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Fitting Loops Into Gaps
Loops often need to undergo conformational changes to fit into gaps defined by
stem residues. ProMod3 implements two algorithms performing this task:
In case of small gaps or small issues in the loop you might also consider the
BackboneRelaxer .
CCD
The ProMod3 implementation of the cyclic coordinate descent first superposes
the nstem of the input loop with the provided nstem positions. In every
iteration of the algorithm, we loop over all residues of the loop and find the
ideal phi/psi angles to minimize the RMSD between the cstem and the target
cstem positions. Iterations continue until a cstem RMSD threshold is reached
or the number of iterations hits a limit. By performing CCD, unfavorable
backbone dihedral pairs can be introduced. It is therefore optionally possible
to use torsion samplers to guide the iterative process. In this case, the
algorithm calculates the probability of observing the dihedral pair before and
after performing the phi/psi update. If the fraction after/before is smaller
than a uniform random number in the range [0,1[, the proposed dihedral pair gets
rejected. Please note, that this increases the probability of nonconvergence.

class
promod3.modelling. CCD
Class, that sets up everything you need to perform a particular loop closing
action.

CCD (sequence, n_stem, c_stem, torsion_sampler, max_steps, rmsd_cutoff, seed)
All runs with this CCD object will be with application of torsion samplers
to avoid moving into unfavourable regions of the backbone dihedrals.
Parameters: 
 sequence (
str ) – Sequence of the backbones to be closed
 n_stem (
ost.mol.ResidueHandle ) – Residue defining the n_stem.
If the residue before n_stem doesn’t exist, the
torsion sampler will use a default residue (ALA) and
and phi angle (1.0472) to evaluate the first angle.
 c_stem (
ost.mol.ResidueHandle ) – Residue defining the c_stem.
If the residue after c_stem doesn’t exist, the
torsion sampler will use a default residue (ALA) and
psi angle (0.7854) to evaluate the last angle.
 torsion_sampler (
TorsionSampler / list
of TorsionSampler ) – To extract probabilities for the analysis of the
backbone dihedrals. Either a list of torsion
samplers (one for for every residue of the loop to
be closed) or a single one (used for all residues).
 max_steps (
int ) – Maximal number of iterations
 rmsd_cutoff (
float ) – The algorithm stops as soon as the c_stem of the loop to
be closed has RMSD below the c_stem
 seed (
int ) – Seed of random number generator to decide whether new phi/psi pair
should be accepted.

Raises:  RuntimeError if a list of torsion samplers is
given with inconsistent length regarding the sequence. Another
requirement is that all backbone atoms of the stems must be
present.


CCD (n_stem, c_stem, max_steps, rmsd_cutoff)
All runs with this CCD object will be without application of torsion samplers.
This is faster but might lead to weird backbone dihedral pairs.
Parameters: 
 n_stem (
ost.mol.ResidueHandle ) – Residue defining the n_stem
 c_stem (
ost.mol.ResidueHandle ) – Residue defining the c_stem
 max_steps (
int ) – Maximal number of iterations
 rmsd_cutoff (
float ) – The algorithm stops as soon as the c_stem of the loop to
be closed has RMSD below the given c_stem


Close (bb_list)
Closes given bb_list with the settings set at initialization.
Parameters:  bb_list (BackboneList ) – Loop to be closed 
Returns:  Whether rmsd_cutoff has been reached 
Return type:  bool 
Raises:  RuntimeError if the CCD object has been
initialized with TorsionSampler support
and the length of the bb_list is not consistent with the initial
sequence. 
KIC
The kinematic closure leads to a fragmentation of the loop based on given
pivot residues. It then calculates possible relative orientations
of these fragments by considering constraints of bond length and bond angles
at these pivot residues. Due to the internal mathematical formalism, up to
16 solutions can be found for a given loop closing problem.

class
promod3.modelling. KIC
Class, that sets up everything you need to perform a particular loop closing
action.

KIC (n_stem, c_stem)
All runs of this KIC closing object will adapt the input loops to these
stem residues.
Parameters: 
 n_stem – Residue describing the stem towards n_ter
 c_stem – Residue describing the stem towards c_ter


Close (bb_list, pivot_one, pivot_two, pivot_three)
Applies KIC algorithm, so that the output loops match the given stem residues
Parameters: 
 bb_list (
BackboneList ) – Loop to be closed
 pivot_one (
int ) – Index of first pivot residue
 pivot_two (
int ) – Index of second pivot residue
 pivot_three (
int ) – Index of third pivot residue

Returns:  List of closed loops (maximum of 16 entries)

Return type:  list of BackboneList

Raises:  RuntimeError in case of invalid pivot indices.

Relaxing Backbones
In many cases one wants to quickly relax a loop. This can be useful to close
small gaps in the backbone or resolve the most severe clashes. The
BackboneRelaxer internally sets up a topology for the input loop.
Once setup, every loop of the same length and sequence can be relaxed by
the relaxer.

class
promod3.modelling. BackboneRelaxer (bb_list, ff, fix_nterm=True, fix_cterm=True)
Sets up a molecular mechanics topology for given bb_list. Every
BackboneList of same length and sequence can then be
relaxed. The parametrization is taken from ff, simply neglecting all
interactions to non backbone atoms. The electrostatics get neglected
completely by setting all charges to 0.0.
Parameters: 
 bb_list (
BackboneList ) – Basis for topology creation
 ff (
promod3.loop.ForcefieldLookup ) – Source for parametrization
 fix_nterm (
bool ) – Whether Nterminal backbone positions (N, CA, CB) should
be kept rigid during relaxation
(C and O are left to move).
 fix_cterm (
bool ) – Whether Cterminal backbone positions (CA, CB, C, O)
should be kept rigid during relaxation
(N is left to move).


class
promod3.modelling. BackboneRelaxer (bb_list, density, resolution, fix_nterm=True, fix_cterm=True)
Parameters: 
 bb_list (
BackboneList ) – Basis for topology creation
 fix_nterm (
bool ) – Whether Nterminal backbone positions (N, CA, CB) should
be kept rigid during relaxation.
 fix_cterm (
bool ) – Whether Cterminal backbone positions (CA, CB, C, O)
should be kept rigid during relaxation.

Raises:  RuntimeError if size of bb_list is below 2


Run (bb_list, steps=100, stop_criterion=0.01)
Performs steepest descent on given BackboneList. The function possibly fails
if there are particles (almost) on top of each other, resulting in NaN
positions in the OpenMM system. The positions of bb_list are not touched
in this case and the function returns an infinit potential energy.
In Python you can check for that with float(“inf”).
Parameters: 
 bb_list (
BackboneList ) – To be relaxed
 steps (
int ) – number of steepest descent steps
 stop_criterion (
float ) – If maximum force acting on a particle
falls below that threshold, the
relaxation aborts.

Returns:  Forcefield energy upon relaxation, infinity in case of OpenMM Error

Return type:  float

Raises:  RuntimeError if bb_list has not the same
size or sequence as the initial one.


AddNRestraint (idx, pos, force_constant=100000)
Adds harmonic position restraint for nitrogen atom at specified residue
Parameters: 
 idx (
int ) – Idx of residue
 pos (
ost.geom.Vec3 ) – Restraint Position (in Angstrom)
 force_constant (
float ) – Force constant in kJ/mol/nm^2

Raises:  RuntimeError if idx is too large


AddCARestraint (idx, pos, force_constant=100000)
Adds harmonic position restraint for CA atom at specified residue
Parameters: 
 idx (
int ) – Idx of residue
 pos (
ost.geom.Vec3 ) – Restraint Position (in Angstrom)
 force_constant (
float ) – Force constant in kJ/mol/nm^2

Raises:  RuntimeError if idx is too large


AddCBRestraint (idx, pos, force_constant=100000)
Adds harmonic position restraint for CB atom at specified residue,
doesn’t do anything if specified residue is a glycine
Parameters: 
 idx (
int ) – Idx of residue
 pos (
ost.geom.Vec3 ) – Restraint Position (in Angstrom)
 force_constant (
float ) – Force constant in kJ/mol/nm^2

Raises:  RuntimeError if idx is too large


AddCRestraint (idx, pos, force_constant=100000)
Adds harmonic position restraint for C atom at specified residue
Parameters: 
 idx (
int ) – Idx of residue
 pos (
ost.geom.Vec3 ) – Restraint Position (in Angstrom)
 force_constant (
float ) – Force constant in kJ/mol/nm^2

Raises:  RuntimeError if idx is too large


AddORestraint (idx, pos, force_constant=100000)
Adds harmonic position restraint for O atom at specified residue
Parameters: 
 idx (
int ) – Idx of residue
 pos (
ost.geom.Vec3 ) – Restraint Position (in Angstrom)
 force_constant (
float ) – Force constant in kJ/mol/nm^2

Raises:  RuntimeError if idx is too large


SetNonBondedCutoff (nonbonded_cutoff)
Defines cutoff to set for non bonded interactions. By default, all atom
pairs are compared which is the fastest for small backbones (e.g. in
CloseSmallDeletions() ). Otherwise, a cutoff around 5 is reasonable as
we ignore electrostatics.
Parameters:  nonbonded_cutoff (float ) – Cutoff to set for non bonded interactions. Negative
means no cutoff. 

GetNonBondedCutoff (nonbonded_cutoff)
Returns:  Cutoff for non bonded interactions. 
Return type:  float 
Relaxing All Atom Loops
After the reconstruction of loop sidechains with the
Reconstruct() method of
SidechainReconstructor , it may be desired to
quickly relax the loop. The AllAtomRelaxer class takes care of that.
Example usage:
from ost import io
from promod3 import modelling, loop
# load example (has res. numbering starting at 1)
prot = io.LoadPDB('data/1CRN.pdb')
res_list = prot.residues
seqres_str = ''.join([r.one_letter_code for r in res_list])
# initialize AllAtom environment and sidechain reconstructor
env = loop.AllAtomEnv(seqres_str)
env.SetInitialEnvironment(prot)
sc_rec = modelling.SidechainReconstructor()
sc_rec.AttachEnvironment(env)
# "reconstruct" subset (res. num. 6..10) > sidechains kept here
sc_result = sc_rec.Reconstruct(6, 5)
# setup sys creator
ff_lookup = loop.ForcefieldLookup.GetDefault()
mm_sys = loop.MmSystemCreator(ff_lookup)
relaxer = modelling.AllAtomRelaxer(sc_result, mm_sys)
# relax loop
pot_e = relaxer.Run(sc_result, 300, 0.1)
print("Potential energy after: %g" % pot_e)
# update environment with solution
env.SetEnvironment(sc_result.env_pos)
# store all positions of environment
io.SavePDB(env.GetAllAtomPositions().ToEntity(), 'aa_relax_test.pdb')

class
promod3.modelling. AllAtomRelaxer (sc_data, mm_system_creator)
Setup relaxer for a given sidechain reconstruction result and a given MM
system creator, which takes care of generating a simulation object.
N/C stems of loop are fixed if they are nonterminal.

Run (sc_data, steps=100, stop_criterion=0.01)
Performs steepest descent for this system and writes updated positions into
sc_data.env_pos.all_pos. The function possibly fails
if there are particles (almost) on top of each other, resulting in NaN
positions in the OpenMM system. The positions of sc_data.env_pos.all_pos
are not touched in this case and the function returns an infinit potential
energy. In Python you can check for that with float(“inf”).
Parameters: 
 sc_data (
SidechainReconstructionData ) – Sidechain reconstruction result to be updated
 steps (
int ) – Number of steepest descent steps
 stop_criterion (
float ) – If maximum force acting on a particle falls below
that threshold, the relaxation aborts.

Returns:  Potential energy after relaxation, infinity in case of OpenMM Error

Return type:  float

Raises:  RuntimeError if sc_data is incompatible with
the one given in the constructor.


UpdatePositions (sc_data)
Resets simulation positions to a new set of positions. It is assumed that
this sc_data object has the same amino acids as loops and surrounding and
the same disulfid bridges as the one given in the constructor.
Parameters:  sc_data (SidechainReconstructionData ) – Get new positions from sc_data.env_pos.all_pos 
Raises:  RuntimeError if sc_data is incompatible with
the one given in the constructor. 

GetSystemCreator ()
Returns:  MM system creator passed in the constructor 
Return type:  MmSystemCreator 

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