# Native contacts analysis — pmda.contacts¶

This module contains classes to analyze native contacts Q over a trajectory. Native contacts of a conformation are contacts that exist in a reference structure and in the conformation. Contacts in the reference structure are always defined as being closer then a distance radius. The fraction of native contacts for a conformation can be calculated in different ways. This module supports 3 different metrics listed below, as well as custom metrics.

1. Hard Cut: To count as a contact the atoms i and j have to be at least as close as in the reference structure.

2. Soft Cut: The atom pair i and j is assigned based on a soft potential that is 1 if the distance is 0, 1/2 if the distance is the same as in the reference and 0 for large distances. For the exact definition of the potential and parameters have a look at function soft_cut_q().

3. Radius Cut: To count as a contact the atoms i and j cannot be further apart than some distance radius.

The “fraction of native contacts” Q(t) is a number between 0 and 1 and calculated as the total number of native contacts for a given time frame divided by the total number of contacts in the reference structure.

## Examples for contact analysis¶

### One-dimensional contact analysis¶

As an example we analyze the opening (“unzipping”) of salt bridges when the AdK enzyme opens up; this is one of the example trajectories in MDAnalysis.

import MDAnalysis as mda
from pmda import contacts
from MDAnalysis.tests.datafiles import PSF,DCD
import matplotlib.pyplot as plt
# example trajectory (transition of AdK from closed to open)
u = mda.Universe(PSF,DCD)
# crude definition of salt bridges as contacts between NH/NZ in ARG/LYS and
# OE*/OD* in ASP/GLU. You might want to think a little bit harder about the
# problem before using this for real work.
sel_basic = "(resname ARG LYS) and (name NH* NZ)"
sel_acidic = "(resname ASP GLU) and (name OE* OD*)"
# reference groups (first frame of the trajectory, but you could also use a
# separate PDB, eg crystal structure)
acidic = u.select_atoms(sel_acidic)
basic = u.select_atoms(sel_basic)
# set up analysis of native contacts ("salt bridges"); salt bridges have a
# distance <6 A
ca1 = contacts.Contacts(mobiles=(acidic, basic),
refs=(acidic, basic),
# analyze trajectory and perform analysis of "native contacts" Q
ca1.run(n_jobs=-1)
# print number of averave contacts
average_contacts = np.mean(ca1.timeseries[:, 1])
print('average contacts = {}'.format(average_contacts))
# plot time series q(t)
f, ax = plt.subplots()
ax.plot(ca1.timeseries[:, 0], ca1.timeseries[:, 1])
ax.set(xlabel='frame', ylabel='fraction of native contacts',
title='Native Contacts, average = {:.2f}'.format(average_contacts))
fig.show()


The first graph shows that when AdK opens, about 20% of the salt bridges that existed in the closed state disappear when the enzyme opens. They open in a step-wise fashion (made more clear by the movie AdK_zipper_cartoon.avi).

Notes

Suggested cutoff distances for different simulations

• For all-atom simulations, cutoff = 4.5 Å

• For coarse-grained simulations, cutoff = 6.0 Å

### Two-dimensional contact analysis (q1-q2)¶

Analyze a single DIMS transition of AdK between its closed and open conformation and plot the trajectory projected on q1-q2 [Franklin2007]

import MDAnalysis as mda
from pmda import contacts
from MDAnalysisTests.datafiles import PSF, DCD
u = mda.Universe(PSF, DCD)
q1q2.run()

f, ax = plt.subplots(1, 2, figsize=plt.figaspect(0.5))
ax[0].plot(q1q2.timeseries[:, 0], q1q2.timeseries[:, 1], label='q1')
ax[0].plot(q1q2.timeseries[:, 0], q1q2.timeseries[:, 2], label='q2')
ax[0].legend(loc='best')
ax[1].plot(q1q2.timeseries[:, 1], q1q2.timeseries[:, 2], '.-')
f.show()


Compare the resulting pathway to the MinActionPath result for AdK [Franklin2007].

### Writing your own contact analysis¶

The Contacts class has been designed to be extensible for your own analysis. As an example we will analyze when the acidic and basic groups of AdK are in contact which each other; this means that at least one of the contacts formed in the reference is closer than 2.5 Å.

For this we define a new function to determine if any contact is closer than 2.5 Å; this function must implement the API prescribed by Contacts:

def is_any_closer(r, r0, dist=2.5):
return np.any(r < dist)


The first two parameters r and r0 are provided by Contacts when it calls is_any_closer() while the others can be passed as keyword args using the kwargs parameter in Contacts.

Next we are creating an instance of the Contacts class and use the is_any_closer() function as an argument to method and run the analysis:

# crude definition of salt bridges as contacts between NH/NZ in ARG/LYS and
# OE*/OD* in ASP/GLU. You might want to think a little bit harder about the
# problem before using this for real work.
sel_basic = "(resname ARG LYS) and (name NH* NZ)"
sel_acidic = "(resname ASP GLU) and (name OE* OD*)"

# reference groups (first frame of the trajectory, but you could also use a
# separate PDB, eg crystal structure)
acidic = u.select_atoms(sel_acidic)
basic = u.select_atoms(sel_basic)

nc = contacts.Contacts(mobiles=(acidic, basic), refs=(acidic, basic)
method=is_any_closer,
kwargs={'dist': 2.5}).run(n_jobs=-1)

bound = nc.timeseries[:, 1]
frames = nc.timeseries[:, 0]

f, ax = plt.subplots()

ax.plot(frames, bound, '.')
ax.set(xlabel='frame', ylabel='is Bound',
ylim=(-0.1, 1.1))

f.show()


## Functions¶

pmda.contacts.q1q2(atomgroup, radius=4.5)[source]

Perform a q1-q2 analysis.

Compares native contacts between the starting structure and final structure of a trajectory [Franklin2007].

Parameters
• atomgroup (mda.core.groups.AtomGroup) – atomgroup to analyze

• radius (float, optional) – distance at which contact is formed

Returns

contacts – Contact Analysis that is set up for a q1-q2 analysis

Return type

Contacts

References

Franklin2007(1,2,3)

Franklin, J., Koehl, P., Doniach, S., & Delarue, M. (2007). MinActionPath: Maximum likelihood trajectory for large-scale structural transitions in a coarse-grained locally harmonic energy landscape. Nucleic Acids Research, 35(SUPPL.2), 477–482. doi: 10.1093/nar/gkm342

## Classes¶

class pmda.contacts.Contacts(mobiles, refs, method='hard_cut', radius=4.5, kwargs=None)[source]

Calculate contacts based observables.

The standard methods used in this class calculate the fraction of native contacts Q from a trajectory.

By defining your own method it is possible to calculate other observables that only depend on the distances and a possible reference distance. The Contact API prescribes that this method must be a function with call signature func(r, r0, **kwargs) and must be provided in the keyword argument method.

timeseries

list containing Q for all refgroup pairs and analyzed frames

Type

list

Parameters
• mobiles (tuple(AtomGroup, AtomGroup)) – two contacting groups that change over time

• refs (tuple(AtomGroup, AtomGroup)) – two contacting atomgroups in their reference conformation. This can also be a list of tuples containing different atom groups

• radius (float, optional (4.5 Angstroms)) – radius within which contacts exist in refgroup

• method (string | callable (optional)) – Can either be one of ['hard_cut' , 'soft_cut'] or a callable with call signature func(r, r0, **kwargs) (the “Contacts API”).

• kwargs (dict, optional) – dictionary of additional kwargs passed to method. Check respective functions for reasonable values.

readonly_attributes()

Set the attributes of this class to be read only

Useful to avoid the class being modified when passing it around.

To be used as a context manager:

with analysis.readonly_attributes():
some_function(analysis)

run(start=None, stop=None, step=None, n_jobs=1, n_blocks=None)

Perform the calculation

Parameters
• start (int, optional) – start frame of analysis

• stop (int, optional) – stop frame of analysis

• step (int, optional) – number of frames to skip between each analysed frame

• n_jobs (int, optional) – number of jobs to start, if -1 use number of logical cpu cores. This argument will be ignored when the distributed scheduler is used

• n_blocks (int, optional) – number of blocks to divide trajectory into. If None set equal to n_jobs or number of available workers in scheduler.