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PubMed1993

Crystal structure of a flavoprotein related to the subunits of bacterial luciferase.

The molecular structure of the luxF protein from the bioluminescent bacterium Photobacterium leiognathi has been determined by X-ray diffraction techniques and refined to a conventional R-factor of 17.8% at 2.3 A resolution. The 228 amino acid polypeptide exists as a symmetrical homodimer and 33% of the monomer's solvent-accessible surface area is buried upon dimerization. The monomer displays a novel fold that contains a central seven-stranded beta-barrel. The solvent-exposed surface of the monomer is covered by seven alpha-helices, whereas the dimer interface is primarily a flat surface composed of beta-strands. The protein monomer binds two molecules of flavin mononucleotide, each of which has C6 of the flavin isoalloxazine moiety covalently attached to the C3' carbon atom of myristic acid. Both myristyl groups of these adducts are buried within the hydrophobic core of the protein. One of the cofactors contributes to interactions at the dimer interface. The luxF protein displays considerable amino acid sequence homology with both alpha- and beta-subunits of bacterial luciferase, especially the beta-subunit. Conserved amino acid residues shared between luxF and the luciferase subunits cluster predominantly in two distinct regions of the luxF protein molecule. These homologous regions in the luciferase subunits probably share a three-dimensional fold similar to that of the luxF protein.

Amino Acid Sequence↗

PubMed2004

Structural proteomics of the poxvirus family.

Recent concerns over the potential use of variola virus-commonly known as smallpox-and other orthopox viruses as weapons of bioterrorism have increased research efforts towards creating new antiviral drugs and safer more effective vaccines. Here we introduce a new resource for structural information of poxvirus proteins: the poxvirus proteomics database (PPDB). In the PPDB, we leverage recently developed bioinformatics structure prediction tools on a genomic scale and provide results in a publicly accessible format. The current version of the system contains both experimentally determined and predicted information about protein structural features, such as secondary structure and relative solvent accessibility, as well as tertiary structure and homology information. The system is automated to read the primary sequences from the database, produce the new information for each sequence, and update the database monthly and as new tools are incorporated. The PPDB contains detailed information on the open reading frames (ORFs) in the Copenhagen strain of the vaccinia virus genome. The contents of the PPDB can be accessed through a simple web interface. Inclusion of additional poxvirus genomes in the PPDB is in progress. The PPDB has an upward scalable informatics infrastructure that can readily be applied to viral, bacterial, as well as eukaryotic genomes.

Antiviral Agents↗

PubMed2000

Three-dimensional structures of the free and antigen-bound Fab from monoclonal antilysozyme antibody HyHEL-63(,).

Antigen-antibody complexes provide useful models for studying the structure and energetics of protein-protein interactions. We report the cloning, bacterial expression, and crystallization of the antigen-binding fragment (Fab) of the anti-hen egg white lysozyme (HEL) antibody HyHEL-63 in both free and antigen-bound forms. The three-dimensional structure of Fab HyHEL-63 complexed with HEL was determined to 2.0 A resolution, while the structure of the unbound antibody was determined in two crystal forms, to 1.8 and 2.1 A resolution. In the complex, 19 HyHEL-63 residues from all six complementarity-determining regions (CDRs) of the antibody contact 21 HEL residues from three discontinuous polypeptide segments of the antigen. The interface also includes 11 bound water molecules, 3 of which are completely buried in the complex. Comparison of the structures of free and bound Fab HyHEL-63 reveals that several of the ordered water molecules in the free antibody-combining site are retained and that additional waters are added upon complex formation. The interface waters serve to increase shape and chemical complementarity by filling cavities between the interacting surfaces and by contributing to the hydrogen bonding network linking the antigen and antibody. Complementarity is further enhanced by small (<3 A) movements in the polypeptide backbones of certain antibody CDR loops, by rearrangements of side chains in the interface, and by a slight shift in the relative orientation of the V(L) and V(H) domains. The combining site residues of complexed Fab HyHEL-63 exhibit reduced temperature factors compared with those of the free Fab, suggesting a loss in conformational entropy upon binding. To probe the relative contribution of individual antigen residues to complex stabilization, single alanine substitutions were introduced in the epitope of HEL recognized by HyHEL-63, and their effects on antibody affinity were measured using surface plasmon resonance. In agreement with the crystal structure, HEL residues at the center of the interface that are buried in the complex contribute most to the binding energetics (DeltaG(mutant) - DeltaG(wild type) > 3.0 kcal/mol), whereas the apparent contributions of solvent-accessible residues at the periphery are much less pronounced (<1.5 kcal/mol). In the latter case, the mutations may be partially compensated by local rearrangements in solvent structure that help preserve shape complementarity and the interface hydrogen bonding network.

Amino Acid Sequence↗

PubMed1999

Differential temperature-dependent chaperone-like activity of alphaA- and alphaB-crystallin homoaggregates.

alpha-Crystallin, a heteromultimeric protein made up of alphaA- and alphaB-crystallins, functions as a molecular chaperone in preventing the aggregation of proteins. We have shown earlier that structural perturbation of alpha-crystallin can enhance its chaperone-like activity severalfold. The two subunits of alpha-crystallin have extensive sequence homology and individually display chaperone-like activity. We have investigated the chaperone-like activity of alphaA- and alphaB-crystallin homoaggregates against thermal and nonthermal modes of aggregation. We find that, against a nonthermal mode of aggregation, alphaB-crystallin shows significant protective ability even at subphysiological temperatures, at which alphaA-crystallin or heteromultimeric alpha-crystallin exhibit very little chaperone-like activity. Interestingly, differences in the protective ability of these homoaggregates against the thermal aggregation of beta(L)-crystallin is negligible. To investigate this differential behavior, we have monitored the temperature-dependent structural changes in both the proteins using fluorescence and circular dichroism spectroscopy. Intrinsic tryptophan fluorescence quench-ing by acrylamide shows that the tryptophans in alphaB-crystallin are more accessible than the lone tryptophan in alphaA-crystallin even at 25 degrees C. Protein-bound 8-anilinonaphthalene-1-sulfonate fluorescence demonstrates the higher solvent accessibility of hydrophobic surfaces on alphaB-crystallin. Circular dichroism studies show some tertiary structural changes in alphaA-crystallin above 50 degrees C. alphaB-crystallin, on the other hand, shows significant alteration of tertiary structure by 45 degrees C. Our study demonstrates that despite a high degree of sequence homology and their generally accepted structural similarity, alphaB-crystallin is much more sensitive to temperature-dependent structural perturbation than alphaA- or alpha-crystallin and shows differences in its chaperone-like properties. These differences appear to be relevant to temperature-dependent enhancement of chaperone-like activity of alpha-crystallin and indicate different roles for the two proteins both in alpha-crystallin heteroaggregate and as separate proteins under stress conditions.

Acrylamide↗

PubMed1985

Intramolecular interactions, mesomerism and dynamics in actinomycin D studied by 15N NMR spectroscopy.

We present a detailed conformational study of 15N-labelled actinomycin D in different organic solvents using 1H, 15N and two-dimensional (2D) NMR techniques at 30.4 MHz and 50.6 MHz. The assignment of the threonine and valine 15N resonances to the individual residues on the alpha- or beta-lactone rings was achieved via heteronuclear shift-correlated 2D NMR experiments. The solvent perturbation studies allow an estimation of the solvent accessibility of the nitrogens and carbonyl groups. Evidence is presented that the pentapeptide rings of actinomycin D have different conformations in polar and in apolar solvents. The chromophoric N10 is efficiently solvent-protected, the solvent-dependence of its 15N resonance resulting from solvent interactions at other positions of the molecule and from solvent-dependent changes in the twisting of the chromophoric system. The chromophoric 2-amino nitrogen is shown to exhibit a strong sp2 character due to the formation of a conjugated system with the carbonyl group at C1. Such a conjugation requires a non-planar chromophoric ring system. Additionally, a hydrogen bond connecting the 2-amino and the 1-carbonyl group was detected. In some solvents, two resonances appear for the 2-amino nitrogen implying the presence of the 2-amino group in two different conformations. The possible implications of the non-planarity of the chromophore for the intercalation process and for the biological activity of the drug are discussed.

Chemical Phenomena↗

PubMed2004

Prediction of protein accessible surface areas by support vector regression.

A novel support vector regression (SVR) approach is proposed to predict protein accessible surface areas (ASAs) from their primary structures. In this work, we predict the real values of ASA in squared angstroms for residues instead of relative solvent accessibility. Based on protein residues, the mean and median absolute errors are 26.0 A(2) and 18.87 A(2), respectively. The correlation coefficient between the predicted and observed ASAs is 0.66. Cysteine is the best predicted amino acid (mean absolute error is 13.8 A(2) and median absolute error is 8.37 A(2)), while arginine is the least predicted amino acid (mean absolute error is 42.7 A(2) and median absolute error is 36.31 A(2)). Our work suggests that the SVR approach can be directly applied to the ASA prediction where data preclassification has been used.

Arginine↗

PubMed2002

Structure and dynamics of a helical hairpin and loop region in annexin 12: a site-directed spin labeling study.

A 30-residue nitroxide scan encompassing a helical hairpin and an extended loop in soluble annexin 12 (helices D and E in repeat 2; residues 134-163) has been analyzed in terms of nitroxide side chain mobility and accessibility to collision with paramagnetic reagents (Pi). Values of Pi for both O(2) and a Ni(II) metal complex (NiEDDA) are remarkably well correlated with the fractional solvent accessibility of the native side chains at the corresponding positions computed from the known crystal structure. This result demonstrates the utility of Pi as an experimental measure of side chain accessibility in solution, as well as the lack of structural perturbation due to the presence of the nitroxide side chain. The pattern of side chain mobility is also in excellent agreement with predictions from the crystal structure. The results presented here extend the correlations between mobility and structure described in earlier work on other helical proteins, and suggest their generality. The periodic dependence of Pi and mobility along the sequence of annexin 12 reveals the helical segments and their orientation in the fold, as expected for a nonperturbing nitroxide side chain. However, these data do not distinguish the helix-loop-helix motif from a continuous helix, because immobilized side chains in the short loop sequence maintain the periodicity. As shown here, the ratio of Pi values for O(2) and NiEDDA clearly delineates the loop region, due to size exclusion effects between the two reagents. A new feature evident in a nitroxide scan through multiple secondary elements is a modulation of the basic Pi and mobility patterns along the sequence, apparently due to differences in helix packing and backbone motion. Thus, in the short helix D, residues are consistently more mobile and accessible throughout the sequence compared to the residues in the longer, less-solvated and more ordered helix E.

Annexins↗

PubMed1998

A spectroscopic and molecular dynamics study of native and of a mutant of Xenopus laevis Cu,Zn superoxide dismutase: mechanistic consequences of replacing four charged amino acids on the 'electrostatic' loop.

Neutralisation by site-directed mutagenesis of four charged and highly conserved residues of the electrostatic loop of Cu,Zn superoxide dismutase from Xenopus laevis, involved in the electrostatic attraction of the substrate: Lys120-->Leu, Asp130-->Gln, Glu131-->Gln and Lys134-->Thr, gives rise to a mutant enzyme which displays an affinity for monovalent inhibitor anions, such as N3-, higher than that of the wild type. Analysis of 300 ps of molecular dynamics simulation carried out on the wild type and on the Xenopus laevis Cu,Zn superoxide dismutase mutant indicates that the two proteins display a distinct dynamical behaviour. In particular the root mean square deviation from the starting structure, the number of residues in random coil conformations, the number of residues in unfavourable regions of the Ramachandran plot indicate that the mutant displays a rigidity higher than the native enzyme. This is also evidenced by the loss of dynamical cross correlations in the simulation of the mutant, which on the other hand are present in the wild type. Moreover the mutant protein shows a different organisation of the backbone-to-backbone hydrogen bonds network that generates a rigid structure leading to an increase of the active site accessibility when compared to the native enzyme. It is suggested that the rigid state in which the mutant is confined, accompanied by the increase of the solvent accessible surface of the active site may explain the difference in reactivity toward the inhibitor anion.

Amino Acid Sequence↗

PubMed1986

Antigenic determinants in proteins coincide with surface regions accessible to large probes (antibody domains).

We evaluated surface areas on proteins that would be accessible to contacts with large (1-nm radius) spherical probes. Such spheres are comparable in size to antibody domains that contain antigen-combining sites. We found that all the reported antigenic sites correspond to segments particularly accessible to a large sphere. The antigenic sites were also evident as the most prominently exposed regions (hills and ridges) in contour maps of the solvent-accessible (small-probe) surface. In myoglobin and cytochrome c, virtually all of the van der Waals surface is accessible to the large probe and therefore potentially antigenic; in myohemerythrin, distinct large-probe-inaccessible, and nonantigenic, surface regions are apparent. The correlation between large-sphere-accessibility and antigenicity in myoglobin, lysozyme, and cytochrome c appears to be better than that reported to exist between antigenicity and segmental flexibility; that is, surface regions that are rigid often constitute antigenic epitopes, whereas some of the flexible parts of the molecules do not appear antigenic. We propose that the primary reason why certain polypeptide-chain segments are antigenic is their exceptional surface exposure, making them readily available for contacts with antigen-combining sites. Exposure of these segments frequently results in high mobility and, in consequence, to the reported correlation between antigenicity and segmental flexibility.

Cytochrome c Group↗

PubMed2002

An overview on 2-methyl-2,4-pentanediol in crystallization and in crystals of biological macromolecules.

2-Methyl-2,4-pentanediol (MPD) is the most popular chemical additive used for crystallization of biological macromolecules. However, the mechanism of its action on proteins in aqueous solution is not well understood. We have carried out a systematic analysis of the conformation and environment of MPD molecules bound to proteins. We find that the majority of MPD molecules adopt their most stable conformer. They prefer to bind to hydrophobic sites with a distinct preference for leucine side chains. Most MPD binding sites involve amino-acid residues in helical or beta-sheet structures. MPD binding to proteins is penetrative, leading to displacement of water molecules in grooves and cavities (sometimes ligand-binding and active sites) on the protein surface. This results in a large reduction of solvent-accessible area, which can have significant implications for protein stability. The packing of the MPD molecules by the protein is not optimal and usually some other solvent molecules are also bound along with it. Our analysis suggests that MPD is not as strong a denaturant as often suggested. It promotes stabilization of the protein by preferential hydration, which is facilitated by attachment of MPD molecules to the hydrophobic surface.

Binding Sites↗

PubMed1997

The interactions with solvent, heat stability, and 13C-labelling of alamethicin, an ion-channel-forming peptide.

The peptide alamethicin was labelled with 13C and 15N by growing the fungus Trichoderma viride in a medium containing [U-13C] glucose and K15NO3. Spin-echo difference spectroscopy showed that 13C was incorporated to a level of about 50% and 15N to about 98%. Incorporation of 13C into the peptide provided residue-specific probes of the interactions with solvent and heat stability of this ion-channel-forming peptide. All of the carbonyl carbons and the alpha-carbons of the alpha-aminoisobutyric acid [Ala(Me)] residues of alamethicin in methanol were assigned using two-dimensional and three-dimensional heteronuclear correlation experiments. Measurements of 1JC'N revealed hydrogen bonding with solvent at residues 1 and 19 at the ends of the peptide and at Gly11 in the middle. The data also support the thesis [see Juranic, N., Ilich, P. K. & Macara, S. (1995) J. Am. Chem. Soc. 117, 405-410 that intramolecular hydrogen bonds in proteins and peptides are weaker than hydrogen bonds to solvent. The sensitivity of alamethicin carbonyl and proton chemical shifts to perturbation by dimethyl sulfoxide correlates well with the calculated solvent accessibilities of the carbonyls in the crystal structures and reveals residues in the middle of the peptide and at the C-terminus which interact with solvent. Taken together with the 1JC'N measurements, the data support a model in which hydrogen bonding to solvent at the Gly11/Leu12 amide could provide a site of hydration in the interior of the alamethicin channel structure. The temperature dependencies of the carbonyl chemical shifts support the suggestion that the peptide is flexible in the regions where solvent interacts with the backbone of the peptide. The linear temperature dependence of the carbonyl chemical shifts and molar ellipticity indicate that, due to steric constraints at the Ala(Me) residues, the peptide folding/unfolding transition is non-cooperative and that the peptide is remarkably heat stable.

Alamethicin↗

PubMed1993

Insights into interfacial activation from an open structure of Candida rugosa lipase.

The structure of the Candida rugosa lipase determined at 2.06-A resolution reveals a conformation with a solvent-accessible active site. Comparison with the crystal structure of the homologous lipase from Geotrichum candidum, in which the active site is covered by surface loops and is inaccessible from the solvent, shows that the largest structural differences occur in the vicinity of the active site. Three loops in this region differ significantly in conformation, and the interfacial activation of these lipases is likely to be associated with conformational rearrangements of these loops. The "open" structure provides a new image of the substrate binding region and active site access, which is different from that inferred from the structure of the "closed" form of the G. candidum lipase.

Amino Acid Sequence↗

PubMed1999

Characterization of transient intermediates in lysozyme folding with time-resolved small-angle X-ray scattering.

We have used synchrotron radiation, together with stopped-flow and continuous-flow mixing techniques to monitor refolding of lysozyme at pH 5.2. From data measured at times which range from 14 ms to two seconds, we can monitor changes in the size, the shape and the pair distribution function of the polypeptide chain during the folding process. Comparison of the results with the properties of native and GdmCl-unfolded lysozyme shows that a major chain collapse occurs in the dead-time of mixing. During this process about 50 % of the change in radius of gyration between the unfolded protein and the native state occurs and the polypeptide chain adopts a globular shape. Time-resolved fluorescence spectra of this collapsed state suggest that the hydrophobic side-chains are still highly solvent accessible. A subsequently formed intermediate with helical structure in the alpha-domain is nearly identical in size and shape with native lysozyme and has a solvent-inaccessible hydrophobic core. Despite its native-like properties, this intermediate is only slightly more stable (DeltaG0=-4 kJ/mol) than the collapsed state and still much less stable than native lysozyme (DeltaDeltaG0=36 kJ/mol) at 20 degrees C.

Animals↗

PubMed2000

Structure and dynamics of the pore of inwardly rectifying K(ATP) channels.

Inwardly rectifying K(+) currents are generated by a complex of four Kir (Kir1-6) subunits. Pore properties are conferred by the second transmembrane domain (M2) of each subunit. Using cadmium ions as a cysteine-interacting probe, we examined the accessibility of substituted cysteines in M2 of the Kir6.2 subunit of inwardly rectifying K(ATP) channels. The ability of Cd(2+) ions to inhibit channels was used as the estimate of accessibility. The distribution of Cd(2+) accessibility is consistent with an alpha-helical structure of M2. The apparent surface of reactivity is broad, and the most reactive residues correspond to the solvent-accessible residues in the bacterial KcsA channel crystal structure. In several mutants, single channel measurements indicated that inhibition occurred by a single transition from the open state to a zero-conductance state. Analysis of currents expressed from mixtures of control and L164C mutant subunits indicated that at least three cysteines are required for coordination of the Cd(2+) ion. Application of phosphatidylinositol 4,5-diphosphate to inside-out membrane patches stabilized the open state of all mutants and also reduced cadmium sensitivity. Moreover, the Cd(2+) sensitivity of several mutants was greatly reduced in the presence of inhibitory ATP concentrations. Taken together, these results are consistent with state-dependent accessibility of single Cd(2+) ions to coordination sites within a relatively narrow inner vestibule.

Adenosine Triphosphate↗

PubMed2004

Converging free energy estimates: MM-PB(GB)SA studies on the protein-protein complex Ras-Raf.

Estimating protein-protein interaction energies is a very challenging task for current simulation protocols. Here, absolute binding free energies are reported for the complex H-Ras/C-Raf1 using the MM-PB(GB)SA approach, testing the internal consistency and model dependence of the results. Averaging gas-phase energies (MM), solvation free energies as determined by Generalized Born models (GB/SA), and entropic contributions calculated by normal mode analysis for snapshots obtained from 10 ns explicit-solvent molecular dynamics in general results in an overestimation of the binding affinity when a solvent-accessible surface area-dependent model is used to estimate the nonpolar solvation contribution. Applying the sum of a cavity solvation free energy and explicitly modeled solute-solvent van der Waals interaction energies instead provides less negative estimates for the nonpolar solvation contribution. When the polar contribution to the solvation free energy is determined by solving the Poisson-Boltzmann equation (PB) instead, the calculated binding affinity strongly depends on the atomic radii set chosen. For three GB models investigated, different absolute deviations from PB energies were found for the unbound proteins and the complex. As an alternative to normal-mode calculations, quasiharmonic analyses have been performed to estimate entropic contributions due to changes of solute flexibility upon binding. However, such entropy estimates do not converge after 10 ns of simulation time, indicating that sampling issues may limit the applicability of this approach. Finally, binding free energies estimated from snapshots of the unbound proteins extracted from the complex trajectory result in an underestimate of binding affinity. This points to the need to exercise caution in applying the computationally cheaper "one-trajectory-alternative" to systems where there may be significant changes in flexibility and structure due to binding. The best estimate for the binding free energy of Ras-Raf obtained in this study of -8.3 kcal mol(-1) is in good agreement with the experimental result of -9.6 kcal mol(-1), however, further probing the transferability of the applied protocol that led to this result is necessary.

Calorimetry↗

PubMed1999

Folding pattern of the alpha-crystallin domain in alphaA-crystallin determined by site-directed spin labeling.

The folding pattern of the alpha-crystallin domain, a conserved protein module encoding the molecular determinants of structure and function in the small heat-shock protein superfamily, was determined in the context of the lens protein alphaA-crystallin by systematic application of site-directed spin labeling. The sequence-specific secondary structure was assigned primarily from nitroxide scanning experiments in which the solvent accessibility and mobility of a nitroxide probe were measured as a function of residue number. Seven beta-strands were identified and their orientation relative to the aqueous solvent determined, thus defining the residues lining the hydrophobic core. The pairwise packing of adjacent strands in the primary structure was deduced from patterns of proximities in nitroxide pairs with one member on the exposed surface of each strand. In addition to identifying supersecondary structures, these proximities revealed that the seven strands are arranged in two beta-sheets. The overall packing of the two sheets was determined by application of the general rules of protein structure and from proximities in nitroxide pairs designed to distinguish between known all beta-sheet folds. Our data are consistent with an immunoglobulin-like fold consisting of two aligned beta-sheets. Comparison of this folding pattern to that of the evolutionary distant alpha-crystallin domain in Methanococcus jannaschii heat-shock protein 16.5 reveals a conserved core structure with the differences sequestered at one edge of the beta-sandwich. A beta-strand deletion in alphaA-crystallin disrupts a subunit interface and allows for a different dimerization motif. Putative substrate binding regions appear to include a buried loop and a buried turn, suggesting that the chaperone function involves a disassembly of the oligomer.

Amino Acid Motifs↗

PubMed2005

DNA cytosine C5 methyltransferase Dnmt1: catalysis-dependent release of allosteric inhibition.

We followed the cytosine C(5) exchange reaction with Dnmt1 to characterize its preference for different DNA substrates, its allosteric regulation, and to provide a basis for comparison with the bacterial enzymes. We determined that the methyl transfer is rate-limiting, and steps up to and including the cysteine-cytosine covalent intermediate are in rapid equilibrium. Changes in these rapid equilibrium steps account for many of the previously described features of Dnmt1 catalysis and specificity including faster reactions with premethylated DNA versus unmethylated DNA, faster reactions with DNA in which guanine is replaced with inosine [poly(dC-dG) vs poly(dI-dC)], and 10-100-fold slower catalytic rates with Dnmt1 relative to the bacterial enzyme M.HhaI. Dnmt1 interactions with the guanine within the CpG recognition site can prevent the premature release of the target base and solvent access to the active site that could lead to mutagenic deamination. Our results suggest that the beta-elimination step following methyl transfer is not mediated by free solvent. Dnmt1 shows a kinetic lag in product formation and allosteric inhibition with unmethylated DNA that is not observed with premethylated DNA. Thus, we suggest the enzyme undergoes a slow relief from allosteric inhibition upon initiation of catalysis on unmethylated DNA. Notably, this relief from allosteric inhibition is not caused by self-activation through the initial methylation reaction, as the same effect is observed during the cytosine C(5) exchange reaction in the absence of AdoMet. We describe limitations in the Michaelis-Menten kinetic analysis of Dnmt1 and suggest alternative approaches.

Allosteric Regulation↗

PubMed2002

MASKER: improved solvent-excluded molecular surface area estimations using Boolean masks.

A fast algorithm for computing the solvent-accessible molecular surface area (SAS) using Boolean masks [Le Grand,S.M. and Merz,K.M.J. (1993). J. Comput. Chem., 14, 349-352) has been modified to estimate the solvent-excluded molecular surface area (SES), including contact, toroidal and re-entrant surface components. Numerical estimates of arc lengths of intersecting atomic SAS are used to estimate the toroidal surface and intersections between those arcs are used to estimate the re-entrant surface area. The new method is compared with an exact analytical method. Boolean molecular surface areas are continuous and pairwise differentiable and should be useful for molecular dynamics simulations, especially as the basis for an implicit solvent model.

Algorithms↗