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PMAP (Probability Distribution Map)

PMAP (spatial Probability distribution MAP) is a three-dimensional probability density map representing the spatial distribution of probe molecules.

Table of Contents

  1. PMAP Basics
  2. Calculation Method
  3. Implementation Details

Related Documents:

PMAP Basics

PMAP represents the spatial probability distribution of probe molecules observed in mixed-solvent molecular dynamics (MSMD) simulations.

This information can be utilized both qualitatively and quantitatively:

  • Regions where probes are likely to exist are likely binding sites for compounds (qualitative, hotspot analysis)
  • Regions with high probe existence probability likely indicate stronger binding (quantitative, binding affinity prediction)

Calculation Method

1. Basic Procedure

  1. Division of simulation box into 3D grid
  2. Counting probe atom frequencies at each grid point
  3. Converting frequencies to probabilities

2. Grid Setup

Grid creation is performed using cpptraj from Amber Tools.

  • Grid center: Protein center of mass (set as origin)
  • Default box size: 80 Å × 80 Å × 80 Å
  • Grid spacing: 1 Å

This creates an 80 × 80 × 80 grid with 1 Å spacing, counting the frequency of probe atoms at each grid point.

3. Atom Selection

Atoms used for grid creation are selected by selectors specified in the yaml file. Here are three examples:

  1. Heavy atoms only
    • Selector: (!@VIS)&(!@H*)
    • Excludes hydrogen atoms and virtual atoms
  2. All atoms
    • Selector: (!@VIS)
    • Excludes only virtual atoms
  3. Probe center of mass
    • Selector: @VIS
    • Selects only probe virtual atoms
      • Since probe virtual atoms are placed at the center of mass of each probe, selecting only virtual atoms effectively selects probe centers of mass.

4. Value Conversion

As mentioned above, the grid created so far counts the frequency of probe atoms. Naturally, these counts vary with simulation length (more precisely, the number of snapshots), so they need to be converted to probabilities. Two types of normalization are provided. The default is total normalization (although snapshot normalization may often be more appropriate).

  1. Total normalization $P(r) = N(r) / \sum N(r)$

    • $N(r)$: Frequency at position $r \in \mathbb{R}^3$
    • Sum of probabilities across all grid points equals 1

  2. Snapshot normalization $P(r) = N(r) / N_{\mathrm{frames}}$

    • $N_{\mathrm{frames}}$: Number of snapshots used
    • Directly represents existence probability at each position

Additionally, a method is provided to estimate the interaction energy between protein and probe molecules (grid free energy; GFE) using these probabilities.

$$\mathrm{GFE}(r) = -RT \ln(P(r)/P_{\mathrm{bulk}})$$

  • $R$: Gas constant
  • $T$: Temperature
  • $P_{\mathrm{bulk}}$: Bulk probability (average probability across the entire space)

Implementation Details

1. Single Simulation Processing (gen_pmap() function)

Frequency Grid Calculation with cpptraj

Grid calculation using cpptraj follows these steps. The template for this execution can be found in script/utilities/executables/template/cpptraj_pmap.in.

  1. Trajectory preprocessing Loads the trajectory and performs alignment with the initial structure using backbone carbon atoms.

    trajin [project_name].xtc [start_frame] [end_frame]
reference [project_name].pdb
rms reference @CA

  2. Frequency grid creation Creates a grid based on the specified atom selector using cpptraj's grid command.

    grid [output_map_file_path].dx
  [X_size(Å)] [X_spacing(Å)] [Y_size(Å)] [Y_spacing(Å)] [Z_size(Å)] [Z_spacing(Å)]
  gridcenter 0.0 0.0 0.0 [atom_selector]
    • Default size: 80×80×80 Å
    • Default spacing: 1×1×1 Å

PMAP File Generation

Reads the frequency grid created by cpptraj and generates PMAP.

  1. Conversion to probabilities

    • For total normalization: 
      total_count = np.sum(frequency_map)
probability_map = frequency_map / total_count
    • For snapshot normalization: 
      probability_map = frequency_map / n_frames

  2. GFE calculation (optional) convert_to_gfe()

    R = 0.001987  # kcal/mol/K
T = 300       # K
bulk_prob = np.mean(probability_map)
gfe_map = -R * T * np.log(probability_map / bulk_prob)

    Note that gfe_map may contain infinite values (this occurs at coordinates where probability_map is 0), so if any value in gfe_map is greater than 3.0 kcal/mol, it is clipped to 3.0 kcal/mol.

2. Multiple Simulation Integration

under construction

Note: All maps are output in OpenDX format.