Detect Allosteric Coupling via Time-Lagged Cross Correlation (TLCC)

Overview and Methodology

What It Does

This script detects directional coupling between residue motions in molecular dynamics trajectories. It identifies delayed responses that suggest signal propagation, allosteric communication, or ligand-induced rearrangements.

How It Works

• Objective: Identify whether motion in one group of atoms precedes correlated motion in another, capturing direction and timing of influence.
• Process:
  • Extract Displacements: Computes time-dependent displacements of atom groups relative to a reference frame.
  • Run TLCC: Calculates time-lagged cross-correlations between residue groups to assess influence over time.
  • Determine Peak Influence: Measures the maximum correlation and corresponding lag where one group most strongly affects another.
  • Visualize:
    • Correlation heatmap (−1 to +1)
    • Lag time heatmap (in user-defined units)
    • Sankey diagram tracing directional pathways

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Configuration and Inputs

Prerequisites

• Requires a loaded trajectory.

Key Configuration Options

• Selections:

  • group_sel1, group_name1: Primary group (e.g., segid VSD, VSD).
  • group_sel2, group_name2: Optional secondary group (e.g., ligand, segid TOX, TOX).
  • If both groups are filled out, TLCC operates to detect allosteric coupling resulting from ligand (group 2) binding to receptor (group 1).
  • If group_sel2 is empty, TLCC operates in self-allosteric mode (within Selection 1).
  • distance_cutoff: Restricts Selection 1 to residues near Selection 2 (set to -1 to skip filtering).

• Atom Type:

  • 'CA': Use alpha-carbons only (recommended for proteins).
  • 'all': Use all atoms in a residue (for non-proteins or ligands).
  • 'CA for sel1 & all for sel2': Mixed mode ideal for ligand–protein interfaces.

• Resolution:

  • Group residues for analysis at a coarse level (e.g., resolution=2 = pairwise residue blocks).

• Correlation Filters:

  • correlation_threshold: Hide weak interactions below this value.
  • Only strictly one-way allosteric interactions are considered in pathway detection.

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Outputs

• Heatmaps:

  • *_TLCC_Max.png: Peak cross-correlation matrix (range −1 to +1).
  • *_TLCC_Lag.png: Matrix of lag times (in ns or custom time units) where these peaks occur.

• Sankey Diagram:

  • *_TLCC_Sankey.html: Interactive visualization of directional allosteric pathways.
  • Only pathways meeting the minimum correlation_threshold and lag are shown.

• CSV Files:

  • *_TLCC_Lag.csv: Lag matrix.
  • *_TLCC_Max.csv: Maximum correlation matrix.
  • *_TLCC_Pathways.csv: Summary of top directional pathways (if found).

• Terminal Logs:

  • Selection diagnostics, skipped groups, lag stats, and graph edges for debugging.

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Interpreting the Results

Correlation Heatmap

• +1: Strong directional synchronization.
• -1: Strong directional anti-correlation.
• 0: No influence.

These patterns indicate where information or conformational signals propagate over time.

Lag Time Heatmap

• 0 Lag: Immediate synchronization (e.g., rigid segments).
• > 0 Lag: Time-delayed influence, revealing causal directionality (A causes B to move).

Sankey Diagram

• Visual summary of allosteric signal flow.
• Pathways are ranked and filtered by correlation strength and delay.
• Edges are colored by origin node, showing signal propagation routes.

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Example Scenarios

Ligand–Receptor Allostery

• Scenario: Ligand binds to a voltage-sensor domain (VSD).
• Observation: Delayed influence from ligand residues to the gating machinery.
• Interpretation: Binding initiates allosteric signaling toward functional sites.

Internal Protein Coupling

• Scenario: Analyze intra-protein domain dynamics.
• Observation: One helix causes delayed motion in a loop region.
• Interpretation: Structural pathways mediate mechanical or dynamic coupling.

Receptor Signaling Chains

• Scenario: Multi-step propagation through structural elements.
• Observation: Ligand → Site A → Site B → Active site.
• Interpretation: Multi-hop allostery suggests regulatory architecture.

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How TLCC Differs from DCCM

Feature	DCCM	TLCC
Timing	Instantaneous	Time-delayed (uses lag analysis)
Matrix Type	Symmetric (e.g., A↔B = B↔A)	Asymmetric (A→B ≠ B→A if delay exists)
Captures Direction	No	Yes
Use Case	Detect global coordination	Detect signal propagation or time-lagged response
Interpretation	Who moves together	Who causes whom to move, and when

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Usage Tips

• One vs. Two Groups:

  • Use one group (group_sel2 blank) for internal allostery.
  • Use two groups for ligand–protein or domain–domain signaling.

• Performance:

  • 'CA' atom mode is fast and protein-specific.
  • 'all' atom mode is more flexible but memory-intensive.

• Path Filtering:

  • Use correlation_threshold (e.g., 0.5–0.7) to reduce noise.
  • Set min_path_length = 3 for longer cascade detection.

• Scaling Output:

  • Increase max_paths_to_show to explore alternative signaling routes.
  • Use path_sort_by = 'mean_corr' for tight correlations or 'total_lag' for slow signals.

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