[ term-vw | term14 | term-hb | term-to | term-el | term-sf | term-en | term-af | term-bs | term-cn | term-ss | term-tz | term-ts | term-rs | term-dc | term-xr | term-gc | term-gh | term-gs | term-ge | term-gb | term-gp | term-mf ]
The energy function calculated for any conformation of an ICM molecular
object consists of individual terms described in this section. For most of them
ICM calculates analytical derivatives which use gradient
minimization. The terms can be switched on and off with the
set terms [only] "xx,yy,.." command, e.g.
set terms "el" # activate electrostatic term
set terms only "vw,14" # reactivate only "vw" and "14" terms
Existing terms are returned in s_out after the show term command, or returned
by the Info (term) function.
The following commands also understand shortcuts for groups of energy terms:
The list of shortcuts:
- "energy","ecepp","ecep","ey" is equivalent to "vw,14,to,hb,el,ss"
- "map" or "mp" returns a set of terms according to the existing maps. If a map with a suitable system name is found, the terms is activated (see also Info (map) ).
The following map names trigger the corresponding term activation: "m_gh","m_gc","m_gb","m_ge","m_gs","m_g1",..,"m_g5"
- "mmff" is equivalent to "bs,bb,af,vw,14,to,hb,el,ss"
van der Waals ("vw")
nonbonded interatomic pairwise interactions
(1-5 and further, i.e. two atoms separated by more than 3 covalent bonds).
If not for tests, this terms should
always be used with the "14" energy term which considers 1-4 interactions.
The ECEPP/3 force field is used.
Parameters are specified in the icm.vwt file and are taken from Momany et al., 1975.
Both the usual 6-12 term and a soft van der Waals terms are available.
See also: vwMethod, vwSoftMaxEnergy, vwCutoff .
1-4 van der Waals ("14")
A part of the total van der Waals energy for atoms separated by exactly
three covalent bonds.
Repulsion for 1-4 pairs is cut in half according to the ECEPP energy function.
This term is complementary to the "vw" term and is usually used with the "vw" energy term.
Hydrogen bonding energy ("hb")
A different form of the "vw" term (10-12 instead of 6-12 for "vw") for
hydrogen bonding donors and acceptors as specified in icm.cod and icm.hbt files.
Parameters are taken from Momany et al., 1975.
The electrostatic contribution to a given hydrogen bond is not included in "hb" and
is calculated as part of the electrostatic energy.
The cutoff distance for hydrogen bonding interactions is controlled
by the hbCutoff parameter.
Torsion energy ("to")
dihedral angle deformation energy K*(1+-cos(n*Phi)). The parameters K, sign
and n are given in icm.tot file.
Parameters are taken from Momany et al., 1975,
Electrostatic energy ("el") This term is calculated in four different ways depending on the value of
electroMethod preference.
If electroMethod="boundary element" the
solvation component is in r_out and the envelope surface area in r_2out .
A special case: if the van der Waals energy is calculated with the
vwMethod ="soft" , the electrostatic energy will be automatically
buffered to avoid singularities. You will see that the electrostatic term "el"
changes upon switching from vwMethod=1 to vwMethod=2 .
The buffering artifically increases the distance between two charged atoms
to avoid having negative energy values better than the van der Waals repulsion
and, therefore, will prevents collapse of oppositely charged atoms.
-
A simple electrostatic energy ( electroMethod="Coulomb").
The Coulomb law is used to evaluate the energy. The
dielectric constant
is constant.
-
the distance dependent electrostatics (
electroMethod="distance dependent" ; currentDielConst = dielConst * DISTANCEij )
Advantage: this term has analytical derivatives and can be used in
local energy minization.
-
A better electrostatic free energy ( electroMethod="MIMEL"),
uses the
Modified IMage ELectrostatics
approximation (
Abagyan and Totrov, 1994
) to evaluate both the internal Coulombic energy and electrostatic
polarization free energy. Disadvantage: this term has no analytical
derivatives and has no effect on local energy minimization. It can be
a part of the energy function in global optimization such as montecarlo
or ssearch .
The solvation component is stored separately in r_out .
REBEL provides a more accurate evaluation
of the electrostatic solvation energy. For small molecules, use
mimelDepth = 0.3 (default 0.5 ).
-
The most accurate electrostatic free energy:
( electroMethod="boundary element" )
which uses so called boundary element method
to solve the Poisson equation to calculated a electrostatic free energy of a protein
surrounded by a continuous aqueous solution.
In addition to the total energy, one can extract the two components:
the electrostatic solvation energy from
r_out , and the Coulomb energy can be calculated
as a difference between the total electrostatic energy and r_out.
Surface term ("sf"). Map m_ga
Surface energy is based on atomic solvent-accessible surfaces.
Depending on the surfaceMethod preference this term is either a surface tension which
is evaluated as a product of the total solvent accessible area by the
surfaceTension parameter (currently 0.012 kcal/mole/A2 )
or is a product of atomic accessibilities by the atomic
energy density parameters similar to those proposed by
Wesson and Eisenberg (1992) (check icm.hdt file).
The "sf" term is evaluated at each Monte Carlo or systematic search step,
but not during local minimization (we do not calculate analytical energy
derivatives).
The atomic accessible surfaces are calculated using a faster
modification of the Shrake and Rupley, (1973) algorithm.
This algorithm analyzes all atom neighbors for each atom and
Sometimes a part of molecular system is represented with the grid energy terms
( "gc","gh" ) rather than by explicit atoms. In this case
the atomic accessibilities need to be corrected.
This correction can be introduced with a special map, called m_ga
which stores implicit neighbor information from the parts represented
with the grid potentials.
The m_ga map is calculated with the make map potential "sf" ..
command (see the make map potential command),
along with other grid maps.
The surface term can be weighted with the sfWeight parameter.
Entropic free energy term (conformational entropy of side-chains) ("en")
Configurational entropy of side-chains is evaluated on the basis of
their maximal possible entropy which is read from the residue library.
Note that this term is calculated at room temperature (300 K), so that the
ICM-shell variable
temperature
does not affect the entropic contribution (see
Abagyan and Totrov, 1994
for values) and solvent-accessible area of a side-chain.
Phase angle bending term ("af")
Harmonic term U*(f1-f0)2. Parameters U and f0 are taken from
icm.bbt file. Sometimes referred to as improper torsion.
Bond stretching energy ("bs")
Harmonic term U*(b1-b0)2. Parameters U and b0 taken from icm.bst file.
Distance restraints ("cn") a penalty term restraining two atoms to a certain distance range.
The shape of the potential is soft square well with lower and upper
bounds.
This term may be used to determine three-dimensional structure
from a set of interproton distances (NOEs) resulting from NMR experiments.
There are local and global distance restraints (drestraints).
Local restraints become weaker and vanish as the distance grows
(similar to the van der Waals forces),
while global restraints become stronger
as you deviate further from the required distance range.
See also files: icm.cnt and icm.cn .
Disulfide bonds and covalent bridges ("ss")
a penalty term establishing the additional (extra-tree) covalent bridges.
Currently there are three types of covalent bridges: disulfide bonds, peptide bonds and
thioester bonds.
In each case several distance constraints are imposed to enforce the correct covalent
geometry. The constraints for the disulfide bonds include Sg1-Sg2, Sg1-Cb2, Sg2-Cb1, Cb1-Cb2
atom pairs. The extra CO-NH bond involves C-N, C-H, O-N and O-H constraints.
Similarly, CO-SH bond involves C-S, C-H, O-C, O-H, C-C and O-H constraints.
The functional form of this penalty term is identical to local
distance restraints.
The disulfide SS bonds are automatically formed when you load the object.
The disulfide bonds may be LOCAL, i.e. when two sulfur atoms feel each other ONLY at small
distances.
See also:
icm.cnt, disulfide bond, make disulfide bond,
make peptide bond, delete disulfide bond,
delete peptide bond.
Tethers ("tz")
Quadratic restraint E= tzWeight *Distance2
between atoms in the current object and static atoms in a different
object (as opposed to distance restraints "cn" between atoms
in the same object). The target value of the distance is zero.
See also: read pdb, set tether, term ts , and tether .
Tethers to Self ("ts")
Term "ts" is used in minimization to temporarily
tether the atoms specified in the selftether= as_ argument of the minimize or montecarlo
command to their initial coordinates. The advantage of this term that
you do not need to have any other objects. To self-tether a fraction of atoms, use the
selftether= as_ option of the minimize command.
Example:
build string "lys"
randomize v_//x*
minimize "vw,to,ts" selftether=a_//ca,c,n
See also: TOOLS.tsWeight , TOOLS.tsToleranceRadius , term tz , set selftether, delete selftether , selftether
Multidimensional variable restraints ("rs")
Energy associated with multidimensional ellipsoidal attraction zones
(in which dimension they look like soft square wells with flat bottom)
in a hyperspace of internal variables (e.g. preferred side-chain or backbone
torsion angles). Vrestraints are defined in
icm.rst and
icm.rs files and are earmarked to be used in energy
calculations (as opposed as for the BPMC) with the rse field
(as opposed to rs ).
Use
set vrestraint energy
command to assign vrestraints. Described in
Abagyan, Totrov and Kuznetsov, 1994
(pp. 494,495).
Density correlation ("dc")
Penalty function associated with correlation between the static
map ( the current map is used by default )
and a virtual map generated from atomic positions on the fly.
The dcMethod preference allows you to choose between several
different functional forms of this term:
DC = 1 - Sum( Di - < D > )( Ai - < A > )/( N * Rmsd( D )*Rmsd( A ))
and
DC = 1 - Sum( Di - < D > )( Ai - < A > )/ N
where Di is the map value, and Ai is the density generated
dynamically from atomic positions.
The term has analytical derivatives with respect to the
internal coordinates and can be efficiently locally minimized.
By adding this term one can combine energy minimization with the real space
fitting into electron density.
A more detailed description can be found in the dcMethod section.
Crystallographic correlation between Fobs and Fcalc ("xr")
van der Waals grid potential for carbon probe ("gc")
van der Waals interaction between explicit non-hydrogen atoms of an ICM object and a
van der Waals potential calculated on the grid.
To calculate this term one needs an ICM object and map named m_gc which is calculated
with make map potential "gc" .. .
The calculation also counts the number of atoms in the area with Evw > 0.8 * GRID.maxVw and
stores this number in r_2out .
By default the make map potential "gc" command will create two maps: m_gc map for a carbon probe,
and m_gl map for atoms with the van der Vaals radius larger than 1.8 (e.g. sulphur or phosphorus).
With the "gc" term on both maps will be used.
Note that these two maps, m_gc and m_gl are very similar, but one is calculated for a carbon like
probe, while the other for a sulphur-like probe and, therefore, is an inflated version of the m_gc map.
van der Waals grid potential for hydrogen probe ("gh")
hydrophobic potential ("gs")
electrostatic grid potential ("ge")
Calculates the electrostatic potential contribution from the
atoms specified in the
make map potential as_ command.
The contributions are calculated by the Coulomb formula with
distance dependent-dielectric constant ( 4*Dij )
hydrogen bonding grid potential ("gb")
property grid potential ("gp").an atom property term that can carry up to 7 different
grid maps. The grid maps are generated with the make map potential "gp" command and are controlled by the GRID.gpGaussianRadius parameter. The atom type projection is defined by
the set type property command.
The relative weight of each map of the gp term (g1,g2,...) is controlled by the gpWeights parameters.
Potential of mean force ( "mf" and pmf )
Note that term name is "mf", while icm keyword for some commands is pmf
The mean-force "mf" potential was designed as a generic energy term
which is calculated for pairs of atoms according to their pmf-types
and inter-atomic distances. The definitions of the pmf-types and
energy-distance dependencies for each contributing pair of atom types
can be loaded from a .pmf pmf-file.
To read this file use the following command.
read pmf "icm.pmf" # or any other mf-file
The list of pmf-interacting pairs is calculated dynamically
and only the pairs at smaller that vwCutoff threshold distance are considered.
Note: It is important that vwCutoff = 9.5 is used in binding score
evaluation.
There is a preference called mfMethod which controls if the
atoms in the same molecule can interract.
By default only intermolecular pairs of atoms are considered ( mfMethod = 1 ).
Switching mfMethod to 2 (or "all") allows to include all atomic
pairs regardless of which molecule they belong to
in the "mf" term calculation.
Since this term is quite general one can prepare different pmf-parameter files
for solving different problems. The default file icm.pmf has been derived
from receptor-ligand complexes and allows pmf-scoring of docked ligands.
Another file: ident.pmf was designed to specify attraction of the same
atom types and allows to solve a problem of chemical superposition.
The relative weight of the pmf-term is controlled by the mfWeight parameter.
An example in which we evaluate a binding score:
read object "rec"
read object "anwers1"
move a_2. a_1.
vwCutoff = 9.5
mfMethod = 1
show energy "mf" a_1 a_2
e = Energy("mf")
An example in which flexible superposition of two molecules is performed:
build string "his ; gly trp" # two molecules
read pmf "ident.pmf"
fix v_//omg
display
superimpose a_1 a_2
vwCutoff = 2. # mf uses vwCutoff to calculate lists
montecarlo "mf" v_2//?vt* | v_//!?vt* # internal variables + positional for the second molecule
See also: mfMethod , pmf-file, mfWeight .