Tutorial #5: Building Complex Contact Schemas#

In this tutorial, we’ll explore how to build complex contact representations in prolint2, allowing you to create intricate contact schemas for in-depth analysis of lipid-protein interactions in your molecular dynamics simulations.

Prerequisites#

Ensure you have prolint2 installed in your Python environment.

from prolint2 import Universe
from prolint2.sampledata import GIRKDataSample

GIRK = GIRKDataSample()
u = Universe(GIRK.coordinates, GIRK.trajectory)
u.normalize_by = 'actual_time'  # Choose your preferred normalization method

Overview of Complex Contact Schemas#

prolint2’s modular design allows you to create complex contact schemas by combining contact representations computed at different cutoff values. We will demonstrate how to achieve this, showcasing its power and flexibility.

Compute Contacts at Different Cutoffs#

Let’s start by computing contact representations at three different cutoff values, c1, c2, and c3.

c1 = u.compute_contacts(cutoff=6)
c2 = u.compute_contacts(cutoff=7)
c3 = u.compute_contacts(cutoff=8)

These contact representations will serve as our building blocks for constructing the contact schemas.

Using Double Cutoffs#

We can use a double cutoff as a damping layer to measure contact durations more accurately. This is done by taking the intersection of two contact representations, c1 and c2.

c3 = c1.intersection(c2)

The result, c3, represents the contacts that exist in both c1 and c2. This intuitive approach allows you to build complex contact schemas effortlessly.

Understanding the Logic#

The logic behind this approach is straightforward. When dealing with radial cutoffs, you can think of it as a subset relationship. In other words, if c1 represents contacts with a smaller cutoff, it is a subset of c2, which represents contacts with a larger cutoff. Here’s a quick summary of set operations based on this relationship:

  • Union (\(c1 \cup c2\)): All elements of c1 are already present in c2, so the union results in c2.

  • Intersection (\(c1 \cap c2\)): All elements of c1 are present in c2, so the intersection includes all elements of c1.

  • Difference (\(c2 - c1\)): This is the set of elements that are in c2 but not in c1, representing elements unique to c2.

  • Difference (\(c1 - c\)): This results in the empty set (\(\emptyset\)), as all elements of c1 are present in c2.

  • Symmetric Difference (\(c1 \bigtriangleup c2\)): This is equivalent to the difference (\(c2 - c1\)), as it includes elements unique to c2.

Constructing More Complex Schemas#

You can use the same approach to create contact schemas with more cutoffs. For example, to analyze how contacts with different lipids change with the cutoff, you can combine multiple cutoffs.

_ = c1 + c2  # Double cutoff
_ = c1 + c2 + c3  # Triple cutoff
_ = c1 + c2 + c3 + c4  # Quadruple cutoff
_ = c1 + c2 + c3 + c4 + c5  # Quintuple cutoff

This way, you can explore how the contacts with different lipids evolve as you adjust the cutoff value.

Annular Shell Contacts#

Conversely, you can construct contact schemas that resemble a donut shape. This is useful for studying annular lipids, a critical concept in lipid-protein interactions. To do this, you subtract the core contacts from the shell contacts.

annular_shell = c2 - c1  # or c2.difference(c1)

This analysis allows you to investigate the annular lipids surrounding the protein as a function of the cutoff. You can apply this logic to multiple shells to create more intricate schemas.

first_shell = c2 - c1  # or c2.difference(c1)
second_shell = c3 - c2  # or c3.difference(c2)
third_shell = c4 - c3  # or c4.difference(c3)
fourth_shell = c5 - c4  # or c5.difference(c4)

By combining and subtracting different contact representations, you can create complex contact schemas tailored to your specific analysis needs.