Quantum Dynamics of Electronic Excitations in Biomolecular Chromophores: Role of the Protein Environment and Solvent

A Review of the Current State of Magnetic Force Microscopy to Unravel the Magnetic Properties of Nanomaterials Applied in Biological Systems and Future Directions for Quantum Technologies

Magnetism plays a pivotal role in many biological systems. However, the intensity of the magnetic forces exerted between magnetic bodies is usually low, which demands the development of ultra-sensitivity tools for proper sensing. In this framework, magnetic force microscopy (MFM) offers excellent lateral resolution and the possibility of conducting single-molecule studies like other single-probe microscopy (SPM) techniques. This comprehensive review attempts to describe the paramount importance of magnetic forces for biological applications by highlighting MFM's main advantages but also intrinsic limitations. While the working principles are described in depth, the article also focuses on novel micro- and nanofabrication procedures for MFM tips, which enhance the magnetic response signal of tested biomaterials compared to commercial nanoprobes. This work also depicts some relevant examples where MFM can quantitatively assess the magnetic performance of nanomaterials involved in biological systems, including magnetotactic bacteria, cryptochrome flavoproteins, and magnetic nanoparticles that can interact with animal tissues. Additionally, the most promising perspectives in this field are highlighted to make the reader aware of upcoming challenges when aiming toward quantum technologies.

Molecular Structure, Quantum Coherence, and Solvent Effects on the Ultrafast Electron Transport in BODIPY- Derivatives

Photoinduced electron transfer in multichromophore molecular systems is defined by a critical interplay between their core unit configuration (donor, molecular bridge, and acceptor) and their system-solvent coupling; these lead to energy and charge transport processes that are key in the design of molecular antennas for efficient light harvesting and organic photovoltaics. Here, we quantify the ultrafast non-Markovian dissipative dynamics of electron transfer in D-π-A molecular photosystems comprising 1,3,5,7-tetramethyl-8-phenyl-4,4-difluoroboradiazaindacene (BODIPY), Zn-porphyrin, fulleropyrrolidine, and fulleroisoxazoline. We find that the stabilization energy of the charge transfer states exhibits a significant variation for different polar (methanol, tetrahydrofuran (THF)) and nonpolar (toluene) environments and determine such sensitivity according to the molecular structure and the electron-vibration couplings that arise at room temperature. For the considered donor-acceptor (D-A) dyads, we show that the stronger the molecule-solvent coupling, the larger the electron transfer rates, regardless of the dyads' electronic coherence properties. We find such coupling strengths to be the largest (lowest) for methanol (toluene), with an electron transfer rate difference of 2 orders of magnitude between the polar and nonpolar solvents. For the considered donor-bridge-acceptor (D-B-A) triads, the molecular bridge introduces an intermediate state that allows the realization of Λ or cascaded-type energy mechanisms. We show that the latter configuration, obtained for BDP-ZnP-[PyrC₆₀] in methanol, exhibits the highest transfer rate of all of the computed triads. Remarkably, and in contrast with the dyads, we show that the larger charge transfer rates are obtained for triads that exhibit prolonged electron coherence and population oscillations.

Room temperature quantum coherence vs. electron transfer in a rhodanine derivative chromophore

Understanding electron transfer in organic molecules is of great interest in quantum materials for light harvesting, energy conversion and integration of molecules into solar cells. This, however, poses the challenge of designing specific optimal molecular structure for which the processes of ultrafast quantum coherence and electron transport are not so well understood. In this work, we investigate subpicosecond time scale quantum dynamics and electron transfer in an efficient electron acceptor rhodanine chromophoric complex. We consider an open quantum system approach to model the complex-solvent interaction, and compute the crossover from weak to strong dissipation on the reduced system dynamics for both a polar (methanol) and a non polar solvent (toluene). We show that the electron transfer rates are enhanced in the strong chromophore-solvent coupling regime, being the highest transfer rates those found at room temperature. Even though the computed dynamics are highly non-Markovian, and they may exhibit a quantum character up to hundreds of femtoseconds, we show that quantum coherence does not necessarily optimise the electron transfer in the chromophore.

The Role of Quantum Decoherence in FRET

Resonance energy transfer has become an indispensable experimental tool for single-molecule and single-cell biophysics. Its physical underpinnings, however, are subtle: it involves a discrete jump of excitation from one molecule to another, and so we regard it as a strongly quantum-mechanical process. And yet its kinetics differ from what many of us were taught about two-state quantum systems, quantum superpositions of the states do not seem to arise, and so on. Although J. R. Oppenheimer and T. Förster navigated these subtleties successfully, it remains hard to find an elementary derivation in modern language. The key step involves acknowledging quantum decoherence. Appreciating that aspect can be helpful when we attempt to extend our understanding to situations in which Förster's original analysis is not applicable.

Broad-Band Pump-Probe Spectroscopy Quantifies Ultrafast Solvation Dynamics of Proteins and Molecules

In this work, we demonstrate the use of broad-band pump-probe spectroscopy to measure femtosecond solvation dynamics. We report studies of a rhodamine dye in methanol and cryptophyte algae light-harvesting proteins in aqueous suspension. Broad-band impulsive excitation generates a vibrational wavepacket that oscillates on the excited-state potential energy surface, destructively interfering with itself at the minimum of the surface. This destructive interference gives rise to a node at a certain probe wavelength that varies with time. This reveals the Gibbs free-energy changes of the excited-state potential energy surface, which equates to the solvation time correlation function. This method captures the inertial solvent response of water (∼40 fs) and the bimodal inertial response of methanol (∼40 and ∼150 fs) and reveals how protein-buried chromophores are sensitive to the solvent dynamics inside and outside of the protein environment.

Quantum Chemical Studies of Light Harvesting

The design of optimal light-harvesting (supra)molecular systems and materials is one of the most challenging frontiers of science. Theoretical methods and computational models play a fundamental role in this difficult task, as they allow the establishment of structural blueprints inspired by natural photosynthetic organisms that can be applied to the design of novel artificial light-harvesting devices. Among theoretical strategies, the application of quantum chemical tools represents an important reality that has already reached an evident degree of maturity, although it still has to show its real potentials. This Review presents an overview of the state of the art of this strategy, showing the actual fields of applicability but also indicating its current limitations, which need to be solved in future developments.

Quantum mechanics of excitation transport in photosynthetic complexes: a key issues review

For a long time microscopic physical descriptions of biological processes have been based on quantum mechanical concepts and tools, and routinely employed by chemical physicists and quantum chemists. However, the last ten years have witnessed new developments on these studies from a different perspective, rooted in the framework of quantum information theory. The process that more, than others, has been subject of intense research is the transfer of excitation energy in photosynthetic light-harvesting complexes, a consequence of the unexpected experimental discovery of oscillating signals in such highly noisy systems. The fundamental interdisciplinary nature of this research makes it extremely fascinating, but can also constitute an obstacle to its advance. Here in this review our objective is to provide an essential summary of the progress made in the theoretical description of excitation energy dynamics in photosynthetic systems from a quantum mechanical perspective, with the goal of unifying the language employed by the different communities. This is initially realized through a stepwise presentation of the fundamental building blocks used to model excitation transfer, including protein dynamics and the theory of open quantum system. Afterwards, we shall review how these models have evolved as a consequence of experimental discoveries; this will lead us to present the numerical techniques that have been introduced to quantitatively describe photo-absorbed energy dynamics. Finally, we shall discuss which mechanisms have been proposed to explain the unusual coherent nature of excitation transport and what insights have been gathered so far on the potential functional role of such quantum features.

Vibronic bandshape of the absorption spectra of dibenzoylmethanatoboron difluoride derivatives: analysis based on ab initio calculations

The nature of absorption bandshapes of dibenzoylmethanatoboron difluoride (DBMBF₂) derivatives is investigated using TDDFT and time-dependent linear vibronic coupling model.

Dynamics and quantumness of excitation energy transfer through a complex quantum network

Understanding the mechanisms of efficient and robust energy transfer in organic systems provides us with insights for the optimal design of artificial systems. In this paper, we explore the dynamics of excitation energy transfer (EET) through a complex quantum network by a toy model consisting of three sites coupled to environments. We study how the coherent evolution and the noise-induced decoherence work together to reach efficient EET and illustrate the role of the phase factor attached to the coupling constant in the EET. By comparing the differences between the Markovian and non-Markovian dynamics, we discuss the effect of environment and the spatial structure of system on the dynamics and the efficiency of EET. A intuitive picture is given to show how the exciton is transferred through the system. Employing the simple model, we show the robustness of EET efficiency under the influence of the environment and elucidate the important role of quantum coherence in EET. We go further to study the quantum feature of the EET dynamics by quantumness and show the importance of quantum coherence from a different perspective. We calculate the energy current in the EET and its quantumness, and results for different system parameters are presented and discussed.

Numerical evidence for robustness of environment-assisted quantum transport

Recent theoretical studies show that decoherence process can enhance transport efficiency in quantum systems. This effect is known as environment-assisted quantum transport (ENAQT). The role of ENAQT in optimal quantum transport is well investigated; however, it is less known how robust ENAQT is with respect to variations in the system or its environment characteristic. Toward answering this question, we simulated excitonic energy transfer in Fenna-Matthews-Olson photosynthetic complex. We found that ENAQT is robust with respect to many relevant parameters of environmental interactions and Frenkel-exciton Hamiltonians, including reorganization energy, bath-frequency cutoff, temperature, initial excitations, dissipation rate, trapping rate, disorders, and dipole moments orientations. Our study suggests that the ENAQT phenomenon can be exploited in robust design of highly efficient quantum transport systems.

Intra-molecular refrigeration in enzymes

We present a simple mechanism for intra-molecular refrigeration, where parts of a molecule are actively cooled below the environmental temperature. We discuss the potential role and applications of such a mechanism in biology, in particular in enzymatic reactions.

Dynamics of the sub-Ohmic spin-boson model: a comparison of three numerical approaches

Dynamics of the sub-Ohmic spin-boson model is examined using three numerical approaches, namely the Dirac-Frenkel time-dependent variation with the Davydov D(1) ansatz, the adaptive time-dependent density matrix renormalization group method within the representation of orthogonal polynomials, and a perturbative approach based on a unitary transformation. In order to probe the validity regimes of the three approaches, we study the dynamics of a qubit coupled to a bosonic bath with and without a local field. Comparison of the up-state population evolution shows that the three approaches are in agreement in the weak-coupling regime but exhibit marked differences when the coupling strength is large. The Davydov D(1) ansatz and the time-dependent density matrix renormalization group can both be reliably employed in the weak-coupling regime, while the former is also valid in the strong-coupling regime as judged by how faithfully the trial state follows the Schrödinger equation. We further explore the bipartite entanglement dynamics between two qubits coupled with individual bosonic baths which reveals entanglement sudden death and revival.

Quantum dephasing of a two-state system by a nonequilibrium harmonic oscillator

In this paper, we investigate coherent quantum dynamics in a nonequilibrium environment. We focus on a two-state quantum system strongly coupled to a single classical environmental oscillator, and explore the effect of nonstationary statistical properties of the oscillator on the quantum evolution. A simple nonequilibrium model, consisting of an oscillator with a well-defined initial phase which undergoes subsequent diffusion, is introduced and studied. Approximate but accurate analytic expressions for the evolution of the off-diagonal density matrix element of the quantum system are derived in the second-order cumulant approximation. The effect of the initial phase choice on the subsequent quantum evolution is quantified. It is observed that the initial phase can have a significant effect on the preservation of coherence on short time scales, suggesting this variable as a control parameter for optimizing coherence in many-body quantum systems.

Adiabatic eigenfunction-based approach for coherent excitation transfer: an almost analytical treatment of the Fenna-Matthews-Olson complex

We suggest a method of studying coherence in finite-level systems coupled to the environment and use it for the Hamiltonian that has been used to describe the light-harvesting pigment-protein complex. The method works with the adiabatic states and transforms the Hamiltonian to a form in which the terms responsible for decoherence and population relaxation are separated out. Decoherence is then accounted for nonperturbatively and population relaxation using a Markovian master equation. Almost analytical results can be obtained for the seven-level system, and the calculations are very simple for systems with more levels. We apply the treatment to the seven-level system, and the results are in excellent agreement with the exact numerical results of Nalbach et al. [Nalbach, Braun, and Thorwart, Phys. Rev. E 84, 041926 (2011)]. Our approach is able to account for decoherence and population relaxation separately. It is found that decoherence causes only damping of oscillations and does not lead to transfer to the reaction center. Population relaxation is necessary for efficient transfer to the reaction center, in agreement with earlier findings. Our results show that the transformation to the adiabatic basis followed by a Redfield type of approach leads to results in good agreement with exact simulation.

Exciton transport in thin-film cyanine dye J-aggregates

We present a theoretical model for the study of exciton dynamics in J-aggregated monolayers of fluorescent dyes. The excitonic evolution is described by a Monte-Carlo wave function approach which allows for a unified description of the quantum (ballistic) and classical (diffusive) propagation of an exciton on a lattice in different parameter regimes. The transition between the ballistic and diffusive regime is controlled by static and dynamic disorder. As an example, the model is applied to three cyanine dye J-aggregates: TC, TDBC, and U3. Each of the molecule-specific structure and excitation parameters are estimated using time-dependent density functional theory. The exciton diffusion coefficients are calculated and analyzed for different degrees of film disorder and are correlated to the physical properties and the structural arrangement of molecules in the aggregates. Further, exciton transport is anisotropic and dependent on the initial exciton energy. The upper-bound estimation of the exciton diffusion length in the TDBC thin-film J-aggregate is of the order of hundreds of nanometers, which is in good qualitative agreement with the diffusion length estimated from experiments.

Efficient estimation of energy transfer efficiency in light-harvesting complexes

The fundamental physical mechanisms of energy transfer in photosynthetic complexes is not yet fully understood. In particular, the degree of efficiency or sensitivity of these systems for energy transfer is not known given their realistic with surrounding photonic and phononic environments. One major problem in studying light-harvesting complexes has been the lack of an efficient method for simulation of their dynamics in biological environments. To this end, here we revisit the second order time-convolution (TC2) master equation and examine its reliability beyond extreme Markovian and perturbative limits. In particular, we present a derivation of TC2 without making the usual weak system-bath coupling assumption. Using this equation, we explore the long-time behavior of exciton dynamics of Fenna-Matthews-Olson (FMO) portein complex. Moreover, we introduce a constructive error analysis to estimate the accuracy of TC2 equation in calculating energy transfer efficiency, exhibiting reliable performance for system-bath interactions with weak and intermediate memory and strength. Furthermore, we numerically show that energy transfer efficiency is optimal and robust for the FMO protein complex of green sulfur bacteria with respect to variations in reorganization energy and bath correlation time scales.

Quantum Rabi model for N-state atoms

A tractable N-state Rabi Hamiltonian is introduced by extending the parity symmetry of the two-state model. The single-mode case provides a few-parameter description of a novel class of periodic systems, predicting that the ground state of certain four-state atom-cavity systems will undergo parity change at strong-coupling. A group-theoretical treatment provides physical insight into dynamics and a modified rotating wave approximation obtains accurate analytical energies. The dissipative case can be applied to study excitation energy transfer in molecular rings or chains.

Atomistic study of the long-lived quantum coherences in the Fenna-Matthews-Olson complex

A remarkable amount of theoretical research has been carried out to elucidate the physical origins of the recently observed long-lived quantum coherence in the electronic energy transfer process in biological photosynthetic systems. Although successful in many respects, several widely used descriptions only include an effective treatment of the protein-chromophore interactions. In this work, by combining an all-atom molecular dynamics simulation, time-dependent density functional theory, and open quantum system approaches, we successfully simulate the dynamics of the electronic energy transfer of the Fenna-Matthews-Olson pigment-protein complex. The resulting characteristic beating of populations and quantum coherences is in good agreement with the experimental results and the hierarchy equation of motion approach. The experimental absorption, linear, and circular dichroism spectra and dephasing rates are recovered at two different temperatures. In addition, we provide an extension of our method to include zero-point fluctuations of the vibrational environment. This work thus presents, to our knowledge, one of the first steps to explain the role of excitonic quantum coherence in photosynthetic light-harvesting complexes based on their atomistic and molecular description.

The role of the environment in electronic energy transfer: a molecular modeling perspective

The key role of the environment in electronic energy transfer has been underscored in recent experimental and theoretical studies. In this perspective, we provide an overview of novel quantum-mechanical methodologies aimed at describing environment effects in energy transfers. The techniques described include continuum dielectric and atomistic descriptions of the surroundings. We discuss the advantages and limitations of each technique, as well as the main insights that have emerged from their application to solvated dyads and photosynthetic pigment-protein complexes. We finally highlight the aspects that still need to be solved in order to provide a full theoretical route to the study of energy transfer phenomena in complex environments.

Communication: Decoherence in a nonequilibrium environment: an analytically solvable model

We describe an analytically solvable model of quantum decoherence in a nonequilibrium environment. The model considers the effect of a bath driven from equilibrium by, for example, an ultrafast excitation of a quantum chromophore. The nonequilibrium response of the environment is represented by a nonstationary random function corresponding to the fluctuating transition frequency between two quantum states coupled to the surroundings. The nonstationary random function is characterized by a Fourier series with the phase of each term starting initially with a definite value across the ensemble but undergoing random diffusion with time. The decay of the off-diagonal density matrix element is shown to depend significantly on the particular pattern of initial phases of the terms in the Fourier series, or equivalently, the initial phases of bath modes coupled to the quantum subsystem. This suggests the possibility of control of quantum decoherence by the detailed properties of an environment that is driven from thermal equilibrium.

Multiphonon transitions in the biomolecular energy transfer dynamics

We show that the biomolecular exciton dynamics under the influence of slow polarization fluctuations in the solvent cannot be described by lowest order, one-phonon approaches which are perturbative in the system-bath coupling. Instead, nonperturbative multiphonon transitions induced by the slow bath yield significant contributions. This is shown by comparing results for the decoherence rate of the exciton dynamics of a resumed perturbation theory with numerically exact real-time path-integral data. The exact decoherence rate for realistically slow solvent environments is significantly modified by multiphonon processes even in the weak coupling regime, while a one-phonon description is satisfactory only for fast environmental noise. Slow environments inhibit bath modes that are resonant with the exciton dynamics, thereby suppressing one-phonon transitions and enhancing multiphonon processes, which are typically not captured by lowest order perturbative treatments, such as Redfield or Lindblad approaches, even in more refined variants.

Dynamic entanglement in oscillating molecules and potential biological implications

We demonstrate that entanglement can persistently recur in an oscillating two-spin molecule that is coupled to a hot and noisy environment, in which no static entanglement can survive. The system represents a nonequilibrium quantum system which, driven through the oscillatory motion, is prevented from reaching its (separable) thermal equilibrium state. Environmental noise, together with the driven motion, plays a constructive role by periodically resetting the system, even though it will destroy entanglement as usual. As a building block, the present simple mechanism supports the perspective that entanglement can exist also in systems which are exposed to a hot environment and to high levels of decoherence, which we expect, e.g., for biological systems. Our results also suggest that entanglement plays a role in the heat exchange between molecular machines and environment. Experimental simulation of our model with trapped ions is within reach of the current state-of-the-art quantum technologies.

Non-Markovian quantum jumps in excitonic energy transfer

We utilize the novel non-Markovian quantum jump (NMQJ) approach to stochastically simulate exciton dynamics derived from a time-convolutionless master equation. For relevant parameters and time scales, the time-dependent, oscillatory decoherence rates can have negative regions, a signature of non-Markovian behavior and of the revival of coherences. This can lead to non-Markovian population beatings for a dimer system at room temperature. We show that strong exciton-phonon coupling to low frequency modes can considerably modify transport properties. We observe increased exciton transport, which can be seen as an extension of recent environment-assisted quantum transport concepts to the non-Markovian regime. Within the NMQJ method, the Fenna-Matthew-Olson protein is investigated as a prototype for larger photosynthetic complexes.

Could light harvesting complexes exhibit non-classical effects at room temperature?

Mounting experimental and theoretical evidence suggest that coherent quantum effects play a role in the efficient transfer of an excitation from a chlorosome antenna to a reaction centre in the Fenna–Matthews–Olson protein complex. However, it is conceivable that a satisfying alternate interpretation of the results is possible in terms of a classical theory. To address this possibility, we consider a class of classical theories satisfying the minimal postulates of macrorealism and frame Leggett–Garg-type tests that could rule them out. Our numerical simulations indicate that even in the presence of decoherence, several tests could exhibit the required violations of the Leggett–Garg inequality. Remarkably, some violations persist even at room temperature for our decoherence model.

Protein hydration dynamics and molecular mechanism of coupled water-protein fluctuations

Protein surface hydration is fundamental to its structural stability and flexibility, and water-protein fluctuations are essential to biological function. Here, we report a systematic global mapping of water motions in the hydration layer around a model protein of apomyoglobin in both native and molten globule states. With site-directed mutagenesis, we use intrinsic tryptophan as a local optical probe to scan the protein surface one at a time with single-site specificity. With femtosecond resolution, we examined 16 mutants in two states and observed two types of water-network relaxation with distinct energy and time distributions. The first water motion results from the local collective hydrogen-bond network relaxation and occurs in a few picoseconds. The initial hindered motions, observed in bulk water in femtoseconds, are highly suppressed and drastically slow down due to structured water-network collectivity in the layer. The second water-network relaxation unambiguously results from the lateral cooperative rearrangements in the inner hydration shell and occurs in tens to hundreds of picoseconds. Significantly, this longtime dynamics is the coupled interfacial water-protein motions and is the direct measurement of such cooperative fluctuations. These local protein motions, although highly constrained, are necessary to assist the longtime water-network relaxation. A series of correlations of hydrating water dynamics and coupled fluctuations with local protein's chemical and structural properties were observed. These results are significant and reveal various water behaviors in the hydration layer with wide heterogeneity. We defined a solvation speed and an angular speed to quantify the water-network rigidity and local protein flexibility, respectively. We also observed that the dynamic hydration layer extends to more than 10 A. Finally, from native to molten globule states, the hydration water networks loosen up, and the protein locally becomes more flexible with larger global plasticity and partial unfolding.

Anomalous surplus energy transfer observed with multiple FRET acceptors

BACKGROUND

Förster resonance energy transfer (FRET) is a mechanism where energy is transferred from an excited donor fluorophore to adjacent chromophores via non-radiative dipole-dipole interactions. FRET theory primarily considers the interactions of a single donor-acceptor pair. Unfortunately, it is rarely known if only a single acceptor is present in a molecular complex. Thus, the use of FRET as a tool for measuring protein-protein interactions inside living cells requires an understanding of how FRET changes with multiple acceptors. When multiple FRET acceptors are present it is assumed that a quantum of energy is either released from the donor, or transferred in toto to only one of the acceptors present. The rate of energy transfer between the donor and a specific acceptor (k(D-->A)) can be measured in the absence of other acceptors, and these individual FRET transfer rates can be used to predict the ensemble FRET efficiency using a simple kinetic model where the sum of all FRET transfer rates is divided by the sum of all radiative and non-radiative transfer rates.

METHODOLOGY/PRINCIPAL FINDINGS

The generality of this approach was tested by measuring the ensemble FRET efficiency in two constructs, each containing a single fluorescent-protein donor (Cerulean) and either two or three FRET acceptors (Venus). FRET transfer rates between individual donor-acceptor pairs within these constructs were calculated from FRET efficiencies measured after systematically introducing point mutations to eliminate all other acceptors. We find that the amount of energy transfer observed in constructs having multiple acceptors is significantly greater than the FRET efficiency predicted from the sum of the individual donor to acceptor transfer rates.

CONCLUSIONS/SIGNIFICANCE

We conclude that either an additional energy transfer pathway exists when multiple acceptors are present, or that a theoretical assumption on which the kinetic model prediction is based is incorrect.

Penrose-Hameroff orchestrated objective-reduction proposal for human consciousness is not biologically feasible

Penrose and Hameroff have argued that the conventional models of a brain function based on neural networks alone cannot account for human consciousness, claiming that quantum-computation elements are also required. Specifically, in their Orchestrated Objective Reduction (Orch OR) model [R. Penrose and S. R. Hameroff, J. Conscious. Stud. 2, 99 (1995)], it is postulated that microtubules act as quantum processing units, with individual tubulin dimers forming the computational elements. This model requires that the tubulin is able to switch between alternative conformational states in a coherent manner, and that this process be rapid on the physiological time scale. Here, the biological feasibility of the Orch OR proposal is examined in light of recent experimental studies on microtubule assembly and dynamics. It is shown that the tubulins do not possess essential properties required for the Orch OR proposal, as originally proposed, to hold. Further, we consider also recent progress in the understanding of the long-lived coherent motions in biological systems, a feature critical to Orch OR, and show that no reformation of the proposal based on known physical paradigms could lead to quantum computing within microtubules. Hence, the Orch OR model is not a feasible explanation of the origin of consciousness.

Weak, strong, and coherent regimes of Fröhlich condensation and their applications to terahertz medicine and quantum consciousness

In 1968, Fröhlich showed that a driven set of oscillators can condense with nearly all of the supplied energy activating the vibrational mode of lowest frequency. This is a remarkable property usually compared with Bose-Einstein condensation, superconductivity, lasing, and other unique phenomena involving macroscopic quantum coherence. However, despite intense research, no unambiguous example has been documented. We determine the most likely experimental signatures of Fröhlich condensation and show that they are significant features remote from the extraordinary properties normally envisaged. Fröhlich condensates are classified into 3 types: weak condensates in which profound effects on chemical kinetics are possible, strong condensates in which an extremely large amount of energy is channeled into 1 vibrational mode, and coherent condensates in which this energy is placed in a single quantum state. Coherent condensates are shown to involve extremely large energies, to not be produced by the Wu-Austin dynamical Hamiltonian that provides the simplest depiction of Fröhlich condensates formed using mechanically supplied energy, and to be extremely fragile. They are inaccessible in a biological environment. Hence the Penrose-Hameroff orchestrated objective-reduction model and related theories for cognitive function that embody coherent Fröhlich condensation as an essential element are untenable. Weak condensates, however, may have profound effects on chemical and enzyme kinetics, and may be produced from biochemical energy or from radio frequency, microwave, or terahertz radiation. Pokorný's observed 8.085-MHz microtubulin resonance is identified as a possible candidate, with microwave reactors (green chemistry) and terahertz medicine appearing as other feasible sources.