Quantum Decoherence of Green Fluorescence Proteins Open Access
Chen, Yingrong (Fall 2023)
Abstract
Quantum batteries, rooted in quantum mechanics, are revolutionizing energy storage with their superextensive charging capability, which allows them to charge rapidly as their capacity increases. The previous prototype, utilizing an organic microcavity with polaritons as "qubits," faces limitations due to exciton-exciton annihilation. To address this, we propose replacing organic dyes in the microcavity with fluorescent proteins, leveraging their protein cylinder as a "molecular bumper" to mitigate annihilation. For practical battery function, the fluorescent protein-based microcavity must delay quantum decoherence, where the quantum system collapses into classical states due to environmental interactions. Inspired by biological systems with enduring quantum coherence, our research explores how protein and solvent environments influence energy gap fluctuations and quantum decoherence. The hypothesis posits that mutations reducing interactions and collisions can delay quantum decoherence. Using hybrid quantum mechanics-molecular mechanics (QMMM) simulations with both explicit and implicit models, we studied three GFP mutants—citrine, eGFP, and GFP.
The findings reveal that citrine, with mutations (Q65M and T199Y) introducing π-π interactions and steric clashes, exhibits a shorter estimated decoherence time. In contrast, eGFP shows prolonged coherence, attributed to lower water density surrounding its chromophore. Explicit models also show shorter decoherence times due to dynamic solvent-chromophore interactions. Additionally, we establish a correlation between structural dynamics metrics like RMSD and RMSF and quantum decoherence, emphasizing their value for future rational design. The model is validated with experimental absorption spectra using time-dependent density functional theory (TDDFT). In conclusion, this study enhances our understanding of quantum decoherence in fluorescent proteins, providing a knowledge base for the rational design of quantum batteries.
Table of Contents
Table of Contents
Introduction ______________________________________________________________________ 1
Quantum Battery _________________________________________________________________ 1
Fig. 1 Quantum battery implemented with an ensemble of qubits coupled with external energy source 7. ______________________________________________________________________ 2
Quantum Battery Built from Microcavity ______________________________________________ 2
Fig. 2 Quantum battery prototype implemented with microcavity. ________________________ 3
Exciton-Exciton Annihilation Necessitates the Use of Fluorescent Protein ____________________ 3
Fig. 3 Exciton-exciton annihilation and green fluorescent protein. ________________________ 4
Fig. 4 An innovative quantum battery prototype: fluorescent protein-based microcavity. _______ 5
Energy Retention Issue – Quantum Decoherence ________________________________________ 5
Fig. 5 Quantum decoherence on a quantum superposition state of 'heads' and 'tails'. ___________ 5
Fig. 6 Light-harvesting complexes Fenna−Matthews−Olson (FMO) with multiple chromophores 16. ___________________________________________________________________________ 6
Fig. 7 Energy gap fluctuation and quantum decoherence.________________________________ 7
Rational Design of Fluorescent Proteins to Minimize Decoherence __________________________ 7
Fig. 8 Mutants of GFP and their surrounding environments. _____________________________ 9
Theory ___________________________________________________________________________ 9
Quantum Decoherence _____________________________________________________________ 9
Fig. 9 Math theories behind quantum decoherence represented with Schrödinger’s cat. _______ 11
Decoherence Time and Energy Gap Fluctuation ________________________________________ 11
Molecular Dynamics (MD) ________________________________________________________ 12
Fig. 10 Statistical ensembles in Molecular Dynamics26. ________________________________ 14
Fig. 11 Explicit versus Implicit solvent models in Molecular Dynamics 26. _________________ 14
Fig. 12 Periodic boundary condition in Molecular Dynamics 28. _________________________ 15
Quantum Mechanics−Molecular Mechanics (QM/MM) __________________________________ 15
Unsupervised Learning in Chemistry Simulation _______________________________________ 17
Time-Dependent Density Functional Theory (TDDFT) __________________________________ 17
Computational Details _____________________________________________________________ 18
Fig. 13 Hybrid quantum mechanics-molecular mechanics (QM/MM) workflow 30. __________ 19
Protein Preparation _______________________________________________________________ 19
Table 1. Amino acid mutations in GFP mutants.______________________________________ 19
Molecular Dynamics (MD) ________________________________________________________ 20
Quantum Mechanical−Molecular Mechanical (QM/MM) ________________________________ 21
Simulation Analysis ______________________________________________________________ 21
Time-Dependent Density Functional Theory (TDDFT) __________________________________ 22
Results and Discussion _____________________________________________________________ 22
Simulation Overview _____________________________________________________________ 22
Fig. 14 Total energy and temperature over time.______________________________________ 23
Fig. 15 QM region energy and HOMO-LUMO gap over time. __________________________ 24
Fig. 16 Autocorrelation function of HOMO-LUMO gap. _______________________________ 25
Larger Energy Gap Fluctuation in Explicit Solvent Model and Citrine ______________________ 25
Table 2. Mean values and standard deviations of HOMO-LUMO gaps, as well as estimated decoherence times. _____________________________________________________________ 26
Correlation between Structural Dynamics and Decoherence ______________________________ 26
Fig. 17 Root mean square deviation (RMSD) analysis. ________________________________ 28
Higher Structural Dynamics of Individual Residues in Explicit Solvent Models _______________ 28
Fig 18. Root Mean Square Fluctuation (RMSF) analysis. ______________________________ 29
Q65M and T199Y in Citrine Increase Protein-Chromophore Contact _______________________ 29
Fig 19. Native contacts between the protein and the chromophore. _______________________ 31
Table 3. Mean values and standard deviations of contact distance between chromophore and the protein at selected residues. ______________________________________________________ 31
Greater Water Density Around GFP _________________________________________________ 31
Fig. 20 Solvent radial distribution function. _________________________________________ 32
Dimensionality Reduction and Clustering Analysis of Simulations _________________________ 32
Fig 21. tICA and clustering analysis of the simulations. ________________________________ 32
Mismatch between TDDFT Results and Experimental Absorption Spectrum _________________ 32
Table 4. Experimental absorption spectrum. 32 ______________________________________ 33
Fig. 22 TDDFT modeled absorption spectrum. _______________________________________ 34
Conclusion _______________________________________________________________________ 34
Supplement Code _________________________________________________________________ 39
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