How To Change Solvent Dielectric Constant In Pymol?

Nucleic Acids Res. 2006 Jul 1; 34(Web Server issue): W38–W42.

PDB_Hydro: incorporating dipolar solvents with variable density in the Poisson–Boltzmann treatment of macromolecule electrostatics

Cyril Azuara

ⁱUnité de Dynamique Structurale des Macromolécules, URA 2185 du C.North.R.S., Institut Pasteur, 75015 Paris, French republic

Erik Lindahl

ⁱUnité de Dynamique Structurale des Macromolécules, URA 2185 du C.Due north.R.S., Institut Pasteur, 75015 Paris, France

²Computational Structural Biology, Stockholm Bioinformatics Center, Stockholm, Sweden

Patrice Koehl

^threeInformatics Section and Genome Center, University of California, Davis, CA 95616, USA

Henri Orland

⁴Service de Physique Théorique, CE-Saclay, 91191 Gif/Yvette Cedex, France

Marc Delarue

ⁱUnité de Dynamique Structurale des Macromolécules, URA 2185 du C.Northward.R.Southward., Institut Pasteur, 75015 Paris, France

Received 2006 Feb 14; Revised 2006 Mar 3; Accepted 2006 Mar 3.

Abstract

We draw a new way to calculate the electrostatic properties of macromolecules which eliminates the assumption of a constant dielectric value in the solvent region, resulting in a Generalized Poisson–Boltzmann–Langevin equation (GPBLE). We have implemented a spider web server (http://lorentz.immstr.pasteur.fr/pdb_hydro.php) that both numerically solves this equation and uses the resulting water density profiles to place water molecules at preferred sites of hydration. Surface atoms with loftier or low hydration preference can exist hands displayed using a simple PyMol script, allowing for the tentative prediction of the dimerization interface in homodimeric proteins, or lipid binding regions in membrane proteins. The spider web site includes options that permit mutations in the sequence likewise as reconstruction of missing side chain and/or principal chain atoms. These tools are attainable independently from the electrostatics calculation, and can exist used for other modeling purposes. We expect this web server to exist useful to structural biologists, as the knowledge of solvent density should prove useful to get better fits at low resolution for X-ray diffraction information and to computational biologists, for whom these profiles could better the calculation of interaction energies in water between ligands and receptors in docking simulations.

INTRODUCTION

Understanding the stability and function of biological macromolecules too as their interaction with other ligands (effectors, substrates) requires every bit a prerequisite a quantitative evaluation of their interactions with the solvent. Indeed, being able to predict the solvation energy from just the coordinates of the molecule would exist a tremendous advance in drug-design studies and many other issues in computational structural biology.

Current methods that compute solvation autumn into two classes: those which stand for the solvent explicitly, which are computationally intensive, and those that attempt to model the solvent as a continuous dielectric medium, i.e. implicit solvent models.

In this second class, the Poisson–Boltzmann equation (PBE) is widely used. It is ordinarily solved numerically for solutes of arbitrary shapes using finite departure methods, equally pioneered by Warwicker and Watson (1) and later adult by Honig and colleagues and incorporated in their popular Delphi package (2,3). Many programs that solve either the linearized version of PBE, or directly the non-linear PBE, with a multifariousness of scientific calculating techniques are at present available [see ref. (4) for a contempo review].

While it has been demonstrated that these packages give qualitatively correct values of the electric potential in a number of situations (5) (http://honiglab.cpmc.columbia.edu), information technology is still not entirely satisfying to accept to use somewhat capricious values for the dielectric constant of the poly peptide (around ii–4), which abruptly jumps to 80 at the interface between the protein and the solvent. This problem notwithstanding attracts a lot of attention (6).

In this commodity we depict how a simple solvent clarification every bit an associates of freely orienting dipoles can be readily incorporated into the Poisson–Boltzmann formalism. This is in upshot a generalization of the Langevin Dipoles-Protein Dipoles (LDPD) model advocated past Warshel and colleagues (7–9), with the key additional characteristic that the dipoles are now allowed to have a variable density at each grid point around the solute. Also, information technology leads to a solvent with a variable dielectric abiding that is self-consistently adamant past the system.

There is a variety of situations where one would like to take admission to the solvent density profile, starting from just the PDB atomic coordinates of the molecule (x). Experimentally, this would pb to better fits with depression resolution diffraction information (11,12). As well, better electrostatics calculations would lead to amend estimates of intrinsic pKas of cached ionisable groups (13), which are ofttimes role of catalytic sites. On the modeling side, this would obviously be useful both to compute solvation energies with much more accuracy than shortly (14) and also in understanding the nature of the hydrophobic effect. For instance, in the van der Waals theory of capillarity, the gratis energy at the liquid–vapor h2o interface contains a term proportional to the integral of the squared gradient of the solvent density contour and this is currently being used to study the nature of the hydrophobic consequence at different length scales (15).

The post-obit department describes the web server and its tools, and a flow chart of the different options is presented in Figure i. The main focus is put on the new method used to solve for the electrostatics of the macromolecule. The result section briefly describes two applications, i for predicting putative dimerization region(southward) on the surface of a globular protein, and the other for predicting regions for lipid binding in membrane proteins. The conclusion department provides a perspective and outlines hereafter work.

An external file that holds a picture, illustration, etc. Object name is gkl072f1.jpg

Flow chart of the different options in PDB_hydro.

MATERIALS AND METHODS

PDB fixer

As in other like servers dealing with macromolecular electrostatics [PDB2PQR—ref. (16) (http://agave.wustl.edu/pdb2pqr), 2004; PCE—ref. (17)], we provide some tools to bank check the PDB file of interest before submitting it to a PBE solver. Indeed, some PDB files lack atoms, just because the electron density was non defined for some exposed side chains or disordered loops. If the concerned residues are charged, it may be meliorate to accept even a rough estimate of their locations rather than nada at all. We provide 1 choice that detects missing side chains and builds the rotamer with the lowest van der Waals energy in the context of the (frozen) rest of the protein, for each missing side chain. Another option can detect missing loops, if the numbering of the residues appears to be discontinuous along the chain. The algorithm builds alanines using an idealized conformation of the peptide bond, as described in Hoffmann and Knapp (18). It can bargain with interruptions of the primary chain upwardly to 21 residues long and then proceeds to generate variants of the conformation of the missing loop by using 'window moves'. The algorithm was designed to let for several loops to exist built simultaneously. The user can choose the number of different conformations of the loop (typically 10), audit them visually, and so choose to mutate them past either changing their amino acid blazon from Alanine to the desired sequence in the PDB file (frozen approximation), or apply a more sophisticated algorithm where all the mutated side bondage have their conformation optimized simultaneously using the Hateful Field Optimization technique described by u.s.a. earlier (19). This option, called 'decorate', can actually be used to do protein blueprint and has been used in the past for such purposes (20). Its input is a PDB file and an alignment file (MSF format) containing the aligned onetime and new sequences.

The resulting PDB file can be refined to remove bumps coming from the utilise of rotamers, by minimizing the van der Waals energy of the sidechains using a cohabit gradient minimizer in dihedral angle space, where the needed energy derivatives are calculated according to Abe et al. (21).

Finally, at that place is an choice to refine the network of hydrogen bonds in the PDB file, by allowing 180° flips of the final chi angles of Asn, Gln and His side bondage, as amide O and NH2 atoms cannot really be distinguished in experimental electron density maps obtained by crystallographers. The resulting combinatorics tin can exist explored by Monte Carlo (22) restricting the rotamers to the observed and flipped value of the last chi angle for Asn, Gln or His side chains only. However, here it is washed with Mean Field Optimization techniques as in (19).

PDB solvate

Once the PDB file contains all side chain atoms, we assign partial charges and atomic radii to each atom of the molecule, according to CHARMM22 (similar to PDB2PQR for APBS); this as well works for Dna too every bit RNA molecules. For protein–nucleic acid complexes, the user must submit the files separately and so manually merge them. Alternatively, the user can also directly submit the PDB file to the Generalized Poisson-Boltzmann-Langevin equation (GPBLE) solver, with charges generated according to some other Molecular Mechanics package. In the second step, nosotros solve the GPBLE using a multi-grid method (meet beneath), resulting in a 3D map of the electrostatic potential that specifies the complimentary ions density as well as the dipolar solvent density at each grid point. In the third step, this solvent density is used to place water molecules at preferred sites of hydration, according to a threshold that is calculated from the desired level of hydration (ordinarily 0.four g of jump H2O per g of protein).

To write the analog of PBE in the presence of dipoles p ₀ at position r _i we use the fact that the respective charge density can be written p ₀.grad δ(r − r _i) and and then employ lattice field theory to enforce self-abstention of both complimentary ions and dipoles (23). This is similar in spirit to (24), but differs in detail in the way steric clashes are prevented. The division function Z of the system is evaluated using the saddle-point method (i.east. it is a Hateful Field theory), from which all thermodynamic and physical quantities can be retrieved. Details will be given elsewhere (C. Azuara, H. Orland and K. Delarue, manuscript in training; (25)).

This results in the terminal complimentary-energy functional F(Φ) of the course:

$\begin{array}{l} β F = - \frac{β ɛ}{8 π} \int d \vec{r} {| \vec{\nabla} Φ (\vec{r}) |}^{2} + β \int d \vec{r} ρ_{fixed} Φ (\vec{r}) \\ - \frac{1}{a^{3}} \int d \vec{r} ln (1 + ii λ_{ion} cosh [β e z Φ (\vec{r})] + λ_{dip} \frac{sinh [β p_{0} | \vec{\nabla} Φ (\vec{r}) |]}{β p_{0} | \vec{\nabla} Φ (\vec{r}) |}) \end{array}$

where ρ_fixed is the accuse density of the solute, a is the size of the dipoles and the free ions, β = one/k_B T, ɛ is the dielectric constant of the solute, e the charge of the electron, z the valence, p ₀ the dipole moment of the solvent and Φ the electrical potential; λ_ion and λ_dip are the fugacities of the gratuitous ions and dipoles, respectively, which are functions of their concentrations.

This free free energy has to be minimized as a part of the electrostatic potential Φ, leading to a GPBLE. In the absenteeism of dipolar species and at low βezΦ, i indeed recovers the linear PBE. The minimization tin can be performed in a number of ways, such as the relaxation method or the multi-filigree method. We implemented both methods, checked that the results agreed, and then settled for the multi-filigree method, which is much faster.

IMPLEMENTATION

The web site is organized in ii master sections, namely PDB_fixer and PDB_solvate; each section has several options, which each incorporate a short description, an case, and a form to submit a job. A flow chart of the different steps is presented in Figure 1 and can exist accessed from the bill of fare of the spider web site. Two jobs can be run at the same time and the batch queue status of the server tin can be displayed at whatsoever moment. A number of related links are likewise provided, as well as a pick of reference articles. Once a job is submitted, the user is directed to a web folio that is refreshed every 30 s for 5 min, after which the user is referred to a newly created directory, where the results will be available for 2 weeks. The user may or may not provide his/her email address to be notified of the cease of the job.

For all the options of PDB_fixer, the output volition consist of 1 or several PDB files.

For PDB_solvate information technology volition contain several PDB files besides as formatted CNS-style (26) maps that can be visualized with standard molecular graphics programs, such as O (27) or PyMol (28) (http://pymol.sourceforge.cyberspace). The typical Solvate protocol involves three steps: assign partial charges (assuming that the PDB file is complete), solve the GPBLE using Multi-grid method and place water molecules according to the obtained solvent density map. All three steps tin be performed in a single task chosen All-in-ane. The PDB_solvate output PDB file contains information in the B-gene cavalcade that allows the coloring of the molecular surface with PyMol according to the burying of the surface atom upon addition of the h2o molecules.

The size of the grid is indirectly specified by the two following parameters that must be provided of the user: (i) the number of grid points in the simulation box forth each direction, which must be of the form ii ⁿ +1 and (ii) the number of Bjerrum lengths between the border of the grid and the border of the molecule. L_B is the length at which the electrostatic interaction between 2 unit of measurement charges becomes comparable to thermal free energy kT (fifty_B = 7 Å at 293 K); ordinarily 2l_B is sufficient. The molecule is centered on the grid prior to any electrostatic calculation.

Other input parameters include the size of the ions (taken as the same as the size of the solvent dipoles), the strength of the dipoles (in Debye), equally well equally the concentration and valence of the gratuitous ions. It is important to realize that the system deals with two types of unrelated grids: one that enforces the finite size effect of the gratis ions and the dipoles, and one that is used to solve the not-linear GPBLE. In the futurity, we plan to implement a version of the program that can bargain with unlike sizes for the free ions and the dipoles, or a mixture of dipoles of different concentrations and sizes.

The atomic radii are used to specify the excluded surface of the molecule, which can be of two types: the accessible surface (using the radius of one.4 Å for the probe sphere) or the molecular surface, calculated on a filigree (12) with a probe radius of one Å and a compress radius of 1.ane Å.

RESULTS

For PDB_solvate, we give in Table 1 the CPU times needed for the GPBL solver to converge, for unlike numbers of grid points and different grid sizes. A comparison is given with the CPU times needed in the same configuration past the APBS software (29). Obviously, the solution of the GPBLE takes longer than the PBE, but information technology even so remains reasonable while generating much more information, such every bit the solvent density map, the solvent dielectric constant map, the electric field, the bending between the dipole moment and the solute electric field likewise as the angle between dipole neighbors.

Table 1

CPU needed for the GPBLE solver in dissimilar grid weather condition. Comparing with APBS

Grid size	Nb 50 _B	Grid spacing (Å)		GPBLE		PBE (APBS)
			CPU fourth dimension (south)	$Δ G_{sol}^{elec} (k T)$	CPU time (s)	$Δ G_{sol}^{elec} (k T)$
33^three	1	2.0	34.5	−4581.4	iii.v	−3947.3
33^three	2	2.half-dozen	33.5	−5018.four	2.ix	−3190.7
33³	3	3.0	xxx.7	−4956.iv	2.2	−2813.4
65³	1	ane.0	295.7	−3579.0	fourteen.viii	−3944.3
65ⁱⁱⁱ	2	ane.iii	291.two	−3717.nine	eighteen.7	−3957.0
65³	3	i.v	298.five	−3832.8	17.6	−3940.vi
129³	i	0.v	4759.iii	−3261.5	94.iii	−4030.vii
129³	ii	0.65	4788.5	−3291.0	84.0	−3994.iv
129³	3	0.75	4854.two	−3326.seven	102.nine	−3974.4

As an illustration of the usefulness of the method, we give two examples where the knowledge of the water density profile clearly correlates with known molecular properties. One is a homodimeric protein (4TMK) whose preferred sites of hydration conspicuously are excluded from the dimerization zone (Figure 2A). The other is the KcsA membrane protein, where once more the lipid binding region is conspicuously highlighted in the colored surface output past the program and displayed using a unproblematic PyMol script (Figure 2B). We have checked the generality of these results on a number of different homodimeric and membrane proteins, which will be reported elsewhere (C. Azuara, H. Orland and M. Delarue, unpublished data).

An external file that holds a picture, illustration, etc. Object name is gkl072f2.jpg

(A) Colored molecular surface of thymidine kinase 4TMK (equally a monomer) as a function of surface surface area buried upon add-on of water molecules in the peaks of the solvent density map. The dimerization area appears as the largest poorly solvated (red) patch. Fatigued with PyMol (27) (http://pymol.sourceforge.net). (B) KcsA membrane protein: molecular surface and added water molecules at preferred hydration sites. Fatigued with PyMol (27) (http://pymol.sourceforge.internet). [Supplementary Figure: Radial density profile of the solvent as a function of the surface atom blazon (run into text)].

In addition to the dipole density map, we can calculate the radial solvent density profile, as a function of the nearest surface atom blazon (C, N or O). The resulting profiles (Supplementary Data) indeed show the expected beliefs, with a higher hydration superlative for N and O, compared to C atoms.

Decision AND Futurity WORK

In the present state of the server, the user tin calculate the electrostatic backdrop of a macromolecule (poly peptide or a nucleic acid) using a new methodology which finer merges the two existing PBE and LDPD methods. The solvent is deemed for by an associates of not-overlapping orientable dipoles of variable density. The major advantage of the method is that information technology generates a solvent density map and a variable dielectic constant map of the solvent. All parameters of the theory are given their concrete values. Already, this has proved useful for identifying hydrophobic patches on the surface of proteins.

A number of options and refinements of the method are currently under manner; they include: (i) the possibility to have a pH-dependency of the solute charges (thirty), (ii) the possibility to include the effect of the flexibility of the solute molecule in a dielectric response described by Normal Modes, i.due east. a variable dielectric constant within the solute (31) and (3) the possibility to include the polarisability of the solvent.

SUPPLEMENTARY Information

Supplementary data are bachelor at NAR online

Acknowledgments

Grand. Delarue and H. Orland wish to thank the hospitality of ITP at UCSB, USA, where role of this work was initiated. Funding to pay the Open up Access publication charges for this article was provided by Institut Pasteur.

Conflict of interest statement. None declared.

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