charmmrate (c39b1)
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* CHARMM/POLYRATE INTERFACE *
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with POLYRATE and CHARMM
CHARMMRATE is an interface of CHARMM and POLYRATE to include quantum
mechanical effects in enzyme kinetics. Although CHARMMRATE allows
execution of POLYRATE with all existing capabilities, the present
implementation is primarily intended for predicting reaction rates in
enzyme-catalyzed reactions. CHARMMRATE can be combined with semiempirical
combined QM/MM potentials with numerical second derivatives that are
computed by the POLYRATE interface programs.
The rate constant for an enzymatic reaction depends on the transition
state theory free energy of activation and on an overall transmission
coefficient. Quantum effects on the degrees of freedom perpendicular to
the reaction coordinate can be incorporated by means of a correction for
quantum mechanical vibrational free energy, DeltaW_vib. As described by M.
Garcia-Viloca, C. Alhambra, D. G. Truhlar, and J. Gao, in J. Chem. Phys.
114, 9953-9958 (2001), such a correction is calculated by carrying out
projected instantaneous normal mode analysis at several configurations
along a reaction coordinate as sampled by the umbrella sampling technique
(or by any other suitable method) in molecular dynamics simulations with
projecting out the reaction coordinate of the potential of mean force
(i.e., the coordinate along which umbrella sampling was carried out); thus
it yields different frequencies and modes than would be obtained by
ordinary instantaneous normal mode analysis. The correction for quantized
vibrational free energy in modes normal to the PMF reaction coordinate is
calculated from the average frequencies of the projected instantaneous
normal mode analysis and is added to the classical potential of mean
force.
The quantum effects on the reaction coordinate are represented by an
averaged transmission coefficient obtained by carrying out variational
transition state theory (VTST) calculations for individual members
(configurations) of the transition state ensemble. These calculations
involve a partition of the system into a frozen bath region and a dynamics
region that is used in the dynamics calculation. CHARMMRATE has been used
to determine the rate constants for the proton transfer reactions
catalyzed by enolase and methylamine dehydrogenase and for the hydride
transfer reactions catalyzed by alcohol dehydrogenase, xylose isomerase,
and dihydrofolate reductase. These studies have demonstrated that
inclusion of quantum effects is essential to calculate primary and
secondary kinetic isotopic effects (KIEs) for hydrogen transfer reactions.
The method used in these studies has evolved to its definitive form that
includes free energy simulation to determine the free energy of activation
and calculation of the transmission coefficient. Putting all the elements
together yields a method that is called ensemble-averaged VTST with
multidimensional tunneling (EA-VTST/MT),the formalism of which is
presented in detail in the following recent papers:
C. Alhambra, J. C. Corchado, M. L. Sanchez, M. Garcia-Viloca J. Gao, and
D. G. Truhlar J. Phys. Chem. B. 105, 11326-11340 (2001).
D. G. Truhlar, J. Gao, C. Alhambra, M. Garcia-Viloca, J. Corchado, M. L.
Sanchez, and Jordi Villa, Acc. Chem. Res. 35, 341-349 (2002).
M. Garcia-Viloca, C. Alhambra, D. G. Truhlar, and J. Gao, J. Comput.
Chem. 2002, in press.
This documentation contains a short version and a long, detailed
version following the short CHARMM-command description. Users are
encouraged to read both parts.
* Description | Description of the POLYRATE driver in CHARMM
* Usage | How to run POLYRATE in CHARMM
* Installation | How to install POLYRATE in CHARMM
* Status | Status of the interface code
* CHARMM/POLYRATE INTERFACE *
****************************************
with POLYRATE and CHARMM
CHARMMRATE is an interface of CHARMM and POLYRATE to include quantum
mechanical effects in enzyme kinetics. Although CHARMMRATE allows
execution of POLYRATE with all existing capabilities, the present
implementation is primarily intended for predicting reaction rates in
enzyme-catalyzed reactions. CHARMMRATE can be combined with semiempirical
combined QM/MM potentials with numerical second derivatives that are
computed by the POLYRATE interface programs.
The rate constant for an enzymatic reaction depends on the transition
state theory free energy of activation and on an overall transmission
coefficient. Quantum effects on the degrees of freedom perpendicular to
the reaction coordinate can be incorporated by means of a correction for
quantum mechanical vibrational free energy, DeltaW_vib. As described by M.
Garcia-Viloca, C. Alhambra, D. G. Truhlar, and J. Gao, in J. Chem. Phys.
114, 9953-9958 (2001), such a correction is calculated by carrying out
projected instantaneous normal mode analysis at several configurations
along a reaction coordinate as sampled by the umbrella sampling technique
(or by any other suitable method) in molecular dynamics simulations with
projecting out the reaction coordinate of the potential of mean force
(i.e., the coordinate along which umbrella sampling was carried out); thus
it yields different frequencies and modes than would be obtained by
ordinary instantaneous normal mode analysis. The correction for quantized
vibrational free energy in modes normal to the PMF reaction coordinate is
calculated from the average frequencies of the projected instantaneous
normal mode analysis and is added to the classical potential of mean
force.
The quantum effects on the reaction coordinate are represented by an
averaged transmission coefficient obtained by carrying out variational
transition state theory (VTST) calculations for individual members
(configurations) of the transition state ensemble. These calculations
involve a partition of the system into a frozen bath region and a dynamics
region that is used in the dynamics calculation. CHARMMRATE has been used
to determine the rate constants for the proton transfer reactions
catalyzed by enolase and methylamine dehydrogenase and for the hydride
transfer reactions catalyzed by alcohol dehydrogenase, xylose isomerase,
and dihydrofolate reductase. These studies have demonstrated that
inclusion of quantum effects is essential to calculate primary and
secondary kinetic isotopic effects (KIEs) for hydrogen transfer reactions.
The method used in these studies has evolved to its definitive form that
includes free energy simulation to determine the free energy of activation
and calculation of the transmission coefficient. Putting all the elements
together yields a method that is called ensemble-averaged VTST with
multidimensional tunneling (EA-VTST/MT),the formalism of which is
presented in detail in the following recent papers:
C. Alhambra, J. C. Corchado, M. L. Sanchez, M. Garcia-Viloca J. Gao, and
D. G. Truhlar J. Phys. Chem. B. 105, 11326-11340 (2001).
D. G. Truhlar, J. Gao, C. Alhambra, M. Garcia-Viloca, J. Corchado, M. L.
Sanchez, and Jordi Villa, Acc. Chem. Res. 35, 341-349 (2002).
M. Garcia-Viloca, C. Alhambra, D. G. Truhlar, and J. Gao, J. Comput.
Chem. 2002, in press.
This documentation contains a short version and a long, detailed
version following the short CHARMM-command description. Users are
encouraged to read both parts.
* Description | Description of the POLYRATE driver in CHARMM
* Usage | How to run POLYRATE in CHARMM
* Installation | How to install POLYRATE in CHARMM
* Status | Status of the interface code
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* Syntax for the CHARMMRATE Method *
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POLYRATE is initiated with the POLYrate command.
[Syntax POLYrate]
POLYrate [ atom-selection] [RUNIT int] [PUNIT int] [TSUNit int] [OPUNit
int] [PMFZpe ] [ATMA int ] [ATMB int] [ATMC int]
[POLYRATE commands]
....
[*finish]
atom-spec::= {residue-number atom-name}
{segid resid atom-name}
{BYNUm atom-number}
RUNIt int: Unit specification for input of initial coordinates of the
reactant species. The current limitation is that only
CHARMM format is allowed for the coordinate file.
PUNIt int: Unit specification for input of initial coordinates of the
product species. The current limitation is that only
CHARMM format is allowed for the coordinate file.
TSUNit int: Unit specification for input of initial coordinates of the
transition state. The current limitation is that only
CHARMM format is allowed for the coordinate file.
OPUNit int: Unit to write out coordinates of the optimized structures,
of any of the reactant, product, and TS, depending on
the species being optimized. The current limitation is
that only CHARMM format is used.
PMFZpe ATMA int ATMB int ATMC int: this command switches on the projection
operator that is used to project the reaction coordinate out of
the Hessian matrix of the system. This is used for projected
instantaneous normal mode analysis. The reaction coordinate is
defined as the difference in bond distance between the breaking
and making bonds.
ATMA int: atom number for the donor atom following the numbering in the
general section of POLYRATE commands (see below).
ATMB int: atom number for the transferring atom following the numbering
in the general section of POLYRATE commands (see below).
ATMC int: atom number for the acceptor atom following the numbering in
the general section of POLYRATE commands (see below).
[POLYRATE commands]
This section contains standard POLYRATE commands. They must follow
immediately after the [POLYrate] command in the CHARMM input stream. This
section is terminated by the key word [*finish], lower case with a star in
the beginning. For details of the POLYRATE commands, see the POLYRATE
documentation.
****************************************************
* Syntax for the CHARMMRATE Method *
****************************************************
POLYRATE is initiated with the POLYrate command.
[Syntax POLYrate]
POLYrate [ atom-selection] [RUNIT int] [PUNIT int] [TSUNit int] [OPUNit
int] [PMFZpe ] [ATMA int ] [ATMB int] [ATMC int]
[POLYRATE commands]
....
[*finish]
atom-spec::= {residue-number atom-name}
{segid resid atom-name}
{BYNUm atom-number}
RUNIt int: Unit specification for input of initial coordinates of the
reactant species. The current limitation is that only
CHARMM format is allowed for the coordinate file.
PUNIt int: Unit specification for input of initial coordinates of the
product species. The current limitation is that only
CHARMM format is allowed for the coordinate file.
TSUNit int: Unit specification for input of initial coordinates of the
transition state. The current limitation is that only
CHARMM format is allowed for the coordinate file.
OPUNit int: Unit to write out coordinates of the optimized structures,
of any of the reactant, product, and TS, depending on
the species being optimized. The current limitation is
that only CHARMM format is used.
PMFZpe ATMA int ATMB int ATMC int: this command switches on the projection
operator that is used to project the reaction coordinate out of
the Hessian matrix of the system. This is used for projected
instantaneous normal mode analysis. The reaction coordinate is
defined as the difference in bond distance between the breaking
and making bonds.
ATMA int: atom number for the donor atom following the numbering in the
general section of POLYRATE commands (see below).
ATMB int: atom number for the transferring atom following the numbering
in the general section of POLYRATE commands (see below).
ATMC int: atom number for the acceptor atom following the numbering in
the general section of POLYRATE commands (see below).
[POLYRATE commands]
This section contains standard POLYRATE commands. They must follow
immediately after the [POLYrate] command in the CHARMM input stream. This
section is terminated by the key word [*finish], lower case with a star in
the beginning. For details of the POLYRATE commands, see the POLYRATE
documentation.
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Note: The version number of CHARMMRATE is 2.0/C28b3-P9.0.
This means that CHARMMRATE-version 2.0 is based on POLYRATE-version 9.0
and CHARMM-version c28b3. The version number may be abbreviated to 2.0
when no confusion will result.
CHARMMRATE is a module of CHARMM for interfacing it with POLYRATE;
the POLYRATE main program becomes a subprogram of CHARMM. POLYRATE can be
called to carry out projected instantaneous normal mode analysis and
variational transition state theory calculations with semiclassical
multidimensional tunneling contributions. When POLYRATE needs the value or
gradient of the potential energy surface, it calls a set of interface
routines called hooks. The hooks in turn call CHARMM routines for energies
and gradients calculated by molecular mechanics or QM/MM methods. The
current version has not been parallelized.
Referencing for CHARMMRATE:
"The rate constant (or reaction path or geometry optimization, etc.)
calculations were carried out using the CHARMMRATE program[1-3]".
[1] M. Garcia-Viloca, C. Alhambra, J. C. Corchado, M. L. Sanchez, J.
Villa, J. Gao, and D. G. Truhlar, CHARMMRATE-version 2.0, University
of Minnesota, Minneapolis, 2002, a module of CHARMM (Ref. 2) for
interfacing it with POLYRATE (Ref. 3).
[2] Chemistry at HARvard Macromolecular Mechanics (CHARMM) computer
program, as described in B. R. Brooks, R. E. Bruccoleri,
B. D. Olafson , D. J. States, S. Swaminathan, and M. Karplus, J.
Comput. Chem. 4, 187 (1983).
[3] J. C. Corchado, Y.-Y. Chuang, P. L. Fast, J. Villa, W.-P. Hu, Y.-P.
Liu, G. C. Lynch, K. A. Nguyen, C. F. Jackels, V. S. Melissas,
B.J. Lynch, I. Rossi, E. L. Coitino, A. Fernandez-Ramos, J. Pu, and
T. V. Albu, R. Steckler, B. C. Garrett, A. D. Isaacson, and D. G.
Truhlar, POLYRATE-version 9.0, University of Minnesota, Minneapolis,
2002.
Note: The version number of CHARMMRATE is 2.0/C28b3-P9.0.
This means that CHARMMRATE-version 2.0 is based on POLYRATE-version 9.0
and CHARMM-version c28b3. The version number may be abbreviated to 2.0
when no confusion will result.
CHARMMRATE is a module of CHARMM for interfacing it with POLYRATE;
the POLYRATE main program becomes a subprogram of CHARMM. POLYRATE can be
called to carry out projected instantaneous normal mode analysis and
variational transition state theory calculations with semiclassical
multidimensional tunneling contributions. When POLYRATE needs the value or
gradient of the potential energy surface, it calls a set of interface
routines called hooks. The hooks in turn call CHARMM routines for energies
and gradients calculated by molecular mechanics or QM/MM methods. The
current version has not been parallelized.
Referencing for CHARMMRATE:
"The rate constant (or reaction path or geometry optimization, etc.)
calculations were carried out using the CHARMMRATE program[1-3]".
[1] M. Garcia-Viloca, C. Alhambra, J. C. Corchado, M. L. Sanchez, J.
Villa, J. Gao, and D. G. Truhlar, CHARMMRATE-version 2.0, University
of Minnesota, Minneapolis, 2002, a module of CHARMM (Ref. 2) for
interfacing it with POLYRATE (Ref. 3).
[2] Chemistry at HARvard Macromolecular Mechanics (CHARMM) computer
program, as described in B. R. Brooks, R. E. Bruccoleri,
B. D. Olafson , D. J. States, S. Swaminathan, and M. Karplus, J.
Comput. Chem. 4, 187 (1983).
[3] J. C. Corchado, Y.-Y. Chuang, P. L. Fast, J. Villa, W.-P. Hu, Y.-P.
Liu, G. C. Lynch, K. A. Nguyen, C. F. Jackels, V. S. Melissas,
B.J. Lynch, I. Rossi, E. L. Coitino, A. Fernandez-Ramos, J. Pu, and
T. V. Albu, R. Steckler, B. C. Garrett, A. D. Isaacson, and D. G.
Truhlar, POLYRATE-version 9.0, University of Minnesota, Minneapolis,
2002.
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****************************************************
* Availability of CHARMMRATE *
****************************************************
CHARMMRATE-version 2.0/C28b3-P9.0 is a module of CHARMM-version c28b3
for interfacing it with POLYRATE-version 9.0. An earlier version,
beginning with version 28b1 of CHARMM and was used to interface previous
versions of CHARMM and POLYRATE. CHARMMRATE-2.0/C28b3-P9.0 will be
distributed beginning with version c28b3 of CHARMM. The user will also
require the CRATE utility for modifying POLYRATE to make it compatible
with CHARMM. CRATE-version 8.11 corresponds to CHARMMRATE-1.0, and
CRATE-version 9.0 corresponds to CHARMMRATE-2.0. CRATE-version 9.0
corresponds to interfacing POLYRATE-version 9.0. The prospective user of
University of Minnesota (http://comp.chem.umn.edu).
****************************************************
* Availability of CHARMMRATE *
****************************************************
CHARMMRATE-version 2.0/C28b3-P9.0 is a module of CHARMM-version c28b3
for interfacing it with POLYRATE-version 9.0. An earlier version,
beginning with version 28b1 of CHARMM and was used to interface previous
versions of CHARMM and POLYRATE. CHARMMRATE-2.0/C28b3-P9.0 will be
distributed beginning with version c28b3 of CHARMM. The user will also
require the CRATE utility for modifying POLYRATE to make it compatible
with CHARMM. CRATE-version 8.11 corresponds to CHARMMRATE-1.0, and
CRATE-version 9.0 corresponds to CHARMMRATE-2.0. CRATE-version 9.0
corresponds to interfacing POLYRATE-version 9.0. The prospective user of
University of Minnesota (http://comp.chem.umn.edu).
Top
1. INTRODUCTION
CHARMMRATE is an interface of CHARMM and POLYRATE to include quantum
mechanical effects in enzyme kinetics. Although CHARMMRATE allows
execution of POLYRATE with all existing capabilities for reactions with
only one reactant and only one product, the present implementation is
primarily intended for prediction of the reaction rates of
enzyme-catalyzed reactions. Any CHARMMRATE calculation involves the
partition of the system into a primary subsystem (or primary-zone atoms),
which contains the subset of atoms involved in the reaction, and the rest
of the system (secondary-zone atoms). Only the coordinates of the
primary-zone atoms are passed from CHARMM to POLYRATE for both projected
instantaneous normal mode analysis and dynamics calculations.
Consequently, the quantum mechanical vibrational correction and the
dynamics effects are calculated for the primary subsystem in the field of
the secondary subsystem.
1.A. Capabilities added to CHARMM by CHARMMRATE and references for methods
POLYRATE includes a very large number of options and has multiple
capabilities. The user of CHARMMRATE is encouraged to read the POLYRATE
manual to learn more about these capabilities. The present section
summarizes a few of the capabilities that are liable to be of most
interest to CHARMMRATE users.
1.A.1. Transition state optimization
Saddle point geometry optimizations for the primary (dynamic) zone in
the frozen protein-plus-solvent bath may be performed in various ways; the
default option is the Newton-Raphson method with Brent line minimization
as described in W. H. Press, S. P. Flannery, S. A. Teukolsky, and W. T.
Vetterling, Numerical Recipes (Cambridge University Press, Cambridge,
1986), p.254. The default option for optimization of the stationary points
for reactants and products is to use the BFGS method that has been
implemented in POLYRATE. See the POLYRATE manual for further information
about the optimization methods available in POLYRATE.
1.A.2. Reaction path
In general, reaction paths (RPs) may be defined in various ways.
The simplest general method that is reasonably sure to give physically
meaningful vibrational frequencies for motions transverse to the reaction
path (and hence also physically meaningful free energy of activation
profiles) is the steepest descents path in isoinertial coordinates. (An
isoinertial coordinates system is one in which the kinetic energy is a sum
of square terms and the coordinates are scaled or weighted so that each
kinetic energy term has the same reduced mass. All isoinertial coordinate
systems are related to each other by orthogonal transformations, and
steepest descents paths are invariant under orthogonal transformations.) A
steepest descents path is also called a minimum energy path (MEP). The
signed distance from the saddle point along the reaction path is called
the reaction coordinate, usually denoted s. (This reaction coordinate, s,
should not be confused with the reaction coordinate used for umbrella
sampling, which is called z.) The isoinertial MEP is sometimes just called
the MEP, or it may just be called the RP; other workers prefer to append
the word intrinsic, e.g., intrinsic MEP, intrinsic reaction path,
intrinsic reaction coordinate, etc.
In CHARMMRATE, the reaction path refers to a multidimensional path
for the primary-zone (dynamic) atoms in the presence of the secondary-
zone (frozen) atoms.
CHARMMRATE may be used to calculate the isoinertial minimum energy
path (MEP) as described in B. C. Garrett, M. J. Redmon, R. Steckler, D. G.
Truhlar, K. K. Baldridge, D. Bartol, M. W. Schmidt, M. S. Gordon, J.
Phys. Chem. 92, 1476-1488 (1988).
1.A.3. Free energy of activation profile and variational transition
state theory
Vibrational partition functions and generalized free energies of
activation (which are free energies of activation for tentative transition
states that are not necessarily associated with either a saddle point or
with the final variational transition state) are computed along the
reaction path by using the quantum mechanical harmonic oscillator
approximation in 3N1 - 1 degrees of freedom, where N1 is the number of
atoms in the primary zone, and the reaction coordinate is projected out.
This kind of calculation is described in S. E. Wonchoba, and D. G.
Truhlar, J. Chem. Phys. 99, 9637- 9651 (1993). The generalized free energy
of activation as a function of the reaction coordinate (which is the
signed distance along the MEP) is called the free energy of activation
profile, and it may be used to calculate reaction rate constants by
variational transition state theory (VTST) as described in D. G. Truhlar
and B. C. Garrett, Acc. Chem. Res. 13 , 440-448 (1980). A procedure like
this was used in C. Alhambra, J. Gao, J. C. Corchado, J. Villa, and D. G.
Truhlar, J. Am. Chem. Soc. 121, 2253-2258 (1999), but it is now
recommended to use the more complete EA-VTST/MT method, in which this
quantity is used to compute a transmission coefficient rather than a rate
constant. VTST for a canonical ensemble (i.e., a system at a fixed
temperature) is also called canonical variation theory (CVT). In the
EA-VTST/MT method (described in Section 2), this step is carried out for
several members of the transition state ensemble, and it is used for the
quasiclassical part of the ensemble-averaged transmission coefficient.
1.A.4. Transmission coefficient
In CHARMMRATE the EA-VTST/MT transmission coefficient has two parts:
a quasiclassical dynamical recrossing part (Section 1.A.3) and a part that
accounts for tunneling (transmission through the barrier at energies below
the top) and non-classical reflection (reflection caused by diffraction
from the barrier top even when the energy is above the barrier); often we
just refer to the combination of tunneling and non-classical reflection
effects as tunneling (the tunneling is more important than the non-
classical reflection because the energies where tunneling occurs have
larger Boltzmann factors than the energies where non-classical reflection
occurs).
CHARMMRATE can calculate the tunneling part of the transmission
coefficient in various ways. The most complete method is the
microcanonical optimized multidimensional tunneling (muOMT)
approximation as described in Y.-P. Liu, D.-h. Lu, A. Gonzalez-Lafont, D.
G. Truhlar, and B. C. Garrett, J. Am. Chem. Soc. 115, 7806-7817 (1993). In
this calculation, tunneling and non-classical reflection along the
reaction path are included by calculating both the large-curvature
tunneling (LCT) approximation and the small-curvature tunneling (SCT)
approximation and, at each tunneling energy, accepting whichever tunneling
approximation yields the larger tunneling probability. This is a poor
man's version of a more complete search for the semiclassical tunneling
paths that minimize the imaginary action integrals, and it has been
extensively validated as summarized by T. C. Allison and D. G. Truhlar, in
Modern Methods for Multidimensional Dynamics Computations in Chemistry,
edited by D. L. Thompson (World Scientific, Singapore, 1998), pp. 618-712.
One may also limit the calculation to just the LCT or SCT
approximation or to the zero-curvature tunneling approximation (ZCT) or
even the Wigner approximation. The muOMT, LCT, SCT, and ZCT approximations
are multidimensional, whereas the Wigner approximation is one-dimensional.
The ZCT approximation calculates tunneling along the isoinertial MEP,
whereas the muOMT, LCT, and SCT approximations include various amounts of
corner cutting, i.e., tunneling on the concave side of the isoinertial
MEP, with the amount and nature of the corner cutting depending on the
curvature of the reaction path. The computational cost decreases in the
following order: muOMT, LCT, SCT, ZCT, Wigner. When tunneling is included,
the EA-VTST/MT rate constant is written as
k(T) = gamma(T) kTST(T)
where kTST(T) is the TST rate constant that is determined by the free
energy simulation of of stage 1 (including the quantum mechanical
correction of step 2 of stage 1), and gamma(T) is the transmission
coefficient that accounts for classical recrossing (the quasiclassical
part of section 1.A.3) and for tunneling and non-classical reflection.
Background for the calculation of KIEs by VTST with multidimensional
tunneling approximations is given in D.G. Truhlar, D.-h. Lu, S.C. Tucker ,
X.G. Zhao, A. Gonzalez-Lafont, T.N. Truong, D. Maurice, Y-.P. Liu, and
G.C. Lynch, in Isotope Effects in Chemical Reactions and Photodissociation
Processes, edited by J. A. Kaye (American Chemical Society Symposium
Series 502, Washington, DC, 1992), pp. 16-36.
1.B. CHARMMRATE capabilities that are not included either in POLYRATE or
in prior versions of CHARMM: Projected instantaneous normal mode
analysis
Two source files of POLYRATE (see the CRATE manual) are modified by
the CRATE utility version-9.0 to carry out projected instantaneous normal
mode analysis. With these routines quantum mechanical harmonic frequencies
of the vibrational modes of the primary subsystem orthogonal to the
reaction coordinate may be calculated for a given configuration of the
system. This calculation is used in the second step of the first stage of
the EA-VTST/MT method (described in Section 2) to include quantum effects
on the 3N-7 highest-frequency vibrational modes of the primary zone in a
hypersurface orthogonal to the reaction coordinate that is used for
umbrella sampling in the first step of stage 1. The constraint that the
modes obtained are orthogonal to the reaction coordinate is achieved by a
projection operator described in C. Alhambra , J. C. Corchado, M. L.
Sanchez, M. Garcia-Viloca, J. Gao, and D. G. Truhlar J. Phys. Chem. B
105, 11326-11340 (2001).
1.C. CHARMM options that are of particular interest for use with
CHARMMRATE.
CHARMMRATE is of particular interest for calculations of rate
constants for enzymatic reactions. Although the program would allow the
use of pure molecular mechanics (the CHARMM22 force field) for such
calculations, combined quantum mechanical and molecular mechanical (QM/MM)
potentials are much more realistic than pure molecular mechanics for
chemical reactions. Using CHARMM, QM/MM calculations can now be performed
at the ab initio level using GAMESS (B. Brooks and M. Hodoscek,
unpublished results), at the density functional level using CADPAC (P. D.
Lyne, M. Hodoscek, and M. Karplus, J. Phys. Chem. A 103, 3462-3471
(1999)), and at semiempirical molecular orbital levels (AM1 and PM3, with
general parameters or with specific reaction parameters) with MOPAC (M. J.
Field, P. A. Bash, and M. Karplus, J. Comput. Chem. 11 700-733 (1990)).
There is more than one choice for joining the QM subsystem to the MM one.
The first choice is to use "link atoms" to saturate the valence of the
fragment; this requires that certain atomic charges in the MM fragment
that are close to the QM region be deleted to avoid artificial
polarization of the quantum subsystem. One possibility to avoid these
problems is to use the generalized hybrid orbital (GHO) method described
in J. Gao, P. Amara, C. Alhambra, and M. Field, J. Phys. Chem. A 102,
4714-4721 (1998). The GHO method is currently available for semiempirical
calculations with the AM1 and PM3 methods, and it is being extended (work
in progress) to ab initio and DFT methods. Another way to correct the link
atom artifacts in the original formulation is proposed in C. Alhambra, L.
Wu, Z.-Y. Zhang, and J. Gao, J. Am. Chem. Soc. 120, 3858-3866 (1998).
Molecular dynamics simulations of an enzyme-solvent system can be
carried out on a QM/MM potential energy surface either using periodic
boundary conditions or using stochastic boundary conditions; for the
periodic boundary conditions see M. P. Allen and D. J. Tildesley, Computer
Simulation of Liquids, (Oxford University Press, New York, 1987), Ch. 1,
and for the stochastic boundary conditions see C. L. Brooks, A. Brunger,
and M. Karplus, Biopolymers 24, 843-865 (1985). Free energy perturbation
and umbrella sampling techniques can be used to determine the potential of
mean force or classical free energy profile for the enzymatic reaction
(see C. Alhambra, L. Wu, Z.-Y. Zhang, J. Gao, J. Am. Chem. Soc. 120,
3858-3866 (1998)).
2. THEORETICAL BACKGROUND: Ensemble-averaged variational transition state
theory with multidimensional tunneling (EA-VTST/MT).
This section of the manual summarizes the theoretical framework and
the practical procedure for the EA-VTST/MT method developed in C.
Alhambra, J. C. Corchado, M. L. Sanchez, M. Garcia-Viloca, J. Gao, and D.
G. Truhlar J. Phys. Chem. 105, 11326-11340 (2001).
The capabilities added to CHARMM by CHARMMRATE allow the user to
calculate the rate constant for an enzymatic reaction with the EA-VTST/MT
procedure.
The rate constant for an enzymatic reaction, which is a unimolecular
process, is obtained by combining free energy simulations and variational
transition state theory (VTST) with microcanonical optimized
multidimensional tunneling contributions (muOMT), both in the presence of
the protein environment. The potential energy surface (PES) is modeled by
a QM/MM method, for example by a semiempirical MO method combined with the
treat the boundary between the QM and the MM parts of the system. In
addition, a semiempirical term (» quantum LEPS command) or specific
reaction parameters (SRP) may be used to improve the accuracy of the PES.
The rate constant is expressed as a function of the free energy of
activation, DeltaGCVTact, calculated by variational transition state
theory free energy molecular dynamics simulations, and the transmission
coefficient, gamma. There are two versions of the method that differ in
the approximation used to evaluate gamma, in particular a 2-stage version
and a three-stage version. The procedure for the former approximation,
which has been applied in the study of five hydrogen transfer reactions,
has the following two stages:
1) In stage 1 of the calculation, the free energy of activation,
including the quantum mechanical vibrational free energy, is computed.
This involves the following calculations:
Step 1 - Calculation of the classical mechanical (CM) or transition
state theory free energy of activation by computing the potential of mean
force (PMF) along a distinguished reaction coordinate. For a reaction
AB + C -> A + BC,
the reaction coordinate, z, may be defined as:
z = rAB - rBC
The CM PMF can be evaluated by carrying out classical molecular dynamics
on a QM/MM potential energy surface with the umbrella sampling technique
implemented in CHARMM (» umbrel ) or free energy perturbation theory.
Note, for the discussion below that umbrella sampling involves a sequence
of overlapping windows (whose centers are separated by about 0.1-0.2
angstroms), each of which is later divided into 50-100 bins. The bins are
typically 0.01 angstroms wide. (These specific numerical values are just
given as examples; none of these quantities is restricted to lie within
those limits.)
Step 2 - Calculation of the quantum mechanical vibrational free
energy correction, DeltaW_vib, which is the difference between the quantal
vibrational free energy and the classical vibrational free energy. The
addition of DeltaW_vib to the CM PMF gives the quasi-classical (QC) PMF.
DeltaW_vib may be evaluated by carrying out projected instantaneous normal
mode analysis for the primary-zone atoms for many configurations (100-400
per window) obtained in the umbrella sampling step (see Section 1.B). The
projected instantaneous normal mode frequencies obtained for the different
configurations in a given bin may be averaged and the averaged value used
to determine DeltaW_vib. Strictly speaking, one might argue that one
should average the squared frequencies or some Boltzmann factors, but in
initial applications it has been found sufficient to average the
frequencies themselves.
After these two steps, the value of z with highest QC free energy is
called z*, and the bin containing z* (or a small set of bins centered on
this bin) defines the ensemble of configurations that are representative
of the transition state of the enzymatic reaction.
2) Stage 2 has the objective of computing the transmission
coefficient, gamma (T), that is the average over transition state
configurations i of the product of two factors, Gamma_i and kappa_i. The
first factor, Gamma_i, which is the the quasiclassical transmission
factor, corrects the rate constant for classical mechanical dynamical
recrossing. The second factor, kappa_i, is the semiclassical transmission
coefficient that accounts mainly for tunneling, that is, the quantum
mechanical effect on the reaction coordinate, which is missing in the
calculation of the QC rate constant. The averaged transmission coefficient
is:
gamma = <Gamma_i kappa_i>,
where the brackets indicate average over configurations i. That is, a
number of configurations (5-20 for the enzymatic reactions studied so far)
within the range z = z* Deltaz ( Deltaz = 0.05-0.01 angstroms), are chosen
as representative of the transition state ensemble. For each of them a
kappa_i. As mentioned above, in such stage-2 calculation the system is
divided into a set of primary-zone atoms, which are allowed to move, and
the rest of the system, which is fixed at the transition state
configurations. For each configuration, the saddle point and the reactant
and product structures are optimized. We optimize the saddle point and we
calculate an isoinertial MEP in both directions, i.e., toward the reactant
and toward the product. The reactant and the product calculations are used
only to determine the minimum energy at which tunneling is allowed. The
effective potential used to calculate the tunneling part, kappa_i, of the
transmission coefficient (see Section 1.A) involves the zero-point-
inclusive energy along this MEP. The user should see test run 2 for an
example of how to use a typical solvent configuration.
The approximation described here to obtain the transmission
coefficients is called static secondary-zone approximation (SSZ). The
product of the averaged transmission coefficient obtained in this way and
the quasiclassical rate constant of stage 1 results in the SSZ version of
the EA-VTST/MT rate constant. The results obtained in five studies of
enzymatic hydrogen transfer reactions demonstrate that the SSZ rate
constant is accurate enough to reproduce experimental KIEs.
The SSZ result may be improved by carrying out a further step that
has been called stage 3. In stage 3, the free energy of the secondary zone
is calculated by free energy perturbation theory along the minimum- energy
paths of stage 2. This allows us to include the secondary-zone free energy
in the transmission coefficient. This is called the
equilibrium-secondary-zone (ESZ) approximation.
The EA-VTST/MT method is described in: C. Alhambra, J. C. Corchado,
M. L. Sanchez, M. Garcia-Viloca, J. Gao, and D. G. Truhlar J. Phys. Chem.
B 105, 11326-11340 (2001), and in D. G. Truhlar, J. Gao, C. Alhambra, M.
Garcia-Viloca, J. Corchado, M. L. Sanchez, and J. Villa, Acc. Chem. Res.
35, 341-349 (2002). A complete description of an application study is
provided in M. Garcia-Viloca, C. Alhambra, D. G. Truhlar, and J. Gao, J.
Comput. Chem. 2002, in press.
3. PROGRAM STRUCTURE
3.A. Overall design
The CHARMMRATE interface for CHARMM and POLYRATE takes advantage of
the modular nature of both programs, and, consequently, minimal
modifications of CHARMM and POLYRATE were required. The CHARMM program is
the main driver of the integrated program, which makes a FORTRAN call to
the interface subprogram, CHARMMRATE, to initiate calculations by
POLYRATE. The energy and energy gradients for the primary-zone atoms
required by POLYRATE are determined by CHARMM through the interface
subprogram and are supplied to POLYRATE through a set of subroutines
called the POLYRATE hooks.
3.B. Modifications and additions to CHARMM
Only two modifications have been made in the CHARMM program: (1)
addition of a one-line keyword processing command in the charmm_main.src
module to initiate the subroutine call to CHARMMRATE; (2) addition of the
3.C. Modifications and additions to POLYRATE
Specific modifications of the original POLYRATE program have been
made primarily for efficient transfer of information between CHARMM and
POLYRATE and to eliminate conflicts and other problems during compilation.
These modifications are described in the CRATE manual, available at
http://comp.chem.umn.edu/crate.
4. INSTALLATION OF charmmrate AND ITS USE
4.A. Program distribution
CHARMMRATE-version 2.0/C28b2-P9.0 is distributed as a module in
Karplus's research group at Harvard University and by Accelrys, Inc. In
addition to CHARMM,which includes the CHARMMRATE module, users also need
to obtain the POLYRATE program, which is a copyrighted program distributed
by the University of Minnesota (http://comp.chem.umn.edu) and the CRATE
utility, also available from Minnesota. The CRATE utility will make the
changes to the source code of POLYRATE to allow the interface between the
two programs. When the CHARMM program (which, beginning with version 28,
automatically includes the CHARMMRATE module), the POLYRATE program and
the CRATE utility have been obtained, integration of the codes into a
single executable file is straightforward as described below.
4.B. Installation
The user should carry out the following steps:
1. Install CHARMM.
2. Store the tar file polyrate9.0.tar.Z (obtained from the
University of Minnesota, http://comp.chem.umn.edu) in the
directory chmroot/source/prate and untar it with this command:
tar xvf polyrate9.0.tar
3. Set an environmental variable, called pr, to the
absolute path name of the directory where the polyrate
program is stored. Example:
C shell
% setenv pr /home/chmroot/source/prate/polyrate9.0
Bourne shell
$ pr = /home/chmroot/source/prate/polyrate9.0
$ export pr
4. Store the tar file crate9.0.tar.Z (obtained from the University
of Minnesota, http://comp.chem.umn.edu) in the directory
chmroot/source/prate and untar it with this command:
tar xvf crate9.0.tar
The directory crate9.0 will then contain the files required to
prepare POLYRATE for use with the CHARMMRATE module of CHARMM.
These files are described in the CRATE manual. Change the
dimensions specified in the param.inc file located in the newly
created directory, crate9.0, in order to make them large
enough for the system(s) to be studied, but small enough to run
in the memory available on the computer chosen to carry out the
work. Or use the param.inc file distributed as part of CRATE. See
the POLYRATE manual for further discussion of the dimensions in
in POLYRATE.
5. Set an environmental variable, crate, to the absolute
path name of the directory where the CRATE package is stored.
Example:
C shell
% setenv crate /home/chmroot/source/prate/crate9.0
Bourne shell
$ crate = /home/chmroot/source/prate/crate9.0
$ export crate
6. Go to the /build directory of CHARMM, i.e.
cd /home/chmroot/build/'chm_host',
and edit the file pref.dat. Add the CHARMMRATE module to the
list.
7. If CHARMM has been compiled previously without POLYRATE,
remove all the object files in home/chmroot/lib/'chm_host'
8. Go to the CHARMM directory chmroot and type the command:
install.com 'chm_host' (small/medium/large) POLYR > & log &
(» install in the CHARMM documentation directory). This
step will execute the script install_cr.com, which will put the
CHARMMRATE source code in the directory
/home/chmroot/source/prate.
Any modifications desired should be done here.
9. You do not need to run the script install_cr.com (described in
the CRATE manual) in any further compilations. Therefore it is
recommended to comment the following line in the file
/home/chmroot/install.com:
$crate/install_cr.com
10. After compilation, you will have a new executable in:
/home/chmroot/exec/'chm_host'
NOTE: In order to run projected instantaneous normal mode analysis
with CHARMMRATE-version 2.0 it is necessary to do small changes in two of
the files located in the directory /home/chmroot/source/prate after the
compilation process described above. Instructions for these changes are
provided in the README file contained in the crate9.0 directory of the
CRATE package.
5. DESCRIPTION OF INPUT
CHARMMRATE is run from the CHARMM main input stream. The syntax to
execute polyrate from charmm's input stream for a reaction with only one
reactant (e.g., an enzyme-substrate precursor complex) and only one
product (e.g., an enzyme-substrate successor complex) is:
POLYrate SELEction { atom-spec } end [RUNIt int] [PUNIt int]
[TSUNit int] [OPUNit int]
[ PMFZpe ] [ATMA int ] [ATMB int] [ATMC int]
_polyrate_input_
*finish
We note the use of the CHARMM convention by which one needs to enter
only the first four letters of POLYrate and other words with the first
four letters capitalized. Furthermore the parts in brackets are optional.
The meanings of the various keywords are:
SELEction { atom-spec } specifies the primary-zone atoms in POLYRATE:
atom-spec = { residue-number atom-name }
{ segid resid atom-name }
{ BYNUm atom-number }
RUNit int: Unit specification for input of initial coordinates of the
reactant species. The current limitation is that only CHARMM
format is allowed for the coordinate file.
PUNit int: Unit specification for input of initial coordinates of the
product species. The current limitation is that only CHARMM
format is allowed for the coordinate file.
TSUNit int: Unit specification for input of initial coordinates of the
transition state. The current limitation is that only CHARMM
format is allowed for the coordinate file.
OPUNit int: Unit to write out coordinates of the optimized structures of
the reactant, product, or TS, depending upon which of these
is requested (elsewhere) to be written. The current
limitation is that only CHARMM format is used. The
coordinate files assigned to these units must be in the CARD
format (see CHARMM documentation for details).
PMFZpe ATMA int ATMB int ATMC int: this command switch on the
projection of the reaction coordinate out of the Hessian
matrix of the system. It is used for projected
instantaneous normal mode analysis. The reaction coordinate
is defined as the difference in bond distance between the
breaking and making bonds.
ATMA int: atom number for the donor atom following the numbering in the
general section of POLYRATE commands (see below).
ATMB int: atom number for the transferring atom following the numbering
in the general section of POLYRATE commands (see below).
ATMC int: atom number for the acceptor atom following the numbering in
the general section of POLYRATE commands (see below).
_polyrate_input_: This section contains a standard POLYRATE fu5 input
file. It must follow immediately after the POLYrate command
in the CHARMM input stream. For details of POLYRATE input, see
the POLYRATE documentation. The initial coordinates have
already been setup through the POLYrate command; therefore the
GEOM record in the POLYRATE fu5 input file may be omitted. If,
however, the GEOM record is present, the Cartesian coordinates
given in this record will replace the data set up through the
POLYrate command. This is not recommended.
*finish The last record to be read by POLYRATE from the CHARMM main
input stream. This will terminate I/O operations from unit 5
by POLYRATE, and POLYRATE calculations will proceed.
6. TEST RUNS
This section describes two test runs. Each test job includes a full
input file, initial coordinates and parameter files. They are located in:
/home/chmroot/test/cquantumtest.
6.1. Test Job 1 - Direct dynamics of chorismate to prephenate in the gas
phase
This test job reads in three initial guess coordinates for the
reactant state, product state, and transition state, optimizes their
geometries, and performs a CVT calculation to yield the predicted rate
constants at various temperatures. This test job takes roughly 3 hours on
an SGI Octane 2 computer running under the Irix 6.5 operating system.
(Test Job 2 is a shorter test run.)
6.1.A. Input files
The cr01.inp file contains the CHARMM input stream for a direct
dynamics calculation of the chorismate to prephenate rearrangement
reaction. Similar calculations can be carried out for the substrate in the
enzyme active site, provided that appropriate boundary conditions are set
up in he CHARMM input.
The charmm22.top and charmm22.par files are the CHARMM topology and
parameter files. They are required for all CHARMM calculations.
Three coordinate files are provided for this test job, corresponding
to the initial guess coordinates for the reactant (gs.crd), product
(prod.crd), and transition state (ts.crd) for the dynamics calculation
with POLYRATE.
6.1.B. Description of the CHARMM input stream
The majority of the CHARMM commands are straightforward. The three
initial guess coordinate files must be opened as formatted files in the
FORTRAN unit numbers are default file choices in POLYRATE. Therefore,
these numbers should not be used in the CHARMM input file unless the
POLYRATE defaults are changed. Please consult the POLYRATE documentation
for a full list and description of these files.
Five (5) FORTRAN files will be used by POLYRATE to write out the
computational results. They are files with unit numbers 14, 25, 26, 27,
and 61, which should be opened in the CHARMM input stream before
Section 6.1.C summarizes the contents of these files.
All input instructions immediately following the POLYrate command are
those of POLYRATE. A full description of these commands can be found in
the POLYRATE documentation.
6.1.C. Description of CHARMMRATE output
cr0114.out - computed reaction rates at various temperatures using
the TST and CVT methods.
cr0125.out - potential energy along the reaction coordinate s, which
measures distance along the minimum energy path (MEP), and computed
transmission coefficient, if requested. Since the test run is for a CVT
calculation, no multidimensional tunneling is included in the test run.
cr0126.out - computed vibrational frequencies that hgave been
requested for printing out along s.
cr0127.out - coordinates along s.
cr0161.out - optimized geometries, energies, vibrational frequencies
and the Hessian for the reactant, product, and transition state.
6.2. Test Job 2 - Geometry optimization of chorismate in a water bath
This test job performs geometry optimization of chorismate in the
presence of a frozen water bath, arbitrarily taken from the trajectory of
a molecular dynamics simulation of chorismate in water.
The cr02.inp file is the CHARMM input stream command file. In
addition to the CHARMM topology and parameter files, the cr02.crd file is
required; it contains the instantaneous (initial) coordinates of
chorismate in water from a molecular dynamics simulation.
The file optcr02.crd contains the optimized coordinates of chorismate
in water.
1. INTRODUCTION
CHARMMRATE is an interface of CHARMM and POLYRATE to include quantum
mechanical effects in enzyme kinetics. Although CHARMMRATE allows
execution of POLYRATE with all existing capabilities for reactions with
only one reactant and only one product, the present implementation is
primarily intended for prediction of the reaction rates of
enzyme-catalyzed reactions. Any CHARMMRATE calculation involves the
partition of the system into a primary subsystem (or primary-zone atoms),
which contains the subset of atoms involved in the reaction, and the rest
of the system (secondary-zone atoms). Only the coordinates of the
primary-zone atoms are passed from CHARMM to POLYRATE for both projected
instantaneous normal mode analysis and dynamics calculations.
Consequently, the quantum mechanical vibrational correction and the
dynamics effects are calculated for the primary subsystem in the field of
the secondary subsystem.
1.A. Capabilities added to CHARMM by CHARMMRATE and references for methods
POLYRATE includes a very large number of options and has multiple
capabilities. The user of CHARMMRATE is encouraged to read the POLYRATE
manual to learn more about these capabilities. The present section
summarizes a few of the capabilities that are liable to be of most
interest to CHARMMRATE users.
1.A.1. Transition state optimization
Saddle point geometry optimizations for the primary (dynamic) zone in
the frozen protein-plus-solvent bath may be performed in various ways; the
default option is the Newton-Raphson method with Brent line minimization
as described in W. H. Press, S. P. Flannery, S. A. Teukolsky, and W. T.
Vetterling, Numerical Recipes (Cambridge University Press, Cambridge,
1986), p.254. The default option for optimization of the stationary points
for reactants and products is to use the BFGS method that has been
implemented in POLYRATE. See the POLYRATE manual for further information
about the optimization methods available in POLYRATE.
1.A.2. Reaction path
In general, reaction paths (RPs) may be defined in various ways.
The simplest general method that is reasonably sure to give physically
meaningful vibrational frequencies for motions transverse to the reaction
path (and hence also physically meaningful free energy of activation
profiles) is the steepest descents path in isoinertial coordinates. (An
isoinertial coordinates system is one in which the kinetic energy is a sum
of square terms and the coordinates are scaled or weighted so that each
kinetic energy term has the same reduced mass. All isoinertial coordinate
systems are related to each other by orthogonal transformations, and
steepest descents paths are invariant under orthogonal transformations.) A
steepest descents path is also called a minimum energy path (MEP). The
signed distance from the saddle point along the reaction path is called
the reaction coordinate, usually denoted s. (This reaction coordinate, s,
should not be confused with the reaction coordinate used for umbrella
sampling, which is called z.) The isoinertial MEP is sometimes just called
the MEP, or it may just be called the RP; other workers prefer to append
the word intrinsic, e.g., intrinsic MEP, intrinsic reaction path,
intrinsic reaction coordinate, etc.
In CHARMMRATE, the reaction path refers to a multidimensional path
for the primary-zone (dynamic) atoms in the presence of the secondary-
zone (frozen) atoms.
CHARMMRATE may be used to calculate the isoinertial minimum energy
path (MEP) as described in B. C. Garrett, M. J. Redmon, R. Steckler, D. G.
Truhlar, K. K. Baldridge, D. Bartol, M. W. Schmidt, M. S. Gordon, J.
Phys. Chem. 92, 1476-1488 (1988).
1.A.3. Free energy of activation profile and variational transition
state theory
Vibrational partition functions and generalized free energies of
activation (which are free energies of activation for tentative transition
states that are not necessarily associated with either a saddle point or
with the final variational transition state) are computed along the
reaction path by using the quantum mechanical harmonic oscillator
approximation in 3N1 - 1 degrees of freedom, where N1 is the number of
atoms in the primary zone, and the reaction coordinate is projected out.
This kind of calculation is described in S. E. Wonchoba, and D. G.
Truhlar, J. Chem. Phys. 99, 9637- 9651 (1993). The generalized free energy
of activation as a function of the reaction coordinate (which is the
signed distance along the MEP) is called the free energy of activation
profile, and it may be used to calculate reaction rate constants by
variational transition state theory (VTST) as described in D. G. Truhlar
and B. C. Garrett, Acc. Chem. Res. 13 , 440-448 (1980). A procedure like
this was used in C. Alhambra, J. Gao, J. C. Corchado, J. Villa, and D. G.
Truhlar, J. Am. Chem. Soc. 121, 2253-2258 (1999), but it is now
recommended to use the more complete EA-VTST/MT method, in which this
quantity is used to compute a transmission coefficient rather than a rate
constant. VTST for a canonical ensemble (i.e., a system at a fixed
temperature) is also called canonical variation theory (CVT). In the
EA-VTST/MT method (described in Section 2), this step is carried out for
several members of the transition state ensemble, and it is used for the
quasiclassical part of the ensemble-averaged transmission coefficient.
1.A.4. Transmission coefficient
In CHARMMRATE the EA-VTST/MT transmission coefficient has two parts:
a quasiclassical dynamical recrossing part (Section 1.A.3) and a part that
accounts for tunneling (transmission through the barrier at energies below
the top) and non-classical reflection (reflection caused by diffraction
from the barrier top even when the energy is above the barrier); often we
just refer to the combination of tunneling and non-classical reflection
effects as tunneling (the tunneling is more important than the non-
classical reflection because the energies where tunneling occurs have
larger Boltzmann factors than the energies where non-classical reflection
occurs).
CHARMMRATE can calculate the tunneling part of the transmission
coefficient in various ways. The most complete method is the
microcanonical optimized multidimensional tunneling (muOMT)
approximation as described in Y.-P. Liu, D.-h. Lu, A. Gonzalez-Lafont, D.
G. Truhlar, and B. C. Garrett, J. Am. Chem. Soc. 115, 7806-7817 (1993). In
this calculation, tunneling and non-classical reflection along the
reaction path are included by calculating both the large-curvature
tunneling (LCT) approximation and the small-curvature tunneling (SCT)
approximation and, at each tunneling energy, accepting whichever tunneling
approximation yields the larger tunneling probability. This is a poor
man's version of a more complete search for the semiclassical tunneling
paths that minimize the imaginary action integrals, and it has been
extensively validated as summarized by T. C. Allison and D. G. Truhlar, in
Modern Methods for Multidimensional Dynamics Computations in Chemistry,
edited by D. L. Thompson (World Scientific, Singapore, 1998), pp. 618-712.
One may also limit the calculation to just the LCT or SCT
approximation or to the zero-curvature tunneling approximation (ZCT) or
even the Wigner approximation. The muOMT, LCT, SCT, and ZCT approximations
are multidimensional, whereas the Wigner approximation is one-dimensional.
The ZCT approximation calculates tunneling along the isoinertial MEP,
whereas the muOMT, LCT, and SCT approximations include various amounts of
corner cutting, i.e., tunneling on the concave side of the isoinertial
MEP, with the amount and nature of the corner cutting depending on the
curvature of the reaction path. The computational cost decreases in the
following order: muOMT, LCT, SCT, ZCT, Wigner. When tunneling is included,
the EA-VTST/MT rate constant is written as
k(T) = gamma(T) kTST(T)
where kTST(T) is the TST rate constant that is determined by the free
energy simulation of of stage 1 (including the quantum mechanical
correction of step 2 of stage 1), and gamma(T) is the transmission
coefficient that accounts for classical recrossing (the quasiclassical
part of section 1.A.3) and for tunneling and non-classical reflection.
Background for the calculation of KIEs by VTST with multidimensional
tunneling approximations is given in D.G. Truhlar, D.-h. Lu, S.C. Tucker ,
X.G. Zhao, A. Gonzalez-Lafont, T.N. Truong, D. Maurice, Y-.P. Liu, and
G.C. Lynch, in Isotope Effects in Chemical Reactions and Photodissociation
Processes, edited by J. A. Kaye (American Chemical Society Symposium
Series 502, Washington, DC, 1992), pp. 16-36.
1.B. CHARMMRATE capabilities that are not included either in POLYRATE or
in prior versions of CHARMM: Projected instantaneous normal mode
analysis
Two source files of POLYRATE (see the CRATE manual) are modified by
the CRATE utility version-9.0 to carry out projected instantaneous normal
mode analysis. With these routines quantum mechanical harmonic frequencies
of the vibrational modes of the primary subsystem orthogonal to the
reaction coordinate may be calculated for a given configuration of the
system. This calculation is used in the second step of the first stage of
the EA-VTST/MT method (described in Section 2) to include quantum effects
on the 3N-7 highest-frequency vibrational modes of the primary zone in a
hypersurface orthogonal to the reaction coordinate that is used for
umbrella sampling in the first step of stage 1. The constraint that the
modes obtained are orthogonal to the reaction coordinate is achieved by a
projection operator described in C. Alhambra , J. C. Corchado, M. L.
Sanchez, M. Garcia-Viloca, J. Gao, and D. G. Truhlar J. Phys. Chem. B
105, 11326-11340 (2001).
1.C. CHARMM options that are of particular interest for use with
CHARMMRATE.
CHARMMRATE is of particular interest for calculations of rate
constants for enzymatic reactions. Although the program would allow the
use of pure molecular mechanics (the CHARMM22 force field) for such
calculations, combined quantum mechanical and molecular mechanical (QM/MM)
potentials are much more realistic than pure molecular mechanics for
chemical reactions. Using CHARMM, QM/MM calculations can now be performed
at the ab initio level using GAMESS (B. Brooks and M. Hodoscek,
unpublished results), at the density functional level using CADPAC (P. D.
Lyne, M. Hodoscek, and M. Karplus, J. Phys. Chem. A 103, 3462-3471
(1999)), and at semiempirical molecular orbital levels (AM1 and PM3, with
general parameters or with specific reaction parameters) with MOPAC (M. J.
Field, P. A. Bash, and M. Karplus, J. Comput. Chem. 11 700-733 (1990)).
There is more than one choice for joining the QM subsystem to the MM one.
The first choice is to use "link atoms" to saturate the valence of the
fragment; this requires that certain atomic charges in the MM fragment
that are close to the QM region be deleted to avoid artificial
polarization of the quantum subsystem. One possibility to avoid these
problems is to use the generalized hybrid orbital (GHO) method described
in J. Gao, P. Amara, C. Alhambra, and M. Field, J. Phys. Chem. A 102,
4714-4721 (1998). The GHO method is currently available for semiempirical
calculations with the AM1 and PM3 methods, and it is being extended (work
in progress) to ab initio and DFT methods. Another way to correct the link
atom artifacts in the original formulation is proposed in C. Alhambra, L.
Wu, Z.-Y. Zhang, and J. Gao, J. Am. Chem. Soc. 120, 3858-3866 (1998).
Molecular dynamics simulations of an enzyme-solvent system can be
carried out on a QM/MM potential energy surface either using periodic
boundary conditions or using stochastic boundary conditions; for the
periodic boundary conditions see M. P. Allen and D. J. Tildesley, Computer
Simulation of Liquids, (Oxford University Press, New York, 1987), Ch. 1,
and for the stochastic boundary conditions see C. L. Brooks, A. Brunger,
and M. Karplus, Biopolymers 24, 843-865 (1985). Free energy perturbation
and umbrella sampling techniques can be used to determine the potential of
mean force or classical free energy profile for the enzymatic reaction
(see C. Alhambra, L. Wu, Z.-Y. Zhang, J. Gao, J. Am. Chem. Soc. 120,
3858-3866 (1998)).
2. THEORETICAL BACKGROUND: Ensemble-averaged variational transition state
theory with multidimensional tunneling (EA-VTST/MT).
This section of the manual summarizes the theoretical framework and
the practical procedure for the EA-VTST/MT method developed in C.
Alhambra, J. C. Corchado, M. L. Sanchez, M. Garcia-Viloca, J. Gao, and D.
G. Truhlar J. Phys. Chem. 105, 11326-11340 (2001).
The capabilities added to CHARMM by CHARMMRATE allow the user to
calculate the rate constant for an enzymatic reaction with the EA-VTST/MT
procedure.
The rate constant for an enzymatic reaction, which is a unimolecular
process, is obtained by combining free energy simulations and variational
transition state theory (VTST) with microcanonical optimized
multidimensional tunneling contributions (muOMT), both in the presence of
the protein environment. The potential energy surface (PES) is modeled by
a QM/MM method, for example by a semiempirical MO method combined with the
treat the boundary between the QM and the MM parts of the system. In
addition, a semiempirical term (» quantum LEPS command) or specific
reaction parameters (SRP) may be used to improve the accuracy of the PES.
The rate constant is expressed as a function of the free energy of
activation, DeltaGCVTact, calculated by variational transition state
theory free energy molecular dynamics simulations, and the transmission
coefficient, gamma. There are two versions of the method that differ in
the approximation used to evaluate gamma, in particular a 2-stage version
and a three-stage version. The procedure for the former approximation,
which has been applied in the study of five hydrogen transfer reactions,
has the following two stages:
1) In stage 1 of the calculation, the free energy of activation,
including the quantum mechanical vibrational free energy, is computed.
This involves the following calculations:
Step 1 - Calculation of the classical mechanical (CM) or transition
state theory free energy of activation by computing the potential of mean
force (PMF) along a distinguished reaction coordinate. For a reaction
AB + C -> A + BC,
the reaction coordinate, z, may be defined as:
z = rAB - rBC
The CM PMF can be evaluated by carrying out classical molecular dynamics
on a QM/MM potential energy surface with the umbrella sampling technique
implemented in CHARMM (» umbrel ) or free energy perturbation theory.
Note, for the discussion below that umbrella sampling involves a sequence
of overlapping windows (whose centers are separated by about 0.1-0.2
angstroms), each of which is later divided into 50-100 bins. The bins are
typically 0.01 angstroms wide. (These specific numerical values are just
given as examples; none of these quantities is restricted to lie within
those limits.)
Step 2 - Calculation of the quantum mechanical vibrational free
energy correction, DeltaW_vib, which is the difference between the quantal
vibrational free energy and the classical vibrational free energy. The
addition of DeltaW_vib to the CM PMF gives the quasi-classical (QC) PMF.
DeltaW_vib may be evaluated by carrying out projected instantaneous normal
mode analysis for the primary-zone atoms for many configurations (100-400
per window) obtained in the umbrella sampling step (see Section 1.B). The
projected instantaneous normal mode frequencies obtained for the different
configurations in a given bin may be averaged and the averaged value used
to determine DeltaW_vib. Strictly speaking, one might argue that one
should average the squared frequencies or some Boltzmann factors, but in
initial applications it has been found sufficient to average the
frequencies themselves.
After these two steps, the value of z with highest QC free energy is
called z*, and the bin containing z* (or a small set of bins centered on
this bin) defines the ensemble of configurations that are representative
of the transition state of the enzymatic reaction.
2) Stage 2 has the objective of computing the transmission
coefficient, gamma (T), that is the average over transition state
configurations i of the product of two factors, Gamma_i and kappa_i. The
first factor, Gamma_i, which is the the quasiclassical transmission
factor, corrects the rate constant for classical mechanical dynamical
recrossing. The second factor, kappa_i, is the semiclassical transmission
coefficient that accounts mainly for tunneling, that is, the quantum
mechanical effect on the reaction coordinate, which is missing in the
calculation of the QC rate constant. The averaged transmission coefficient
is:
gamma = <Gamma_i kappa_i>,
where the brackets indicate average over configurations i. That is, a
number of configurations (5-20 for the enzymatic reactions studied so far)
within the range z = z* Deltaz ( Deltaz = 0.05-0.01 angstroms), are chosen
as representative of the transition state ensemble. For each of them a
kappa_i. As mentioned above, in such stage-2 calculation the system is
divided into a set of primary-zone atoms, which are allowed to move, and
the rest of the system, which is fixed at the transition state
configurations. For each configuration, the saddle point and the reactant
and product structures are optimized. We optimize the saddle point and we
calculate an isoinertial MEP in both directions, i.e., toward the reactant
and toward the product. The reactant and the product calculations are used
only to determine the minimum energy at which tunneling is allowed. The
effective potential used to calculate the tunneling part, kappa_i, of the
transmission coefficient (see Section 1.A) involves the zero-point-
inclusive energy along this MEP. The user should see test run 2 for an
example of how to use a typical solvent configuration.
The approximation described here to obtain the transmission
coefficients is called static secondary-zone approximation (SSZ). The
product of the averaged transmission coefficient obtained in this way and
the quasiclassical rate constant of stage 1 results in the SSZ version of
the EA-VTST/MT rate constant. The results obtained in five studies of
enzymatic hydrogen transfer reactions demonstrate that the SSZ rate
constant is accurate enough to reproduce experimental KIEs.
The SSZ result may be improved by carrying out a further step that
has been called stage 3. In stage 3, the free energy of the secondary zone
is calculated by free energy perturbation theory along the minimum- energy
paths of stage 2. This allows us to include the secondary-zone free energy
in the transmission coefficient. This is called the
equilibrium-secondary-zone (ESZ) approximation.
The EA-VTST/MT method is described in: C. Alhambra, J. C. Corchado,
M. L. Sanchez, M. Garcia-Viloca, J. Gao, and D. G. Truhlar J. Phys. Chem.
B 105, 11326-11340 (2001), and in D. G. Truhlar, J. Gao, C. Alhambra, M.
Garcia-Viloca, J. Corchado, M. L. Sanchez, and J. Villa, Acc. Chem. Res.
35, 341-349 (2002). A complete description of an application study is
provided in M. Garcia-Viloca, C. Alhambra, D. G. Truhlar, and J. Gao, J.
Comput. Chem. 2002, in press.
3. PROGRAM STRUCTURE
3.A. Overall design
The CHARMMRATE interface for CHARMM and POLYRATE takes advantage of
the modular nature of both programs, and, consequently, minimal
modifications of CHARMM and POLYRATE were required. The CHARMM program is
the main driver of the integrated program, which makes a FORTRAN call to
the interface subprogram, CHARMMRATE, to initiate calculations by
POLYRATE. The energy and energy gradients for the primary-zone atoms
required by POLYRATE are determined by CHARMM through the interface
subprogram and are supplied to POLYRATE through a set of subroutines
called the POLYRATE hooks.
3.B. Modifications and additions to CHARMM
Only two modifications have been made in the CHARMM program: (1)
addition of a one-line keyword processing command in the charmm_main.src
module to initiate the subroutine call to CHARMMRATE; (2) addition of the
3.C. Modifications and additions to POLYRATE
Specific modifications of the original POLYRATE program have been
made primarily for efficient transfer of information between CHARMM and
POLYRATE and to eliminate conflicts and other problems during compilation.
These modifications are described in the CRATE manual, available at
http://comp.chem.umn.edu/crate.
4. INSTALLATION OF charmmrate AND ITS USE
4.A. Program distribution
CHARMMRATE-version 2.0/C28b2-P9.0 is distributed as a module in
Karplus's research group at Harvard University and by Accelrys, Inc. In
addition to CHARMM,which includes the CHARMMRATE module, users also need
to obtain the POLYRATE program, which is a copyrighted program distributed
by the University of Minnesota (http://comp.chem.umn.edu) and the CRATE
utility, also available from Minnesota. The CRATE utility will make the
changes to the source code of POLYRATE to allow the interface between the
two programs. When the CHARMM program (which, beginning with version 28,
automatically includes the CHARMMRATE module), the POLYRATE program and
the CRATE utility have been obtained, integration of the codes into a
single executable file is straightforward as described below.
4.B. Installation
The user should carry out the following steps:
1. Install CHARMM.
2. Store the tar file polyrate9.0.tar.Z (obtained from the
University of Minnesota, http://comp.chem.umn.edu) in the
directory chmroot/source/prate and untar it with this command:
tar xvf polyrate9.0.tar
3. Set an environmental variable, called pr, to the
absolute path name of the directory where the polyrate
program is stored. Example:
C shell
% setenv pr /home/chmroot/source/prate/polyrate9.0
Bourne shell
$ pr = /home/chmroot/source/prate/polyrate9.0
$ export pr
4. Store the tar file crate9.0.tar.Z (obtained from the University
of Minnesota, http://comp.chem.umn.edu) in the directory
chmroot/source/prate and untar it with this command:
tar xvf crate9.0.tar
The directory crate9.0 will then contain the files required to
prepare POLYRATE for use with the CHARMMRATE module of CHARMM.
These files are described in the CRATE manual. Change the
dimensions specified in the param.inc file located in the newly
created directory, crate9.0, in order to make them large
enough for the system(s) to be studied, but small enough to run
in the memory available on the computer chosen to carry out the
work. Or use the param.inc file distributed as part of CRATE. See
the POLYRATE manual for further discussion of the dimensions in
in POLYRATE.
5. Set an environmental variable, crate, to the absolute
path name of the directory where the CRATE package is stored.
Example:
C shell
% setenv crate /home/chmroot/source/prate/crate9.0
Bourne shell
$ crate = /home/chmroot/source/prate/crate9.0
$ export crate
6. Go to the /build directory of CHARMM, i.e.
cd /home/chmroot/build/'chm_host',
and edit the file pref.dat. Add the CHARMMRATE module to the
list.
7. If CHARMM has been compiled previously without POLYRATE,
remove all the object files in home/chmroot/lib/'chm_host'
8. Go to the CHARMM directory chmroot and type the command:
install.com 'chm_host' (small/medium/large) POLYR > & log &
(» install in the CHARMM documentation directory). This
step will execute the script install_cr.com, which will put the
CHARMMRATE source code in the directory
/home/chmroot/source/prate.
Any modifications desired should be done here.
9. You do not need to run the script install_cr.com (described in
the CRATE manual) in any further compilations. Therefore it is
recommended to comment the following line in the file
/home/chmroot/install.com:
$crate/install_cr.com
10. After compilation, you will have a new executable in:
/home/chmroot/exec/'chm_host'
NOTE: In order to run projected instantaneous normal mode analysis
with CHARMMRATE-version 2.0 it is necessary to do small changes in two of
the files located in the directory /home/chmroot/source/prate after the
compilation process described above. Instructions for these changes are
provided in the README file contained in the crate9.0 directory of the
CRATE package.
5. DESCRIPTION OF INPUT
CHARMMRATE is run from the CHARMM main input stream. The syntax to
execute polyrate from charmm's input stream for a reaction with only one
reactant (e.g., an enzyme-substrate precursor complex) and only one
product (e.g., an enzyme-substrate successor complex) is:
POLYrate SELEction { atom-spec } end [RUNIt int] [PUNIt int]
[TSUNit int] [OPUNit int]
[ PMFZpe ] [ATMA int ] [ATMB int] [ATMC int]
_polyrate_input_
*finish
We note the use of the CHARMM convention by which one needs to enter
only the first four letters of POLYrate and other words with the first
four letters capitalized. Furthermore the parts in brackets are optional.
The meanings of the various keywords are:
SELEction { atom-spec } specifies the primary-zone atoms in POLYRATE:
atom-spec = { residue-number atom-name }
{ segid resid atom-name }
{ BYNUm atom-number }
RUNit int: Unit specification for input of initial coordinates of the
reactant species. The current limitation is that only CHARMM
format is allowed for the coordinate file.
PUNit int: Unit specification for input of initial coordinates of the
product species. The current limitation is that only CHARMM
format is allowed for the coordinate file.
TSUNit int: Unit specification for input of initial coordinates of the
transition state. The current limitation is that only CHARMM
format is allowed for the coordinate file.
OPUNit int: Unit to write out coordinates of the optimized structures of
the reactant, product, or TS, depending upon which of these
is requested (elsewhere) to be written. The current
limitation is that only CHARMM format is used. The
coordinate files assigned to these units must be in the CARD
format (see CHARMM documentation for details).
PMFZpe ATMA int ATMB int ATMC int: this command switch on the
projection of the reaction coordinate out of the Hessian
matrix of the system. It is used for projected
instantaneous normal mode analysis. The reaction coordinate
is defined as the difference in bond distance between the
breaking and making bonds.
ATMA int: atom number for the donor atom following the numbering in the
general section of POLYRATE commands (see below).
ATMB int: atom number for the transferring atom following the numbering
in the general section of POLYRATE commands (see below).
ATMC int: atom number for the acceptor atom following the numbering in
the general section of POLYRATE commands (see below).
_polyrate_input_: This section contains a standard POLYRATE fu5 input
file. It must follow immediately after the POLYrate command
in the CHARMM input stream. For details of POLYRATE input, see
the POLYRATE documentation. The initial coordinates have
already been setup through the POLYrate command; therefore the
GEOM record in the POLYRATE fu5 input file may be omitted. If,
however, the GEOM record is present, the Cartesian coordinates
given in this record will replace the data set up through the
POLYrate command. This is not recommended.
*finish The last record to be read by POLYRATE from the CHARMM main
input stream. This will terminate I/O operations from unit 5
by POLYRATE, and POLYRATE calculations will proceed.
6. TEST RUNS
This section describes two test runs. Each test job includes a full
input file, initial coordinates and parameter files. They are located in:
/home/chmroot/test/cquantumtest.
6.1. Test Job 1 - Direct dynamics of chorismate to prephenate in the gas
phase
This test job reads in three initial guess coordinates for the
reactant state, product state, and transition state, optimizes their
geometries, and performs a CVT calculation to yield the predicted rate
constants at various temperatures. This test job takes roughly 3 hours on
an SGI Octane 2 computer running under the Irix 6.5 operating system.
(Test Job 2 is a shorter test run.)
6.1.A. Input files
The cr01.inp file contains the CHARMM input stream for a direct
dynamics calculation of the chorismate to prephenate rearrangement
reaction. Similar calculations can be carried out for the substrate in the
enzyme active site, provided that appropriate boundary conditions are set
up in he CHARMM input.
The charmm22.top and charmm22.par files are the CHARMM topology and
parameter files. They are required for all CHARMM calculations.
Three coordinate files are provided for this test job, corresponding
to the initial guess coordinates for the reactant (gs.crd), product
(prod.crd), and transition state (ts.crd) for the dynamics calculation
with POLYRATE.
6.1.B. Description of the CHARMM input stream
The majority of the CHARMM commands are straightforward. The three
initial guess coordinate files must be opened as formatted files in the
FORTRAN unit numbers are default file choices in POLYRATE. Therefore,
these numbers should not be used in the CHARMM input file unless the
POLYRATE defaults are changed. Please consult the POLYRATE documentation
for a full list and description of these files.
Five (5) FORTRAN files will be used by POLYRATE to write out the
computational results. They are files with unit numbers 14, 25, 26, 27,
and 61, which should be opened in the CHARMM input stream before
Section 6.1.C summarizes the contents of these files.
All input instructions immediately following the POLYrate command are
those of POLYRATE. A full description of these commands can be found in
the POLYRATE documentation.
6.1.C. Description of CHARMMRATE output
cr0114.out - computed reaction rates at various temperatures using
the TST and CVT methods.
cr0125.out - potential energy along the reaction coordinate s, which
measures distance along the minimum energy path (MEP), and computed
transmission coefficient, if requested. Since the test run is for a CVT
calculation, no multidimensional tunneling is included in the test run.
cr0126.out - computed vibrational frequencies that hgave been
requested for printing out along s.
cr0127.out - coordinates along s.
cr0161.out - optimized geometries, energies, vibrational frequencies
and the Hessian for the reactant, product, and transition state.
6.2. Test Job 2 - Geometry optimization of chorismate in a water bath
This test job performs geometry optimization of chorismate in the
presence of a frozen water bath, arbitrarily taken from the trajectory of
a molecular dynamics simulation of chorismate in water.
The cr02.inp file is the CHARMM input stream command file. In
addition to the CHARMM topology and parameter files, the cr02.crd file is
required; it contains the instantaneous (initial) coordinates of
chorismate in water from a molecular dynamics simulation.
The file optcr02.crd contains the optimized coordinates of chorismate
in water.