Computation of molecular electrostatics with boundary element methods.

In continuum approaches to molecular electrostatics, the boundary element method (BEM) can provide accurate solutions to the Poisson-Boltzmann equation. However, the numerical aspects of this method pose significant problems. We describe our approach, applying an alpha shape-based method to generate a high-quality mesh, which represents the shape and topology of the molecule precisely. We also describe an analytical method for mapping points from the planar mesh to their exact locations on the surface of the molecule. We demonstrate that derivative boundary integral formulation has numerical advantages over the nonderivative formulation: the well-conditioned influence matrix can be maintained without deterioration of the condition number when the number of the mesh elements scales up. Singular integrand kernels are characteristics of the BEM. Their accurate integration is an important issue. We describe variable transformations that allow accurate numerical integration. The latter is the only plausible integral evaluation method when using curve-shaped boundary elements.     

Effect of artificial periodicity in simulations of biomolecules under Ewald boundary conditions: a continuum electrostatics study.

Ewald and related methods are nowadays routinely used in explicit-solvent simulations of biomolecules, although they impose an artificial periodicity in systems which are inherently non-periodic. The consequences of this approximation should be assessed, since they may crucially affect the reliability of computer simulations under Ewald boundary conditions. In the present study we use a method based on continuum electrostatics to investigate the nature and magnitude of possible periodicity-induced artifacts on the potentials of mean force for conformational equilibria in biomolecules. Three model systems and pathways are considered: polyalanine oligopeptides (unfolding), a DNA tetranucleotide (separation of the strands), and the protein Sac7d (conformations from a molecular dynamics simulation). Artificial periodicity may significantly affect these conformational equilibria, in each case stabilizing the most compact conformation of the biomolecule. Three factors enhance periodicity-induced artifacts: (i) a solvent of low dielectric permittivity; (ii) a solute size which is non-negligible compared to the size of the unit cell; and (iii) a non-neutral solute. Neither the neutrality of the solute nor the absence of charge pairs at distances exceeding half the edge of the unit cell do guarantee the absence of artifacts.     

Entropy calculations on a reversibly folding peptide: changes in solute free energy cannot explain folding behavior

The configurational entropy of a beta-heptapeptide in solution at four different temperatures is calculated. The contributions of the backbone and of the side-chain atoms to the total peptide entropy are analyzed separately and the effective contribution to the entropy arising from correlations between these terms determined. The correlation between the backbone and side-chain atoms amounts to about 17% and is rather insensitive to the temperature. The correlation of motion within the backbone and within side-chains is much larger and decreases with temperature. As the peptide reversibly folds at higher temperatures, its change in entropy and enthalpy upon folding is analyzed. The change in entropy and enthalpy upon folding of the peptide alone cannot account for the observed change in free energy on folding of the peptide in solution. Enthalpic and entropic contributions of the solvent thus also play a key role. Proteins 2001;43:45-56.     

Beta-hairpin folding mechanism of a nine-residue peptide revealed from molecular dynamics simulations in explicit water

The beta-hairpin fold mechanism of a nine-residue peptide, which is modified from the beta-hairpin of alpha-amylase inhibitor tendamistat (residues 15-23), is studied through direct folding simulations in explicit water at native folding conditions. Three 300-nanosecond self-guided molecular dynamics (SGMD) simulations have revealed a series of beta-hairpin folding events. During these simulations, the peptide folds repeatedly into a major cluster of beta-hairpin structures, which agree well with nuclear magnetic resonance experimental observations. This major cluster is found to have the minimum conformational free energy among all sampled conformations. This peptide also folds into many other beta-hairpin structures, which represent some local free energy minimum states. In the unfolded state, the N-terminal residues of the peptide, Tyr-1, Gln-2, and Asn-3, have a confined conformational distribution. This confinement makes beta-hairpin the only energetically favored structure to fold. The unfolded state of this peptide is populated with conformations with non-native intrapeptide interactions. This peptide goes through fully hydrated conformations to eliminate non-native interactions before folding into a beta-hairpin. The folding of a beta-hairpin starts with side-chain interactions, which bring two strands together to form interstrand hydrogen bonds. The unfolding of the beta-hairpin is not simply the reverse of the folding process. Comparing unfolding simulations using MD and SGMD methods demonstrate that SGMD simulations can qualitatively reproduce the kinetics of the peptide system.     

Equilibrium structure and folding of a helix-forming peptide: circular dichroism measurements and replica-exchange molecular dynamics simulations

We have performed experimental measurements and computer simulations of the equilibrium structure and folding of a 21-residue alpha-helical heteropeptide. Far ultraviolet circular dichroism spectroscopy is used to identify the presence of helical structure and to measure the thermal unfolding curve. The observed melting temperature is 296 K, with a folding enthalpy of -11.6 kcal/mol and entropy of -39.6 cal/(mol K). Our simulations involve 45 ns of replica-exchange molecular dynamics of the peptide, using eight replicas at temperatures between 280 and 450 K, and the program CHARMM with a continuum solvent model. In a 30-ns simulation started from a helical structure, conformational equilibrium at all temperatures was reached after 15 ns. This simulation was used to calculate the peptide melting curve, predicting a folding transition with a melting temperature in the 330-350 K range, enthalpy change of -10 kcal/mol, and entropy change of -30 cal/(mol K). The simulation results were also used to analyze the peptide structural fluctuations and the free-energy surface of helix unfolding. In a separate 15-ns replica-exchange molecular dynamics simulation started from the extended structure, the helical conformation was first attained after approximately 2.8 ns, and equilibrium was reached after 10 ns of simulation. These results showed a sequential folding process with a systematic increase in the number of hydrogen bonds until the helical state is reached, and confirmed that the alpha-helical state is the global free-energy minimum for the peptide at low temperatures.     

Contact interactions method: a new algorithm for protein folding simulations.

Computer simulations of simple exact lattice models are an aid in the study of protein folding process; they have sometimes resulted in predictions experimentally proved. The contact interactions (CI) method is here proposed as a new algorithm for the conformational search in the low-energy regions of protein chains modeled as copolymers of hydrophobic and polar monomers configured as self-avoiding walks on square or cubic lattices. It may be regarded as an extension of the standard Monte Carlo method improved by the concept of cooperativity deriving from nonlocal contact interactions. A major difference with respect to other algorithms is that criteria for the acceptance of new conformations generated during the simulations are not based on the energy of the entire molecule, but cooling factors associated with each residue define regions of the model protein with higher or lower mobility. Nine sequences of length ranging from 20 to 64 residues were used on the square lattice and 15 sequences of length ranging from 46 to 136 residues were used on the cubic lattice. The CI algorithm proved very efficient both in two and three dimensions, and allowed us to localize energy minima not localized by other searching algorithms described in the literature. Use of this algorithm is not limited to the conformational search, because it allows the exploration of thermodynamic and kinetic behavior of model protein chains.     

Ion-channel properties of mastoparan, a 14-residue peptide from wasp venom, and of MP3, a 12-residue analogue.

Mastoparan, a 14-residue peptide, has been investigated with respect to its ability to form ion channels in planar lipid bilayers. In the presence of 0.3-3.0 microM mastoparan, two types of activity are seen. Type I activity is characterized by discrete channel openings, exhibiting multiple conductance levels in the range 15-700 pS. Type II activity is characterized by transient increases in bilayer conductance, up to a maximum of about 650 pS. Both type I and type II activities are voltage dependent. Channel activation occurs if the compartment containing mastoparan is held at a positive potential; channel inactivation if the same compartment is held at a negative potential. Channel formation is dependent on ionic strength; channel openings are only observed at KCl concentrations of 0.3 M or above. Furthermore, raising the concentration of KCl to 3.0 M stabilizes the open form of the channel. Mastoparan channels are weakly cation selective, PK/Cl approximately 2. A 12-residue analogue, des-Ile1,Asn2-mastoparan, preferentially forms type I channels. The ion channels formed by these short peptides may be modelled in terms of bundles of transmembrane alpha-helices.     

The conformation of dehydroalanine in short homopeptides: molecular dynamics simulations of a 6-residue chain

A molecular dynamics study about the conformational preferences in a chloroform solution of a homo-oligomer constituted by six residues of dehydroalanine is presented. For this purpose, two sets of force-field parameters and explicit solvent molecules have been used. Furthermore, ab initio calculations have been performed in order to estimate 1[H]-NMR chemical shifts. Results have been compared with experimental data.     

Structure and folding of disulfide-rich miniproteins: insights from molecular dynamics simulations and MM-PBSA free energy calculations

The fold of small disulfide-rich proteins largely relies on two or more disulfide bridges that are main components of the hydrophobic core. Because of the small size of these proteins and their high cystine content, the cysteine connectivity has been difficult to ascertain in some cases, leading to uncertainties and debates in the literature. Here, we use molecular dynamics simulations and MM-PBSA free energy calculations to compare similar folds with different disulfide pairings in two disulfide-rich miniprotein families, namely the knottins and the short-chain scorpion toxins, for which the connectivity has been discussed. We first show that the MM-PBSA approach is able to discriminate the correct knotted topology of knottins from the laddered one. Interestingly, a comparison of the free energy components for kalata B1 and MCoTI-II suggests that cyclotides and squash inhibitors, although sharing the same scaffold, are stabilized through different interactions. Application to short-chain scorpion toxins suggests that the conventional cysteine pairing found in many homologous toxins is significantly more stable than the unconventional pairing reported for maurotoxin and for spinoxin. This would mean that native maurotoxin and spinoxin are not at the lowest free energy minimum and might result from kinetically rather than thermodynamically driven oxidative folding processes. For both knottins and toxins, the correct or conventional disulfide connectivities provide lower flexibilities and smaller deviations from the initial conformations. Overall, our work suggests that molecular dynamics simulations and the MM-PBSA approach to estimate free energies are useful tools to analyze and compare disulfide bridge connectivities in miniproteins.     

Boundary element solution of macromolecular electrostatics: interaction energy between two proteins.

The boundary element technique is implemented to solve for the electrostatic potential of macromolecules in an ionic solution. This technique entails solving surface integral equations that are equivalent to the Poisson and the Poisson-Boltzmann equations governing the electrostatic potential inside the macromolecules and and in the solvent. A simple but robust method is described for discretizing the macromolecular surfaces in order to approximate the integral equations by linear algebraic equations. Particular attention is paid to the interaction energy between two macromolecules, and an iterative procedure is devised to make the calculation more efficient. This iterative procedure is illustrated in the electron transfer system of cytochrome c and cytochrome c peroxidase.     

iFold: a platform for interactive folding simulations of proteins

We built a novel web-based platform for performing discrete molecular dynamics simulations of proteins. In silico protein folding involves searching for minimal frustration in the vast conformational landscape. Conventional approaches for simulating protein folding insufficiently address the problem of simulations in relevant time and length scales necessary for a mechanistic understanding of underlying biomolecular phenomena. Discrete molecular dynamics (DMD) offers an opportunity to bridge the size and timescale gaps and uncover the structural and biological properties of experimentally undetectable protein dynamics. The iFold server supports large-scale simulations of protein folding, thermal denaturation, thermodynamic scan, simulated annealing and p(fold) analysis using DMD and coarse-grained protein model with structure-based Gō-interactions between amino acids. AVAILABILITY: http://ifold.dokhlab.org     

Explicit-solvent molecular dynamics simulations of a DNA tetradecanucleotide duplex: lattice-sum versus reaction-field electrostatics

Five long-timescale (10 ns) explicit-solvent molecular dynamics simulations of a DNA tetradecanucleotide dimer are performed using the GROMOS 45A4 force field and the simple-point-charge water model, in order to investigate the effect of the treatment of long-range electrostatic interactions as well as of the box shape and size on the structure and dynamics of the molecule (starting from an idealised B-DNA conformation). Long-range electrostatic interactions are handled using either a lattice-sum (LS) method (particle–particle–particle–mesh; one simulation performed within a cubic box) or a cutoff-based reaction-field (RF) method (four simulations, with long-range cutoff distances of 1.4 or 2.0 nm and performed within cubic or truncated octahedral periodic boxes). The overall double-helical structure, including Watson–Crick (WC) base-pairing, is well conserved in the simulation employing the LS scheme. In contrast, the WC base-pairing is nearly completely disrupted in the four simulations employing the RF scheme. These four simulations result in highly distorted compact (cutoff distance of 1.4 nm) or extended (cutoff distance of 2 nm) structures, irrespective of the shape and size of the computational box. These differences observed between the two schemes seem correlated with large differences in the radial distribution function between charged entities (backbone phosphate groups and sodium counterions) within the system.     

The role of tryptophan in the antibacterial activity of a 15-residue bovine lactoferricin peptide.

Bovine lactoferricin is a 25-residue antibacterial peptide isolated after gastric cleavage of the iron transporting protein lactoferrin. A 15-residue fragment, FKCRRWQWRMKKLGA of this peptide sustains most of the antibacterial activity. In this truncated sequence, the two Trp residues are found to be essential for antibacterial activity. The anchoring properties of Trp, as have been observed in membrane proteins, are believed to be important for the interaction of Trp containing antibacterial peptides with bacterial cell membranes. We have investigated the molecular properties which make Trp important for the antibacterial activity of the 15-residue peptide by replacing Trp with natural and unnatural aromatic amino acids. This series of peptides was tested for antibacterial activity against Echerichia coli and Staphylococcus aureus. We found that neither the hydrogen bonding ability nor the amphipathicity of the indole system are essential properties for the effect of Trp on the antibacterial activity of the peptides. Replacement of Trp with residues containing aromatic hydrocarbon side chains gave the most active peptides. We propose that aromatic hydrocarbon residues are able to position themselves deeper into the bacterial cell membrane, making the peptide more efficient in disrupting the bacterial cell membrane. From our results the size, shape and aromatic character of Trp seem to be the most important features for the activity of this class of Trp containing antibacterial peptides.     

A novel surface autolysin of Listeria monocytogenes serotype 4b, IspC, contains a 23-residue N-terminal signal peptide being processed in E. coli

The 86-kDa protein IspC of 774 amino acids in Listeria monocytogenes serotype 4b has been recently identified as the target of humoral immune response to listerial infection and as a novel surface autolysin. A signal peptide is predicted at the N-terminal end of IspC, but no biochemical data has been shown to confirm the presence of the cleavage site of a signal peptidase. To address this and prepare sufficient amount of the protein for biochemical and structural characterization, we present a strategy for efficient expression and purification of IspC and analyze the purified protein by N-terminal sequencing and mass spectrometry. Expression of IspC in Escherichia coli using a pET30a-based expression construct was efficiently improved by incubating the culture at 37 degrees C for 2h followed by 4 degrees C for 16-18 h. The recombinant product rIspC remained as a soluble form in the cellular extract and was purified to electrophorectic homogeneity by the combination of metal chelate affinity chromatography with cation-exchange chromatography. The IspC was shown to contain a 23-residue N-terminal signal peptide being processed between Thr 23 and Thr 24 in E. coli, resulting in an 84-kDa mature protein. The highly purified form of rIspC from this study, exhibiting both peptidoglycan hydrolase activity and immunogenicity as previously reported, would facilitate further biochemical, structural, and functional studies of this autolysin.     

The scs' boundary element: characterization of boundary element-associated factors.

Boundary elements are thought to define the peripheries of chromatin domains and to restrict enhancer-promoter interactions to their target genes within their domains. We previously characterized a cDNA encoding the BEAF-32A protein (32A), which binds with high affinity to the scs' boundary element from the Drosophila melanogaster 87A7 hsp70 locus. Here, we report a second protein, BEAF-32B, that differs from 32A only in its amino terminus. Unlike 32A, it has the same DNA binding specificity as the complete BEAF activity affinity purified from Drosophila. We characterize three domains in these proteins. Heterocomplex formation is mediated by their identical carboxy-terminal domains, and DNA binding is mediated by their unique amino-terminal domains. The identical middle domains of 32A and 32B are dispensable for the functions described here, although they may be important for boundary element function. 32A and 32B apparently form trimers, and the ratio of 32A to 32B varies at different loci on polytene chromosomes as judged by immunofluorescence. The scs' element contains a high- and low-affinity binding site for BEAF. We observed that interaction with the low-affinity site is facilitated by binding to the high-affinity site some 200 bp distant.     

Comparison of atomic solvation parametric sets: applicability and limitations in protein folding and binding.

Atomic solvation parameters (ASP) are widely used to estimate the solvation contribution to the thermodynamic stability of proteins as well as the free energy of association for protein-ligand complexes. They are also included in several molecular mechanics computer programs. In this work, a total of eight atomic solvation parametric sets has been employed to calculate the solvation contribution to the free energy of folding delta Gs for 17 proteins. A linear correlation between delta Gs and the number of residues in each protein was found for each ASP set. The calculations also revealed a great variety in the absolute value and in the sign of delta Gs values such that certain ASP sets predicted the unfolded state to be more stable than the folded, whereas others yield precisely the opposite. Further, the solvation contribution to the free energy of association of helix pairs and to the disassociation of loops (connection between secondary structural elements in proteins) from the protein tertiary structures were computed for each of the eight ASP sets and discrepancies were evident among them.     

Identification of structured peptide segments in folding proteins.

Prediction of the structures of long polypeptides and small proteins has been carried out using conformational energy calculations. These calculations can be applied to large proteins if structured regions of their sequences can be identified. Three different approaches to identifying such sequences are presented. First, sequences of five or more contiguous hydrophobic residues tend to nucleate alpha-helices. Second, peptide sequences from parent proteins that have the same biological activities as the parent proteins are highly structured. Third, structured synthetic peptide segments from proteins inhibit the folding of the parent proteins by competing with the corresponding segment of the protein chain for associating with complementary regions. Examples of each of these approaches are presented.     

Antimicrobial activity of a 14-residue peptide against Escherichia coli O157:H7

An amphiphilic, cationic peptide composed of eight leucines and six lysines was synthesized by solid phase peptide synthesis (SPPS). The synthetic peptide was bactericidal within 10 min at concentrations as low as 3 microg ml - 1 against mid-exponential Escherichia coli O157:H7 suspended in buffer. Concentrations of 25 microg ml - 1 caused up to 7 log10 cfu ml - 1 reductions. When tested against E. coli O157:H7 grown in TSB, the peptide was bactericidal and bacteriostatic at concentrations of 50 and 25 microg ml - 1, respectively. An inhibitory effect was also observed against stationary phase cells. The synthetic peptide caused the release of u.v.-absorbing materials from the E. coli O157:H7 as well as an increase in its O.D.600 nm. Intracellular K+ and ATP depletion were also observed. These results suggest that the peptide increased the cell membrane permeability but it did not lyse the cells.