LennardJonesKaranicolasBrooks

The LennardJonesKaranicolasBrooks potential is a modified version of the Lennard-Jones potential, introduced by Karanicolas and Brooks to model protein folding [Karanicolas2002]. It includes a well depth scaling factor that depends on the types of interacting residues.

\[U = \epsilon_{ij} \left[ 13\left(\frac{\sigma_{ij}}{r}\right)^{12} - 18\left(\frac{\sigma_{ij}}{r}\right)^{10} + 4\left(\frac{\sigma_{ij}}{r}\right)^6 \right]\]

where:

  • \(\epsilon_{ij}\) is the interaction energy between the particles

  • \(\sigma_{ij}\) is the distance at which the potential is zero

  • \(r\) is the distance between the particles

  • type: Bond2, LennardJonesKaranicolasBrooks

  • parameters: None

  • data:

    • id_i: int: Id of one particle

    • id_j: int: Id of the other particle

    • epsilon: real: Well depth \([energy]\)

    • sigma: real: Distance at which the potential is zero \([distance]\)

Example:

"ljKBBonds":{
  "type":["Bond2","LennardJonesKaranicolasBrooks"],
  "parameters":{},
  "labels":["name_i", "name_j", "epsilon", "sigma"],
  "data":[[0, 1, 1.0, 1.0],
          [1, 2, 0.8, 1.1]]
}

LennardJonesKaranicolasBrooksCommon_epsilon

LennardJonesKaranicolasBrooks bonds variant with a common well depth (epsilon) for all bonds.

  • type: Bond2, LennardJonesKaranicolasBrooksCommon_epsilon

  • parameters:

    • epsilon: real: Common well depth for all bonds \([energy]\)

  • data:

    • id_i: int: Id of one particle

    • id_j: int: Id of the other particle

    • sigma: real: Distance at which the potential is zero \([distance]\)

Example:

"ljKBBondsCommonEpsilon":{
  "type":["Bond2","LennardJonesKaranicolasBrooksCommon_epsilon"],
  "parameters":{"epsilon":1.0},
  "labels":["id_i", "id_j", "sigma"],
  "data":[[0, 1, 1.0],
          [1, 2, 1.1]]
}
[Karanicolas2002]

Karanicolas, John, and Charles L. Brooks III. “The origins of asymmetry in the folding transition states of protein L and protein G.” Protein Science 11, no. 10 (2002): 2351-2361.