ICM Manual v.3.8
by Ruben Abagyan,Eugene Raush and Max Totrov
Copyright © 2018, Molsoft LLC
Jan 4 2018

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Energy and Penalty Terms

[ term-vw | term14 | term-hb | term-to | term-el | term-sf | term-en | term-af | term-bb | 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.
  1. A simple electrostatic energy ( electroMethod="Coulomb"). The Coulomb law is used to evaluate the energy. The dielectric constant is constant.
  2. the distance dependent electrostatics ( electroMethod="distance dependent" ; currentDielConst = dielConst * DISTANCEij ) Advantage: this term has analytical derivatives and can be used in local energy minization.
  3. 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 ).
  4. 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 where the surfaceAccuracy parameter defines the resolution. 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 and is affected by the surfaceAccuracy parameter (set it to 5 for higher accuracy).
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 angle bending term ("bb")
This term is defined for the 'mmff' and icmff' force fields only. It is a harmonic term U*(a1-a0)2 or a skewed term depending on the force field. Parameters U and a0 are taken from icm.bbt file.
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.


  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. Term "gc" depends on the following system variables:

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. Term "gp" represents seven maps:

  • g1 : hydrogen bond donor field
  • g2 : hydrogen bond acceptor field
  • g3 : sp2 hybridization field
  • g4 : lipophilicity field
  • g5 : large-size atom field
  • g6 : positive and negative charge
  • g7 : electronegativity/electropositivity field

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 one 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 one 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 
 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 .


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