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) main protease (Mpro) has been targeted for the development of anti-SARS-CoV-2 agents against COVID-19 infection because Mpro processes essential viral polyproteins and plays a key role in SARS-CoV-2 replication. In this study, we report the development of novel SARS-CoV-2 Mpro inhibitors derived from carmofur, a previously identified compound that has shown moderate potency as a covalent inhibitor of SARS-CoV-2 Mpro. To employ a structure-guided drug design strategy, a putative intact binding mode of carmofur at catalytic active site of Mpro was initially predicted by docking simulation. Based on the predicted binding mode, a series of carmofur derivatives aiming to occupy the Mpro substrate binding regions were investigated for structure-activity relationship analysis. As a result, an indole-based derivative, speculated to interact with the S4 binding pocket, 21b (IC50 = 1.5 ± 0.1 μM) was discovered. Its structure was further modified and evaluated in silico by combining docking simulation, free energy perturbation calculation and subpocket interaction analysis to optimize the interactions at the S2 and S4 binding pockets. Among the newly designed novel derivatives, 21h and 21i showed the best inhibitory potencies against Mpro with IC50 values of 0.35 and 0.37 μM, respectively. Moreover, their antiviral activities were confirmed with EC50 values of 20-30 μM in the SARS-CoV-2-infected cell-based assay, suggesting that these novel Mpro inhibitors could be applied as potential lead compounds for the development of substantial anti-SARS-CoV-2 agents.

Length matters: Functional flip of the short TatA transmembrane helix

The twin arginine translocase (Tat) exports folded proteins across bacterial membranes. The putative pore-forming or membrane-weakening component (TatA_d in B. subtilis) is anchored to the lipid bilayer via an unusually short transmembrane α-helix (TMH), with less than 16 residues. Its tilt angle in different membranes was analyzed under hydrophobic mismatch conditions, using synchrotron radiation circular dichroism and solid-state NMR. Positive mismatch (introduced either by reconstitution in short-chain lipids or by extending the hydrophobic TMH length) increased the helix tilt of the TMH as expected. Negative mismatch (introduced either by reconstitution in long-chain lipids or by shortening the TMH), on the other hand, led to protein aggregation. These data suggest that the TMH of TatA is just about long enough for stable membrane insertion. At the same time, its short length is a crucial factor for successful translocation, as demonstrated here in native membrane vesicles using an in vitro translocation assay. Furthermore, when reconstituted in model membranes with negative spontaneous curvature, the TMH was found to be aligned parallel to the membrane surface. This intrinsic ability of TatA to flip out of the membrane core thus seems to play a key role in its membrane-destabilizing effect during Tat-dependent translocation.

Two physics-based models for pH-dependent calculations of protein solubility

When engineering a protein for its biological function, many physicochemical properties are also optimized throughout the engineering process, and the protein's solubility is among the most important properties to consider. Here, we report two novel computational methods to calculate the pH-dependent protein solubility, and to rank the solubility of mutants. The first is an empirical method developed for fast ranking of the solubility of a large number of mutants of a protein. It takes into account electrostatic solvation energy term calculated using Generalized Born approximation, hydrophobic patches, protein charge, and charge asymmetry, as well as the changes of protein stability upon mutation. This method has been tested on over 100 mutations for 17 globular proteins, as well as on 44 variants of five different antibodies. The prediction rate is over 80%. The antibody tests showed a Pearson correlation coefficient, R, with experimental data from .83 to .91. The second method is based on a novel, completely force-field-based approach using CHARMm program modules to calculate the binding energy of the protein to a part of the crystal lattice, generated from X-ray structure. The method predicted with very high accuracy the solubility of Ribonuclease SA and its 3K and 5K mutants as a function of pH without any parameter adjustments of the existing BIOVIA Discovery Studio binding affinity model. Our methods can be used for rapid screening of large numbers of design candidates based on solubility, and to guide the design of solution conditions for antibody formulation.

A computational study of somatostatin subtype-4 receptor agonist binding

The somatostatin subtype-4 receptor (sst4) is highly expressed in neocortical and hippocampal areas, which are affected by amyloid beta accumulation. Sst4 agonists enhance downstream activity of amyloid beta peptide catabolism through neprilysin and may slow the progression of Alzheimer’s disease (AD). Sst4 is a G protein coupled receptor (GPCR), the structure of which has yet to be resolved. A newly constructed sst4 homology model, along with a previously reported model-built sst4 receptor structure, were used in the present study to gain insights into binding requirements of sst4 agonists employing a set of compounds patented by Boehringer Ingelheim. Besides aiming at delineating binding at the macromolecular level of these recently disclosed compounds, our objectives included the generation of a quantitative structure-activity relationship (QSAR) global model to explore the relationship between chemical structure and affinity. Through the implementation of model building, docking, and QSAR, plausible correlations between structural properties and the binding affinity are established. This study sheds light on understanding binding requirements at the sst4 receptor.

Graphical abstract

How tetraspanin-mediated cell entry of SARS-CoV-2 can dysregulate the shedding of the ACE2 receptor by ADAM17

COVID-19, the respiratory infection caused by the novel coronavirus SARS-CoV-2, presents a clinical picture consistent with the dysregulation of many of the pathways mediated by the metalloprotease ADAM17. ADAM17 is a sheddase that plays a key role in the modulation of ACE2, the receptor which also functions as the point of attachment leading to cell entry by the virus. This work investigates the possibility that ADAM17 dysregulation and attachment of the SARS-CoV-2 virion to the ACE2 receptor are linked events, with the latter causing the former. Tetraspanins, the transmembrane proteins that function as scaffolds for the construction of viral entry platforms, are mooted as key components in this connection.

Structure Based Affinity Maturation and Characterizing of SARS-CoV Antibody CR3022 against SARS-CoV-2 by Computational and Experimental Approaches

The COVID-19 epidemic is raging around the world. Neutralizing antibodies are powerful tools for the prevention and treatment of SARS-CoV-2 infection. Antibody CR3022, a SARS-CoV neutralizing antibody, was found to cross-react with SARS-CoV-2, but its affinity was lower than that of its binding with SARS-CoV, which greatly limited the further development of CR3022 against SARS-CoV-2. Therefore, it is necessary to improve its affinity to SARS-CoV-2 in vitro. In this study, the structure-based molecular simulations were utilized to virtually mutate the possible key residues in the complementarity-determining regions (CDRs) of the CR3022 antibody. According to the criteria of mutation energy, the mutation sites that have the potential to impact the antibody affinity were then selected. Then optimized CR3022 mutants with the enhanced affinity were further identified and verified by enzyme-linked immunosorbent assay (ELISA), surface plasma resonance (SPR) and autoimmune reactivity experiments. Finally, molecular dynamics (MD) simulation and binding free energy calculation (MM/PBSA) were performed on the wild-type CR3022 and its two double-site mutants to understand in more detail the contribution of these sites to the higher affinity. It was found that the binding affinity of the CR3022 antibody could be significantly enhanced more than ten times after the introduction of the S103F/Y mutation in HCDR–3 and the S33R mutation in LCDR–1. The additional hydrogen-bonding, hydrophobic interactions, as well as salt-bridges formed between the modified double-site mutated antibody and SARS-CoV-2 RBD were identified. The computational and experimental results clearly demonstrated that the affinity of the modified antibody has been greatly enhanced. This study indicates that CR3022 as a neutralizing antibody recognizing the conserved region of RBD against SARS-CoV with cross-reactivity with SARS-CoV-2, a different member in a large family of coronaviruses, could be improved by the computational and experimental approaches which provided insights for developing antibody drugs against SARS-CoV-2.

A model for COVID-19-induced dysregulation of ACE2 shedding by ADAM17

The angiotensin Converting Enzyme 2 (ACE2) receptor is a key component of the renin-angiotensin-aldesterone system (RAAS) that mediates numerous effects in the cardiovascular system. It is also the cellular point of contact for the coronavirus spike protein. Cleavage of the receptor is both important to its physiological function as well as being necessary for cell entry by the virus. Shedding of ACE2 by the metalloprotease ADAM17 releases a catalytically active soluble form of ACE2, but cleavage by the serine protease TMPRSS2 is necessary for virion internalization. Complicating the issue is the observation that circulating ACE2 can also bind to the virus effectively blocking attachment to the membrane-bound receptor. This work investigates the possibility that the inflammatory response to coronavirus infection can abrogate shedding by ADAM17, thereby favoring cleavage by TMPRSS2 and thus cell entry by the virion.

Protein Structure Prediction and Design in a Biologically Realistic Implicit Membrane

Protein design is a powerful tool for elucidating mechanisms of function and engineering new therapeutics and nanotechnologies. Although soluble protein design has advanced, membrane protein design remains challenging because of difficulties in modeling the lipid bilayer. In this work, we developed an implicit approach that captures the anisotropic structure, shape of water-filled pores, and nanoscale dimensions of membranes with different lipid compositions. The model improves performance in computational benchmarks against experimental targets, including prediction of protein orientations in the bilayer, ΔΔG calculations, native structure discrimination, and native sequence recovery. When applied to de novo protein design, this approach designs sequences with an amino acid distribution near the native amino acid distribution in membrane proteins, overcoming a critical flaw in previous membrane models that were prone to generating leucine-rich designs. Furthermore, the proteins designed in the new membrane model exhibit native-like features including interfacial aromatic side chains, hydrophobic lengths compatible with bilayer thickness, and polar pores. Our method advances high-resolution membrane protein structure prediction and design toward tackling key biological questions and engineering challenges.

Membrane Curvature Sensing by Amphipathic Helices: Insights from Implicit Membrane Modeling

Sensing and generation of lipid membrane curvature, mediated by the binding of specific proteins onto the membrane surface, play crucial roles in cell biology. A number of mechanisms have been proposed, but the molecular understanding of these processes is incomplete. All-atom molecular dynamics simulations have offered valuable insights but are extremely demanding computationally. Implicit membrane simulations could provide a viable alternative, but current models apply only to planar membranes. In this work, the implicit membrane model 1 is extended to spherical and tubular membranes. The geometric change from planar to curved shapes is straightforward but insufficient for capturing the full curvature effect, which includes changes in lipid packing. Here, these packing effects are taken into account via the lateral pressure profile. The extended implicit membrane model 1 is tested on the wild-types and mutants of the antimicrobial peptide magainin, the ALPS motif of arfgap1, α-synuclein, and an ENTH domain. In these systems, the model is in qualitative agreement with experiments. We confirm that favorable electrostatic interactions tend to weaken curvature sensitivity in the presence of strong hydrophobic interactions but may actually have a positive effect when those are weak. We also find that binding to vesicles is more favorable than binding to tubes of the same diameter and that the long helix of α-synuclein tends to orient along the axis of tubes, whereas shorter helices tend to orient perpendicular to it. Adoption of a specific orientation could provide a mechanism for coupling protein oligomerization to tubule formation.

Generalized Born Implicit Solvent Models for Biomolecules

It would often be useful in computer simulations to use an implicit description of solvation effects, instead of explicitly representing the individual solvent molecules. Continuum dielectric models often work well in describing the thermodynamic aspects of aqueous solvation and can be very efficient compared to the explicit treatment of the solvent. Here, we review a particular class of so-called fast implicit solvent models, generalized Born (GB) models, which are widely used for molecular dynamics (MD) simulations of proteins and nucleic acids. These approaches model hydration effects and provide solvent-dependent forces with efficiencies comparable to molecular-mechanics calculations on the solute alone; as such, they can be incorporated into MD or other conformational searching strategies in a straightforward manner. The foundations of the GB model are reviewed, followed by examples of newer, emerging models and examples of important applications. We discuss their strengths and weaknesses, both for fidelity to the underlying continuum model and for the ability to replace explicit consideration of solvent molecules in macromolecular simulations.

A Membrane Burial Potential with H-Bonds and Applications to Curved Membranes and Fast Simulations

We use the statistics of a large and curated training set of transmembrane helical proteins to develop a knowledge-based potential that accounts for the dependence on both the depth of burial of the protein in the membrane and the degree of side-chain exposure. Additionally, the statistical potential includes depth-dependent energies for unsatisfied backbone hydrogen bond donors and acceptors, which are found to be relatively small, ∼2 RT. Our potential accurately places known proteins within the bilayer. The potential is applied to the mechanosensing MscL channel in membranes of varying thickness and curvature, as well as to the prediction of protein structure. The potential is incorporated into our new Upside molecular dynamics algorithm. Notably, we account for the exchange of protein-lipid interactions for protein-protein interactions as helices contact each other, thereby avoiding overestimating the energetics of helix association within the membrane. Simulations of most multimeric complexes find that isolated monomers and the oligomers retain the same orientation in the membrane, suggesting that the assembly of prepositioned monomers presents a viable mechanism of oligomerization.

Molecular Dynamics Simulations Are Redefining Our View of Peptides Interacting with Biological Membranes

Ever since the first molecular mechanics computer simulations of biological molecules became possible, there has been the dream to study all complex biological phenomena in silico, simply bypassing the enormous experimental challenges and their associated costs. For this, two inherent requirements need to be met: First, the time scales achievable in simulations must reach up to the millisecond range and even longer. Second, the computational model must accurately reproduce what is measured experimentally. Despite some recent successes, the general consensus in the field to date has been that neither of these conditions have yet been met and that the dream will be realized, if at all, only in the distant future. In this Account, we show that this view is wrong; instead, we are actually in the middle of the in silico molecular dynamics (MD) revolution, which is reshaping how we think about protein function. The example explored in this Account is a recent advance in the field of membrane-active peptides (MAPs). MD simulations have succeeded in accurately capturing the process of peptide binding, folding, and partitioning into lipid bilayers as well as revealing how channels form spontaneously from polypeptide fragments and conduct ionic and other cargo across membranes, all at atomic resolution. These game-changing advances have been made possible by a combination of steadily advancing computational power, more efficient algorithms and techniques, clever accelerated sampling schemes, and thorough experimental verifications. The great advantage of MD is the spatial and temporal resolution, directly providing a molecular movie of a protein undergoing folding and cycling through a functional process. This is especially important for proteins with transitory functional states, such as pore-forming MAPs. Recent successes are demonstrated here for the large class of antimicrobial peptides (AMPs). These short peptides are an essential part of the nonadaptive immune system for many organisms, ubiquitous in nature, and of particular interest to the pharmaceutical industry in the age of rising bacterial resistance to conventional antibiotic treatments. Unlike integral membrane proteins, AMPs are sufficiently small to allow converged sampling with the unbiased high-temperature sampling methodology outlined here and are relatively easy to handle experimentally. At the same time, AMPs exhibit a wealth of complex and poorly understood interactions with lipid bilayers, which allow not only tuning and validation of the simulation methodology but also advancement of our knowledge of protein-lipid interactions at a fundamental level. Space constraints limit our discussion to AMPs, but the MD methodologies outlined here can be applied to all phenomena involving peptides in membranes, including cell-penetrating peptides, signaling peptides, viral channel forming peptides, and fusion peptides, as well as ab initio membrane protein folding and assembly. For these systems, the promise of MD simulations to predict the structure of channels and to provide complete-atomic-detail trajectories of the mechanistic processes underlying their biological functions appears to rapidly become a reality. The current challenge is to design joint experimental and computational benchmarks to verify and tune MD force fields. With this, MD will finally fulfill its promise to become an inexpensive, powerful, and easy-to-use tool providing atomic-detail insights to researchers as part of their investigations into membrane biophysics and beyond.

Computational studies of peptide-induced membrane pore formation

A variety of peptides induce pores in biological membranes; the most common ones are naturally produced antimicrobial peptides (AMPs), which are small, usually cationic, and defend diverse organisms against biological threats. Because it is not possible to observe these pores directly on a molecular scale, the structure of AMP-induced pores and the exact sequence of steps leading to their formation remain uncertain. Hence, these questions have been investigated via molecular modelling. In this article, we review computational studies of AMP pore formation using all-atom, coarse-grained, and implicit solvent models; evaluate the results obtained and suggest future research directions to further elucidate the pore formation mechanism of AMPs.This article is part of the themed issue 'Membrane pores: from structure and assembly, to medicine and technology'.

A Finite Element Solution of Lateral Periodic Poisson-Boltzmann Model for Membrane Channel Proteins

Membrane channel proteins control the diffusion of ions across biological membranes. They are closely related to the processes of various organizational mechanisms, such as: cardiac impulse, muscle contraction and hormone secretion. Introducing a membrane region into implicit solvation models extends the ability of the Poisson–Boltzmann (PB) equation to handle membrane proteins. The use of lateral periodic boundary conditions can properly simulate the discrete distribution of membrane proteins on the membrane plane and avoid boundary effects, which are caused by the finite box size in the traditional PB calculations. In this work, we: (1) develop a first finite element solver (FEPB) to solve the PB equation with a two-dimensional periodicity for membrane channel proteins, with different numerical treatments of the singular charges distributions in the channel protein; (2) add the membrane as a dielectric slab in the PB model, and use an improved mesh construction method to automatically identify the membrane channel/pore region even with a tilt angle relative to the z-axis; and (3) add a non-polar solvation energy term to complete the estimation of the total solvation energy of a membrane protein. A mesh resolution of about 0.25 Å (cubic grid space)/0.36 Å (tetrahedron edge length) is found to be most accurate in linear finite element calculation of the PB solvation energy. Computational studies are performed on a few exemplary molecules. The results indicate that all factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic strength, have individually considerable influence on the solvation energy of a channel protein. This demonstrates the necessity to treat all of those effects in the PB model for membrane protein simulations.

Accuracy Comparison of Generalized Born Models in the Calculation of Electrostatic Binding Free Energies

The need for accurate yet efficient representation of the aqueous environment in biomolecular modeling has led to the development of a variety of generalized Born (GB) implicit solvent models. While many studies have focused on the accuracy of available GB models in predicting solvation free energies, a systematic assessment of the quality of these models in binding free energy calculations, crucial for rational drug design, has not been undertaken. Here, we evaluate the accuracies of eight common GB flavors (GB-HCT, GB-OBC, GB-neck2, GBNSR6, GBSW, GBMV1, GBMV2, and GBMV3), available in major molecular dynamics packages, in predicting the electrostatic binding free energies ( ΔΔ G_el) for a diverse set of 60 biomolecular complexes belonging to four main classes: protein-protein, protein-drug, RNA-peptide, and small complexes. The GB flavors are examined in terms of their ability to reproduce the results from the Poisson-Boltzmann (PB) model, commonly used as accuracy reference in this context. We show that the agreement with the PB of ΔΔ G_el estimates varies widely between different GB models and also across different types of biomolecular complexes, with R² correlations ranging from 0.3772 to 0.9986. A surface-based "R6" GB model recently implemented in AMBER shows the closest overall agreement with reference PB ( R² = 0.9949, RMSD = 8.75 kcal/mol). The RNA-peptide and protein-drug complex sets appear to be most challenging for all but one model, as indicated by the large deviations from the PB in ΔΔ G_el. Small neutral complexes present the least challenge for most of the GB models tested. The quantitative demonstration of the strengths and weaknesses of the GB models across the diverse complex types provided here can be used as a guide for practical computations and future development efforts.

Determination of Hydrophobic Lengths of Membrane Proteins with the HDGB Implicit Membrane Model

A protocol for predicting the hydrophobic length of membrane proteins using the heterogeneous dielectric generalized Born (HDGB) implicit membrane model is presented. The method involves optimal positioning in the membrane and identification of lipid-facing and inward-facing residues, followed by energy optimization of the implicit membrane model to obtain the hydrophobic length from the optimal membrane width. The latest HDGB version 3 (HDGBv3) and HDGB van der Waals (HDGBvdW) models were applied to a test set containing 15 proteins (seven β-barrel and eight α-helical proteins), for which matching membrane widths are available from experiment, and an additional set contains ten α-helical and ten β-barrel proteins without any experimental data. The results with the HDGB model compare favorably with predictions from methods used in the Orientations of Proteins in Membranes (OPM) and Protein Data Bank of Transmembrane Proteins (PDB-TM) databases.

A Continuum Poisson-Boltzmann Model for Membrane Channel Proteins

Membrane proteins constitute a large portion of the human proteome and perform a variety of important functions as membrane receptors, transport proteins, enzymes, signaling proteins, and more. Computational studies of membrane proteins are usually much more complicated than those of globular proteins. Here, we propose a new continuum model for Poisson-Boltzmann calculations of membrane channel proteins. Major improvements over the existing continuum slab model are as follows: (1) The location and thickness of the slab model are fine-tuned based on explicit-solvent MD simulations. (2) The highly different accessibilities in the membrane and water regions are addressed with a two-step, two-probe grid-labeling procedure. (3) The water pores/channels are automatically identified. The new continuum membrane model is optimized (by adjusting the membrane probe, as well as the slab thickness and center) to best reproduce the distributions of buried water molecules in the membrane region as sampled in explicit water simulations. Our optimization also shows that the widely adopted water probe of 1.4 Å for globular proteins is a very reasonable default value for membrane protein simulations. It gives the best compromise in reproducing the explicit water distributions in membrane channel proteins, at least in the water accessible pore/channel regions. Finally, we validate the new membrane model by carrying out binding affinity calculations for a potassium channel, and we observe good agreement with the experimental results.

Molecular modelling studies of kdr mutations in voltage gated sodium channel revealed significant conformational variations contributing to insecticide resistance

Voltage gated sodium channels (VGSC) of mosquito vectors are the primary targets of dichlorodiphenyltrichloroethane (DDT) and other synthetic pyrethroids used in public health programmes. The knockdown resistant (kdr) mutations in VGSC are associated with the insecticide resistance especially in Anophelines. The present study is aimed to emphasize and demarcate the impact of three kdr-mutations such as L1014S, L1014F and L1014H on insecticide resistance. The membrane model of sodium transport domain of VGSC (STD-VGSC) was constructed using de novo approach based on domain and trans-membrane predictions. The comparative molecular modelling studies of wild type and mutant models of STD-VGSC revealed that L1014F mutant was observed to be near native to the wild type model in all the respects, but, L1014S and L1014H mutations showed drastic variations in the energy levels, root mean square fluctuations (RMSF) that resulted in conformational variations. The predicted binding sites also showed variable cavity volumes and RMSF in L1014S and L1014H mutants. Further, DDT also found be bound in near native manner to wild type in L1014F mutant and with variable orientation and affinities in L1014S and L1014H mutants. The variations and fluctuations observed in mutant structures explained that each mutation has its specific impact on the conformation of VGSC and its binding with DDT. The study provides new insights into the structure-function-correlations of mutant STD-VGSC structures and demonstrates the role and effects of kdr mutations on insecticide resistance in mosquito vectors.

Physical insights into the blood-brain barrier translocation mechanisms

The number of individuals suffering from diseases of the central nervous system (CNS) is growing with an aging population. While candidate drugs for many of these diseases are available, most of these pharmaceutical agents cannot reach the brain rendering most of the drug therapies that target the CNS inefficient. The reason is the blood-brain barrier (BBB), a complex and dynamic interface that controls the influx and efflux of substances through a number of different translocation mechanisms. Here, we present these mechanisms providing, also, the necessary background related to the morphology and various characteristics of the BBB. Moreover, we discuss various numerical and simulation approaches used to study the BBB, and possible future directions based on multi-scale methods. We anticipate that this review will motivate multi-disciplinary research on the BBB aiming at the design of effective drug therapies.

Heterogeneous dielectric generalized Born model with a van der Waals term provides improved association energetics of membrane-embedded transmembrane helices

The heterogeneous dielectric generalized Born (HDGB) implicit membrane formalism is extended by the addition of a van der Waals dispersion term to better describe the nonpolar components of the free energy of solvation. The new model, termed HDGBvdW, improves the energy estimates in the hydrophobic interior of the membrane, where polar and charged species are rarely found and nonpolar interactions become significant. The implicit van der Waals term for the membrane environment extends the model from Gallicchio et al. (J. Comput. Chem. 2004, 25, 479) by combining separate contributions from each of the membrane components. The HDGBvdW model is validated with a series of test cases ranging from membrane insertion and pair association profiles of amino acid side chain analogs and transmembrane helices. Overall, the HDGBvdW model leads to increased agreement with explicit membrane simulation results and experimental data. © 2016 Wiley Periodicals, Inc.

Dimerization effects on coacervation property of an elastin-derived synthetic peptide (FPGVG)5

Elastin, a core protein of the elastic fibers, exhibits the coacervation (temperature-dependent reversible association/dissociation) under physiological conditions. Because of this characteristic, elastin and elastin-derived peptides have been considered to be useful as base materials for developing various biomedical products, skin substitutes, synthetic vascular grafts, and drug delivery systems. Although elastin-derived polypeptide (Val-Pro-Gly-Val-Gly)n also has been known to demonstrate coacervation property, a sufficiently high (VPGVG)n repetition number (n>40) is required for coacervation. In the present study, a series of elastin-derived peptide (Phe-Pro-Gly-Val-Gly)5 dimers possessing high coacervation potential were newly developed. These novel dimeric peptides exhibited coacervation at significantly lower concentrations and temperatures than the commonly used elastin-derived peptide analogs; this result suggests that the coacervation ability of the peptides is enhanced by dimerization. Circular dichroism (CD) measurements indicate that the dimers undergo similar temperature-dependent and reversible conformational changes when coacervation occurs. The molecular dynamics calculation results reveal that the sheet-turn-sheet motif involving a type II β-turn-like structure commonly observed among the dimers and caused formation of globular conformation of them. These synthesized peptide dimers may be useful not only as model peptides for structural analysis of elastin and elastin-derived peptides, but also as base materials for developing various temperature-sensitive biomedical and industrial products.

Implicit Solvent Model for Million-Atom Atomistic Simulations: Insights into the Organization of 30-nm Chromatin Fiber

Molecular dynamics (MD) simulations based on the implicit solvent generalized Born (GB) models can provide significant computational advantages over the traditional explicit solvent simulations. However, the standard GB becomes prohibitively expensive for all-atom simulations of large structures; the model scales poorly, ∼n2, with the number of solute atoms. Here we combine our recently developed optimal point charge approximation (OPCA) with the hierarchical charge partitioning (HCP) approximation to present an ∼n log n multiscale, yet fully atomistic, GB model (GB-HCPO). The HCP approximation exploits the natural organization of biomolecules (atoms, groups, chains, and complexes) to partition the structure into multiple hierarchical levels of components. OPCA approximates the charge distribution for each of these components by a small number of point charges so that the low order multipole moments of these components are optimally reproduced. The approximate charges are then used for computing electrostatic interactions with distant components, while the full set of atomic charges are used for nearby components. We show that GB-HCPO can deliver up to 2 orders of magnitude speedup compared to the standard GB, with minimal impact on its accuracy. For large structures, GB-HCPO can approach the same nominal speed, as in nanoseconds per day, as the highly optimized explicit-solvent simulation based on particle mesh Ewald (PME). The increase in the nominal simulation speed, relative to the standard GB, coupled with substantially faster sampling of conformational space, relative to the explicit solvent, makes GB-HCPO a suitable candidate for MD simulation of large atomistic systems in implicit solvent. As a practical demonstration, we use GB-HCPO simulation to refine a ∼1.16 million atom structure of 30 nm chromatin fiber (40 nucleosomes). The refined structure suggests important details about spatial organization of the linker DNA and the histone tails in the fiber: (1) the linker DNA fills the core region, allowing the H3 histone tails to interact with the linker DNA, which is consistent with experiment; (2) H3 and H4 tails are found mostly in the core of the structure, closer to the helical axis of the fiber, while H2A and H2B are mostly solvent exposed. Potential functional consequences of these findings are discussed. GB-HCPO is implemented in the open source MD software NAB in Amber 2016.

Modeling Membrane Protein-Ligand Binding Interactions: The Human Purinergic Platelet Receptor

Membrane proteins, due to their roles as cell receptors and signaling mediators, make prime candidates for drug targets. The computational analysis of protein-ligand binding affinities has been widely employed as a tool in rational drug design efforts. Although efficient implicit solvent-based methods for modeling globular protein-ligand binding have been around for many years, the extension of such methods to membrane protein-ligand binding is still in its infancy. In this study, we extended the widely used Amber/MMPBSA method to model membrane protein-ligand systems, and we used it to analyze protein-ligand binding for the human purinergic platelet receptor (P2Y12R), a prominent drug target in the inhibition of platelet aggregation for the prevention of myocardial infarction and stroke. The binding affinities, computed by the Amber/MMPBSA method using standard parameters, correlate well with experiment. A detailed investigation of these parameters was conducted to assess their impact on the accuracy of the method. These analyses show the importance of properly treating the nonpolar solvation interactions and the electrostatic polarization in the binding of nucleotide agonists and non-nucleotide antagonists to P2Y12R. On the basis of the crystal structures and the experimental conditions in the binding assay, we further hypothesized that the nucleotide agonists lose their bound magnesium ion upon binding to P2Y12R, and our computational study supports this hypothesis. Ultimately, this work illustrates the value of computational analysis in the interpretation of experimental binding reactions.

A pH-dependent computational approach to the effect of mutations on protein stability

This article describes a novel software implementation for high-throughput scanning mutagenesis with a focus on protein stability. The approach combines molecular mechanics calculations with calculations of protein ionization and a Gaussian-chain model of electrostatic interactions in unfolded state. Comprehensive testing demonstrates a state-of-the-art accuracy for predicted free energy differences on single, double, and triple mutations with a correlation coefficient R above 0.7, which takes about 1.5 min per mutation on a single CPU. Unlike most of existing in silico methods for fast mutagenesis, the stability changes are reported as a continuous function of solution pH for wide pH intervals. We also propose a novel in silico strategy for searching stabilized protein variants that is based on combinatorial scanning mutagenesis using representative amino acid types. Our in silico predictions are in excellent agreement with the hyper-stabilized variants of mesophilic cold shock protein found using the Proside method of direct evolution. © 2016 Wiley Periodicals, Inc.

A Novel Di-Leucine Motif at the N-Terminus of Human Organic Solute Transporter Beta Is Essential for Protein Association and Membrane Localization

The heteromeric membrane protein Organic Solute Transporter alpha/beta is the major bile acid efflux transporter in the intestine. Physical association of its alpha and beta subunits is essential for their polarized basolateral membrane localization and function in the transport of bile acids and other organic solutes. We identified a highly conserved acidic dileucine motif (-EL20L21EE) at the extracellular amino-tail of organic solute transporter beta from multiple species. To characterize the role of this protein interacting domain in the association of the human beta and alpha subunits and in membrane localization of the transporter, Leu20 and Leu21 on the amino-tail of human organic solute transporter beta were replaced with alanines by site-directed mutagenesis. Co-immunoprecipitation study in HEK293 cells demonstrated that substitution of the leucine residues with alanines prevented the interaction of the human beta mutant with the alpha subunit. Membrane biotinylation demonstrated that the LL/AA mutant eliminated membrane expression of both subunits. Computational-based modelling of human organic solute transporter beta suggested that the LL/AA mutation substantially alters both the structure and lipophilicity of the surface, thereby not only affecting the interaction with the alpha subunit but also possibly impacting the capacity of the beta subunit to traffick through the cell and interact with the membrane. In summary, our findings indicate that the dileucine motif in the extracellular N-terminal region of human organic solute transporter beta subunit plays a critical role in the association with the alpha subunit and in its polarized plasma membrane localization.

Identification of novel natural inhibitor for NorM - a multidrug and toxic compound extrusion transporter - an insilico molecular modeling and simulation studies

The emergence of bacterial multidrug resistance is an increasing problem in treatment of infectious diseases. An important cause for the multidrug resistance of bacteria is the expression of multidrug efflux transporters. The multidrug and toxic compound extrusion (MATE) transporters are most recently recognized as unique efflux system for extrusion of antimicrobials and therapeutic drugs due to energy stored in either Na⁺ or H⁺ electrochemical gradient. In the present study, high throughput virtual screening of natural compound collections against NorM - a MATE transporter from Neisseria gonorrhea (NorM-NG) has been carried out followed by flexible docking. The molecular simulation in membrane environment has been performed for understanding the stability and binding energetic of top lead compounds. Results identified a compound from the Indian medicinal plant "Terminalia chebula" which has good binding free energy compared to substrates (rhodamine 6 g, ethidium) and more favorable interactions with the central cavity forming active site residues. The compound has restricted movement in TM7, TM8, and TM1, thus blocking the disruption of Na+ - coordination along with equilibrium state bias towards occlude state of NorM transporter. Thus, this compound blocks the effluxing pathway of antimicrobial drugs and provides as a natural bioactive lead inhibitor against NorM transporter in drug-resistant gonorrhea.

Constant-pH Molecular Dynamics Study of Kyotorphin in an Explicit Bilayer

To our knowledge, we present the first constant-pH molecular dynamics study of the neuropeptide kyotorphin in the presence of an explicit lipid bilayer. The overall conformation freedom of the peptide was found to be affected by the interaction with the membrane, in accordance with previous results using different methodologies. Analysis of the interactions between the N-terminus amine group of the peptide and several lipid atoms shows that the membrane is able to stabilize both ionized and neutral forms of kyotorphin, resulting in a pKa value that is similar to the one obtained in water. This illustrates how a detailed molecular model of the membrane leads to rather different results than would be expected from simply regarding it as a low-dielectric slab.

Speed of conformational change: comparing explicit and implicit solvent molecular dynamics simulations

Adequate sampling of conformation space remains challenging in atomistic simulations, especially if the solvent is treated explicitly. Implicit-solvent simulations can speed up conformational sampling significantly. We compare the speed of conformational sampling between two commonly used methods of each class: the explicit-solvent particle mesh Ewald (PME) with TIP3P water model and a popular generalized Born (GB) implicit-solvent model, as implemented in the AMBER package. We systematically investigate small (dihedral angle flips in a protein), large (nucleosome tail collapse and DNA unwrapping), and mixed (folding of a miniprotein) conformational changes, with nominal simulation times ranging from nanoseconds to microseconds depending on system size. The speedups in conformational sampling for GB relative to PME simulations, are highly system- and problem-dependent. Where the simulation temperatures for PME and GB are the same, the corresponding speedups are approximately onefold (small conformational changes), between ∼1- and ∼100-fold (large changes), and approximately sevenfold (mixed case). The effects of temperature on speedup and free-energy landscapes, which may differ substantially between the solvent models, are discussed in detail for the case of miniprotein folding. In addition to speeding up conformational sampling, due to algorithmic differences, the implicit solvent model can be computationally faster for small systems or slower for large systems, depending on the number of solute and solvent atoms. For the conformational changes considered here, the combined speedups are approximately twofold, ∼1- to 60-fold, and ∼50-fold, respectively, in the low solvent viscosity regime afforded by the implicit solvent. For all the systems studied, 1) conformational sampling speedup increases as Langevin collision frequency (effective viscosity) decreases; and 2) conformational sampling speedup is mainly due to reduction in solvent viscosity rather than possible differences in free-energy landscapes between the solvent models.

Molecular dynamics simulations of biological membranes and membrane proteins using enhanced conformational sampling algorithms

This paper reviews various enhanced conformational sampling methods and explicit/implicit solvent/membrane models, as well as their recent applications to the exploration of the structure and dynamics of membranes and membrane proteins. Molecular dynamics simulations have become an essential tool to investigate biological problems, and their success relies on proper molecular models together with efficient conformational sampling methods. The implicit representation of solvent/membrane environments is reasonable approximation to the explicit all-atom models, considering the balance between computational cost and simulation accuracy. Implicit models can be easily combined with replica-exchange molecular dynamics methods to explore a wider conformational space of a protein. Other molecular models and enhanced conformational sampling methods are also briefly discussed. As application examples, we introduce recent simulation studies of glycophorin A, phospholamban, amyloid precursor protein, and mixed lipid bilayers and discuss the accuracy and efficiency of each simulation model and method. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Folding Simulations of the Transmembrane Helix of Virus Protein U in an Implicit Membrane Model

Vpu is an 81-amino-acid auxiliary membrane protein encoded by human immunodeficiency virus type 1 (HIV-1). One of its roles is to amplify viral release by self-assembling in homo-oligomers to form functional water-filled pores enabling the flux of ions across the membrane. Various NMR and CD studies have shown that the transmembrane domain of Vpu has a helical conformation. With a recently developed implicit membrane model and an efficient Monte Carlo (MC) algorithm using concerted backbone rotations, we simulate the folding of the transmembrane domain of Vpu at atomic resolution. The implicit membrane environment is based on the generalized Born theory and enables very long time scale events, such as folding to be observed using detailed all-atom representation of the protein. Such studies are currently computationally unfeasible with fully explicit lipid bilayer molecular dynamics simulations. The correct helical transmembrane structure of Vpu is predicted from extended conformations and remains stably inserted. Tilt and kink angles agree well with experimental estimates from NMR measurements. The experimentally observed change in tilt angle in membranes of varying hydrophobic width is accurately reproduced. The extensive simulation of a pentamer of the Vpu transmembrane domain in the implicit membrane gives results similar to the ones reported previously for fully explicit bilayer simulations.

Membrane/Toxin Interaction Energetics via Serial Multiscale Molecular Dynamics Simulations

Computing free energies of complex biomolecular systems via atomistic (AT) molecular dynamics (MD) simulations remains a challenge due to the need for adequate sampling and convergence. Recent coarse-grained (CG) methodology allows simulations of significantly larger systems (∼10(6) to 10(8) atoms) over longer (μs/ms) time scales. Such CG models appear to be capable of making semiquantitative predictions. However, their ability to reproduce accurate thermodynamic quantities remains uncertain. We have recently used CG MD simulations to compute the potential of mean force (PMF) or free energy profile of a small peptide toxin interacting with a lipid bilayer along a 1D reaction coordinate. The toxin studied was VSTx1 (Voltage Sensor Toxin 1) from spider venom which inhibits the archeabacterial voltage-gated potassium (Kv) channel KvAP by binding to the voltage-sensor (VS) domains. Here, we re-estimate this PMF profile using (i) AT MD simulations with explicit membrane and solvent and (ii) an implicit membrane and solvent (generalized Born; GBIM) model where only the peptide was explicit. We used the CG MD free energy simulations to guide the setup of the corresponding AT MD simulations. The aim was to avoid local minima in the AT simulations which would be difficult over shorter AT time scales. A cross-comparison of the PMF profiles revealed a conserved topology, although there were differences in the magnitude of the free energies. The CG and AT simulations predicted a membrane/water interface free energy well of -27 and -23 kcal/mol, respectively (with respect to water). The GBIM model, however, gave a reduced interfacial free energy well (-12 kcal/mol). In addition, the CG and GBIM models predicted a free energy barrier of +61 and +96 kcal/mol, respectively, for positioning the toxin at the center of the bilayer, which was considerably smaller in the AT simulations (+26 kcal/mol). Thus, we present a framework for serially combining CG and AT simulations to estimate the free energy of peptide/membrane interactions. Such approaches for combining simulations at different levels of granularity will become increasingly important in future studies of complex membrane/protein systems.

Applications of MMPBSA to Membrane Proteins I: Efficient Numerical Solutions of Periodic Poisson-Boltzmann Equation

Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membranes into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multigrid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations.

Protein-Ligand Electrostatic Binding Free Energies from Explicit and Implicit Solvation

Accurate yet efficient computational models of solvent environment are central for most calculations that rely on atomistic modeling, such as prediction of protein-ligand binding affinities. In this study, we evaluate the accuracy of a recently developed generalized Born implicit solvent model, GBNSR6 (Aguilar et al. J. Chem. Theory Comput. 2010, 6, 3613-3639), in estimating the electrostatic solvation free energies (ΔG(pol)) and binding free energies (ΔΔG(pol)) for small protein-ligand complexes. We also compare estimates based on three different explicit solvent models (TIP3P, TIP4PEw, and OPC). The two main findings are as follows. First, the deviation (RMSD = 7.04 kcal/mol) of GBNSR6 binding affinities from commonly used TIP3P reference values is comparable to the deviations between explicit models themselves, e.g. TIP4PEw vs TIP3P (RMSD = 5.30 kcal/mol). A simple uniform adjustment of the atomic radii by a single scaling factor reduces the RMS deviation of GBNSR6 from TIP3P to within the above "error margin" - differences between ΔΔG(pol) estimated by different common explicit solvent models. The simple radii scaling virtually eliminates the systematic deviation (ΔΔG(pol)) between GBNSR6 and two out of the three explicit water models and significantly reduces the deviation from the third explicit model. Second, the differences between electrostatic binding energy estimates from different explicit models is disturbingly large; for example, the deviation between TIP4PEw and TIP3P estimates of ΔΔG(pol) values can be up to ∼50% or ∼9 kcal/mol, which is significantly larger than the "chemical accuracy" goal of ∼1 kcal/mol. The absolute ΔG(pol) calculated with different explicit models could differ by tens of kcal/mol. These discrepancies point to unacceptably high sensitivity of binding affinity estimates to the choice of common explicit water models. The absence of a clear "gold standard" among these models strengthens the case for the use of accurate implicit solvation models for binding energetics, which may be orders of magnitude faster.

Capturing Spontaneous Membrane Insertion of the Influenza Virus Hemagglutinin Fusion Peptide

Hemagglutinin (HA) is a protein located on the surface of the influenza virus that mediates viral fusion to the host cellular membrane. During the fusion process the HA fusion peptide (HAfp), formed by the first 23 N-terminal residues of HA and structurally characterized by two alpha helices (Helix A and Helix B) tightly packed in a hairpin-like arrangement, is the only part of the virus in direct contact with the host membrane. After encountering the host cell, HAfp is believed to insert into the membrane, thereby initiating the fusion of the viral and host membranes. Detailed characterization of the interactions between the HAfp and cellular membrane is therefore of high relevance to the mechanism of viral entry into the host cell. Employing HMMM membrane representation with enhanced lipid mobility, we have performed a large set of independent simulations of unbiased membrane binding of HAfp. We have been able to capture spontaneous binding and insertion of HAfp consistently in nearly all the simulations. A reproducible membrane-bound configuration emerges from these simulations, despite employing a diverse set of initial configurations. Extension of several of the simulations into full membrane systems confirms the stability of the membrane-bound form obtained from HMMM binding simulations. The resulting model allows for the characterization of important interactions between the peptide and the membrane and the details of the binding process of the peptide for the first time. Upon membrane binding, Helix A inserts much deeper into the membrane than Helix B, suggesting that the former is responsible for hydrophobic anchoring of the peptide into the membrane. Helix B, in contrast, is found to establish major amphipathic interactions at the interfacial region thereby contributing to binding strength of HAfp.

SLIM: an improved generalized Born implicit membrane model

In most implicit continuum models, membranes are represented as heterogeneous dielectric environments, but their treatment within computationally efficient generalized Born (GB) models is challenging. Despite several previous attempts, an adequate description of multiple dielectric regions in implicit GB-based membrane models that reproduce the qualitative and quantitative features of Poisson-Boltzmann (PB) electrostatics remains an unmet prerequisite of qualitatively correct implicit membrane models. A novel scheme (SLIM) to decompose one environment consisting of multiple dielectric regions into a sum of multiple environments consisting only of two dielectric regions each is proposed to solve this issue. These simpler environments can be treated with established GB methods. This approach captures qualitative features of PB electrostatic that are not present in previous models. Simulations of three membrane proteins demonstrate that this model correctly reproduces known properties of these proteins in agreement with experimental or other computational studies.

Membrane environment modulates the pKa values of transmembrane helices

In this work, we apply the recently developed constant pH molecular dynamics technique to study protonation equilibria of titratable side chains in the context of simple transmembrane (TM) helices and explore the effect of pH on their configurations in membrane bilayers. We observe that, despite a significant shift toward neutral states, considerable population of different side chains stay in the charged state that give rise to pK_a values around 9.6 for Asp and Glu and 4.5 to 6 for His and Lys side chains, respectively. These charged states are highly stabilized by favorable interactions between head groups, water molecules, and the charged side chains that are facilitated by substantial changes in the configuration of the peptides. The pH dependent configurations and the measured pK_a values are in good agreement with relatively recent solid state NMR measurements. Our results presented here demonstrate that all-atom constant pH molecular dynamics can be applied to membrane proteins and peptides to obtain reliable pK_a values and pH dependent behavior for these systems.

Computational modeling of membrane proteins

The determination of membrane protein (MP) structures has always trailed that of soluble proteins due to difficulties in their overexpression, reconstitution into membrane mimetics, and subsequent structure determination. The percentage of MP structures in the protein databank (PDB) has been at a constant 1-2% for the last decade. In contrast, over half of all drugs target MPs, only highlighting how little we understand about drug-specific effects in the human body. To reduce this gap, researchers have attempted to predict structural features of MPs even before the first structure was experimentally elucidated. In this review, we present current computational methods to predict MP structure, starting with secondary structure prediction, prediction of trans-membrane spans, and topology. Even though these methods generate reliable predictions, challenges such as predicting kinks or precise beginnings and ends of secondary structure elements are still waiting to be addressed. We describe recent developments in the prediction of 3D structures of both α-helical MPs as well as β-barrels using comparative modeling techniques, de novo methods, and molecular dynamics (MD) simulations. The increase of MP structures has (1) facilitated comparative modeling due to availability of more and better templates, and (2) improved the statistics for knowledge-based scoring functions. Moreover, de novo methods have benefited from the use of correlated mutations as restraints. Finally, we outline current advances that will likely shape the field in the forthcoming decade.

Transferring the PRIMO Coarse-Grained Force Field to the Membrane Environment: Simulations of Membrane Proteins and Helix-Helix Association

An extension of the recently developed PRIMO coarse-grained force field to membrane environments, PRIMO-M, is described. The membrane environment is modeled with the heterogeneous dielectric generalized Born (HDGB) methodology that simply replaces the standard generalized Born model in PRIMO without further parametrization. The resulting model was validated by comparing amino acid insertion free energy profiles and application in molecular dynamics simulations of membrane proteins and membrane-interacting peptides. Membrane proteins with 148–661 amino acids show stable root-mean-squared-deviations (RMSD) between 2 and 4 Å for most systems. Transmembrane helical peptides maintain helical shape and exhibit tilt angles in good agreement with experimental or other simulation data. The association of two glycophorin A (GpA) helices was simulated using replica exchange molecular dynamics simulations yielding the correct dimer structure with a crossing angle in agreement with previous studies. Finally, conformational sampling of the influenza fusion peptide also generates structures in agreement with previous studies. Overall, these findings suggest that PRIMO-M can be used to study membrane bound peptides and proteins and validates the transferable nature of the PRIMO coarse-grained force field.

Biological applications of classical electrostatics methods

Continuum electrostatics modeling of solvation based on the Poisson–Boltzmann (PB) equation has gained wide acceptance in biomolecular applications such as energetic analysis and structural visualization. Successful application of the PB solvent models requires careful calibration of the solvation parameters. Extensive testing and validation is also important to ensure accuracy in their applications. Limitation in the continuum modeling of solvation is also a known issue in certain biomolecular applications. Growing interest in membrane systems has further spurred developmental efforts to allow inclusion of membrane in the PB solvent models. Despite their past successes due to careful parameterization, algorithm development and parallel implementation, there is still much to be done to improve their transferability from the small molecular systems upon which they were developed and validated to complex macromolecular systems as advances in technology continue to push forward, providing ever greater computational resources to researchers to study more interesting biological systems of higher complexity.

Accuracy of continuum electrostatic calculations based on three common dielectric boundary definitions

We investigate the influence of three common definitions of the solute/solvent dielectric boundary (DB) on the accuracy of the electrostatic solvation energy ΔG_el computed within the Poisson Boltzmann and the generalized Born models of implicit solvation. The test structures include small molecules, peptides and small proteins; explicit solvent ΔG_el are used as accuracy reference. For common atomic radii sets BONDI, PARSE (and ZAP9 for small molecules) the use of van der Waals (vdW) DB results, on average, in considerably larger errors in ΔG_el than the molecular surface (MS) DB. The optimal probe radius ρ_w for which the MS DB yields the most accurate ΔG_el varies considerably between structure types. The solvent accessible surface (SAS) DB becomes optimal at ρ_w ~ 0.2 Å (exact value is sensitive to the structure and atomic radii), at which point the average accuracy of ΔG_el is comparable to that of the MS-based boundary. The geometric equivalence of SAS to vdW surface based on the same atomic radii uniformly increased by ρ_w gives the corresponding optimal vdW DB. For small molecules, the optimal vdW DB based on BONDI + 0.2 Å radii can yield ΔG_el estimates at least as accurate as those based on the optimal MS DB. Also, in small molecules, pairwise charge-charge interactions computed with the optimal vdW DB are virtually equal to those computed with the MS DB, suggesting that in this case the two boundaries are practically equivalent by the electrostatic energy criteria. In structures other than small molecules, the optimal vdW and MS dielectric boundaries are not equivalent: the respective pairwise electrostatic interactions in the presence of solvent can differ by up to 5 kcal/mol for individual atomic pairs in small proteins, even when the total ΔG_el are equal. For small proteins, the average decrease in pairwise electrostatic interactions resulting from the switch from optimal MS to optimal vdW DB definition can be mimicked within the MS DB definition by doubling of the solute dielectric constant. However, the use of the higher interior dielectric does not eliminate the large individual deviations between pairwise interactions computed within the two DB definitions. It is argued that while the MS based definition of the dielectric boundary is more physically correct in some types of practical calculations, the choice is not so clear in some other common scenarios.