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3.3
Sampling Dihedral Angles
The torsion sampler is the basic object used to sample the backbone torsion
angles phi and psi. It can be used to calculate the probability distributions
of backbone torsion angles from structures and save them, as well as loading
distributions and drawing from them.
It uses distributions specific for triplets of residues, so that when drawing
a phi/psi pair for a certain residue, the distribution from which the pair is
drawn also depends on the identity of the residues before and after the residue
in question.
The distributions of the sampler are internally stored in a vector, so that
most methods which need to access a specific distribution can either take 3
residue names or an index as input.
As a showcase example, we randomly sample from a given torsion sample and
store the resulting samples as a scatter plot:
from promod3 import loop
from ost import conop
# this requires matplotlib and numpy
import matplotlib
# change next line, if you wish to use a GUIbased plotoutput
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np
# load a default sampler
t_sampler = loop.LoadTorsionSampler()
# dihedral angles will be stored in here
phi = list()
psi = list()
# draw from a random distribution
for i in range(1000):
dihedral_pair = t_sampler.Draw(conop.ALA,
conop.PRO,
conop.ALA)
phi.append(dihedral_pair[0])
psi.append(dihedral_pair[1])
# and plot it
plt.xlim(np.pi, np.pi)
plt.ylim(np.pi, np.pi)
plt.plot(phi, psi, '.')
plt.xlabel("phi", fontsize='large')
plt.ylabel("psi", fontsize='large')
plt.title("ALAPROALA")
# store plot as png file
plt.savefig("torsion_plot.png")
Defining Amino Acid triplets
Since the torsion sampler considers triplets of amino acids, we need to define
them. This is done with the so called torsion group definitions.
Three strings represent the according positions of the consecutive
amino acids. They are combined by “”. It is either possible to
use the keyword “all”, or write out all allowed amino acids by their
three letter code and separate them by ”,”. An example would be: “all
VAL,ILEPRO”. There are cases where a tripeptide can match several
group definitions. The list of group definitions is iterated for every
combination of three consecutive amino acids and the first hit is
decisive.
The Torsion Sampler Class

class
promod3.loop. TorsionSampler (group_definitions, bins_per_dimension, seed)
Basic object used to sample the backbone torsion angles phi and psi.
Parameters: 
 group_definitions (
list of str ) – List of group definitions defining amino acid triplets
 bins_per_dimension – Number of bins to represent the 360 degrees of each
torsion angle
 seed (
int ) – Seed for random number generator

Raises:  RuntimeException when there is a
possible combination of the 20 standard amino
acids not matching any of the group definitions.

Extracts backbone torsion angles from the structure and adds them to the appropriate histograms in the sampler.

UpdateDistributions ()
Recalculates the probability distributions from the histograms.

static
Load (filename, seed)

static
LoadPortable (filename, seed)
Loads raw binary file generated with Save() (optimized for fast
reading) / portable file generated with SavePortable() (slower but
less machinedependent).
Parameters: 
 filename (
str ) – Path to the file from which to load the sampler.
 seed (
int ) – Seed for random number generator (not saved in file).

Returns:  A torsion sampler

Return type:  TorsionSampler

Raises:  RuntimeError if file cannot be opened or if
file cannot be parsed (see here for details).


Save (filename)

SavePortable (filename)
Saves a raw / portable binary representation. Use portable files for
distribution and convert locally to raw files. See here
for details.
Parameters:  filename (str ) – Path to the file where the sampler will be saved 
Raises:  RuntimeError if file cannot be opened. 

GetHistogramIndex (before, central, after)
Parameters: 

Returns:  The index of the histogram corresponding to the triplet of residues specified.


GetHistogramIndices (sequence)
Parameters:  sequence (str ) – Sequence of length n from which histogram indices
should created. 
Returns:  List of length n2 containing histogram indices of
all consecutive amino acid triplets in sequence 
Raises:  RuntimeError if sequence contains non
standard amino acid 

Draw (before, central, after)
Draws a pair of dihedral angles for the central residue from the distribution specific for such a triplet of residues.
Parameters: 

Returns:  A pair of phi/psi angles


Draw (index)
Draws a pair of dihedral angles from the distribution specified by the index.
Parameters:  index (int ) – The index of the distribution from which a phi/psi pair will be drawn. 
Returns:  A pair of phi/psi angles 

DrawPhiGivenPsi (before, central, after, psi)
Draws a phi angle for the central residue from the conditional distribution P( phi  psi ) specific for such a triplet of residues.
Parameters: 

Returns:  An angle


DrawPhiGivenPsi (index, psi)
Draws a phi angle from the conditional distribution P( phi  psi ) specified by the index.
Parameters: 
 index (
int ) – The index of the distribution from which a phi angle will be drawn.
 psi (
float ) – psi angle

Returns:  An angle


DrawPsiGivenPhi (before, central, after, phi)
Draws a phi angle for the central residue from the conditional distribution P( psi  phi ) specific for such a triplet of residues.
Parameters: 

Returns:  An angle


DrawPsiGivenPhi (index, phi)
Draws a phi angle from the conditional distribution P( psi  phi ) specified by the index.
Parameters: 
 index (
int ) – The index of the distribution from which a psi angle will be drawn.
 phi (
float ) – phi angle

Returns:  An angle


GetProbability (before, central, after, phi, psi)
Returns the probability of a specific pair of phi/psi angles for the central residue from the corresponding distribution.
Parameters: 

Returns:  A probability


GetProbability (index, phi, psi)
Returns the probability of a specific pair of phi/psi angles calulated from the distribution specified by index.
Parameters: 
 index (
int ) – The index of the distribution.
 phi (
float ) – phi angle
 psi (
float ) – psi angle

Returns:  A probability


GetPhiProbabilityGivenPsi (before, central, after, phi, psi)
Returns P( phi  psi ) for the central residue from the corresponding distribution.
Parameters: 

Returns:  A probability


GetPsiProbabilityGivenPhi (before, central, after, psi, phi)
Returns P( psi  phi ) for the central residue from the corresponding distribution.
Parameters: 

Returns:  A probability


GetPhiProbabilityGivenPsi (index, phi, psi)
Returns P( phi  psi ) for the central residue from the corresponding distribution.
Parameters: 
 index (
int ) – The index of the distribution.
 psi (
float ) – phi angle
 phi (
float ) – psi angle

Returns:  A probability


GetPsiProbabilityGivenPhi (index, psi, phi)
Returns P( psi  phi ) for the central residue from the corresponding distribution.
Parameters: 
 index (
int ) – The index of the distribution.
 psi (
float ) – phi angle
 phi (
float ) – psi angle

Returns:  A probability


GetBinsPerDimension ()
Returns the number of bins per dimension of the distributions.

GetBinSize ()
Returns the size of the bins (in radians) of the distributions.

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