mirror of
https://github.com/Electrostatics/apbs-pdb2pqr.git
synced 2026-06-04 14:49:37 +08:00
Nathan Baker
@@ -1,76 +0,0 @@
|
||||
Binding energies with APBS
|
||||
==========================
|
||||
|
||||
In general, implicit solvent models are used to calculation the contribution of solvation to binding free energies.
|
||||
Additional binding free energy contributions (molecular mechanics energies, entropic changes, etc.) must be calculated separately and are not discussed in this tutorial.
|
||||
|
||||
=================
|
||||
Free energy cycle
|
||||
=================
|
||||
|
||||
Our framework for calculating solvation contributions to binding free energies is shown in the figure below:
|
||||
|
||||
.. image:: /media/apbs_bind_eng.png
|
||||
|
||||
This binding free energy cycle illustrates binding in terms of transfer free energies from a homogeneous dielectric environment (where interactions are described by Coulomb's law) to an inhomogeneous dielectric environment with differing internal (green) and external (cyan) dielectric constants.
|
||||
The binding (dissociation) free energy is depicted in Step 3.
|
||||
The binding free energy is given by
|
||||
|
||||
.. math::
|
||||
|
||||
\Delta_b G = -\Delta_3 G =\Delta_4 G-\Delta_1 G-\Delta_2 G.
|
||||
|
||||
The following sections provide more detail on calculating individual terms of this equation.
|
||||
|
||||
===================================
|
||||
Binding energy calculations
|
||||
===================================
|
||||
|
||||
The most general method for calculating binding free energies divides the binding process up into solvation :math:`\Delta\Delta_s G` and Coulombic :math:`\Delta\Delta_c G` components:
|
||||
|
||||
.. math::
|
||||
|
||||
\Delta\Delta_b G = \Delta\Delta_s G + \Delta\Delta_c G.
|
||||
|
||||
As mentioned above, this framework neglects the numerous other mechanical and entropic components actually involved in the binding process.
|
||||
|
||||
---------------------------------
|
||||
Solvation contribution to binding
|
||||
---------------------------------
|
||||
|
||||
If we're just interested in calculating the solvation contributions to binding (steps 4 and 2 in the binding free energy cycle), then we simply need to follow the instructions from the :doc:`solvation-energies` section for the complex and isolated components.
|
||||
The solvation energy contribution to the binding is then given by
|
||||
|
||||
.. math::
|
||||
|
||||
\Delta\Delta_s G = \Delta_4 G - \Delta_2 G = \Delta_s G_{cmpx} - \Delta_s G_{mol1} - \Delta_s G_{mol2}
|
||||
|
||||
---------------------------------
|
||||
Coulombic contribution to binding
|
||||
---------------------------------
|
||||
|
||||
To complete the binding free energy cycle, we need to add intermolecular Coulombic contributions to the solvation energy change upon binding to get the total electrostatic/solvent contribution to the binding free energy.
|
||||
In particular, we're interested in the change in Coulombic electrostatic energy upon binding, as given by
|
||||
|
||||
.. math::
|
||||
|
||||
\Delta\Delta_c G = -\Delta_1 G = \Delta_c G_{cmpx} - \Delta_c G_{mol1} - \Delta_c G_{mol2}
|
||||
|
||||
Each of the quantities in this equation is the sum of pairwise Coulombic interactions between all atoms in the molecule (or complex) for a particular uniform dielectric.
|
||||
In order to combine these Coulombic binding energies with the solvation energies described above, we need to make sure consistent dielectric constants are used.
|
||||
In particular, Coulombic interactions should be calculated using the same uniform dielectric constant as the reference state of the solvation energy above.
|
||||
For example, if solvation energies are calculated for transferring a protein from a homogeneous medium with uniform dielectric of to an inhomogeneous medium with internal dielectric :math:`\epsilon_u` and external dielectric :math:`\epsilon_v`, then Coulombic energies should be calculated using a dielectric of :math:`\epsilon_u`.
|
||||
The APBS accessory program :file:`tools/manip/coulomb` was created to help with the calculation of these analytic individual per-molecule Coulombic energies.
|
||||
Given a PQR file as input, the :file:`tools/manip/coulomb` program calculates Coulombic energies for a vacuum dielectric (e.g., a uniform dielectric of 1).
|
||||
If the reference dielectric is :math:`\epsilon_u`, then all energies returned by :file:`tools/manip/coulomb` need to be divided by :math:`\epsilon_u`.
|
||||
|
||||
|
||||
==============
|
||||
Other examples
|
||||
==============
|
||||
|
||||
Several binding energy examples are distributed in the :file:`examples` directory with APBS.
|
||||
|
||||
.. todo::
|
||||
|
||||
Link binding energy examples directly from the source tree.
|
||||
@@ -1,50 +0,0 @@
|
||||
APBS-PDB2PQR examples and tutorials
|
||||
===================================
|
||||
|
||||
Please see the `PDB2PQR documentation <http://pdb2pqr.readthedocs.io>`_ for PDB2PQR-specific examples.
|
||||
|
||||
===================
|
||||
APBS examples
|
||||
===================
|
||||
|
||||
APBS examples start with a PQR file (e.g., generated by PDB2PQR).
|
||||
Some of these examples can be performed through the PDB2PQR web interface but most require a command-line APBS program.
|
||||
|
||||
.. toctree::
|
||||
:caption: APBS examples
|
||||
:maxdepth: 1
|
||||
|
||||
solvation-energies
|
||||
binding-energies
|
||||
salt-linkage
|
||||
parallel-apbs
|
||||
|
||||
.. todo::
|
||||
|
||||
Migrate geoflow, pbsam, pbam examples over from :file:`examples` directory.
|
||||
|
||||
.. _visualizing:
|
||||
|
||||
===================
|
||||
Visualizing results
|
||||
===================
|
||||
|
||||
There are several programs available for visualizing APBS results.
|
||||
The easiest is the PDB2PQR web server which provides `3Dmol.js <http://3dmol.csb.pitt.edu/>` and `Jmol <http://jmol.sourceforge.net/>` browser-based visualization capabilities.
|
||||
|
||||
Other programs include:
|
||||
|
||||
* `PyMOL <http://www.pymol.org>`_
|
||||
* `VMD <http://www.ks.uiuc.edu/Research/vmd/>`_
|
||||
* `PMV <http://mgltools.scripps.edu/>`_
|
||||
* `Chimera <https://www.cgl.ucsf.edu/chimera/>`_
|
||||
|
||||
.. toctree::
|
||||
:caption: Visualization examples
|
||||
|
||||
using-pymol
|
||||
unitymol
|
||||
|
||||
.. todo::
|
||||
|
||||
Add VMD tutorial.
|
||||
@@ -1,92 +0,0 @@
|
||||
Parallel APBS execution for large calculations
|
||||
==============================================
|
||||
|
||||
=============
|
||||
Why parallel?
|
||||
=============
|
||||
|
||||
APBS finite difference multigrid calculations require approximately 200 B memory per grid point.
|
||||
These memory requirements can be distributed in two ways during a calculation:
|
||||
|
||||
* APBS calculations can be performed in parallel across multiple processors (hopefully, sharing distributed memory!). This functionality is provided by using the :ref:`mgpara` keyword.
|
||||
|
||||
* APBS calculations can be broken into a series of smaller, asynchronous runs which (individually) require less memory. This functionality is provided by using both the :ref:`mgpara` and :ref:`async` keywords.
|
||||
|
||||
=================================
|
||||
Synchronous parallel calculations
|
||||
=================================
|
||||
|
||||
The actin dimer example provided with the APBS distribution :file:`examples/actin-dimer/` is a fairly large system that can often require too much memory for some systems.
|
||||
This example will use the actin dimer complex PQR file (:file:`complex.pqr`) to illustrate parallel focusing.
|
||||
|
||||
We're going to use an 8-processor parallel calculation to write out the electrostatic potential map for this complex.
|
||||
Each processor will solve a portion of the overall problem using the parallel focusing method on a 973 mesh with 20% overlap between meshes for neighboring processors.
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||||
An example input file for this calculation might look like:
|
||||
|
||||
.. code-block:: bash
|
||||
|
||||
read
|
||||
mol pqr complex.pqr
|
||||
end
|
||||
elec name complex
|
||||
mg-para
|
||||
ofrac 0.1
|
||||
pdime 2 2 2
|
||||
dime 97 97 97
|
||||
fglen 150 115 160
|
||||
cglen 156 121 162
|
||||
cgcent mol 1
|
||||
fgcent mol 1
|
||||
mol 1
|
||||
npbe
|
||||
bcfl sdh
|
||||
ion 1 0.150 2.0
|
||||
ion -1 0.150 2.0
|
||||
pdie 2.0
|
||||
sdie 78.54
|
||||
srfm mol
|
||||
chgm spl0
|
||||
srad 1.4
|
||||
swin 0.3
|
||||
sdens 10.0
|
||||
temp 298.15
|
||||
calcenergy total
|
||||
calcforce no
|
||||
write pot dx pot
|
||||
end
|
||||
quit
|
||||
|
||||
where the ":ref:`pdime` 2 2 2" statement specifies the 8-processor array dimensions, the ":ref:`ofrac` 0.1" statement specifies the 20% overlap between processor calculations, and the ":ref:`dime` 97 97 97` statement specifies the size of each processor's calculation.
|
||||
The ":ref:`write` pot dx potential" instructs APBS to write out OpenDX-format maps of the potential to 8 files :file:`potential-{#}.dx`, where *#* is the number of the particular processor.
|
||||
|
||||
An MPI-compiled version of APBS can be used with this input file to run 8 parallel focusing calculations, with each calculation generating fine-scale solutions on a different region of the (:ref:`fglen`) problem domain.
|
||||
Note that 8 separate OpenDX files are written by the 8 processors used to perform the calculation.
|
||||
Writing separate OpenDX< files allows us to avoid communication in the parallel run and keeps individual file sizes (relatively) small.
|
||||
Additionally, if a user is interested in a specific portion of the problem domain, only a few files are needed to get local potential information.
|
||||
However, most users are interested in global potentials.
|
||||
APBS provides the :ref:`mergedx` program to reassemble the separate OpenDX files into a single file.
|
||||
`mergedx` is a simple program that allows users to combine several OpenDX files from a parallel focusing calculation into a single map.
|
||||
This map can be down-sampled from the original resolution to provide coarser datasets for fast visualization, etc.
|
||||
For example, the command
|
||||
|
||||
.. code-block:: bash
|
||||
|
||||
$ mergedx 65 65 65 pot0.dx pot1.dx pot2.dx pot3.dx pot4.dx pot5.dx pot6.dx pot7.dx
|
||||
|
||||
will generate a file :file:`gridmerged.dx` which has downsampled the much larger dataset contained in the 8 OpenDX files into a 65\ :sup:`3` file which would be suitable for rough visualization.
|
||||
An example of mergedx output visualization is shown in the attached figure.
|
||||
Note that downsampling isn't necessary -- and often isn't desirable for high quality visualization or quantitative analysis.
|
||||
|
||||
.. image:: /media/actin_dimer-iso_trans.jpg
|
||||
|
||||
==================================
|
||||
Asynchronous parallel calculations
|
||||
==================================
|
||||
|
||||
The steps described in the previous section can also be performed for systems or binaries which are not equipped for parallel calculations via MPI.
|
||||
In particular, you can add the statement ":ref:`async` *n*" to the ELEC :ref:`mgpara` section of the APBS input file to make the single-processor calculation masquerade as processor *n* of a parallel calculation.
|
||||
|
||||
Scalar maps from asynchronous APBS calculations can be combined using the mergedx program as described above.
|
||||
Currently, energies and forces from asynchronous APBS calculations need to merged manually (e.g., summed) from the individual asynchronous calculation output.
|
||||
This can be accomplished by simple shell scripts.
|
||||
|
||||
@@ -1,196 +0,0 @@
|
||||
Protein-RNA binding linked equilibria
|
||||
=====================================
|
||||
|
||||
Before reading this example, please review :doc:`/apbs/errors` for relevant caveats.
|
||||
|
||||
============
|
||||
Introduction
|
||||
============
|
||||
|
||||
This example is taken from `a paper by García-García and Draper <http://dx.doi.org/10.1016/S0022-2836\(03\)00615-6>`_.
|
||||
Special thanks to `David Draper <http://pmcb.jhu.edu/inactive%20pages/draper-profile.html>`_ who provided the PDB files.
|
||||
This example explores the electrostatic contributions to the binding interaction between a 22-residue α-helical peptide of protein λ with the "box B" RNA hairpin structure.
|
||||
In particular, this example uses nonlinear Poisson-Boltzmann equation calculations to look at the non-specific screening effects of monovalent salt on the peptide-RNA complex.
|
||||
García-García and Draper isolated the contribution of KCl concentration to the binding of the folded peptide with the folded RNA hairpin and determined a fairly linear relationship between the binding free energy :math:`\Delta_{b} G` and the logarithm of the KCl concentration which yields
|
||||
|
||||
.. math::
|
||||
|
||||
\frac{\partial\Delta_{b}G}{\partial\log_{10}[{\rm KCl}]} = {6.0 \pm 0.2 ~ } {\rm kcal/mol}
|
||||
|
||||
This slope can be used to determine the number of KCl ions linked to the binding equilibrium through the expression
|
||||
|
||||
.. math::
|
||||
|
||||
n = -\frac{\partial \Delta_b G}{{RT} \partial \log_{10}[{\rm KCl}]} = {-4.52 \pm 0.08~ } {\rm kcal/mol}
|
||||
|
||||
where :math:`RT` is the thermal energy, to determine :math:`n = -4.4 \pm 0.2` for the RNA-peptide binding equilibrium.
|
||||
:math:`RT` is equal to :math:`kT * N_a` where :math:`kT` is the product of the Boltzmann constant :math:`k` (equal to the gas constant :math:`R/N_a`), and the temperature :math:`T` (at STP it is 298.15 K) and :math:`N_a` is Avogadro's constant.
|
||||
Thus :math:`RT` is equal to
|
||||
|
||||
.. math::
|
||||
|
||||
R ~ ({\mathrm{Joules}}/{\mathrm{Kelvin}}) * T~({\mathrm {Kelvin}}) * N_a~({\mathrm {mols}}) * {1~\mathrm{kJ}}/{1000~\mathrm J}
|
||||
|
||||
which roughly equals
|
||||
|
||||
.. math::
|
||||
|
||||
(1.38 \times 10^{-23}) \times (6.022 \times 10^{23}) \times (298.15)/(1000)
|
||||
|
||||
which is approximately 2.479 kJ/mol or 0.593 kcal/mol.
|
||||
|
||||
García-García and Draper used nonlinear Poisson-Boltzmann equation calculations to estimate the electrostatic contributions to the binding free energy as a function of the monovalent salt concentration.
|
||||
As :doc:`discussed elsewhere </apbs/errors>`, the Poisson-Boltzmann equation is only able to describe non-specific interactions of ions with solutes, including the effects of ion size and charge but otherwise ignoring the important differences between ionic species.
|
||||
Interestingly (and perhaps surprisingly), they find excellent agreement between the experimental binding energy dependence on KCl and their Poisson-Boltzmann calculations with equivalent concentrations of monovalent ions.
|
||||
This agreement strongly suggests that the binding of RNA and the peptide is primarily determined by electrostatic interactions.
|
||||
It also suggests that the primary interaction of the KCl with this system is through non-specific screening interactions.
|
||||
The García-García and Draper nonlinear Poisson-Boltzmann equation calculations gave:
|
||||
|
||||
.. math::
|
||||
|
||||
\frac{\partial\Delta_{b}G}{\partial\log_{10}[{\rm KCl}]} = {5.9 \pm 0.2 ~ } {\rm kcal/mol}
|
||||
|
||||
and :math:`n = -4.3 \pm 0.2` for KCl linkage to the RNA-peptide binding equilibrium.
|
||||
|
||||
===================
|
||||
APBS implementation
|
||||
===================
|
||||
|
||||
This example follows the calculations from their paper.
|
||||
|
||||
The PQR files are included in the :file:`examples/protein-rna/` directory of the apbs-pdb2pqr repository.
|
||||
This directory also includes a :file:`template.txt` file that serves as a template for the APBS input files with ``IONSTR`` as a placeholder for the ionic strength.
|
||||
This file is also shown here:
|
||||
|
||||
.. code-block:: bash
|
||||
|
||||
read
|
||||
mol pqr model_outNB.pqr
|
||||
mol pqr model_outNpep.pqr
|
||||
mol pqr model_outBoxB19.pqr
|
||||
end
|
||||
elec name complex
|
||||
mg-auto
|
||||
dime 65 97 129
|
||||
cglen 45.3322 54.9498 82.2633
|
||||
fglen 45.3322 52.3234 68.3902
|
||||
cgcent mol 1
|
||||
fgcent mol 1
|
||||
mol 1
|
||||
npbe
|
||||
bcfl sdh
|
||||
pdie 4.0
|
||||
ion charge 1 conc IONSTR radius 2.0
|
||||
ion charge -1 conc IONSTR radius 2.0
|
||||
sdie 80.0
|
||||
srfm mol
|
||||
chgm spl2
|
||||
sdens 10.00
|
||||
srad 1.40
|
||||
swin 0.30
|
||||
temp 298.15
|
||||
calcenergy total
|
||||
calcforce no
|
||||
write qdens dx qdens-complex-IONSTR
|
||||
write ndens dx ndens-complex-IONSTR
|
||||
end
|
||||
elec name peptide
|
||||
mg-auto
|
||||
dime 65 97 129
|
||||
cglen 45.3322 54.9498 82.2633
|
||||
fglen 45.3322 52.3234 68.3902
|
||||
cgcent mol 1
|
||||
fgcent mol 1
|
||||
mol 2
|
||||
npbe
|
||||
bcfl sdh
|
||||
pdie 4.0
|
||||
sdie 80.0
|
||||
ion charge 1 conc IONSTR radius 2.0
|
||||
ion charge -1 conc IONSTR radius 2.0
|
||||
srfm mol
|
||||
chgm spl2
|
||||
sdens 10.00
|
||||
srad 1.40
|
||||
swin 0.30
|
||||
temp 298.15
|
||||
calcenergy total
|
||||
calcforce no
|
||||
write qdens dx qdens-peptide-IONSTR
|
||||
write ndens dx ndens-peptide-IONSTR
|
||||
end
|
||||
elec name rna
|
||||
mg-auto
|
||||
dime 65 97 129
|
||||
cglen 45.3322 54.9498 82.2633
|
||||
fglen 45.3322 52.3234 68.3902
|
||||
cgcent mol 1
|
||||
fgcent mol 1
|
||||
mol 3
|
||||
npbe
|
||||
bcfl sdh
|
||||
pdie 4.0
|
||||
sdie 80.0
|
||||
ion charge 1 conc IONSTR radius 2.0
|
||||
ion charge -1 conc IONSTR radius 2.0
|
||||
srfm mol
|
||||
chgm spl2
|
||||
sdens 10.00
|
||||
srad 1.40
|
||||
swin 0.30
|
||||
temp 298.15
|
||||
calcenergy total
|
||||
calcforce no
|
||||
write qdens dx qdens-rna-IONSTR
|
||||
write ndens dx ndens-rna-IONSTR
|
||||
end
|
||||
print elecEnergy complex - peptide - rna end
|
||||
quit
|
||||
|
||||
As used in the template file, the READ command, our calculation will have three parts:
|
||||
|
||||
* Calculation of the total electrostatic energy (including self-interaction energies) of the peptide-RNA complex. This calculation is named complex in the input file.
|
||||
* Calculation of the total electrostatic energy (including self-interaction energies) of the peptide. This calculation is named peptide in the input file.
|
||||
* Calculation of the total electrostatic energy (including self-interaction energies) of the RNA. This calculation is named rna in the input file.
|
||||
|
||||
The calculations themselves will not be overly demanding, since we will use relatively coarse grids.
|
||||
This grid coarseness has a significant impact on the absolute electrostatic binding energy we obtain from this particular calculation: the calculated energy isn't converged with respect to grid spacing.
|
||||
However, the overall slope of binding energy with respect to monovalent ion concentration is rather insensitive with respect to the grid spacing, allowing us to save computational time and effort during the calculations.
|
||||
The calculation will conclude with a :doc:`/apbs/input/print` command which will combine the total energies from the three parts to obtain our approximate absolute electrostatic binding energy for the complex at 0.225 M monovalent salt concentration.
|
||||
It is very important to note that this absolute energy no meaning in isolation for several reasons:
|
||||
|
||||
* It is not converged with respect to grid spacing
|
||||
* It does not contain other very important non-electrostatic aspects of the binding energy which are important for the measured affinity
|
||||
|
||||
``IONSTR`` is a placeholder that represents the ion concentration for the APBS calculation.
|
||||
|
||||
You will also have to create a :file:`dxmath.txt` file which contains the following.
|
||||
|
||||
.. code-block:: bash
|
||||
|
||||
qdens-complex-IONSTR.dx
|
||||
qdens-pep-IONSTR.dx -
|
||||
qdens-rna-IONSTR.dx -
|
||||
qdens-diff-IONSTR.dx =
|
||||
|
||||
:doc:`/apbs/utilities/dxmath` will subtract the dx maps of the individual peptide and RNA from the overall structure (and prints to the :file:`qdens-diff-IONSTR.dx` file.
|
||||
|
||||
======================
|
||||
Automation with Python
|
||||
======================
|
||||
|
||||
We have provided Python scripts :file:`apbs_{win, unix}_dx.py` that run the necessary APBS calculations and analyze the results.
|
||||
When you run these programs, you need to be in the same directory as ``template.txt`` and ``dxmath.txt``.
|
||||
This script will create all the input files for the tests as well as run apbs and dxmath on your :file:`template.txt` and :file:`dxmath.txt` files.
|
||||
Most of the syntax fills in the ion concentrations in the template file, and the call commands actually run the calculations on each input.
|
||||
|
||||
========================
|
||||
Visualization
|
||||
========================
|
||||
|
||||
The :file:`qdens-diff-0.225.dx` file produced by the script can be viewed in PyMOL or another visualization program to give something similar to the following imaged which show the difference in charge density before and after binding.
|
||||
|
||||
.. image:: /media/rna-qdens-pymol.jpg
|
||||
|
||||
.. image:: /media/rna-qdens-vmd.jpg
|
||||
|
||||
@@ -1,172 +0,0 @@
|
||||
Solvation energies with APBS
|
||||
============================
|
||||
|
||||
Solvation energies are usually decomposed into a free energy cycle as shown in the free energy cycle below.
|
||||
Note that such solvation energies often performed on fixed conformations; as such, they are more correctly called "potentials of mean force".
|
||||
More details on using APBS for the polar and nonpolar portions of such a cycle are given in the following sections.
|
||||
|
||||
.. figure:: /media/apbs_sol_eng.png
|
||||
|
||||
Our model solvation free energy cycle illustrating several steps:
|
||||
1. The solvation energy to be calculated.
|
||||
2. Charging of the solute in solution (e.g., inhomogeneous dielectric, ions present).
|
||||
3. Introduction of attractive solute-solvent dispersive interaction interactions (e.g., an integral of Weeks-Chandler-Andersen interactions over the solvent-accessible volume).
|
||||
4. Introduction of repulsive solute-solvent interaction (e.g., cavity formation).
|
||||
5. Basically a null step although it could be used to offset unwanted energies added in Steps 3 and 4 above.
|
||||
6. Charging of the solute in a vacuum or homogeneous dielectric environment in the absence of mobile ions.
|
||||
|
||||
===============
|
||||
Polar solvation
|
||||
===============
|
||||
|
||||
The full free energy cycle is usually decomposed into polar and nonpolar parts.
|
||||
The polar portion is usually represented by the charging energies in Steps 2 and 6:
|
||||
|
||||
.. math::
|
||||
|
||||
\Delta_p G = \Delta_2 G - \Delta_6 G
|
||||
|
||||
Energies returned from APBS electrostatics calculations are charging free energies.
|
||||
Therefore, to calculate the polar contribution to the solvation free energy, we simply need to setup two calculations corresponding to Steps 2 and 6 in the free energy cycle.
|
||||
Note that the electrostatic charging free energies returned by APBS include self-interaction terms.
|
||||
These are the energies of a charge distribution interacting with itself.
|
||||
Such self-interaction energies are typically very large and extremely sensitive to the problem discretization (grid spacing, location, etc.).
|
||||
Therefore, it is very important that the two calculations in Steps 2 and 6 are performed with identical grid spacings, lengths, and centers, in order to ensure appropriate matching (or "cancellation") of self-energy terms.
|
||||
|
||||
--------
|
||||
Born ion
|
||||
--------
|
||||
|
||||
One of the canonical examples for polar solvation is the Born ion: a nonpolarizable sphere with a single charge at its center surrounded by an aqueous medium.
|
||||
Consider the transfer of a non-polarizable ion between two dielectrics.
|
||||
In the initial state, the dielectric coefficient inside and outside the ion is :math:`\epsilon\_{\mathrm {in}}`, and in the final state, the dielectric coefficient inside the ion is :math:`\epsilon\_{\mathrm {in}}` and the dielectric coefficient outside the ion is :math:`\epsilon\_{\mathrm {in}}`.
|
||||
In the absence of external ions, the polar solvation energy of this transfer for this system is given by:
|
||||
|
||||
.. math::
|
||||
|
||||
\Delta\_p G\_{\mathrm{Born}}= \frac{q^2}{8\pi\epsilon\_0 a}\left (\frac{1}{\epsilon\_{\mathrm {out}}}-\frac{1}{\epsilon\_{\mathrm {in}}}\right)
|
||||
|
||||
where q is the ion charge, a is the ion radius, and the two ε variables denote the two dielectric coefficients.
|
||||
This model assumes zero ionic strength.
|
||||
|
||||
Note that, in the case of transferring an ion from vacuum, where :math:`\epsilon\_{\mathrm {in}} = 1`, the expression becomes
|
||||
|
||||
.. math::
|
||||
|
||||
\Delta\_p G\_{\mathrm{Born}}= \frac{q^2}{8\pi\epsilon\_0 a}\left (\frac{1}{\epsilon\_{\mathrm {out}}}-1\right)
|
||||
|
||||
We can setup a PQR file for the Born ion for use with APBS with the contents:
|
||||
|
||||
.. code-block:: bash
|
||||
|
||||
REMARK This is an ion with a 3 A radius and a +1 e charge
|
||||
ATOM 1 I ION 1 0.000 0.000 0.000 1.00 3.00
|
||||
|
||||
We're interested in performing two APBS calculations for the charging free energies in homogeneous and heterogeneous dielectric coefficients.
|
||||
We'll assume the internal dielectric coefficient is 1 (e.g., a vacuum) and the external dielectric coefficient is 78.54 (e.g., water).
|
||||
For these settings, the polar Born ion solvation energy expression has the form
|
||||
|
||||
.. math::
|
||||
|
||||
\Delta_p G_{\mathrm{Born}} = -691.85 \biggl( \frac{z^2}{R} \biggr) \mathrm {kJ \, A/mol}
|
||||
|
||||
where z is the ion charge in electrons and R is the ion size in Å.
|
||||
|
||||
This solvation energy calculation can be setup in APBS with the following input file:
|
||||
|
||||
.. code-block:: bash
|
||||
|
||||
# READ IN MOLECULES
|
||||
read
|
||||
mol pqr born.pqr
|
||||
end
|
||||
elec name solv # Electrostatics calculation on the solvated state
|
||||
mg-manual # Specify the mode for APBS to run
|
||||
dime 97 97 97 # The grid dimensions
|
||||
nlev 4 # Multigrid level parameter
|
||||
grid 0.33 0.33 0.33 # Grid spacing
|
||||
gcent mol 1 # Center the grid on molecule 1
|
||||
mol 1 # Perform the calculation on molecule 1
|
||||
lpbe # Solve the linearized Poisson-Boltzmann equation
|
||||
bcfl mdh # Use all multipole moments when calculating the potential
|
||||
pdie 1.0 # Solute dielectric
|
||||
sdie 78.54 # Solvent dielectric
|
||||
chgm spl2 # Spline-based discretization of the delta functions
|
||||
srfm mol # Molecular surface definition
|
||||
srad 1.4 # Solvent probe radius (for molecular surface)
|
||||
swin 0.3 # Solvent surface spline window (not used here)
|
||||
sdens 10.0 # Sphere density for accessibility object
|
||||
temp 298.15 # Temperature
|
||||
calcenergy total # Calculate energies
|
||||
calcforce no # Do not calculate forces
|
||||
end
|
||||
elec name ref # Calculate potential for reference (vacuum) state
|
||||
mg-manual
|
||||
dime 97 97 97
|
||||
nlev 4
|
||||
grid 0.33 0.33 0.33
|
||||
gcent mol 1
|
||||
mol 1
|
||||
lpbe
|
||||
bcfl mdh
|
||||
pdie 1.0
|
||||
sdie 1.0
|
||||
chgm spl2
|
||||
srfm mol
|
||||
srad 1.4
|
||||
swin 0.3
|
||||
sdens 10.0
|
||||
temp 298.15
|
||||
calcenergy total
|
||||
calcforce no
|
||||
end
|
||||
# Calculate solvation energy
|
||||
print energy solv - ref end
|
||||
quit
|
||||
|
||||
Running this example with a recent version of APBS should give an answer of -229.59 kJ/mol which is in good agreement with the -230.62 kJ/mol predicted by the analytic formula above.
|
||||
|
||||
.. note::
|
||||
|
||||
The Born example above can be easily generalized to other polar solvation energy calculations.
|
||||
For example, ions could be added to the solv ELEC, dielectric constants could be modified, surface definitions could be changed (in both ELEC sections!), or more complicated molecules could be examined.
|
||||
Many of the examples included with APBS also demonstrate solvation energy calculations.
|
||||
|
||||
.. note::
|
||||
|
||||
As molecules get larger, it is important to examine the sensitivity of the calculated polar solvation energies with respect to grid spacings and dimensions.
|
||||
|
||||
================
|
||||
Apolar solvation
|
||||
================
|
||||
|
||||
Referring back to the solvation free energy cycle, the nonpolar solvation free energy is usually represented by the energy changes in Steps 3 through 5:
|
||||
|
||||
.. math::
|
||||
|
||||
\Delta_n G = (\Delta_3 G - \Delta_5 G) + \Delta_4 G
|
||||
|
||||
|
||||
where Step 4 represents the energy of creating a cavity in solution and Steps 3-5 is the energy associated with dispersive interactions between the solute and solvent.
|
||||
There are many possible choices for modeling this nonpolar solvation process.
|
||||
APBS implements a relatively general model described by `Wagoner and Baker (2006) <http://www.pnas.org/content/103/22/8331>`_ and references therein.
|
||||
The implementation and invocation of this model is described in more in the :ref:`apolar` documentation.
|
||||
Our basic model for the cavity creation term (Step 4) is motivated by scaled particle theory and has the form
|
||||
|
||||
.. math::
|
||||
|
||||
\Delta_4 G = pV + \gamma A
|
||||
|
||||
where :math:`p` is the solvent pressure (:ref:`press` keyword), :math:`V` is the solute volume, :math:`\gamma` is the solvent surface tension (:ref:`gamma` keyword), and :math:`A` is the solute surface area.
|
||||
|
||||
Our basic model for the dispersion terms (Steps 3 and 5) follow a Weeks-Chandler-Anderson framework as proposed by `Levy et al (2002) <http://onlinelibrary.wiley.com/doi/10.1002/jcc.10045/abstract>`_:
|
||||
|
||||
.. math::
|
||||
|
||||
\Delta_3 G - \Delta_5 G = \overset{-} \rho \int_\omega u^{(att)}(y)\theta(y)dy
|
||||
|
||||
where :math:`\overline{\rho}` is the bulk solvent density (:ref:`bconc` keyword), :math:`\Omega` is the problem domain, :math:`u^{\mathrm{(att)}}(y)` is the attractive dispersion interaction between the solute and the solvent at point y with dispersive Lennard-Jones parameters specified in APBS parameter files, and :math:`\theta(y)` describes the solvent accessibility of point y.
|
||||
|
||||
The ability to independently adjust :ref:`press`, :ref:`gamma`, and :ref:`bconc` means that the general nonpolar solvation model presented above can be easily adapted to other popular nonpolar solvation models.
|
||||
For example, setting :ref:`press` and :ref:`bconc` to zero yields a typical solvent-accessible surface area model.
|
||||
|
||||
@@ -1,28 +0,0 @@
|
||||
Virtual reality with UnityMol
|
||||
=============================
|
||||
|
||||
Molecular visualization software packages provide the ability for users to explore the 3D representations molecular structures and properties.
|
||||
Typical user interaction is limited to panning, zooming, and rotating the molecule using a mouse and keyboard while viewing on a standard computing monitor.
|
||||
These techniques support a pseudo 3-dimensional view of a molecule to understand its structure but lack the true depth perception people are used to with stereoscopic vision in the real world.
|
||||
|
||||
New advancements in virtual reality (VR) technologies has resulted in lower costs and systems that are easier to use to many consumers.
|
||||
Compared to past VR hardware, these new systems have several key advancements including lower latency, higher frame rates, and improved resolution.
|
||||
Additionally, these systems are equipped with better optics and motion tracking and a more robust software ecosystem.
|
||||
|
||||
We are extending the visualization capabilities for APBS through the incorporation of a VR device with molecular rendering software.
|
||||
We are currently experimenting with the HTC Vive, which allows a person to walk around a 15' by 15' physical space while wearing a head mounted display.
|
||||
Precise head movements are matched in virtual reality with no noticeable latency.
|
||||
Additionally, the HTC Vive controllers are motion tracked with millimeter precision and provide a valuable method for interacting with virtual objects.
|
||||
We have enabled VR using the HTC Vive in the `UnityMol molecular visualization software <http://www.baaden.ibpc.fr/umol/>`_ (created by Baaden, et al.) and incorporated electrostatic surface data (see figure below and a `YouTube video <https://www.youtube.com/watch?v=Xxb3W8jnnp8&t=21s>`_).
|
||||
New viewing capabilities now include walking around, grabbing (using the motion controllers), and scaling (gestures) of molecules.
|
||||
We are actively working with Dr. Baaden and his group to determine the best use of interaction techniques for users to interact with molecular models through his software.
|
||||
|
||||
.. figure:: /media/1fas_VR.png
|
||||
|
||||
View of UnityMol form the monitor as it is being used in VR with controllers.
|
||||
|
||||
For future work, we would like to further extend UnityMol in the HTC Vive to include natural user interactions for viewing multiple molecules, vary the electrostatic results from APBS, and change molecular attributes.
|
||||
We envision this tool will also enable virtual collaboration for participant in different locations.
|
||||
Each participant will be able to view, gesture and interact with the same data in the same VR space.
|
||||
Finally, we would like to explore the use of VR for research related to docking of different molecules.
|
||||
|
||||
@@ -1,70 +0,0 @@
|
||||
Using the PyMOL APBS plugin
|
||||
===========================
|
||||
|
||||
The `PyMOL <http://www.pymol.org/>`_ molecular graphics software package can both run APBS and visualize resulting electrostatic potentials.
|
||||
Below are instructions for performing a basic demonstration of how to go from a PDB entry to a plot of structure and potential in PyMOL using APBS.
|
||||
|
||||
========================
|
||||
Run the APBS calculation
|
||||
========================
|
||||
|
||||
* Load your PQR file you created into PyMOL (:guilabel:`File → Open...`) and choose your favorite graphical representation of the molecular structure.
|
||||
|
||||
* Go to :guilabel:`Plugin → APBS Tools...` to open the APBS calculation plugin.
|
||||
|
||||
* Under the :guilabel:`Main` tab of the PyMOL APBS Tools window, select :guilabel:`Use another PQR` and either browse to (via the :guilabel:`Choose Externally Generated PQR` button) or input the path to your PQR file. This step is necessary to ensure you use the radii and charges assigned by PDB2PQR.
|
||||
|
||||
* Under the :guilabel:`APBS Location` tab of the PyMOL APBS Tools window, either browse to (via the APBS binary location: button) or input the path to your local APBS binary. It is not necessary to provide a path to the APBS :file:`psize.py` binary for most biomolecules.
|
||||
|
||||
* Under the :guilabel:`Temporary File Locations` tab of the PyMOL APBS Tools window, customize the locations of the various temporary files created during the run. This can be useful if you want to save the generated files for later use.
|
||||
|
||||
* Under the :guilabel:`Configuration` tab of the PyMOL APBS Tools window, press :guilabel:`Set grid` to set the grid spacings. The default values are usually sufficient for all but the most highly charged biomolecules.
|
||||
|
||||
* Under the :guilabel:`Configuration` tab of the PyMOL APBS Tools window, customize the remaining parameters; the defaults are usually OK.
|
||||
|
||||
.. note::
|
||||
|
||||
0.150 M concentrations for the +1 and −1 ion species are often useful to ensure that electrostatic properties are not overly exaggerated.
|
||||
|
||||
* Under the :guilabel:`Configuration` tab of the PyMOL APBS Tools window, press the Run :guilabel:`APBS button` to start the APBS calculation. Depending on the speed of your computer, this could take a few minutes. The :guilabel:`Run APBS` button will become unselected when the calculation is finished.
|
||||
|
||||
=====================
|
||||
Visualize the results
|
||||
=====================
|
||||
|
||||
Before proceeding, you must load the electrostatic potential data into PyMOL. Under the :guilabel:`Visualization` tab of the PyMOL APBS Tools window, press the :guilabel:`Update` button.
|
||||
|
||||
-------------------------
|
||||
Electrostatic isocontours
|
||||
-------------------------
|
||||
|
||||
PyMOL makes this step very easy: adjust the positive and negative "Contour" fields to the desired values (usually ±1, ±5, or ±10 kT/e)
|
||||
and press the :guilabel:`Positive Isosurface`, :guilabel:`Negative Isosurface`, and :guilabel:`Show buttons`.
|
||||
|
||||
At this point, you probably have a figure that looks something like the image below.
|
||||
|
||||
.. figure:: /media/fas2-iso-pymol.png
|
||||
|
||||
±1 kT/e electrostatic potential isocontours of FAS2 in PyMOL
|
||||
|
||||
If the colors are not as you expect, you can change the colors of the objects iso_neg and iso_pos in the main menu.
|
||||
By convention (for electrostatics in chemistry), red is negative (think oxygen atoms in carboxyl groups) and blue positive (think nitrogen atoms in amines).
|
||||
|
||||
------------------
|
||||
Surface potentials
|
||||
------------------
|
||||
|
||||
If you haven't already, hide the isocontours by pressing the :guilabel:`Positive Isosurface`, :guilabel:`Negative Isosurface`, and :guilabel:`Hide` buttons.
|
||||
The surface potential is also straightforward to visualize.
|
||||
Set the "Low" and "High"values to the desired values (usually ±1, ±5, or ±10 kT/e) at which the surface colors are clamped at red (-) or blue (+).
|
||||
Check the "Solvent accessible surface" and "Color by potential on sol. acc. surf." buttons to plot the potential on the solvent-accessible (probe-inflated or Lee-Richards) surface.
|
||||
Press the :guilabel:`Molecular Surface` :guilabel:`Show` button to load the surface potential.
|
||||
|
||||
.. figure:: /media/fas2-surf-pymol.png
|
||||
|
||||
±5 kT/e electrostatic potential of FAS2 in PyMOL plotted on the solvent-accessible surface.
|
||||
|
||||
The solvent-accessible surface tends to reveal more global features of the surface potential.
|
||||
Tighter surfaces (e.g., van der Waals and molecular or Connolly surfaces) provide more information about the shape of the biomolecule but otherwise tend to simply map atomic surface charges onto the biomolecular surface.
|
||||
PyMOL can simultaneously provide geometric information (from the molecular surface) and useful electrostatic potential information (from the solvent-accessible surface).
|
||||
To visualize the molecule in this way, simply uncheck the "Solvent accessible surface"box and check the "Color by potential on sol. acc. surf." box on the :guilabel:`Visualization` tab.
|
||||
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Reference in New Issue
Block a user