Membrane Bending and Deformation Mapping

Overview and Methodology

What It Does

This tool quantifies local membrane bending, curvature, and deformation caused by protein-lipid interactions during molecular dynamics simulations. By analyzing the z-position of lipid headgroup atoms across the membrane surface, it constructs curvature maps and leaflet height profiles to identify spatial distortions and bilayer asymmetry induced by embedded proteins.

How It Works

• Objective: Visualize bilayer shape deformation and quantify membrane curvature near protein surfaces.
• Process:
  • Leaflet Identification: Lipid headgroups are split into upper and lower leaflets based on their z-coordinates.
  • Grid Mapping: The membrane plane is divided into a grid centered on the protein. Heights of lipid headgroups are averaged within each grid cell.
  • Surface Smoothing: Gaussian smoothing reduces noise and clarifies curvature patterns.
  • Curvature Calculation: Mean curvature is computed as the height difference between smoothed upper and lower leaflets.
  • Protein Proximity Analysis: Regions near the protein (within a user-defined cutoff) are isolated to quantify localized deformation.
  • Time Modes:
    • Time-Averaged Mode: Aggregates membrane shape and curvature over all frames for a global view.
    • Per-Frame Mode: Captures dynamic changes and fluctuations over time.

---

Configuration and Inputs

Prerequisites

• A loaded trajectory containing both protein and lipid atoms.
• Headgroup atom (e.g., P) must be specified for surface detection.

Key Configuration Options

• Atom Selections:

  • protein_sel: Atom group defining the protein.
  • lipid_sel: Atom group for membrane lipids.
  • headgroup_atom: Atom name used to define leaflet surfaces (e.g., P).

• Curvature Grid and Smoothing:

  • grid_resolution: Defines xy-plane spacing for curvature mapping (Å).
  • smoothing_radius: Gaussian blur radius to smooth surface noise (Å).
  • proximity_cutoff: Radial distance cutoff (Å) for analyzing curvature near protein.

• Analysis Modes:

  • 'Time-Averaged': Aggregate curvature across frames.
  • 'Per-Frame': Time-series analysis with curvature map from final frame.

• Parallelization:

  • num_threads: Number of CPU threads used. -1 utilizes all available cores.

---

Output

• Time-Series Plot:

  • Displays curvature near the protein over time (Per-Frame mode only).

• 2D Heatmaps:

  • Mean Curvature Map: Highlights bilayer bending zones.
  • Upper/Lower Leaflet Height Maps: Show topography of each leaflet.

• 3D Surface Plot:

  • Interactive visualization of upper and lower membrane surfaces in 3D.
  • Includes protein silhouette overlay to highlight proximity-induced deformation.

• Console Output:

  • Reports progress, centroid position, selected frames, and analysis parameters.

---

Interpreting the Results

• Positive/Negative Curvature:

  • Positive values = bulging toward upper leaflet.
  • Negative values = invagination or thinning near the protein.

• Leaflet Asymmetry:

  • Greater disparity between upper and lower leaflet heights may reflect lipid sorting or tilt.

• Time-Resolved Fluctuations:

  • Curvature spikes in time-series data can indicate gating events or transient leaflet perturbations.

• Protein-Centered Mapping:

  • Centering on the protein enables consistent comparisons across time and between systems.

---

Example Scenarios

Detecting Localized Membrane Deformation

• Scenario: Evaluate how a transmembrane protein perturbs the surrounding lipid bilayer.
• Observation: Curvature maps show pronounced leaflet asymmetry and thinning adjacent to helices.
• Interpretation: Indicates protein-induced deformation zones, potentially linked to functional domains or gating interfaces.

Monitoring Gating-Linked Bilayer Changes

• Scenario: Analyze membrane shape during activation of a voltage-gated channel.
• Observation: Transient curvature spikes and leaflet height shifts occur in synchrony with gating helices.
• Interpretation: Suggests coupling between channel conformational change and lipid bilayer mechanics.

Assessing Curvature Sensing by Peripheral Proteins

• Scenario: Investigate an amphipathic helix interacting with the membrane surface.
• Observation: Positive mean curvature and upper leaflet elevation near the helix insertion site.
• Interpretation: Consistent with curvature sensing or scaffolding behavior, supporting proposed mechanism of membrane remodeling.

---

Usage Tips

• Headgroup Selection:

  • For phospholipids, use 'P' for phosphorus atoms or lipid-specific head atoms ('O21', 'O11').
  • Ensure atoms are present in both leaflets.

• Grid and Smoothing:

  • Use grid_resolution = 5 Å for balance between resolution and performance.
  • Increase smoothing_radius for noisy membranes or low lipid density.

• Frame Selection:

  • For long simulations, analyze representative windows to reduce computational cost.
  • Per-frame mode is ideal for capturing rare events.

---