TBC1D5-Rab7-NHE6 Proton Diffusion Model

This repository contains computational models and analyses for studying proton diffusion in the TBC1D5-Rab7-NHE6 protein complex. The project investigates how protons released from NHE6 (Na+/H+ exchanger 6) diffuse through the complex to reach the pH sensor site in TBC1D5 (Rab7 GTPase-activating protein).

Overview

The TBC1D5-Rab7-NHE6 complex is involved in pH sensing and regulation. This project models:

• Proton emission: Protons are released from the outward-facing proton binding site of NHE6 (residue D260)
• Proton diffusion: Protons diffuse through the protein complex
• pH sensing: Protons reach the allosteric pH sensor site in TBC1D5 (residue H207)

Directory Structure

model_processing/

Contains notebooks and scripts for processing the structural model:

• trim_af_model.ipynb: Processes AlphaFold model by removing poorly modeled loop regions

  • Input: AlphaFold model with low confidence regions
  • Output: Trimmed model (NHE6_TBC1D5_GTP_MG_noloops18plus_score40plus.pdb)

• align_center.ipynb: Aligns and centers the structural model

  • Reorients the model for analysis
  • Output: rotated.pdb

• PDB files:

  • PDBmodel_0.pdb: Original AF3 model
  • NHE6_TBC1D5_GTP_MG_noloops18plus_score40plus.pdb: Trimmed AlphaFold model
  • rotated.pdb: Aligned and centered model

proton_pathway/

Contains analysis of the putative proton diffusion pathway through the protein complex:

• diffusion_pathway.ipynb: Identifies the minimum-length pathway for proton diffusion

  • Uses HOLLOW casting to define the cavity/pathway
  • Finds shortest path from NHE6 D260 (D292' in rotated model) to TBC1D5 H207 (H207')
  • Uses graph-based approach with nearest neighbor analysis
  • Uses Dijkstra's algorithm for path finding

• hollow.pdb: Hollow casting of the protein cavity

• path.pdb: Coordinates of the identified diffusion pathway

• constraint.txt, atom_based_constraint.txt: Constraint files for hollow casting

• RUN_hollow.sh: Shell script for running hollow casting analysis

diffusion/

Contains Jupyter notebooks implementing analytical solutions for proton diffusion in different geometries:

• Diffusion1D_cylindrical.ipynb: Models proton diffusion in 1D cylindrical geometry

  • Solves Laplace's equation for steady-state concentration profiles
  • Assumes rotational symmetry and no radial dependence
  • Boundary conditions: constant flux at z=0, bulk concentration at z=L
  • Analytical solution: linear concentration profile
  • Includes discussion of the thermodynamics of Na+, K+, and H+ transport under realistic concentrations in the cytosol and endosome.
  • Shows that under plausible assumptions, proton transport is likely not thermodynamically limited; under assumption of kinetical limitations, the local pH near H207 may be sufficiently acidic to change its protonation state and thus couple proton efflux from NHE to Rab7 signaling.

• Diffusion3D_spherical.ipynb: Models proton diffusion in 3D hemispherical geometry

  • Solves Laplace's equation in spherical coordinates with radial symmetry
  • Models protons emitted from a sphere of radius r₀ diffusing outward
  • Boundary conditions: constant flux density at inner sphere, bulk concentration at outer boundary
  • Analytical solution: 1/r concentration profile
  • Investigates effects of reduced diffusion coefficients
  • The hemispherical model does not generate a sufficiently acidic local pH near H207.

visualization/

Contains a VMD tcl file drawing.tcl with functions for drawing

• a hemisphere draw_hemisphere
• a cylinder between two coordinates draw_cylinder_along
• two parallel planes to indicate a membrane draw_membrane

Usage: Within VMD's tcl window

source drawing.tcl

to make all functions available.

See drawing.tcl for details.

Key Residues

• NHE6 proton binding site: D260 (D292' in rotated model)
• TBC1D5 pH sensor: H207 (H207' in rotated model)
• Note: Primed residue numbers refer to the AlphaFold model, unprimed are canonical UniProt sequence numbers

Methods

Diffusion Modeling

• Steady-state solutions to Laplace's equation (∇²c = 0)
• Fick's law: j = -D∇c
• Boundary conditions: constant flux at source, bulk concentration at sink
• Parameters include:
  • Diffusion coefficient D (with reduced values for protein environment)
  • Proton emission rate k₀
  • Bulk pH (typically pH 7.2)

Pathway Analysis

• Uses hollow casting to identify protein cavities
• Graph-based path finding using nearest neighbor networks
• Minimum distance path calculation via Dijkstra's algorithm

Dependencies

• HOLLOW
  • Bosco K. Ho and Franz Grusewitz. HOLLOW: Generating accurate representations of channel and interior surfaces in molecular structures. BMC Struct Biol, 8 (49), 2008. doi: 10.1186/1472-6807-8-49
  • Use the patched version from https://github.com/Becksteinlab/hollow and install in a Python 2.7 environment.
  • Only needed for creating a casting of the cavities and tunnels that is then used to find a putative diffusion path. The casting is already included in the repository so it is not needed for running the notebooks.
• Python packages in notebooks (required Python ≥ 3.10)
  • MDAnalysis: For structural analysis
  • networkx: For graph-based path finding
  • numpy, scipy: Numerical computations
  • matplotlib: Plotting
  • sympy: Symbolic mathematics

Usage

1. Process the structural model:

   • Run model_processing/trim_af_model.ipynb to trim the AlphaFold model
   • Run model_processing/align_center.ipynb to align and center the model

2. Identify the proton pathway:

   • optional: Run proton_pathway/RUN_hollow.sh to create the casting (optional because casting hollow.pdb is already included)
   • Run proton_pathway/diffusion_pathway.ipynb to find the diffusion pathway

3. Model proton diffusion:

   • Run diffusion/Diffusion1D_cylindrical.ipynb for 1D cylindrical model
   • Run diffusion/Diffusion3D_spherical.ipynb for 3D spherical model

License

All content licensed under the MIT License.

Citation

YouJin Lee, Qing Ouyang, Li Ma, Morgan Fleishman, Hasib Aamir Riaz, Michael Schmidt, Jeffrey L. Dupree, Anupam Mondal, Priyesh Mohanty, Jeetain Mittal, Oliver Beckstein, David G. Lambright, and Eric M. Morrow. Endosome maturation is orchestrated by inside-out proton signaling through a Na⁺/H⁺ exchanger and pH-dependent Rab GTPase cycling. Nature Communications (2026) accepted.

The software and data are archived on zenodo under the DOI 10.5281/zenodo.19011503.