Calculation of the total electrostatic energy of a macromolecular system: solvation energies, binding energies, and conformational analysis

In this report we describe an accurate numerical method for calculating the total electrostatic energy of molecules of arbitrary shape and charge distribution, accounting for both Coulombic and solvent polarization terms. In addition to the solvation energies of individual molecules, the method can be used to calculate the electrostatic energy associated with conformational changes in proteins as well as changes in solvation energy that accompany the binding of charged substrates. The validity of the method is examined by calculating the hydration energies of acetate, methyl ammonium, ammonium, and methanol. The method is then used to study the relationship between the depth of a charge within a protein and its interaction with the solvent. Calculations of the relative electrostatic energies of crystal and misfolded conformations of Themiste dyscritum hemerythrin and the VL domain of an antibody are also presented. The results indicate that electrostatic charge-solvent interactions strongly favor the crystal structures. More generally, it is found that charge-solvent interactions, which are frequently neglected in protein structure analysis, can make large contributions to the total energy of a macromolecular system.     

Intrinsic pKas of ionizable residues in proteins: An explicit solvent calculation for lysozyme

Molecular dynamics simulations of triclinic hen egg white lysozyme in aqueous solution were performed to calculate the intrinsic pK_as of 14 ionizable residues. An all-atom model was used for both solvent and solute, and a single 180 ps simulation in conjunction with a Gaussian fluctuation analysis method was used. An advantage of the Gaussian fluctuation method is that it only requires a single simulation of the system in a reference state to calculate all the pK_as in the protein, in contrast to multiple simulations for the free energy perturbation method. pK_int shifts with respect to reference titratable residues were evaluated and compared to results obtained using a finite difference Poisson-Boltzmann (FDPB) method with a continuum solvent model; overall agreement with the direction of the shifts was generally observed, though the magnitude of the shifts was typically larger with the explicit solvent model. The contribution of the first solvation shell to the total charging free energies of the titratable groups was explicitly evaluated and found to be significant. Dielectric shielding between pairs of titratable groups was examined and found to be smaller than expected. The effect of the approximations used to treat the long-range interactions on the pK_int shifts is discussed. © 1994 Wiley-Liss, Inc.     

Simplified methods for pKa and acid pH-dependent stability estimation in proteins: removing dielectric and counterion boundaries

Much computational research aimed at understanding ionizable group interactions in proteins has focused on numerical solutions of the Poisson-Boltzmann (PB) equation, incorporating protein exclusion zones for solvent and counterions in a continuum model. Poor agreement with measured pKas and pH-dependent stabilities for a (protein, solvent) relative dielectric boundary of (4,80) has lead to the adoption of an intermediate (20,80) boundary. It is now shown that a simple Debye-Huckel (DH) calculation, removing both the low dielectric and counterion exclusion regions associated with protein, is equally effective in general pKa calculations. However, a broad-based discrepancy to measured pH-dependent stabilities is maintained in the absence of ionizable group interactions in the unfolded state. A simple model is introduced for these interactions, with a significantly improved match to experiment that suggests a potential utility in predicting and analyzing the acid pH-dependence of protein stability. The methods are applied to the relative pH-dependent stabilities of the pore-forming domains of colicins A and N. The results relate generally to the well-known preponderance of surface ionizable groups with solvent-mediated interactions. Although numerical PB solutions do not currently have a significant advantage for overall pKa estimations, development based on consideration of microscopic solvation energetics in tandem with the continuum model could combine the large deltapKas of a subset of ionizable groups with the overall robustness of the DH model.     

Modeling of peptides and proteins in a membrane environment: II. Structural and energetic aspects of glycophorin A in a lipid bilayer

The conformational space of a hydrophobic peptide fragment of glycophorin A in a lipid membrane was studied with the Monte Carlo method using the solvation model described in the first communication of this series. The simulation was performed for various starting orientations of the peptide relative the membrane bilayer: outside, inside, partially immersed, and transbilayer. We showed that the membrane substantially stabilizes the α-helical conformation of the central hydrophobic part of the glycophorin A molecule, which for the most part is immersed in the apolar core of the bilayer. For various conformational states, energy values were calculated and the orientations of the peptide relative to the membrane were characterized. Depending on the thickness of the bilayer, either an entirely α-helical conformation in transbilayer orientation or a conformation with a kink in the central part of the helix with theN- andC-termini exposed on one side of the membrane corresponds to the minimal-energy structure. The transmembrane orientation of glycophorin A is energetically advantageous when the membrane thickness is close to the length of its hydrophobic helical portion, which is consistent with the effect ofhydrophobic match observed experimentally. The prospects for further refinement of the model are discussed. For communication I, see [1].     

Protein conformational transitions coupled to binding in molecular recognition of unstructured proteins: hierarchy of structural loss from all-atom Monte Carlo simulations of p27Kip1 unfolding-unbinding and structural determinants of the binding mechanism

Conformational transitions coupled to binding are studied for the p27(Kip1) protein which undergoes a functional disorder-to-order folding transition during tertiary complex formation with the phosphorylated cyclin A-cyclin-dependent kinase 2 (Cdk2) binary complex. Temperature-induced Monte Carlo simulations of p27(Kip1) unfolding-unbinding carried out from the crystal structure of the tertiary complex have revealed a systematic trend in the hierarchy of structural loss for p27(Kip1) and a considerable difference in mobility of p27(Kip1) secondary structure elements. The most persistent interactions of p27(Kip1) at the intermolecular interface during unfolding-unbinding simulations are formed by beta-hairpin and beta-strand that on average maintain their structural integrity considerably longer than other p27(Kip1) elements. We have found that the ensemble of unfolded p27(Kip1) conformations is characterized by transitions between mostly unbound, collapsed conformations and entropically favorable p27(Kip1) conformations, which are weakly bound to the cyclin A side of the binary complex. The results of this study are consistent with the experimental evidence pointing to this region of the intermolecular interface as a potential initiation docking site during binding reaction and may reconcile conflicting experimental hypotheses on the recognition of substrate recruitment motifs.     

Molecular dynamics simulation of highly charged proteins: comparison of the particle-particle particle-mesh and reaction field methods for the calculation of electrostatic interactions

Molecular dynamics (MD) simulations of the activation domain of porcine procarboxypeptidase B (ADBp) were performed to examine the effect of using the particle-particle particle-mesh (P3M) or the reaction field (RF) method for calculating electrostatic interactions in simulations of highly charged proteins. Several structural, thermodynamic, and dynamic observables were derived from the MD trajectories, including estimated entropies and solvation free energies and essential dynamics (ED). The P3M method leads to slightly higher atomic positional fluctuations and deviations from the crystallographic structure, along with somewhat lower values of the total energy and solvation free energy. However, the ED analysis of the system leads to nearly identical results for both simulations. Because of the strong similarity between the results, both methods appear well suited for the simulation of highly charged globular proteins in explicit solvent. However, the lower computational demand of the RF method in the present implementation represents a clear advantage over the P3M method.     

Surface energy components of a dye-ligand immobilized pHEMA membranes: effects of their molecular attracting forces for non-covalent interactions with IgG and HSA in aqueous media

In the present paper, we report the study of the adsorption behaviour of human immunoglobulin G (IgG), human serum albumin (HSA) and polyethylenimine (PEI) onto surfaces of Procion Green HE-4BD (PG) immobilized poly(hydroxyethylmethacrylate) (pHEMA) membranes. The adsorption behaviour of the IgG and HSA onto surfaces of the PG–PEI complexed membrane was also studied. Surface wettability and hydrophilicity of all the membranes were investigated by static contact angle measurements. The measurements of the contact angle to various test liquids, i.e., water, glycerol, formamide, diiodomethane (DIM) and ethylene glycol on the investigated membranes were made by sessile drop method. In accordance to the Young equation, the smaller the surface tension of the test liquid, the smaller becomes the contact angles measured on all the investigated membranes surfaces. The highest contact angles were obtained with water, whereas ethylene glycol gave the lowest contact angles for all the tested membranes. Component and parameters of the surface free energy of all the investigated membranes were calculated from measured contact angle values using two methods (the geometric mean by Fowkes and acid–base by van Oss). HSA adsorption was enhanced after complexation of PEI with the immobilized dye-ligand. The adsorption of proteins and PEI significantly changed both the contact angles and component of surface free energies of the investigated membranes.     

Heat shock proteins as biomarkers for the rapid detection of brain and spinal cord ischemia: a review and comparison to other methods of detection in thoracic aneurysm repair

The heat shock proteins (HSPs) are members of highly conserved families of molecular chaperones that have multiple roles in vivo. We discuss the HSPs in general, and Hsp70 and Hsp27 in particular, and their rapid induction by severe stress in the context of tissue and organ expression in physiology and disease. We describe the current state of knowledge of the relationship and interactions between extra- and intracellular HSPs and describe mechanisms and significance of extracellular expression of HSPs. We focus on the role of the heat shock proteins as biomarkers of central nervous system (CNS) ischemia and other severe stressors and discuss recent and novel technologies for rapid measurement of proteins in vivo and ex vivo. The HSPs are compared to other proposed small molecule biomarkers for detection of CNS injury and to other methods of detecting brain and spinal cord ischemia in real time. While other biomarkers may be of use in prognosis and in design of appropriate therapies, none appears to be as rapid as the HSPs; therefore, no other measurement appears to be of use in the immediate detection of ongoing severe ischemia with the intention to immediately intervene to reduce the severity or risk of permanent damage.