Final Project: Sequence-Dependent Structure in Lennard-Jones Polymers Using OpenMM#

Bacgrkound and Motivation#

In many soft-matter and biological systems, the arrangement of interactions along a polymer chain—i.e., the sequence—has profound effects on its structure and function. This is especially important in:

  • Synthetic block copolymers (e.g., AB diblocks),

  • Intrinsically disordered proteins with patchy stickers/spacers,

  • Engineered self-assembling materials.

In this project, you’ll use OpenMM to simulate single polymers with different sequences of monomer types (A and B), which interact via Lennard-Jones potentials. You’ll explore how sequence patterning affects polymer compactness, shape, and dynamics.

Project Objective#

Simulate coarse-grained LJ polymers with two types of monomers (A and B), each with different pairwise attractions. Compare how different sequences (random, alternating, blocky, etc.) affect the polymer’s conformation and dynamics.

Tasks#

1. Set Up Polymer Model in OpenMM#

  • Build a linear polymer of \( N = 20\text{–}100 \) beads.

  • Assign each bead a type (A or B) based on a user-defined sequence.

  • Connect beads with harmonic bonds:

    CustomBondForce("0.5 * K * (r - r0)^2")

2. Define Nonbonded Interactions#

  • Use a CustomNonbondedForce or NonbondedForce to define Lennard-Jones interactions: $\( V(r) = 4\varepsilon_{ij} \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{\sigma}{r} \right)^6 \right] \)$

  • Choose interaction strengths:

    • \( \varepsilon_{AA} = 1.0 \)

    • \( \varepsilon_{BB} = 0.5 \)

    • \( \varepsilon_{AB} = 0.1 \) (weak attraction)

  • Ignore interactions between directly bonded neighbors (using an exclusion list).

Try Different Sequences#

Examples:

  • Homopolymer AAAAAA…

  • Alternating ABABAB…

  • Random AB

  • Block copolymer (e.g., 10 A’s followed by 10 B’s)

  • Patterned repeats (e.g., ABBA ABBA…)

4. Run Simulations#

  • Langevin dynamics at fixed temperature (e.g., \( T = 0.5 \), \( \gamma = 1.0 \))

  • Use implicit solvent (no cutoff)

  • Equilibrate and run for \( 10^5 \)–\( 10^6 \) steps

  • Save trajectories for analysis

5. Analyze Polymer Structure#

  • Measure radius of gyration \( R_g \)

  • Measure end-to-end distance

  • Visualize trajectories (e.g., using PyMol or nglview)

  • Plot \( R_g \) vs. sequence or interaction strength

Optional#

  • Compute contact maps from trajectory (binary contact matrix based on distance cutoff)

  • Compare collapse temperature for different sequences (simulate cooling)

  • Add angle/bending terms to make semiflexible chains

  • Simulate multiple polymers and study coacervation (condensate-like behavior)

Learning Goals**#

  • Understand how sequence encodes polymer structure

  • Practice building custom force fields in OpenMM

  • Learn basic trajectory analysis: \( R_g \), \( R_{ee} \), contact maps

  • Explore relationships between interactions, temperature, and collapse

Starter Parameters#

Parameter

Value

\( N \)

30–50

\( \sigma \)

1.0

\( \varepsilon_{AA} \)

1.0

\( \varepsilon_{BB} \)

0.5

\( \varepsilon_{AB} \)

0.1–0.3

Temperature \( T \)

0.5–1.0

Time step

0.01–0.02 ps