SOLVATE is a program to construct an atomic solvent environment model for a given atomic macromolecule model (solute) for use in molecular dynamics simulations.
SOLVATE
) obeying
a Debye-Hückel distribution,
Solvate 1.0 can be obtained as a compressed tar-file from anonymous ftp (ftp.imo.physik.uni-muenchen.de/pub/solvate_1.0/solvate_1.0.tar.Z).
To install it, move the tar-file to your favourite directory and enter:
zcat solvate_1.0.tar.Z | tar -xvf -
The source solvate.c is just one ANSI-C-file without any system-specific stuff (except for malloc() --- RS6000 and NeXT users: pay attention!), so it should compile right away with something like
cc -ansi -O -o solvate solvate.c -lm
It is tested under IRIX System V.4 (SGI), HP-UX, and Digital UNIX V3.2C; appropriate Makefiles are included.
The distribution contains a postscript version of this manual ( docu.ps) as well as an html-version ( html/docu.html with references to all other files in the html-directory).
The distribution also contains two sample-solutes, bpti.pdb/ bpti.psf and globh.pdb/ globh.psf. To check your installation, try:
solvate -t 5.0 -n 2 -ion bpti solbpti
After a while (approx. 10 minutes on a DEC ALPHA/2100)
you should see the following output:
.:::::.. SOLVATE 1.0 (C) 1996 Helmut Grubmueller ::oOOOoo:: Purpose: make a water shell around solutes ::OOO:::: http://www.imo.physik.uni-muenchen.de/~grubi ::::: Helmut.Grubmueller@Physik.uni-muenchen.de Reading solute from file bpti.pdb ... 568 atoms read. Reading atomic charges from file bpti.psf ... total charge is +6.00 e. Calculating bounding sphere ... done. Creating convex volume (max. radius is 100000.000000) ... done. Gauss-sampling convex volume ... done. Approximating volume with 2 gaussians: Phase 1/4...2/4...3/4...4/4...done. Saving parameter for 2 gaussians to file gaussians.lis ... done. Adjusting boundary distance by varying gaussian widths ... 5.046 A Gaussian widths are being scaled by a factor of 1.579210 Saving boundary parameters to file boundary.lis ... done. Creating volume within boundary ... done. Sorting grid points according to distance from solute ... done. Performing distance approximation statistics with 58283 grid points ... 100% Checking approximation for distance from boundary ... 100% Estimated number of water molecules: 2297 Placing water molecules ... found 1692 Grouping water molecules ... 100% The water molecules form 2 groups. Group 1 contains 1691 water molecules Group 2 contains 1 water molecule So we have one single, 0 twins, and 0 triplets Placing ions ... placed 2 sodium ions and 8 chloride ions. Equilibrating ions (2000000 Monte Carlo moves) ... 100% Saving solute, 1682 water molecules, and 10 ions to file solbpti.pdb ... done. Solvate ready. No errors.
Molecular dynamics (MD) studies of biological macromolecules (such as proteins or DNA) require a large amount of computations, mainly due to the large number of atoms (typically several thousands) such molecules consist of. Even when using supercomputers, this computational complexity limits such simulations to very short time scales, typically a few nanoseconds.
Furthermore, just considering the macromolecule of interest is not enough, for the physiological environment of the molecule (e.g., for globular proteins, water solvent and salt ions) strongly interacts with the dissolved macromolecule. Therefore, also part of that environment has to be included within the simulation system, which then usually contains several tens of thousands of atoms [1,2]. Obviously, one wishes to include only as many solvent molecules within the simulation system as really necessary, while keeping the influence of the (artificial) system boundary (the surface of the solvent) onto the dissolved macromolecule as small as possible. SOLVATE serves this purpose.
SOLVATE is a program to construct an atomic model of a solvent environment for a given atomic macromolecule model (solute). Its main feature is that it can create irregularly-shaped solvent volumes specifically adapted to the (mostly also irregular) shape of the solute. As a result, the number of atoms that have to be considered in the MD-simulation is significantly reduced in comparison to the usual box- or sphere-shaped volumes, so that the simulations run considerably faster.
SOLVATE accepts pdb-files (Brookhaven Data Bank/X-PLOR format) of the solute as input; the output is a pdb-file of the solute plus a number of water molecules and, optionally, sodium and chloride ions placed in accordance with a Debye-Hückel-distribution. To generate ions, an X-PLOR protein structure (psf-)file of the solute (which contains the partial charges of the solute atoms) is required in addition to the pdb-file. An X-PLOR-script to create a protein structure file of the solute/water/ion-system can be generated. Note that the output structure is not equilibrated, since this can be done with the usual programs, e.g., CHARMm [3], X-PLOR [4], or EGO [5].
Clearly, just creating solute-adapted solvent volumes is not an art --- it can easily be done, e.g., with the around-function of X-PLOR. However, just to have such a solvent/solute-system is not enough for an MD-simulation. Rather, water molecules near the surface of the solvent volume must be subjected to `boundary-forces' in order to prevent these water molecules from evaporating into the vacuum. Ideally, these forces should substitute all those forces (e.g., electrostatic interactions and van der Waals contacts), which would originate from solvent molecules outside the simulation system. The socalled `stochastic boundary'-approach [6,7] provides such forces in a simple approximation by use of a suitable boundary potential.
Such boundary potentials are generally functions of the distance between the particle, onto which the force acts, and the boundary of the simulation system. Hence, for an efficient computation of the forces derived from this potential, it should be of simple analytic form. This is the reason why, typically, box- or sphere-shaped solvent-volumes are used.
SOLVATE provides an (almost) arbitrarily-shaped solvent volume and a simple analytic description of its boundary using few multivariate gaussian functions. That choice of description enables efficient computation of distances between water molecules and the boundary during subsequent MD-simulations. The necessary algorithms will soon be implemented into the MD-program EGO, but they can also easily be implemented within CHARMm or X-PLOR.
SOLVATE creates the solute/solvent/ion simulation system in a number of steps. For optimal use of SOLVATE, knowledge of these steps is advantageous. As an example, the accompanying pictures show the generation of a solvent shell around a protein complex (immunoglobulin/lysozyme), 6Å thick, including ions. Starting from the coordinate- and structure-file of the complex ( glob.pdb and glob.psf), the shell was created with the command
solvate -t 6.0 -n 8 -ion glob globsol
yielding the file globsol.pdb.
SOLVATE reads the atom
coordinates 
and atom names
of the solute (Figure) from the pdb-file specified on the
command line.
From the atom names SOLVATE derives approximate
van der Waals parameters (radii 
and interaction
strengths 
). If ions are to be placed (as in
our case), SOLVATE must
know about the electrostatics of the solute, which it derives
from the atomic partial charges read from the psf-file.
If no pdb-file is given, or if the pdb-file contains no atoms, one `dummy-atom' (with zero radius) is created at the cartesian origin as the `solute'. By that means a `pure' spherical water droplet can be created.
(a) Bounding sphere
On the basis of the atomic positions of the solute
the smallest convex volume containing
the solute is computed and represented by a regular
set of `grid points' with 
Å spacing.
To that end, in a first step center and radius of the solute's
`bounding sphere',
i.e., the smallest sphere containing the solute,
are computed. This bounding sphere is then filled with grid points
(see Figure; the solute seems not to completely fill the bounding sphere;
however it does, since
the sphere and the solute are three-dimensional objects).
(b) Slicing
From that spherical volume the minimal convex volume is
subsequently constructed
by `slicing away' parts of the spherical volume in many different
directions by a `knife' (solid lines) that just touches the solute.
To vary the flatness of the surface of the minimal convex volume, a
`bended knife' (dashed lines) can be used by specifying a
maximum boundary curvature radius. The 
grid points
which
survive the slicing procedure span the desired
minimal convex volume.
An ideal solute-adapted boundary would be given by a surface enclosing the minimal convex volume at a given constant distance d.
To a good approximation, such an ideal surface can be defined as an
iso-surface of a density function 
,
by requiring 
with suitably
chosen 
.
The figure shows a cut through this density function, 
,
for our example solute.
This boundary certainly fulfills the geometric requirements,
but its computational treatment is highly inefficient, since the
number 
of exponentials to be computed in Eq. 1
(the number of grid points spanning the convex volume) is
typically of the order 
.
Note, however, that the density function 
defined above
is quite smooth, since the distance between
grid points (
Å) is much smaller than the width of the (univariate)
gaussians used (typically 
Å).
Therefore, 
can be approximated to sufficient accuracy by a sum
of much fewer (
) multivariate gaussians,
where 
are the heights and
are the centers of the
gaussians. The matrices
specify the shapes of the gaussians; their overall
extension in space can be varied
by a scale-factor s. Experience shows that usually very few (less than 10)
gaussians are sufficient, so that the computational cost for the
necessary distance
computations in MD simulations becomes negligible. To find optimal
heights, centers and shape matrices, SOLVATE uses a recently proposed
maximum likelihood density estimation method [8].
After having computed these parameters, they are written to the file
gaussians.lis.
The Figure shows a set of dots, the density of which obeys the density function f.
SOLVATE uses a fixed isosurface level 
(where 
is the average height of the gaussians).
Obviously, the distance of the solvent surface from
the solute, as defined by 
, is not known at this point.
To ensure that the smallest distance equals a given distance d,
SOLVATE iteratively varies the scale-factor s (i.e.,
the widths of the gaussians) until the
minimum distance between solute and solvent surface approaches
the desired value.
All parameters necessary to
define 
(
,
,
and 
)
are now written to the file boundary.lis for later use by an
MD-program, e.g., by
EGO.
In a similar way as in STEP 2, the
boundary surface 
is filled with
a number of grid points 
(see figure). For every grid point
the minimum distance to the solute, 
,
is determined and stored; the grid points are then sorted by
increasing minimum distance,
which will be useful to efficiently place the solute (water) molecules.
Those grid points which are located very close to the boundary
can be used to visualize that boundary and are therefore written to the file
surface_stat.lis if desired.
As will be described in Sec. 6, the distance
of a given point 
of the solvent volume to the boundary can be efficiently
estimated from 
(shown in the figure, colour-coded)
to a sufficient accuracy (
Å).
To check the accuracy of
the distance computation, for each grid point 
the efficiently
estimated distance is compared with the accurate distance,
and, if the -s option is set, the resulting error
statistics is appended to the file surface_stat.lis.
In our example, this statistics reads
[MINIMUM INVALID DENSITY]
0.935194
[DISTANCE ERROR STATISTICS (ABS. ERR / DENSITY / DISTANCE)]
0.01 0.401408 3.245818
0.02 0.451980 4.120950
0.05 0.538697 5.512379
0.10 0.631438 6.651468
0.20 0.753683 8.271388
0.50 0.985918 10.718131
1.00 100000000000000000000.000000 62.000000
which means that all distances smaller than 3.245818 Å (for these, f<0.401408), are computed within an error of 0.01 Å; all distances smaller than 4.120950 Å (f<0.451980) within an error of 0.02 Å and so on. No error of 1.0 Å or larger occurred. Distance computations are valid for all locations within the boundary where f is below the minimum invalid density (0.935194).
Using the sorted grid points 
, and starting at points
closest to the solute, the solvent volume is
filled with water molecules, one molecule after the other.
In this process, for each grid point 
SOLVATE
checks whether the distances of 
to all
solute atoms as well as to all water molecules already placed
is larger or equal to the appropriate van der Waals distance.
If not, the respective grid point is discarded; if yes,
a water molecule is placed at location 
and, by steepest
descent, subsequently moved to a nearby energetically favorable position
(only van der Waals energies are considered here).
By this procedure, water molecules close to the solute are placed
first (drawn in blue in the figure), followed by water molecules further apart
(the ones placed last are drawn in red).
Water molecules closest to the solute are likely ones placed
in `caves' inside the solute (such caves exist, e.g., inside
proteins). To distinguish such `buried' water molecules (drawn as
balls in the figure) from
bulk water (small angles), all water molecules are grouped according to their
connectivity. Typically a few dozen `groups' consisting of just
one isolated molecule, of a pair or a triplet of molecules
(depending on the size of the `cave') will be identified as well
as the bulk group containing all the other water molecules.
The groups are consecutively numbered, starting with 
for
the bulk group.
Note that solvate places buried water molecules only according to steric criteria, not according to energetic criteria. If buried water molecules found by solvate are to be included within a subsequent MD-simulations, it has to be checked whether their free energy is low enough so that they are likely to really be there. A good estimate is provided by the program Dowser (http://femto.med.unc.edu/Research/dowser.html or similar software.
Sodium (light blue) and chloride ions (green) are placed in the solvent volume
at isotonic (physiological) concentration (
mol/l) obeying
the Debye-Hückel distribution, which depends on
the locations of charged atoms of the solute (red, blue): on average,
each charged atom at the surface of the
solute is surrounded by a `cloud' of socalled counter-ions. The
size of this cloud is given by the Debye-Hückel length 
,
, where
e is the
elementary charge, 
is the dielectric constant,
is the Boltzmann constant,
and T=300K the temperature.
The density 
(i=Na,Cl) of an ion cloud caused by a solute
atom with partial charge 
is a function of the
distance r from the charged atom, approaches the isotonic concentration
for large
r, and is computed in linear approximation,
with 
and
. Due to the linear approximation,
may become negative, in which case it is set to zero.
The total ionic density is the determined from the linear superposition of
all the ion clouds around the charged solute atoms.
In a first step, all ions (the number of which is
determined from the charge
density integral over the solvent volume) are placed at random
according to that Debye-Hückel total ionic density.
Since the Debye-Hückel approximation is a mean field description, at this point ion-ion correlations are not yet described. To find ionic positions which obey also these higher order correlations, and to avoid artifacts due to the linear approximation, the ions are subsequently subjected to a large number (2,000,000) of Monte-Carlo moves, where the Coulomb field of the solute, and now also the inter-ionic Coulomb field is considered.
The current version of SOLVATE does not yet allow
to use a salt concentration
different from the isotonic concentration, neither is it
possible to include ions other tan sodium and chloride or to
set a temperature different from 
K.
Since up to now, the water molecules have been treated as simple van der Waals spheres (one per molecule) representing only the oxygen positions, two hydrogen atoms per water molecule have to be added. These are oriented at random; a realistic short range order of these dipoles can be created within a short MD run (10 picoseconds is long enough).
Finally, a pdb-file is written, containing the solute, the positions of the water molecules, and, if present, the positions of the ions.
In the pdb-file each group of water molecules is assigned a unique segment-identifier, starting with W100 for the innermost group, W101 for the second and so on. Bulk water is stored last.
If present, ions are appended at the end of the pdb-file; sodium ions first (atom name NA, `molecule' INA, segment-identifier NA), then the chloride ions (atom name CL, `molecule' ICL, segment-identifier CL)
Optionally, SOLVATE generates an X-PLOR-script to create a (psf-) structure file for the final solute/solvent-system. Appropriate topology-files and parameter-files to describe the water molecules from the X-PLOR distribution (e.g., toph19.sol and param19.sol) are required to generate a psf-file.
SOLVATE receives all input parameters from the command line, so it can easily be used within shell-scripts.
Available options are:
solvate [-t thick] [-r radius] [-n ngauss] [-ug] [-ub]
[-s] [-v] [-bulk] [-w] [-ion] [-psf] [infile] outfile
of the density function at this
point,
its accurate distance and the approximate distance (which is the
efficient estimate used in subsequent MD-simulations) from the
solute surface, as well as
an approximate value of the curvature of the surface at the point
next to 
(which also is an efficient estimate that can be used
in MD-simulations).
The command line options can be given in arbitrary sequence.
Once a density function 
is computed by SOLVATE and the
parameters defining f are stored in the file boundary.lis,
any MD-program can access that file and use f to compute
boundary forces acting on water molecules near the surface of the
solute/solvent system. This force is always a function of the
distance to that surface, which therefore must be computed efficiently.
In this section we describe how this can be done to an accuracy
sufficient for most purposes.
For the computation of the distance r between the location of a water
molecule, 
, and the surface point closest to
we first have to find
that surface point. We assume that, from the construction of f
as a sum of few gaussians, this surface point is sufficiently
close to the intersection
of a line through 
, the direction of which is given by the
gradient 
, with the surface
. So we have to compute that intersection point.
Since this cannot be done analytically, and to avoid a possible (but slow)
iterative method, we approximate f for points on the line defined above
beween 
and the intersection point. In that region,
f (solid white line) is
by construction (a sum of gaussians, red, dashed lines)
dominated by the gaussian next to 
(thin, vertical line) and thus
can be approximated by a simple (one-dimensional) gaussian function g
(white dashed line),
The parameters k,
a, and
, which define
g, are obtained
from the value 
,
the gradient 
,
as well as the second derivative along the gradient,
(where J
is the Jacobian matrix of
f at
),
The intersection point 
, approximated by
requiring 
,
can now be calculated analytically, and the distance r we are interested in
reads
As a rule of thumb, all distances required in an MD-simulation are computed with an error smaller than 0.2 Å, which becomes even smaller (0.02 Å) for water molecules close to the surface.
Through a similar approximation, also the average curvature of the solvent at the intersection point, which may enter the boundary forces as a second parameter, can be obtained.
This software is distributed in the hope that it will be useful but without any warranty. The author does not accept responsibility to anyone for the consequences of using it or for whether it serves any particular purpose or works at all. No warranty is made about the software or its performance.
Use and copying of this software and the preparation of derivative works based on this software are permitted, so long as the following conditions are met:
SOLVATE is written by Helmut Grubmüller,
Theoretical Biophysics Group, Institut für Medizinische Optik,
Ludwig-Maximilians-Universität München, München, Germany.
Copyright © 1996. All rights reserved.
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