A method to determine dielectric constants in nonhomogeneous systems: application to biological membranes

Sensing membrane voltage by reorientation of dipolar transmembrane peptides

Membrane voltage plays a vital role in the behavior and functions of the lipid bilayer membrane. For instance, it regulates the exchange of molecules across the membrane through transmembrane proteins such as ion channels. In this paper, we study the membrane voltage-sensing mechanism, which entails the reorientation of α-helices with a change in the membrane voltage. We consider a helix having a large electrical macrodipole embedded in a lipid bilayer as a model system. We performed extensive molecular dynamics simulations to study the effect of variation of membrane voltage on the tilt angle of peptides and ascertain the optimal parameters for designing such a voltage-sensing peptide. A theoretical model for the system is also developed to investigate the interplay of competing effects of hydrophobic mismatch and dipole-electric field coupling on the tilt of the peptide and further explore the parameter space. This work opens the possibility for the design and fabrication of artificial dipolar membrane voltage-sensing elements for biomedical applications.

Treating Polarization Effects in Charged and Polar Bio-Molecules Through Variable Electrostatic Parameters

Polarization plays important roles in charged and hydrogen bonding containing systems. Much effort ranging from the construction of physics-based models to quantum mechanism (QM)-based and machine learning (ML)-assisted models have been devoted to incorporating the polarization effect into the conventional force fields at different levels, such as atomic and coarse grained (CG). The application of polarizable force fields or polarization models was limited by two aspects, namely, computational cost and transferability. Different from physics-based models, no predetermining parameters were required in the QM-based approaches. Taking advantage of both the accuracy of QM calculations and efficiency of molecular mechanism (MM) and ML, polarization effects could be treated more efficiently while maintaining the QM accuracy. The computational cost could be reduced with variable electrostatic parameters, such as the charge, dipole, and electronic dielectric constant with the help of linear scaling fragmentation-based QM calculations and ML models. Polarization and entropy effects on the prediction of partition coefficient of druglike molecules are demonstrated by using both explicit or implicit all-atom molecular dynamics simulations and machine learning-assisted models. Directions and challenges for future development are also envisioned.

Combined in-silico and in-vitro experiments support acid-base equilibrium as a tool to estimate the localization depth of 4-nitrophenol within a phospholipid bilayer

The interaction and location of 4-nitrophenol (PNP) in biomembranes are relevant in the bioaccumulation and potentiation of the intensive toxic effects of this persistent organic pollutant. In this work, in-silico analyses predicted that, in a fluid phospholipid bilayer, the minimum energy of the protonated (PNPH) and deprotonated (PNP^-) species is located within the glycerol and choline region, respectively. This was experimentally confirmed by acid-base equilibrium experiments and theory, allowing the estimation of the mean location of PNP within a bilayer region with a dielectric constant D = 50.6 compatible with the phosphate/choline moiety of egg-yolk phosphatidylcholine unilamellar (EPC) vesicles. The comparison with the D = 43.2 value obtained in Triton X-100 micelles allow predicting a mean surface potential of ψ = 25.37 mV for the EPC-water interface. Changes in the chemical shifts and longitudinal relaxation times of EPC hydrogens by ¹H NMR confirm the deeper location of the PNPH within the glycerol region and at the choline region (PNP^-) at higher pH. Intermolecular PNP^-EPC dipolar interactions within the choline region was also demonstrated at pH 10.2 using ROESY experiments. Additional information was obtained trough ³¹P NMR, that detected an increase in the anisotropy at the membrane interface after insertion of PNP which probably act as a bridge between choline moieties rigidizing the crystalline structure at that spot. Concluding, here we provide experimental support to the "pH-piston hypothesis" proposed some decades ago in the pharmaceutical field, and that reinforce the importance of the environmental conditions (e.g. pH) to modulate the bioavailability of this highly toxic pollutant.

Measuring anion binding at biomembrane interfaces

The quantification of anion binding by molecular receptors within lipid bilayers remains challenging. Here we measure anion binding in lipid bilayers by creating a fluorescent macrocycle featuring a strong sulfate affinity. We find the determinants of anion binding in lipid bilayers to be different from those expected that govern anion binding in solution. Charge-dense anions H2PO4- and Cl- that prevail in dimethyl sulfoxide fail to bind to the macrocycle in lipids. In stark contrast, ClO4- and I- that hardly bind in dimethyl sulfoxide show surprisingly significant affinities for the macrocycle in lipids. We reveal a lipid bilayer anion binding principle that depends on anion polarisability and bilayer penetration depth of complexes leading to unexpected advantages of charge-diffuse anions. These insights enhance our understanding of how biological systems select anions and guide the design of functional molecular systems operating at biomembrane interfaces.

The permeability of human red blood cell membranes to hydrogen peroxide is independent of aquaporins

Hydrogen peroxide (H₂O₂) not only is an oxidant but also is an important signaling molecule in vascular biology, mediating several physiological functions. Red blood cells (RBCs) have been proposed to be the primary sink of H₂O₂ in the vasculature because they are the main cellular component of blood with a robust antioxidant defense and a high membrane permeability. However, the exact permeability of human RBC to H₂O₂ is neither known nor is it known if the mechanism of permeation involves the lipid fraction or protein channels. To gain insight into the permeability process, we measured the partition constant of H₂O₂ between water and octanol or hexadecane using a novel double-partition method. Our results indicated that there is a large thermodynamic barrier to H₂O₂ permeation. The permeability coefficient of H₂O₂ through phospholipid membranes containing cholesterol with saturated or unsaturated acyl chains was determined to be 4 × 10⁻⁴ and 5 × 10⁻³ cm s⁻¹, respectively, at 37 °C. The permeability coefficient of human RBC membranes to H₂O₂ at 37 °C, on the other hand, was 1.6 × 10⁻³ cm s⁻¹. Different aquaporin-1 and aquaporin-3 inhibitors proved to have no effect on the permeation of H₂O₂. Moreover, human RBCs devoid of either aquaporin-1 or aquaporin-3 were equally permeable to H₂O₂ as normal human RBCs. Therefore, these results indicate that H₂O₂ does not diffuse into RBCs through aquaporins but rather through the lipid fraction or a still unidentified membrane protein.

Dielectric Properties of Phosphatidylcholine Membranes and the Effect of Sugars

Simple carbohydrates are associated with the enhanced risk of cardiovascular disease and adverse changes in lipoproteins in the organism. Conversely, sugars are known to exert a stabilizing effect on biological membranes, and this effect is widely exploited in medicine and industry for cryopreservation of tissues and materials. In view of elucidating molecular mechanisms involved in the interaction of mono- and disaccharides with biomimetic lipid systems, we study the alteration of dielectric properties, the degree of hydration, and the rotational order parameter and dipole potential of lipid bilayers in the presence of sugars. Frequency-dependent deformation of cell-size unilamellar lipid vesicles in alternating electric fields and fast Fourier transform electrochemical impedance spectroscopy are applied to measure the specific capacitance of phosphatidylcholine lipid bilayers in sucrose, glucose and fructose aqueous solutions. Alteration of membrane specific capacitance is reported in sucrose solutions, while preservation of membrane dielectric properties is established in the presence of glucose and fructose. We address the effect of sugars on the hydration and the rotational order parameter for 1-palmitoyl-2-oleoyl-sn-glycero-3- phosphocholine (POPC) and 1-stearoyl-2-oleoyl-sn-glycero-3- phosphocholine (SOPC). An increased degree of lipid packing is reported in sucrose solutions. The obtained results provide evidence that some small carbohydrates are able to change membrane dielectric properties, structure, and order related to membrane homeostasis. The reported data are also relevant to future developments based on the response of lipid bilayers to external physical stimuli such as electric fields and temperature changes.

Mechanistic Understanding from Molecular Dynamics in Pharmaceutical Research 2: Lipid Membrane in Drug Design

We review the use of molecular dynamics (MD) simulation as a drug design tool in the context of the role that the lipid membrane can play in drug action, i.e., the interaction between candidate drug molecules and lipid membranes. In the standard "lock and key" paradigm, only the interaction between the drug and a specific active site of a specific protein is considered; the environment in which the drug acts is, from a biophysical perspective, far more complex than this. The possible mechanisms though which a drug can be designed to tinker with physiological processes are significantly broader than merely fitting to a single active site of a single protein. In this paper, we focus on the role of the lipid membrane, arguably the most important element outside the proteins themselves, as a case study. We discuss work that has been carried out, using MD simulation, concerning the transfection of drugs through membranes that act as biological barriers in the path of the drugs, the behavior of drug molecules within membranes, how their collective behavior can affect the structure and properties of the membrane and, finally, the role lipid membranes, to which the vast majority of drug target proteins are associated, can play in mediating the interaction between drug and target protein. This review paper is the second in a two-part series covering MD simulation as a tool in pharmaceutical research; both are designed as pedagogical review papers aimed at both pharmaceutical scientists interested in exploring how the tool of MD simulation can be applied to their research and computational scientists interested in exploring the possibility of a pharmaceutical context for their research.

A Graphic Encoding Method for Quantitative Classification of Protein Structure and Representation of Conformational Changes

In order to successfully predict a proteins function throughout its trajectory, in addition to uncovering changes in its conformational state, it is necessary to employ techniques that maintain its 3D information while performing at scale. We extend a protein representation that encodes secondary and tertiary structure into fix-sized, color images, and a neural network architecture (called GEM-net) that leverages our encoded representation. We show the applicability of our method in two ways: (1) performing protein function prediction, hitting accuracy between 78 and 83 percent, and (2) visualizing and detecting conformational changes in protein trajectories during molecular dynamics simulations.

Quantitative Determination of Relative Permittivity Based on the Fluorescence Property of Pyrene Derivatives: An Interpretation of Hydrophobicity in Self-Assembled Aggregates of Nonionic Amphiphiles

Aggregates in aqueous solutions can embed hydrophobic molecules, and their interactions depend on the properties of the aggregates. The electric surface potential, molecular mobility, and gradual hydrophobicity are the properties that regulate the interactions, and it is essential to understand these to quantify the properties. Electric surface potential and molecular mobility are quantified using the zeta potential and NMR measurements. In this study, the quantification of gradual hydrophobicity within the aggregate based on the relative permittivity, also called the dielectric constant, has been estimated from fluorescence spectra of pyrene-dicarboxylic acid conjugates. The localization of the pyrene moiety was modified by conjugation with succinic acid, suberic acid, or dodecanedioic acid, and the conjugates were evaluated in the shallow, middle, and deep regions of the aggregates. Span and Tween surfactants have been employed to prepare these aggregates, because they form various kinds of aggregates such as micelles and vesicles. It was realized that the hydrophobicity gradually increased from the interface to the hydrophobic core. Alternatively, a comparison of hydrophobicity within the aggregates showed no remarkable difference. Moreover, the analyses suggested that there are a few water molecules in the deep region. These results support the idea of the localization of embedded molecules in aggregates.

Dynamic "Molecular Portraits" of Biomembranes Drawn by Their Lateral Nanoscale Inhomogeneities

To date, it has been reliably shown that the lipid bilayer/water interface can be thoroughly characterized by a sophisticated so-called "dynamic molecular portrait". The latter reflects a combination of time-dependent surface distributions of various physicochemical properties, inherent in both model lipid bilayers and natural multi-component cell membranes. One of the most important features of biomembranes is their mosaicity, which is expressed in the constant presence of lateral inhomogeneities, the sizes and lifetimes of which vary in a wide range-from 1 to 10³ nm and from 0.1 ns to milliseconds. In addition to the relatively well-studied macroscopic domains (so-called "rafts"), the analysis of micro- and nanoclusters (or domains) that form an instantaneous picture of the distribution of structural, dynamic, hydrophobic, electrical, etc., properties at the membrane-water interface is attracting increasing interest. This is because such nanodomains (NDs) have been proven to be crucial for the proper membrane functioning in cells. Therefore, an understanding with atomistic details the phenomena associated with NDs is required. The present mini-review describes the recent results of experimental and in silico studies of spontaneously formed NDs in lipid membranes. The main attention is paid to the methods of ND detection, characterization of their spatiotemporal parameters, the elucidation of the molecular mechanisms of their formation. Biological role of NDs in cell membranes is briefly discussed. Understanding such effects creates the basis for rational design of new prospective drugs, therapeutic approaches, and artificial membrane materials with specified properties.

Theory of cell membrane interaction with glass

There are three regimes of cell membrane interaction with glass: Tight and loose adhesion, separated by repulsion. Explicitly including hydration, this paper evaluates the pressure between the surfaces as functions of distance for ion correlation and ion-screened electrostatics and electromagnetic fluctuations. The results agree with data for tight adhesion energy (0.5-3 vs 0.4-4 mJ/m^{2}), detachment pressure (7.9 vs. 9 MPa), and peak repulsion (3.4-7.5 vs. 5-10 kPa), also matching the repulsion's distance dependence on renormalization by steric pressure mainly from undulations.

Strategies for enzymological studies and measurements of biological molecules with the cytolysin A nanopore

Pore-forming toxins are used in a variety of biotechnological applications. Typically, individual membrane proteins are reconstituted in artificial lipid bilayers where they form water-filled nanoscale apertures (nanopores). When a voltage is applied, the ionic current passing through a nanopore can be used for example to sequence biopolymers, identify molecules, or to study chemical or enzymatic reactions at the single-molecule level. Here we present strategies for studying individual enzymes and measuring molecules, also in highly complex biological samples such as blood.

Stepwise Insertion of Cobra Cardiotoxin CT2 into a Lipid Bilayer Occurs as an Interplay of Protein and Membrane "Dynamic Molecular Portraits"

For many peripheral membrane-binding polypeptides(MBPs), especially β-structural ones, the precise molecular mechanisms of membrane insertion remain unclear. In most cases, only the terminal water-soluble and membrane-bound states have been elucidated, whereas potential functionally important intermediate stages are still not understood in sufficient detail. In this study, we present one of the first successful attempts to describe step-by-step embedding of the MBP cardiotoxin 2 (CT2) from cobra Naja oxiana venom into a lipid bilayer at the atomistic level. CT2 possesses a highly conservative and rigid β-structured three-finger fold shared by many other exogenous and endogenous proteins performing a wide variety of functions. The incorporation of CT2 into the lipid bilayer was analyzed via a 2 μs all-atom molecular dynamics (MD) simulation without restraints. This process was shown to occur over a number of distinct steps, while the geometry of initial membrane attachment drastically differs from that of the final equilibrated state. In the latter one, the hydrophobic platform ("bottom") formed by the tips of the three loops is deeply buried into the lipid bilayer. This agrees well with the NMR data obtained earlier for CT2 in detergent micelles. However, the bottom is too bulky to insert itself into the membrane at once. Instead, the gradual immersion of CT2 initiated by the loop-1 was observed. This initial binding stage was also demonstrated in a series of MD runs with varying starting orientations of the toxin with respect to the bilayer surface. Apart from the nonspecific long-range electrostatic attraction and hydrophobic match/mismatch factor, several specific lipid-binding sites were identified in CT2. They were shown to promote membrane insertion by engaging in strong interactions with lipid head groups, fine-tuning the toxin-membrane accommodation. We therefore propose that the toxin insertion relies on the interplay of nonspecific and specific interactions, which are determined by the "dynamic molecular portraits" of the two players, the protein and the membrane. The proposed model does not require protein oligomerization for membrane insertion and can be further employed to design MBPs with predetermined properties with regard to particular membrane targets.

Comparative roles of charge, π, and hydrophobic interactions in sequence-dependent phase separation of intrinsically disordered proteins

Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid-liquid phase separation (LLPS) of proteins, we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess roles of electrostatic, hydrophobic, cation-π, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated three different residue-residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation-π interactions consistently accounted for available experimental LLPS data on the wild-type, a charge-scrambled, a phenylalanine-to-alanine (FtoA), and an arginine-to-lysine (RtoK) mutant of Ddx4 IDR. In contrast, interactions based on contact statistics among folded globular protein structures reproduce the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. Consistency between simulation and experiment was also found for RtoK mutants of P-granule protein LAF-1, underscoring that, to a degree, important LLPS-driving π-related interactions are embodied in classical statistical potentials. Further elucidation is necessary, however, especially of phenylalanine's role in condensate assembly because experiments on FtoA and tyrosine-to-phenylalanine mutants suggest that LLPS-driving phenylalanine interactions are significantly weaker than posited by common statistical potentials. Protein-protein electrostatic interactions are modulated by relative permittivity, which in general depends on aqueous protein concentration. Analytical theory suggests that this dependence entails enhanced interprotein interactions in the condensed phase but more favorable protein-solvent interactions in the dilute phase. The opposing trends lead to only a modest overall impact on LLPS.

Accurate Estimation of Membrane Capacitance from Atomistic Molecular Dynamics Simulations of Zwitterionic Lipid Bilayers

Lipid membranes are indispensable to life, and they regulate countless cellular processes. To investigate the properties of membranes under controlled conditions, numerous reconstitution methods have been developed over the last few decades. Several of these methods result in the formation of lipid bilayers containing residual hydrophobic molecules between the two monolayers. These contaminants might alter membrane properties, including bilayer thickness, that is usually inferred from measurements of membrane capacitance assuming a simple slab model. However, recent measurements on solvent-free bilayers raised significant questions on the reliability of this approach. To reconcile the observed discrepancies, we developed a protocol to predict membrane capacitance from the dielectric profile of lipid bilayers computed from molecular dynamics simulations. Our methodology shows excellent agreement against available data on solvent-free noncharged bilayers, and it confirms that the uniform slab model is a reliable approximation from which to infer membrane capacitance. We find that the effective electrical thickness contributing to membrane capacitance is different from the hydrophobic thickness inferred from X-ray scattering form factors. We apply our model to estimate the concentration of residual solvent in reconstituted systems, and we propose that our protocol could be used to infer membrane properties in the presence of hydrophobic solvents.

Long-range electron-electron interaction and charge transfer in protein complexes: a numerical approach

With application to the nitrite reductase hexameric protein complex of Desulfovibrio vulgaris, NrfH2A4, we suggest a strategy to compute the energy landscape of electron transfer in large systems of biochemical interest. For small complexes, the energy of all electronic configurations can be scanned completely on the level of a numerical solution of the Poisson-Boltzmann equation. In contrast, larger systems have to be treated using a pair approximation, which is verified here. Effective Coulomb interactions between neighbouring sites of excess electron localization may become as large as 200 meV, and they depend in a nontrivial manner on the intersite distance. We discuss the implications of strong Coulomb interactions on the thermodynamics and kinetics of charging and decharging a protein complex. Finally, we turn to the effect of embedding the system into a biomembrane.

A super-Gaussian Poisson-Boltzmann model for electrostatic free energy calculation: smooth dielectric distribution for protein cavities and in both water and vacuum states

Calculations of electrostatic potential and solvation free energy of macromolecules are essential for understanding the mechanism of many biological processes. In the classical implicit solvent Poisson-Boltzmann (PB) model, the macromolecule and water are modeled as two-dielectric media with a sharp border. However, the dielectric property of interior cavities and ion-channels is difficult to model realistically in a two-dielectric setting. In fact, the detection of water molecules in a protein cavity remains to be an experimental challenge. This introduces an uncertainty, which affects the subsequent solvation free energy calculation. In order to compensate this uncertainty, a novel super-Gaussian dielectric PB model is introduced in this work, which devices an inhomogeneous dielectric distribution to represent the compactness of atoms and characterizes empty cavities via a gap dielectric value. Moreover, the minimal molecular surface level set function is adopted so that the dielectric profile remains to be smooth when the protein is transferred from water phase to vacuum. An important feature of this new model is that as the order of super-Gaussian function approaches the infinity, the dielectric distribution reduces to a piecewise constant of the two-dielectric model. Mathematically, an effective dielectric constant analysis is introduced in this work to benchmark the dielectric model and select optimal parameter values. Computationally, a pseudo-time alternative direction implicit (ADI) algorithm is utilized for solving the super-Gaussian PB equation, which is found to be unconditionally stable in a smooth dielectric setting. Solvation free energy calculation of a Kirkwood sphere and various proteins is carried out to validate the super-Gaussian model and ADI algorithm. One macromolecule with both water filled and empty cavities is employed to demonstrate how the cavity uncertainty in protein structure can be bypassed through dielectric modeling in biomolecular electrostatic analysis.

Heterogeneous Dielectric Implicit Membrane Model for the Calculation of MMPBSA Binding Free Energies

Membrane-bound protein receptors are a primary biological drug target, but the computational analysis of membrane proteins has been limited. In order to improve molecular mechanics Poisson-Boltzmann surface area (MMPBSA) binding free energy calculations for membrane protein-ligand systems, we have optimized a new heterogeneous dielectric implicit membrane model, with respect to free energy simulations in explicit membrane and explicit water, and implemented it into the Amber software suite. This new model supersedes our previous uniform, single dielectric implicit membrane model by allowing the dielectric constant to vary with depth within the membrane. We calculated MMPBSA binding free energies for the human purinergic platelet receptor (P2Y₁₂R) and two of the muscarinic acetylcholine receptors (M2R and M3R) bound to various antagonist ligands using both membrane models, and we found that the heterogeneous dielectric membrane model has a stronger correlation with experimental binding affinities compared to the older model under otherwise identical conditions. This improved membrane model increases the utility of MMPBSA calculations for the rational design and improvement of future drug candidates.

Dielectric-Dependent Strength of Interlipid Hydrogen Bonding in Biomembranes: Model Case Study

Atomistic aspects of the structural organization, dynamics, and functioning of hydrated lipid bilayers-model cell membranes-are primarily governed by the fine balance of intermolecular interactions between all constituents of these systems. Besides the hydrophobic effect, which shapes the overall skeleton of lipid membranes, a very important contribution to their behavior is made by hydrogen bonds (H-bonds) between lipid head groups. The latter determine crucial phenomena in cell membranes, such as dynamic ultrananodomain organization, hydration, and fine-tuning of microscopic physicochemical properties that allow the membrane to adapt quickly when binding/insertion external agents (proteins, etc.). The characteristics of such H-bonds (strength, spatial localization, etc.) dramatically depend on the local polarity properties of the lipid-water environment. In this work, we calculated free energies of H-bonded complexes between typical donor (NH₃⁺, NH, OH) and acceptor (C═O, OH, COO^-, COOH) groups of lipids in vacuo and in a set of explicit solvents with dielectric constants (ε) from 1 to 78.3, which mimic membrane environment at different depths. This was done using Monte Carlo simulations and an assessment of the corresponding potential of mean force profiles. The strongest H-bonded complexes were observed in the nonpolar environment, and their strength increased sharply with decreasing ε below 17. When ε changed, the largest free energy gain (>10.8 kcal/mol) was observed for pairs of acceptors C═O and O(H) with donor NH₃⁺. The complexation of the same acceptors with NH donor in this range of ε values was rather less sensitive to the environmental polarity, by ∼1.5 kcal/mol. Dielectric-dependent interactions of polar lipid groups with water were evaluated as well. The results explain the delicate balance that determines the unique pattern of H-bonds for a particular lipid bilayer. Understanding the factors that regulate the propensity for H-bonding in lipid bilayers provides a fundamental basis for the rational design of new membrane nano objects with predefined properties.

YidC: Evaluating the Importance of the Native Environment

In this issue of Structure, Baker et al. (2018) take advantage of recent technological breakthroughs in solid-state NMR spectroscopy and electron cryogenic tomography to characterize structural and functional differences between reconstituted YidC in E. coli lipids and YidC as overexpressed in the E. coli inner cellular membrane.

Specific refolding pathway of viscumin A chain in membrane-like medium reveals a possible mechanism of toxin entry into cell

How is a water-soluble globular protein able to spontaneously cross a cellular membrane? It is commonly accepted that it undergoes significant structural rearrangements on the lipid-water interface, thus acquiring membrane binding and penetration ability. In this study molecular dynamics (MD) simulations have been used to explore large-scale conformational changes of the globular viscumin A chain in a complex environment – comprising urea and chloroform/methanol (CHCl₃/MeOH) mixture. Being well-packed in aqueous solution, viscumin A undergoes global structural rearrangements in both organic media. In urea, the protein is “swelling” and gradually loses its long-distance contacts, thus resembling the “molten globule” state. In CHCl₃/MeOH, viscumin A is in effect turned “inside out”. This is accompanied with strengthening of the secondary structure and surface exposure of hydrophobic epitopes originally buried inside the globule. Resulting solvent-adapted models were further subjected to Monte Carlo simulations with an implicit hydrophobic slab membrane. In contrast to only a few point surface contacts in water and two short regions with weak protein-lipid interactions in urea, MD-derived structures in CHCl₃/MeOH reveal multiple determinants of membrane interaction. Consequently it is now possible to propose a specific pathway for the structural adaptation of viscumin A with respect to the cell membrane – a probable first step of its translocation into cytoplasmic targets.

Sensitivity analysis of the Poisson Nernst-Planck equations: a finite element approximation for the sensitive analysis of an electrodiffusion model

Biological structures exhibiting electric potential fluctuations such as neuron and neural structures with complex geometries are modelled using an electrodiffusion or Poisson Nernst-Planck system of equations. These structures typically depend upon several parameters displaying a large degree of variation or that cannot be precisely inferred experimentally. It is crucial to understand how the mathematical model (and resulting simulations) depend on specific values of these parameters. Here we develop a rigorous approach based on the sensitivity equation for the electrodiffusion model. To illustrate the proposed methodology, we investigate the sensitivity of the electrical response of a node of Ranvier with respect to ionic diffusion coefficients and the membrane dielectric permittivity.

Static dielectric constant of water within a bilayer using recent water models: a molecular dynamics study

The water confined within a surfactant bilayer is studied using different water models via molecular dynamics simulations. We considered four representative rigid models of water: the SPC/E and the TIP4P/2005, which are commonly used in numerical calculations and the more recent TIP4Q and SPC/ε models, developed to reproduce the dielectric behaviour of pure water. The static dielectric constant of the confined water was analyzed as a function of the temperature for the four models. In all cases it decreases as the temperature increases. Additionally, the static dielectric constant of the bilayer-water system was estimated through its expression in terms of the fluctuations in the total dipole moment, usually applied for isotropic systems. The estimated dielectric was compared with the available experimental data. We found that the TIP4Q and the SPC/ε produce closer values to the experimental data than the other models, particularly at room temperature. It was found that the probability of finding the sodium ion close to the head of the surfactant decreases as the temperature increases, thus the head of the surfactant is more exposed to the interaction with water when the temperature is higher.

Perturbations of Native Membrane Protein Structure in Alkyl Phosphocholine Detergents: A Critical Assessment of NMR and Biophysical Studies

Membrane proteins perform a host of vital cellular functions. Deciphering the molecular mechanisms whereby they fulfill these functions requires detailed biophysical and structural investigations. Detergents have proven pivotal to extract the protein from its native surroundings. Yet, they provide a milieu that departs significantly from that of the biological membrane, to the extent that the structure, the dynamics, and the interactions of membrane proteins in detergents may considerably vary, as compared to the native environment. Understanding the impact of detergents on membrane proteins is, therefore, crucial to assess the biological relevance of results obtained in detergents. Here, we review the strengths and weaknesses of alkyl phosphocholines (or foscholines), the most widely used detergent in solution-NMR studies of membrane proteins. While this class of detergents is often successful for membrane protein solubilization, a growing list of examples points to destabilizing and denaturing properties, in particular for α-helical membrane proteins. Our comprehensive analysis stresses the importance of stringent controls when working with this class of detergents and when analyzing the structure and dynamics of membrane proteins in alkyl phosphocholine detergents.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

Entropy and Polarity Control the Partition and Transportation of Drug-like Molecules in Biological Membrane

Partition and transportation of drug in the plasma membrane of a mammalian cell are the prerequisite for its function on target protein. Therefore, comprehensive understanding of the physicochemical properties and mechanism behind these complex phenomena is crucial in pharmaceutical research. By using the state-of-art molecular simulations with polarization effect implicitly or explicitly included, we studied the permeation behavior of 2-aminoethoxydiphenyl borate (2-APB), a broad-spectrum modulator for a number of membrane proteins. We showed that the protonation state and therefore the polarity of the drug is critical for its partition, and that the drug is likely to switch between different protonation states along its permeation pathway. By changing the degrees of freedom, protonation further affects the thermodynamic of the permeation pathway of 2-APB, leading to different entropic contributions. A survey on 54 analog structures with similar backbone to 2-APB showed that delicate balance between entropy and polarity plays an important role in drugs’ potency.

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.

Structural assemblies of the di- and oligomeric G-protein coupled receptor TGR5 in live cells: an MFIS-FRET and integrative modelling study

TGR5 is the first identified bile acid-sensing G-protein coupled receptor, which has emerged as a potential therapeutic target for metabolic disorders. So far, structural and multimerization properties are largely unknown for TGR5. We used a combined strategy applying cellular biology, Multiparameter Image Fluorescence Spectroscopy (MFIS) for quantitative FRET analysis, and integrative modelling to obtain structural information about dimerization and higher-order oligomerization assemblies of TGR5 wildtype (wt) and Y111 variants fused to fluorescent proteins. Residue 111 is located in transmembrane helix 3 within the highly conserved ERY motif. Co-immunoprecipitation and MFIS-FRET measurements with gradually increasing acceptor to donor concentrations showed that TGR5 wt forms higher-order oligomers, a process disrupted in TGR5 Y111A variants. From the concentration dependence of the MFIS-FRET data we conclude that higher-order oligomers - likely with a tetramer organization - are formed from dimers, the smallest unit suggested for TGR5 Y111A variants. Higher-order oligomers likely have a linear arrangement with interaction sites involving transmembrane helix 1 and helix 8 as well as transmembrane helix 5. The latter interaction is suggested to be disrupted by the Y111A mutation. The proposed model of TGR5 oligomer assembly broadens our view of possible oligomer patterns and affinities of class A GPCRs.

Specific electrical capacitance and voltage breakdown as a function of temperature for different planar lipid bilayers

The breakdown voltage and specific electrical capacitance of planar lipid bilayers formed from lipids isolated from the membrane of archaeon Aeropyrum pernix K1 as a function of temperature were studied and compared with data obtained previously in MD simulation studies. Temperature dependence of breakdown voltage and specific electrical capacitance was measured also for dipalmitoylphosphatidylcholine (DPPC) bilayers and bilayers formed from mixture of diphytanoylphosphocholine (DPhPC) and DPPC in ratio 80:20. The breakdown voltage of archaeal lipids planar lipid bilayers is more or less constant until 50°C, while at higher temperatures a considerable drop is observed, which is in line with the results from MD simulations. The breakdown voltage of DPPC planar lipid bilayer at melting temperature is considerably higher than in the gel phase. Specific electrical capacitance of planar lipid bilayers formed from archaeal lipids is approximately constant for temperatures up to 40°C and then gradually decreases. The difference with MD simulation predictions is discussed. Specific electrical capacitance of DPPC planar lipid bilayers in fluid phase is 1.75 times larger than that of the gel phase and it follows intermediated phases before phase transition. Increase in specific electrical capacitance while approaching melting point of DPPC is visible also for DPhPC:DPPC mixture.

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.

Differential dielectric responses of chondrocyte and Jurkat cells in electromanipulation buffers

Electromanipulation of cells as a label-free cell manipulation and characterization tool has gained particular interest recently. However, the applicability of electromanipulation, particularly dielectrophoresis (DEP), to biological cells is limited to cells suspended in buffers containing lower amounts of salts relative to the physiological buffers. One might question the use of low conductivity buffers (LCBs) for DEP separation, as cells are stressed in buffers lacking physiological levels of salt. In LCB, cells leak ions and undergo volume regulation. Therefore, cells exhibit time-dependent DEP response in LCB. In this work, cellular changes in LCB are assessed by dielectric spectroscopy, cell viability assay, and gene expression of chondrocytes and Jurkats. Results indicate leakage of ions from cells, increases in cytoplasmic conductivity, membrane capacitance, and conductance. Separability factor, which defines optimum conditions for DEP cell separation, for the two cell types is calculated using the cellular dielectric data. Optimum DEP separation conditions change as cellular dielectric properties evolve in LCB. Genetic analyses indicate no changes in expression of ionic channel proteins for chondrocytes suspended in LCB. Retaining cellular viability might be important during dielectrophoretic separation, especially when cells are to be biologically tested at a downstream microfluidic component.

Advances in the use of nanoscale bilayers to study membrane protein structure and function

Within the last decade, nanoscale lipid bilayers have emerged as powerful experimental systems in the analysis of membrane proteins (MPs) for both basic and applied research. These discoidal lipid lamellae are stabilized by annuli of specially engineered amphipathic polypeptides (nanodiscs) or polymers (SMALPs/Lipodisqs®). As biomembrane mimetics, they are well suited for the reconstitution of MPs within a controlled lipid environment. Moreover, because they are water-soluble, they are amenable to solution-based biochemical and biophysical experimentation. Hence, due to their solubility, size, stability, and monodispersity, nanoscale lipid bilayers offer technical advantages over more traditional MP analytic approaches such as detergent solubilization and reconstitution into lipid vesicles. In this article, we review some of the most recent advances in the synthesis of polypeptide- and polymer-bound nanoscale lipid bilayers and their application in the study of MP structure and function.

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.

Polarizable molecular interactions in condensed phase and their equivalent nonpolarizable models

Earlier, using phenomenological approach, we showed that in some cases polarizable models of condensed phase systems can be reduced to nonpolarizable equivalent models with scaled charges. Examples of such systems include ionic liquids, TIPnP-type models of water, protein force fields, and others, where interactions and dynamics of inherently polarizable species can be accurately described by nonpolarizable models. To describe electrostatic interactions, the effective charges of simple ionic liquids are obtained by scaling the actual charges of ions by a factor of 1/√(ε(el)), which is due to electronic polarization screening effect; the scaling factor of neutral species is more complicated. Here, using several theoretical models, we examine how exactly the scaling factors appear in theory, and how, and under what conditions, polarizable Hamiltonians are reduced to nonpolarizable ones. These models allow one to trace the origin of the scaling factors, determine their values, and obtain important insights on the nature of polarizable interactions in condensed matter systems.

Water response to intense electric fields: A molecular dynamics study

This paper investigated polarization properties of water molecules in close proximity to an ionic charge in the presence of external electric fields by using an approach based on simulations at the atomic level. We chose sodium and chloride ions in water as examples of dilute ionic solutions and used molecular dynamics simulations to systematically investigate the influence of an external static electric field on structural, dipolar, and polarization properties of water near charged ions. Results showed that a threshold electric field higher than 10(8) V/m is needed to affect water polarization and increase mean dipole moment of water molecules close to the ion. A similar threshold holds for water permittivity profiles, although a field 10× higher is needed to ensure that water permittivity is almost constant independently of the position close to the ion. Electric fields of such intensities can greatly enhance polarizability of water in hydration shells around ions.

Unstable, metastable, or stable halogen bonding interaction involving negatively charged donors? A statistical and computational chemistry study

The noncovalent halogen bonding could be attributed to the attraction between the positively charged σ-hole and a nucleophile. Quantum mechanics (QM) calculation indicated that the negatively charged organohalogens have no positively charged σ-hole on their molecular surface, leading to a postulation of repulsion between negatively charged organohalogens and nucleophiles in vacuum. However, PDB survey revealed that 24% of the ligands with halogen bonding geometry could be negatively charged. Moreover, 36% of ionizable drugs in CMC (Comprehensive Medicinal Chemistry) are possibly negatively charged at pH 7.0. QM energy scan showed that the negatively charged halogen bonding is probably metastable in vacuum. However, the QM calculated bonding energy turned negative in various solvents, suggesting that halogen bonding with negatively charged donors should be stable in reality. Indeed, QM/MM calculation on three crystal structures with negatively charged ligands revealed that the negatively charged halogen bonding was stable. Hence, we concluded that halogen bonding with negatively charged donors is unstable or metastable in vacuum but stable in protein environment, and possesses similar geometric and energetic characteristics as conventional halogen bonding. Therefore, negatively charged organohalogens are still effective halogen bonding donors for medicinal chemistry and other applications.

Membrane protein structural validation by oriented sample solid-state NMR: diacylglycerol kinase

The validation of protein structures through functional assays has been the norm for many years. Functional assays perform this validation for water-soluble proteins very well, but they need to be performed in the same environment as that used for the structural analysis. This is difficult for membrane proteins that are often structurally characterized in detergent environments, although functional assays for these proteins are most frequently performed in lipid bilayers. Because the structure of membrane proteins is known to be sensitive to the membrane mimetic environment, such functional assays are appropriate for validating the protein construct, but not the membrane protein structure. Here, we compare oriented sample solid-state NMR spectral data of diacylglycerol kinase previously published with predictions of such data from recent structures of this protein. A solution NMR structure of diacylglycerol kinase has been obtained in detergent micelles and three crystal structures have been obtained in a monoolein cubic phase. All of the structures are trimeric with each monomer having three transmembrane and one amphipathic helices. However, the solution NMR structure shows typical perturbations induced by a micelle environment that is reflected in the predicted solid-state NMR resonances from the structural coordinates. The crystal structures show few such perturbations, especially for the wild-type structure and especially for the monomers that do not have significant crystal contacts. For these monomers the predicted and observed data are nearly identical. The thermostabilized constructs do show more perturbations, especially the A41C mutation that introduces a hydrophilic residue into what would be the middle of the lipid bilayer inducing additional hydrogen bonding between trimers. These results demonstrate a general technique for validating membrane protein structures with minimal data obtained from membrane proteins in liquid crystalline lipid bilayers by oriented sample solid-state NMR.

Extension of the free energy workflow FEW towards implicit solvent/implicit membrane MM-PBSA calculations

BACKGROUND

The number of high-resolution structures of pharmacologically relevant membrane proteins has been strongly increasing. This makes computing relative affinities of chemically similar compounds binding to a membrane protein possible in order to guide decision making in drug design. However, the preparation step of such calculations is time-consuming and complex.

METHODS

We extended the free energy workflow tool FEW, available in AMBER, towards facilitating the setup of molecular dynamics simulations with explicit membrane, and the setup and execution of effective binding energy calculations according to a 1-trajectory implicit solvent/implicit membrane MM-PBSA approach for multiple ligands binding to the same membrane protein.

RESULTS

We validated the implemented protocol initially on two model systems, a sodium ion in the presence of an implicit membrane slab and a proton traversing the M2 proton-channel of the influenza A virus. For the latter, we found a good agreement for several important events along the proton pathway with those obtained in a recent computational study. Finally, we performed a case study on effective binding energy calculations for a set of inhibitors binding to the M2 proton-channel.

CONCLUSIONS

From the case study, we estimate a considerable speed up in the setup and analysis times for implicit solvent/implicit membrane MM-PBSA calculations by the extended version of FEW compared to a manual preparation.

GENERAL SIGNIFICANCE

Together with the overall runtime and the analysis results, this suggests that such type of calculations can be valuable in later stages of drug design projects on membrane proteins. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

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.

Lattice simulations of phase morphology on lipid bilayers: renormalization, membrane shape, and electrostatic dipole interactions

When liquid phases coexist at equilibrium but are not driven to minimize domain interfacial contact energy, the resulting patterns of phase domains can have important implications for living cells. In this study we explore some of the interactions and conditions that produce the stable patterned phases that are observed in model lipid mixtures. By use of Monte Carlo simulations we find that background curvature is important for the formation of patterned (modulated) phases. The interactions that stabilize nanoscopic phase separation are still not well understood. We show that inclusion of an electrostatic dipole repulsion with decay lengths as short as two to four lipid diameters can break up domains at the nanometer scale and that the location of the miscibility critical point is sensitive to this interaction. The use of a coarse-grained simulation raises questions about comparing parameters in simulations performed at different length scales. Using renormalization group techniques we show how to reconcile this problem, treating line tension as a running coupling constant.

Solid state NMR: The essential technology for helical membrane protein structural characterization

NMR spectroscopy of helical membrane proteins has been very challenging on multiple fronts. The expression and purification of these proteins while maintaining functionality has consumed countless graduate student hours. Sample preparations have depended on whether solution or solid-state NMR spectroscopy was to be performed - neither have been easy. In recent years it has become increasingly apparent that membrane mimic environments influence the structural result. Indeed, in these recent years we have rediscovered that Nobel laureate, Christian Anfinsen, did not say that protein structure was exclusively dictated by the amino acid sequence, but rather by the sequence in a given environment (Anfinsen, 1973) [106]. The environment matters, molecular interactions with the membrane environment are significant and many examples of distorted, non-native membrane protein structures have recently been documented in the literature. However, solid-state NMR structures of helical membrane proteins in proteoliposomes and bilayers are proving to be native structures that permit a high resolution characterization of their functional states. Indeed, solid-state NMR is uniquely able to characterize helical membrane protein structures in lipid environments without detergents. Recent progress in expression, purification, reconstitution, sample preparation and in the solid-state NMR spectroscopy of both oriented samples and magic angle spinning samples has demonstrated that helical membrane protein structures can be achieved in a timely fashion. Indeed, this is a spectacular opportunity for the NMR community to have a major impact on biomedical research through the solid-state NMR spectroscopy of these proteins.

Helical membrane protein conformations and their environment

Evidence that membrane proteins respond conformationally and functionally to their environment is growing. Structural models, by necessity, have been characterized in preparations where the protein has been removed from its native environment. Different structural methods have used various membrane mimetics that have recently included lipid bilayers as a more native-like environment. Structural tools applied to lipid bilayer-embedded integral proteins are informing us about important generic characteristics of how membrane proteins respond to the lipid environment as compared with their response to other nonlipid environments. Here, we review the current status of the field, with specific reference to observations of some well-studied α-helical membrane proteins, as a starting point to aid the development of possible generic principles for model refinement.

Progress in developing Poisson-Boltzmann equation solvers

This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects.

Nanoscale measurement of the dielectric constant of supported lipid bilayers in aqueous solutions with electrostatic force microscopy

We present what is, to our knowledge, the first experimental demonstration of dielectric constant measurement and quantification of supported lipid bilayers in electrolyte solutions with nanoscale spatial resolution. The dielectric constant was quantitatively reconstructed with finite element calculations by combining thickness information and local polarization forces which were measured using an electrostatic force microscope adapted to work in a liquid environment. Measurements of submicrometric dipalmitoylphosphatidylcholine lipid bilayer patches gave dielectric constants of ε(r) ~ 3, which are higher than the values typically reported for the hydrophobic part of lipid membranes (ε(r) ~ 2) and suggest a large contribution of the polar headgroup region to the dielectric response of the lipid bilayer. This work opens apparently new possibilities in the study of biomembrane electrostatics and other bioelectric phenomena.