Molecular dynamics simulations have revealed a dramatic increase, with increasing temperature, of the amplitude of electrostatic fluctuations caused by water at the active site of metalloprotein plastocyanin. The increased breadth of electrostatic fluctuations, expressed in terms of the reorganization energy of changing the redox state of the protein, is related to the formation of the hydrophobic protein/water interface allowing large-amplitude collective fluctuations of the water density in the protein's first solvation shell. On the top of the monotonic increase of the reorganization energy with increasing temperature, we have observed a spike at 220 K also accompanied by a significant slowing of the exponential collective Stokes shift dynamics. In contrast to the local density fluctuations of the hydration-shell waters, these spikes might be related to the global property of the water solvent crossing the Widom line.
The behavior of proteins near interfaces is relevant for biological and medical purposes. Previous results in bulk show that, when the protein concentration increases, the proteins unfold and, at higher concentrations, aggregate. Here, we study how the presence of a hydrophobic surface affects this course of events. To this goal, we use a coarse-grained model of proteins and study by simulations their folding and aggregation near an ideal hydrophobic surface in an aqueous environment by changing parameters such as temperature and hydrophobic strength, related, e.g., to ions concentration. We s…
Scaling law for geometrical and dynamical quantities of biological molecules is an interesting topic. According to Flory's theory, a power law between radius of gyration and the length of homopolymer chain is found, with exponent 3/5 for good solvent and 1/3 for poor solvent. For protein in physiological condition, a solvent condition in between, a power law with exponent ~2/5 is obtained. In this paper, we present a unified formula to cover all above cases. It shows that the scaling exponents are generally correlated with fractal dimension of a chain under certain solvent condition. While app…
The hydrophobic effect stabilizes the native structure of proteins by minimizing the unfavourable interactions between hydrophobic residues and water through the formation of a hydrophobic core. Here we include the entropic and enthalpic contributions of the hydrophobic effect explicitly in an implicit solvent model. This allows us to capture two important effects: a length-scale dependence and a temperature dependence for the solvation of a hydrophobic particle. This consistent treatment of the hydrophobic effect explains cold denaturation and heat capacity measurements of solvated proteins.
An understanding of the hydrophobicity of complex heterogeneous molecular assemblies is crucial to characterize and predict interactions between biomolecules. As such, uncovering the subtleties of assembly processes hinges on an accurate classification of the relevant interfaces involved, and much effort has been spent on developing so-called "hydrophobicity maps." In this work, we introduce a novel electrostatics-based mapping of aqueous interfaces that focuses on the collective, long-wavelength electrostatic response of water to the presence of nearby surfaces. In addition to distinguishing …
A theoretical approach is developed to quantify hydrophobic hydration and interactions on a molecular scale, with the goal of gaining insight into the molecular origins of hydrophobic effects. The model is based on the fundamental relation between the probability for cavity formation in bulk water resulting from molecular-scale density fluctuations, and the hydration free energy of the simplest hydrophobic solute, a hard particle. This probability is estimated using an information theory (IT) approach, incorporating experimentally available properties of bulk water -- the density and radial di…
Numerical simulations of hydrated proteins show that protein hydration shells are polarized into a ferroelectric cluster with a large magnitude of its average dipole moment. The emergence of this new mesophase dramatically alters the statistics of electrostatic fluctuations at the protein/water interface. The linear-response relation between the average electrostatic potential and its variance breaks down, with the breadth of the electrostatic noise far exceeding the expectations of the linear response theories. The dynamics of these non-Gaussian electrostatic fluctuations are dominated by a s…
Water and water-mediated interactions determine thermodynamic and kinetics of protein folding, protein aggregation and self-assembly in confined spaces. To obtain insights into the role of water in the context of folding problems, we describe computer simulations of a few related model systems. The dynamics of collapse of eicosane shows that upon expulsion of water the linear hydrocarbon chain adopts an ordered helical hairpin structure with 1.5 turns. The structure of dimer of eicosane molecules has two well ordered helical hairpins that are stacked perpendicular to each other. As a prelude t…
We study membrane-protein interactions and membrane-mediated protein-protein interactions by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers with cylindrical hydrophobic inclusions. The strength of the hydrophobic force and the hydrophobic thickness of the proteins are systematically varied. The results are compared with analytical predictions of two popular analytical theories: The Landau-de Gennes theory and the elastic theory. The elastic theory provides an excellent description of the fluctuation spectra of pure membranes and successfully reproduces the deforma…
We propose a dissipative electro-elastic network model (DENM) to describe the dynamics and statistics of electrostatic fluctuations at active sites of proteins. The model combines the harmonic network of residue beads with overdamped dynamics of the normal modes of the network characterized by two friction coefficients. The electrostatic component is introduced to the model through atomic charges of the protein force field. The overall effect of the electrostatic fluctuations of the network is recorded through the frequency-dependent response functions of the electrostatic potential and electr…
Recent work has shown that the hydrophobic protein surfaces in aqueous solution sit near a drying transition. The tendency for these surfaces to expel water from their vicinity leads to self assembly of macromolecular complexes. In this article we show with a realistic model for a biologically pertinent system how this phenomenon appears at the molecular level. We focus on the association of the C-terminal domain (CA-C) of the human immunodeficiency virus (HIV) capsid protein. By combining all-atom simulations with specialized sampling techniques we measure the water density distribution durin…
Topological properties of native folds are obtained from statistical analysis of 160 low homology proteins covering the four structural classes. This is done analysing one, two and three-vertex joint distribution of quantities related to the corresponding network of amino acid residues. Emphasis on the amino acid residue hydrophobicity leads to the definition of their center of mass as vertices in this contact network model with interactions represented by edges. The network analysis helps us to interpret experimental results such as hydrophobic scales and fraction of buried accessible surface…
We present an extension of the Poisson-Boltzmann model in which the solute of interest is immersed in an assembly of self-orienting Langevin water dipoles, anions, cations, and hydrophobic molecules, all of variable densities. Interactions between charges are controlled by electrostatics, while hydrophobic interactions are modeled with a Yukawa potential. We impose steric constraints by assuming that the system is represented on a cubic lattice. We also assume incompressibility, i.e. all sites of the lattice are occupied. This model, which we refer to as the Hydrophobic Dipolar Poisson Boltzma…
We investigate membrane-mediated interactions between transmembrane proteins using coarse-grained models. We compare the effective potential of mean force (PMF) between two proteins, which are always aligned parallel to the z-axis of the simulation box, with those PMFs obtained for proteins with fluctuating orientations. The PMFs are dominated by an oscillatory packing-driven contribution and a smooth attractive hydrophobic mismatch contribution, which vanishes if the hydrophobic length of the protein matches the thickness of the membrane. If protein orientations are allowed to fluctuate, the …
Prion diseases are invariably fatal neurodegenerative diseases that affect humans and animals. Unlike most other amyloid forming neurodegenerative diseases, these can be highly infectious. Prion diseases occur in a variety of species. They include the fatal human neurodegenerative diseases Creutzfeldt-Jakob Disease (CJD), Fatal Familial Insomnia (FFI), Gerstmann-Straussler-Scheinker syndrome (GSS), Kuru, the bovine spongiform encephalopathy (BSE or 'mad-cow' disease) in cattle, the chronic wasting disease (CWD) in deer and elk, and scrapie in sheep and goats, etc. Transmission across the speci…
Knowledge of the mechanisms of interaction between self-aggregating peptides and nucleic acids or other polyanions is key to the understanding of many aggregation processes underlying several human diseases (e.g. Alzheimer's and Parkinson's diseases). Determining the affinity and kinetic steps of such interactions is challenging due to the competition between hydrophobic self-aggregating forces and electrostatic binding forces. Kahalalide F (KF) is an anticancer hydrophobic peptide which contains a single positive charge that confers strong aggregative properties with polyanions. This makes KF…
The contribution of electrostatic interactions to the free energy of binding between model protein and a ceramic implant surface in the aqueous solvent, considered in the framework of the non-local electrostatic model, is calculated as a function of the implant low-frequency dielectric constant. We show that the existence of a dynamically ordered (low-dielectric) interfacial solvent layer at the protein-solvent and ceramic-solvent interface markedly increases charging energy of the protein and ceramic implant, and consequently makes the electrostatic contribution to the protein-ceramic binding…
We assume that the protein folding process follows two autonomous steps: the conformational search for the native, mainly ruled by the hydrophobic effect; and, the final adjustment stage, which eventually gives stability to the native. Our main tool of investigation is a 3D lattice model provided with a ten-letter alphabet, the stereochemical model. This model was conceived for Monte Carlo (MC) simulations when one keeps in mind the kinetic behavior of protein-like chains in solution. In order to characterize the folding characteristic time (τ) by two distinct sampling methods, first we presen…
The thermodynamic behavior and structural properties of hydrophobic-polar (HP) lattice proteins interacting with attractive surfaces are studied by means of Wang-Landau sampling. Three benchmark HP sequences (48mer, 67mer, and 103mer) are considered with different types of surfaces, each of which attract either all monomers, only hydrophobic (H) monomers, or only polar (P) monomers, respectively. The diversity of folding behavior in dependence of surface strength is discussed. Analyzing the combined patterns of various structural observables, such as, e.g., the derivatives of the numbers of su…
For a model deca-alanine peptide the cavity (ideal hydrophobic) contribution to hydration favors the helix state in the coil-to-helix transition and the paired helix bundle in the assembly of two helices. The energetic contributions of attractive protein-solvent interactions are separated into a short-range part arising from interactions with solvent in the first hydration shell and the remaining long-range part. In the helix-coil transition, short-range attractive protein-solvent interactions outweigh hydrophobic hydration and favor the unfolded coil states. Analysis of enthalpic effects show…
Many proteins have the potential to aggregate into amyloid fibrils, which are associated with a wide range of human disorders including Alzheimer's and Parkinson's disease. In contrast to that of folded proteins, the thermodynamic stability of amyloid fibrils is not well understood: specifically the balance between entropic and enthalpic terms, including the chain entropy and the hydrophobic effect, are poorly characterised. Using simulations of a coarse-grained protein model we delineate the enthalpic and entropic contributions dominating amyloid fibril elongation, predicting a characteristic…
This paper reviews the molecular theory of hydrophobic effects relevant to biomolecular structure and assembly in aqueous solution. Recent progress has resulted in simple, validated molecular statistical thermodynamic theories and clarification of confusing theories of decades ago. Current work is resolving effects of wider variations of thermodynamic state, e.g. pressure denaturation of soluble proteins, and more exotic questions such as effects of surface chemistry in treating stability of macromolecular structures in aqueous solution
Atomic displacements of hydrated proteins are dominated by phonon vibrations at low temperatures and by dissipative large-amplitude motions at high temperatures. A crossover between the two regimes is known as a dynamical transition. Recent experiments indicate a connection between the dynamical transition and the dielectric response of the hydrated protein. We analyze two mechanisms of the coupling between the protein atomic motions and the protein-water interface. The first mechanism considers viscoelastic changes in the global shape of the protein plasticized by its coupling to the hydratio…
We examine the role of electrostatic interactions in the assembly of empty spherical viral capsids. The charges on the protein subunits that make the viral capsid mutually interact and are expected to yield electrostatic repulsion acting against the assembly of capsids. Thus, attractive protein-protein interactions of non-electrostatic origin must act to enable the capsid formation. We investigate whether the interplay of repulsive electrostatic and attractive interactions between the protein subunits can result in the formation of spherical viral capsids of a preferred radius. For this to be …
Prion diseases caused by the conversion from a soluble normal cellular prion protein into insoluble abnormally folded infectious prions, are invariably fatal and highly infectious degenerative diseases that affect a wide variety of mammalian species. The palindrome and the Glycine-rich conserved segment in the hydrophobic region 109-136 control the conversion from normal prion protein to form into diseased prions. This paper gives detailed reviews on the 109-136 region and presents the studies of its 3D structures and structural dynamics.
The interaction between surface patches of proteins with different surface properties has a vital role to play driving conformational changes of proteins in different salt solutions. We demonstrate the existence of ion-specific attractive double-layer forces between neutral hydrophobic and hydrophilic surfaces in the presence of certain salt solutions. This is done by solving a generalized Poisson-Boltzmann equation for two unequal surfaces. In the calculations we utilize parameterized ion-surface-potentials and dielectric-constant-profiles deduced from recent non-primitive-model molecular dyn…
Bovine heart cytochrome c has been immobilized into the mesoporous silica host material SBA-15 in both its native folded and urea-unfolded state. The comparison of the two folding states' behavior casts doubt on the commonly used explanation of cytochrome c adsorption, i.e. the electrostatic interaction model. A detailed investigation of the protein binding as a function of pH and ionic strength of the buffer solution reveals the complex nature of the protein-silica interaction. Electrostatic interaction, van der Waals forces and entropic contributions by counterion release each contribute to …
A global optimization method called Greedy Neighborhood Search (GNS) and a novel conformational sampling method using a spherical distribution is proposed to find the minimum energy conformation of a protein-like heteropolymer model called AB model. The AB model consists of hydrophobic (A) and hydrophilic (B) monomers analogous to the real proteins. The AB model in three-dimensional space is represented by simple bead-rod chain system which is identical to the one-bead protein model. The minimum energy conformations of four different sequences consisting of 13, 21, 34, and 55 monomers are obta…
The precise sequence of aminoacids plays a central role in the tertiary structure of proteins and their functional properties. The Hydrophobic-Polar lattice models have provided valuable insights regarding the energy landscape. We demonstrate here the isomorphism between the protein sequences and designable structures for two and three dimensional lattice proteins of very long aminoacid chains using exact enumerations and intuitive considerations.We emphasize that the topological arrangement of the aminoacid residues alone is adequate to deduce the designable and non-designable sequences witho…
We present a mechanism for a generic and powerful force of assembly and mobility for transmembrane proteins in lipid bilayers. This force is a pre-transition (or pre-melting) effect for the first-order transition between ordered and disordered phases in the host membrane. Using large scale molecular simulation, we show that a protein with hydrophobic thickness equal to that of the disordered phase embedded in an ordered bilayer stabilizes a microscopic order-disorder interface, and the stiffness of that interface is finite. When two such proteins approach each other, they assemble because asse…
Abeta is a disordered peptide central to Alzheimer's Disease. Aggregation of Abeta has been widely explored, but its molecular crowding less so. The synaptic cleft where Abeta locates only holds 60-70 water molecules along its width. We subjected Abeta40 to 100 different simulations with variable water cell size. We show that even for this disordered aggregation-prone peptide, many properties are not cell-size dependent, i.e. a small cell is easily justified. The radius of gyration, intra-peptide, and peptide-water hydrogen bonds are well-sampled by short (50 ns) time scales at any cell size. …
Prion is a misfolded protein found in mammals that causes infectious diseases of the nervous system in humans and animals. Prion diseases are invariably fatal and highly infectious neurodegenerative diseases that affect a wide variety of mammalian species such as sheep and goats, cattle, deer, elk and humans etc. Recent studies have shown that rabbits have a low susceptibility to be infected by prion diseases with respect to other animals including humans. The present study employs molecular dynamics (MD) means to unravel the mechanism of rabbit prion proteins (RaPrPC) based on the recently av…
The possibility for proteins to aggregate in different superstructures, i.e. large-scale polymorphism, has been widely observed, but an understanding of the physico-chemical mechanisms behind it is still out of reach. Here we present a theoretical model for the description of a generic aggregate formed from an ensemble of charged proteins. The model predicts the formation of multi-fractal structures with the geometry of the growth determined by the electrostatic interactions between single proteins. The model predictions are successfully verified in comparison with experimental curves for aggr…
We present a coarse-grained lattice model to study the influence of water on the recognition process of two rigid proteins. The basic model is formulated in terms of the hydrophobic effect. We then investigate several modifications of our basic model showing that the selectivity of the recognition process can be enhanced by considering the explicit influence of single solvent particles. When the number of cavities at the interface of a protein-protein complex is fixed as an intrinsic geometric constraint, there typically exists a characteristic fraction that should be filled with water molecul…
Wang-Landau sampling has been applied to investigate the thermodynamics and structural properties of a lattice hydrophobic-polar heteropolymer (the HP protein model) interacting with an attractive substrate. For simplicity, we consider a short HP sequence consisting of only 36 monomers interacting with a substrate which attracts all monomers in the sequence. The conformational "phase transitions" have been identified by a canonical analysis of the specific heat and suitable structural observables. Three major "transitions", namely, adsorption, hydrophobic core formation and "flattening" of ads…
In the present work we study and compare unfolding of a small protein, chicken villin headpiece (HP-36) in two different aqueous binary mixtures, namely water-ethanol (EtOH) and water-dimethyl sulphoxide (DMSO). In both the binary mixtures, HP-36 is found to unfold (fully or partially, depending on the mixture) under ambient conditions, that otherwise requires temperature as high as ~600 K to denature in pure aqueous solvent. In all the cases, first step of unfolding is found to be similar, i.e. separation of the cluster formed by three hydrophobic (phenylalanine) residues, namely Phe-7, Phe-1…
We present a novel statistical mechanics formalism for the theoretical description of the process of protein folding$\leftrightarrow$unfolding transition in water environment. The formalism is based on the construction of the partition function of a protein obeying two-stage-like folding kinetics. Using the statistical mechanics model of solvation of hydrophobic hydrocarbons we obtain the partition function of infinitely diluted solution of proteins in water environment. The calculated dependencies of the protein heat capacities upon temperature are compared with the corresponding results of e…
Aggregation of amphiphiles through the action of hydrophobic interactions is a common feature in soft condensed matter systems and is of particular importance in the context of biophysics as it underlies both the generation of functional biological machinery as well as the formation of pathological misassembled states of proteins. Here we explore the aggregation behaviour of amphiphilic polymers using lattice Monte-Carlo calculations and show that the distribution of hydrophobic residues within the polymer sequence determines the facility with which dry/wet interfaces can be created and that s…
We present an approximate method for calculating the electrostatic free energy of concentrated protein solutions. Our method uses a cell model and accounts for both the coulomb energy and the entropic cost of Donnan salt partitioning. The former term is calculated by linearizing the Poisson-Boltzmann equation around a nonzero average potential, while the second term is calculated using a jellium approximation that is empirically modified to reproduce the dilute solution limit. When combined with a short-ranged binding interaction, calculated using the mean spherical approximation, our model re…
Single-stranded RNA viruses efficiently encapsulate their genome into a protein shell called the capsid. Electrostatic interactions between the positive charges in the capsid protein's N-terminal tail and the negatively charged genome have been postulated as the main driving force for virus assembly. Recent experimental results indicate that the N-terminal tail with the same number of charges and same lengths package different amounts of RNA, which reveals that electrostatics alone cannot explain all the observed outcomes of the RNA self-assembly experiments. Using a mean-field theory, we show…
The objective of this paper is to provide a mathematical model to construct a barrier that may be useful to prevent the penetration of different viruses (Eg. SARS-COV-2) as well as charged aerosols through the concept of electrostatic charge negotiation. (Fusion for the opposite types of charges and repulsion for the similar types of charges). Reviewing the works of different authors, regarding charges, surface charge densities (σ), charge mobility (μ) and electrostatic potentials of different aerosols under varied experimental conditions, a similar intensive study has also been carried out to…
Simulations of macromolecular diffusion and adsorption in confined environments can offer valuable mechanistic insights into numerous biophysical processes. In order to model solutes at atomic detail on relevant time scales, Brownian Dynamics simulations can be carried out with the approximation of rigid body solutes moving through a continuum solvent. This allows the precomputation of interaction potential grids for the solutes, thereby allowing the computationally efficient calculation of forces. However, hydrodynamic and long-range electrostatic interactions cannot be fully treated with gri…
Gene expression and regulation rely on an apparently finely tuned set of reactions between some proteins and DNA. Such DNA-binding proteins have to find specific sequences on very long DNA molecules and they mostly do so in absence of any active process. It has been rapidly recognized that to achieve this task these proteins should be efficient at both searching (i.e. sampling fast relevant parts of DNA) and finding (i.e. recognizing the specific site). A two-mode search and variants of it have been suggested since the 70s to explain either a fast search or an efficient recognition. Combining …
Micro-domains of modified surface potential (SP) were created on hydroxyapatite (HAp) films by direct patterning by midenergy focused electron beam, typically available as a microprobe of Scanning Electron Microscopes. The SP distribution of these patterns has been studied on sub-micrometer scale by the Kelvin Probe Force Microscopy method as well as lysozyme adsorption. Since the lysozyme is positively charged at physiological pH, it allows us to track positively and negatively charged areas of the SP patterns. Distribution of the adsorbed proteins over the domains was in good agreement with …
Motivated by experimentally observed biocompatibility enhancement of nanoengineered cubic zirconia ZrO2 coatings to mesenchymal stromal cells, we have carried out computational analysis of the initial immobilization of one of known structural fragment of the adhesive protein (fibronectin) on the corresponding surface. We constructed an atomistic model of the zirconia nano-hillock of 3-fold symmetry based on AFM and TEM images. First-principle quantum-mechanical calculations show a substantial variation of electrostatic potential at the hillock due to the presence of surface features such as ed…
Effects of the mismatch between the hydrophobic length, d, of transmembrane alpha helices of integral proteins and the hydrophobic thickness, D_h, of the membranes they span are studied theoretically utilizing a microscopic model of lipids. In particular, we examine the dependence of the period of a lamellar phase on the hydrophobic length and volume fraction of a rigid, integral, peptide. We find that the period decreases when a short peptide, such that d<D_h, is inserted. More surprising, we find that the period increases when a long peptide, such that d>D_h, is inserted. The effect is due t…
The mechanism allowing a protein to search of a target sequence on DNA is currently described as an intermittent process composed of 3D diffusion in bulk and 1D diffusion along the DNA molecule. Due to the relevant charge of protein and DNA, electrostatic interaction should play a crucial role during this search. In this paper, we explicitly derive the mean field theory allowing for a description of the protein-DNA electrostatics in solution. This approach leads to a unified model of the search process, where 1D and 3D diffusion appear as a natural consequence of the diffusion on an extended i…
