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.     

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.     

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     

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.     

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.     

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.     

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 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.     

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.     

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.     

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.     

Explicit and implicit water simulations of a beta-hairpin peptide.

The conformational properties of a beta-hairpin peptide (YITNSDGTWT) were studied by using both explicit and implicit water simulations. The conformational space of the peptide was scanned by using a restricted hydrogen-bonding search method. The search method used generated the conformational space with enough diversity and good representation of beta-hairpin structures. By using a total surface area-based treatment of hydrophobic interactions, implicit water simulations failed to discriminate between experimental beta-hairpin structures from the rest of the conformers present in the authors' conformation library. However, with inclusion of vibrational free energy and accounting separately for polar and nonpolar surface areas, the nuclear magnetic resonance structure was ranked successfully as the most stable conformation. There is a loose correlation between the conformational energies by the continuum model and the conformational energies by explicit water simulation for conformers with similar structures. However, in terms of solvation energy, both approaches have a much better correlation. By using proper treatment of surface effect (partition of the surface area into polar and nonpolar areas) and including vibrational free-energy contribution, the continuum models should be reliable. Furthermore, the authors found that, for this peptide, beta-hairpin structures have large vibrational entropy that contributes decisively to the stability of folded beta-hairpin structures. Proteins 1999;37:73-87.     

Rapid folding of calcium-free subtilisin by a stabilized pro-domain mutant.

In vitro folding of mature subtilisin is extremely slow. The isolated pro-domain greatly accelerates in vitro folding of subtilisin in a bimolecular reaction whose product is a tight complex between folded subtilisin and folded pro-domain. In our studies of subtilisin, we are trying to answer two basic questions: why does subtilisin fold slowly without the pro-domain and what does the pro-domain do to accelerate the folding rate? To address these general questions, we are trying to characterize all the rate constants governing individual steps in the bimolecular folding reaction of pro-domain with subtilisin. Here, we report the results of a series of in vitro folding experiments using an engineered pro-domain mutant which is independently stable (proR9) and two calcium-free subtilisin mutants. The bimolecular folding reaction of subtilisin and proR9 occurs in two steps: an initial binding of proR9 to unfolded subtilisin, followed by isomerization of the initial complex into the native complex. The central findings are as follows. First, the independently stable proR9 folds subtilisin much faster than the predominantly unfolded wild-type pro-domain. Second, at micromolar concentrations of proR9, the subtilisin folding reaction becomes limited by the rate at which prolines in the unfolded state can isomerize to their native conformation. The simpliest mechanism which closely describes the data includes two denatured forms of subtilisin, which form the initial complex with proR9 at the same rate but which isomerize to the fully folded complex at much different rates. In this model, 77% of the subtilisin isomerizes to the native form slowly and the remaining 23% isomerizes more rapidly (1.5 s-1). The slow-folding population may be unfolded subtilisin with the trans form of proline 168, which must isomerize to the cis form during refolding. Third, in the absence of proline isomerization, the rate of subtilisin folding is rapid and at [proR9] 3 s-1. The implications of these results concerning why subtilisin folds slowly without the pro-domain are discussed.     

Theory and applications of the generalized Born solvation model in macromolecular simulations.

Generalized Born (GB) models provide an attractive way to include some thermodynamic aspects of aqueous solvation into simulations that do not explicitly model the solvent molecules. Here we discuss our recent experience with this model, presenting in detail the way it is implemented and parallelized in the AMBER molecular modeling code. We compare results using the GB model (or GB plus a surface-area based "hydrophobic" term) to explicit solvent simulations for a 10 base-pair DNA oligomer, and for the 108-residue protein thioredoxin. A slight modification of our earlier suggested parameters makes the GB results more like those found in explicit solvent, primarily by slightly increasing the strength of NH [bond] O and NH [bond] N internal hydrogen bonds. Timing and energy stability results are reported, with an eye toward using these model for simulations of larger macromolecular systems and longer time scales.     

Molecular simulations of mutually exclusive folding in a two-domain protein switch

A major challenge with testing designs of protein conformational switches is the need for experimental probes that can independently monitor their individual protein domains. One way to circumvent this issue is to use a molecular simulation approach in which each domain can be directly observed. Here we report what we believe to be the first molecular simulations of mutually exclusive folding in an engineered two-domain protein switch, providing a direct view of how folding of one protein drives unfolding of the other in a barnase-ubiquitin fusion protein. These simulations successfully capture the experimental effects of interdomain linker length and ligand binding on the extent of unfolding in the less stable domain. In addition, the effect of linker length on the potential for oligomerization, which eliminates switch activity, is in qualitative agreement with analytical ultracentrifugation experiments. We also perform what we believe to be the first study of protein unfolding via progressive localized compression. Finally, we are able to explore the kinetics of mutually exclusive folding by determining the effect of linker length on rates of unfolding and refolding of each protein domain. Our results demonstrate that molecular simulations can provide seemingly novel biological insights on the behavior of individual protein domains, thereby aiding in the rational design of bifunctional switches.