In an article published in Frontiers in Physics, researchers explored superradiance in tryptophan (Trp) networks within microtubules, actin filaments, and amyloid fibrils, modeling them as open quantum systems using a non-Hermitian Hamiltonian. The study revealed that all three structures exhibited highly superradiant states, which enhanced quantum yield and demonstrated resilience against static disorder and thermal noise.
Study: Quantum-enhanced photoprotection in neuroprotein architectures emerges from collective light-matter interactions. Image Credit: Juan Gaertner/Shutterstock.com
Background
Previous research has focused on the cytoskeleton's key components, particularly microtubules and actin filaments, which are critical for cellular structure and transport.
Microtubules are essential for cell communication and mitosis, while actin filaments stabilize the cytoskeleton and support cell movement. Additionally, amyloid fibrils have been extensively studied for their role in neurodegenerative diseases. Toy models with varying transition dipole orientations have shown that packing density significantly affects superradiance and quantum yield, demonstrating that high superradiance does not always correlate with high quantum yield.
Fluorescent Amino Modeling
In this study, tryptophan (Trp), a highly fluorescent amino acid in the ultraviolet spectrum, was modeled as a two-level system with a transition energy of around 280 nm and a decay rate of approximately 0.00273 cm⁻¹. Trp possesses a significant transition dipole moment of roughly 6.0 debye.
The interaction between a network of Trp molecules and the electromagnetic field was described using a non-Hermitian Hamiltonian, incorporating terms for the system's Hamiltonian, detuning, and decay rates. The dynamics of the system followed the Schrödinger equation with this non-Hermitian Hamiltonian, accounting for non-unitary evolution and probability leakage.
Quantum yield (QY) was used as a measure of the efficiency of photon emission relative to absorption, ranging from 0 to 1. In the case of Trp, a high QY reflects its effective photoprotection, as it absorbs high-energy ultraviolet (UV) photons and re-emits them at lower energies.
The thermal average of QY was calculated using the partition function and decay rates, taking into account both radiative and non-radiative processes. The non-radiative decay rate, assumed to be constant across the network, influences QY, with recent research suggesting that Trp network formation may increase non-radiative decay rates and modulate QY.
Static disorder, representing random fluctuations in site energies and decay rates, was incorporated by modifying the Hamiltonian. A uniform random number was added to the diagonal elements for site energies, and QY was averaged over multiple realizations. Random variations were introduced for decay rates, and off-diagonal rates were averaged based on the on-diagonal values to maintain symmetry. The effects of static disorder were analyzed by calculating the average QY across several realizations, accounting for variations in both site energies and decay rates.
Biological structures, including microtubules, actin filaments, and amyloid fibrils, were modeled using specific Protein Data Bank (PDB) entries and detailed geometric transformations.
Microtubules were constructed from tubulin dimers arranged into a helical structure. Actin filaments were created from individual actin subunits, with actin bundles packed into concentric hexagons. Amyloid fibrils were modeled using PDB data, with subunits arranged in a spiral pattern to ensure proper spacing between beta strands. Matrix diagonalization for these systems was performed using Python's NumPy library and the zgeev routine, enabling efficient handling of large matrices on high-performance computing systems.
QY Insights
The eigen solutions of the effective Hamiltonian provided insights into the relationship between quantum yield (QY) and structural length, as well as the impact of static disorder in microtubules, actin filaments, and amyloid fibrils. The effective Hamiltonian, a non-Hermitian matrix, consists of a Hermitian and non-Hermitian part, leading to complex eigenvalues due to the non-Hermitian component.
In the case of microtubules, the QY remained highly robust against static disorder, showing only a 3.08 % decrease even when disorder strength was increased fivefold. This robustness aligns with experimental observations and indicates that collective light-matter interactions can significantly enhance quantum effects in these structures.
Similarly, the QY of actin filaments and bundles increased with size, though this enhancement saturated sooner than in microtubules. Despite a slight decrease in QY with increasing length in actin bundles, their overall quantum yield remained relatively high.
Interestingly, actin bundles exhibited higher predicted QY values than microtubules, which can be attributed to the stronger Trp-Trp couplings in actin. This suggests that while both structures benefit from collective quantum effects, actin bundles have a distinct advantage in quantum yield due to their stronger internal interactions.
In comparisons between human and mouse amyloid fibrils, the maximum superradiant enhancement was found to be significantly higher than that of actin bundles despite having fewer Trp chromophores. The QY of amyloid fibrils, ranging from 0.44 to 0.60, increased with system size and remained robust in the presence of static disorder.
Energy gap analysis revealed that amyloid fibrils have a higher energy gap compared to microtubules and actin bundles. Additionally, variations in the single-Trp decay rate only had a minor effect on QY, supporting the assumption of a constant decay rate in the modeling.
Conclusion
In conclusion, the analysis of Trp chromophore networks in microtubules, actin filaments, and amyloid fibrils demonstrated significant superradiant behavior and robust quantum yields, even in the presence of static disorder.
These findings suggest that quantum coherent effects may play a critical role in the behavior of neuroprotein architectures, offering new insights into the understanding of neurodegenerative diseases and brain information processing. Future work will focus on experimentally validating these quantum yield predictions, paving the way for exploring collective quantum optical behavior in protein polymers.
Journal Reference
Patwa, H. et al. (2024). Quantum-enhanced photoprotection in neuroprotein architectures emerges from collective light-matter interactions. Frontiers in Physics, 12, 1387271. DOI: 10.3389/fphy.2024.1387271, https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2024.1387271/full
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