LHCII Quantum Zeno Threshold Mapping

Author: Hassan Farooq, Sargodha Medical College
OSF Pre-registration: https://doi.org/10.17605/OSF.IO/SXTHP
Status: Manuscript in preparation

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Research Question

In the LHCII light-harvesting chromophore network, at what pure dephasing rate γ does the system transition from environment-assisted quantum transport (ENAQT) into the Quantum Zeno localisation regime — and does this threshold depend on chromophore network geometry?

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Key Findings

Quantity	Value
ENAQT optimum γ_ENAQT (symmetric, σ=0)	112.5 cm⁻¹
Zeno threshold γ_c (symmetric, σ=0)	701.2 cm⁻¹ (95% CI: 692.4–710.1)
Physiological dephasing range at 300 K	50–200 cm⁻¹
Geometry dependence of γ_c	1.02× fold (not significant)
LHCII regime in vivo	ENAQT optimum — γ_phys ≈ γ_ENAQT

Headline result: The ENAQT optimum (γ_ENAQT = 112.5 cm⁻¹, dephasing timescale ≈ 47 fs) falls within the physiological protein conformational fluctuation range at 300 K. The Quantum Zeno threshold is 6.2-fold above physiological conditions. LHCII appears to be tuned to operate at its quantum transport optimum in vivo.

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Method

• Model: 15-dimensional Lindblad master equation (14 chromophores + ground state)
• Boundary conditions: Incoherent source at Chl b 601; irreversible sink at Chl a 610
• Hamiltonian: Müh et al. 2010 J. Phys. Chem. B (QM/MM, 14-site LHCII monomer)
• Metric: Inverse Participation Ratio (IPR) of the non-equilibrium steady-state density matrix
• Solver: Pure NumPy/SciPy — scipy.linalg.solve on the 225×225 Liouville superoperator
• Sweep: 40 γ × 3 σ × 2 geometry × 100 realisations = 24,000 simulations in 3.9 min

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The Core Physics Fix

Pure dephasing with no source or sink always drives the system to the maximally mixed state: IPR = 1/N = 0.0714 for all γ. This is mathematically guaranteed — not a code bug — and means a naive sweep measures nothing physical.

The fix is a 15-dimensional Hilbert space (14 chromophores + electronic ground state |g⟩) with three categories of collapse operator:

Operator	Form	Physics
Dephasing	L_n = √γ |n⟩⟨n| for n = 0..13	Site-energy fluctuations from protein bath
Source	L_src = √κ_in |b601⟩⟨g|	Incoherent photon absorption at Chl b 601
Sink	L_snk = √κ_out |g⟩⟨a610|	Irreversible trapping toward reaction centre

This creates a non-equilibrium steady state where IPR depends non-trivially on γ. See src/lindblad.py for the full derivation and implementation.

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Repository Structure

LHCII-Zeno-threshold/
│
├── src/
│   ├── hamiltonian.py        # LHCII Hamiltonian loader and builder
│   ├── lindblad.py           # 15-site source-sink Lindblad model (physics fix)
│   ├── metrics.py            # IPR, participation ratio, sigmoid model
│   └── visualization.py      # Publication-quality plotting utilities
│
├── scripts/
│   ├── 00_quick_diagnostic.py    # Run this FIRST — validates source-sink fix
│   ├── 01_dimer_validation.py    # 2-site dimer Lindblad limiting cases
│   ├── 02_build_hamiltonian.py   # Build LHCII Hamiltonian from Müh 2010
│   ├── 03_ipr_validation.py      # IPR formula validation and 5-point preview
│   ├── 05_parameter_sweep.py     # Full γ sweep (optimised NumPy/SciPy solver)
│   ├── 06_threshold_extraction.py # Sigmoid fit and γ_c extraction
│   ├── 07_spatial_localization.py # Exciton density maps on PDB coordinates
│   ├── 08_robustness_controls.py  # Parameter sensitivity analysis
│   └── 09_figure_finalization.py  # Manuscript figures + Results section draft
│
├── data/
│   └── hamiltonians/         # Source documentation; place 1RWT.pdb here
│
├── config.yaml               # All tunable parameters
├── Snakefile                 # Full reproducible pipeline
├── COLAB_SETUP.py            # Paste into Colab Cell 1 to configure session
└── requirements.txt          # Python dependencies

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Quick Start (Google Colab)

Cell 1 — Session setup

from google.colab import drive
drive.mount('/content/drive')
import os
os.chdir('/content/drive/MyDrive/LHCII-Zeno-threshold')
!pip install qutip==4.7.3 numpy scipy matplotlib h5py pandas tqdm pyyaml -q

Cell 2 — Keepalive thread (prevents disconnection during sweep)

import threading, time, sys
def _keep():
    for i in range(9999):
        time.sleep(55)
        sys.stdout.write(f'\r keepalive {i+1}'); sys.stdout.flush()
threading.Thread(target=_keep, daemon=True).start()

Cell 3 — Validate the source-sink model (30 seconds)

%run scripts/00_quick_diagnostic.py

Cell 4 — Run the full sweep (~4 minutes)

%run scripts/05_parameter_sweep.py

Cell 5 — Extract γ_c and generate figures

%run scripts/06_threshold_extraction.py
%run scripts/09_figure_finalization.py

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Hamiltonian Setup (Required Before First Run)

Open scripts/02_build_hamiltonian.py and replace all values marked ← REPLACE with exact numbers from:

Müh, F., Madjet, M. E., & Renger, T. (2010). Structure-based identification of energy sinks in plant light-harvesting complex II. J. Phys. Chem. B, 114, 13517–13535. DOI: 10.1021/jp106323e

Then run the script once to generate results/lhcii_hamiltonian_mueh2010.h5. Every downstream script loads from this file.

Site ordering (0-indexed, Müh 2010):

Index	Site	Energy (cm⁻¹)	Role
0–7	Chl a 602–609	15,020–15,220	Antenna
8–11	Chl a 610–613	14,730–15,020	Low-energy cluster
12	Chl b 601	15,880	Source site
13	Chl b 606	15,970	Antenna

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Reproducing All Results

From a clean Colab session with the repo on Google Drive:

%run COLAB_SETUP.py                    # install + navigate
%run scripts/02_build_hamiltonian.py   # requires Müh 2010 values
%run scripts/05_parameter_sweep.py     # ~4 min, saves sweep_raw_v2.h5
%run scripts/06_threshold_extraction.py
%run scripts/09_figure_finalization.py

Or with Snakemake (local environment):

pip install snakemake
snakemake --cores 1 --forceall

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Scope Reduction Note

The pre-registered sweep (OSF) specified 80 γ × 5 σ × 2 geom × 200 realisations = 160,000 simulations. This was reduced to 40 × 3 × 2 × 100 = 24,000 simulations due to Google Colab compute constraints (Pivot Trigger 3, documented in OSF pre-registration before execution). The NumPy/SciPy solver completed the reduced sweep in 3.9 minutes on Colab CPU. Qualitative conclusions are unchanged.

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Data Availability

Dataset	Location
Primary sweep (sweep_raw_v2.h5)	OSF: https://doi.org/10.17605/OSF.IO/SXTHP
LHCII Hamiltonian (lhcii_hamiltonian_mueh2010.h5)	OSF (same DOI)
Pre-registration (timestamped)	OSF (same DOI)
Analysis code	This repository

Large binary files (HDF5, PDB) are not committed to this repository.

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Unit Conventions

Quantity	API unit	Internal unit
Site energies, coupling J	cm⁻¹	rad ps⁻¹ (× 0.1884)
Dephasing rate γ	cm⁻¹	rad ps⁻¹
Source κ_in, sink κ_out	cm⁻¹	rad ps⁻¹

Conversion: 1 cm⁻¹ = 2π × 2.998 × 10⁻² rad ps⁻¹ ≈ 0.1884 rad ps⁻¹

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Citation

If you use this code or data, please cite:

Farooq, H. (2025). Quantum Zeno threshold mapping in LHCII chromophore networks:
physiological dephasing rates coincide with the ENAQT optimum.
Manuscript in preparation.
OSF pre-registration: https://doi.org/10.17605/OSF.IO/SXTHP
GitHub: https://github.com/hadbierox196/LHCII-Zeno-threshold

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License

MIT License. See LICENSE for details.