Vibrations, quanta and biology

In the paper

“No noise or very strong noise are counterproductive for the performance of the transport network.”

In the paper

“A numerical optimization employing Redfield equations to take account of the spectral structure of the environment (see [34, 61] for theoretical and numerical details) now finds that the optimal position of site 2 is close to site 1 such that it exhibits a strong coherent dipolar interaction and close in excitation energy.”

What the sources say

• Not checked yetcites [34]
• Not checked yetcites [61]

In the paper

“Even more remarkable is the observation in recent experiments that Drosophila flies are capable of discriminating between molecules in their hydrogenated and their deuterated form and, importantly, are able to generalize from deuterated molecules to other molecules that exhibit a vibrational modes similar in frequency to the Carbon-Deuterium stretch mode [21]”

What the sources say

• Not checked yetcites [21]

In the paper

“Hence, in 50% of the cases the system will remain in the anti-symmetric state while in the other 50% of the cases the excitation reaches the reaction center. Therefore the transfer efficiency is limited to 50% in this setting.”

In the paper

“In the exchange of energy between two quantum systems these features will then enforce highest efficiency if the respective energy levels, such as vibrational eigenfrequencies, are well matched.”

In the paper

“there is some evidence for proton tunneling in enzymes (see e.g. [8])”

What the sources say

• Not checked yetcites [8] source

In the paper

“This includes coherence and interference, that is, wave-like features of particles which may lead to faster propagation for example in quantum random walks [9].”

What the sources say

• Not checked yetcites [9] source

In the paper

“This requires a wide variety of transport processes including excitation energy transfer but extending to charge transport including electrons, protons and ions as well as the transport of larger molecules, peptides and proteins.”

In the paper

“This in turn permits the unambiguous identification of frequencies and thus can facilitate the construction of sensing devices [20].”

What the sources say

• Not checked yetcites [20]

In the paper

“It is noteworthy though that, distinct from evolutionary optimization, via the control of conformation within an existing structure nature also possesses the means to switch between different states of operation.”

In the paper

“The uncontrolled fluctuations of these environments will lead to changes in the local structures in which the electronic degrees of freedom are embedded and may therefore lead to decoherence.”

In the paper

“and at the same time the properties of the environmental fluctuations that this transport networks are subjected to are determined and tuned mainly via the secondary protein structure.”

In the paper

“In order to optimize this interplay between system and environment, biological systems cannot simply be random conglomerates but must possess structure that they can control.”

In the paper

“While thermal fluctuations imparted by the environment may be beneficial for example to overcome potential barriers between distinct classical configurations and therefore facilitating processes such as protein folding or chemical reactions”

In the paper

“So much is unknown about biological systems that assumptions that are entering theoretical models as well as the predictions of these models must be tested against experiment.”

In the paper

“The discussions so far suggest that quantum dynamics, structured environments and their mutual interplay may provide increased efficiencies and potentially even novel functionalities.”

In the paper

“The rich structure of biological environments leads to non-Markovian dynamics which is also non-perturbative being neither weak nor strong compared to the intrasystem dynamics.”

In the paper

“If, on the other hand, a narrow spectral feature, relating to a long-lived vibrational mode, is excited then this will lead to long lasting quasi-coherent motion of the environment with the possibility of triggering quasi-coherent exchange with the system.”

In the paper

“This optimization that is required here will have taken place on evolutionary time scales.”

In the paper

“The ensuing out-of-equilibrium dynamics then leads to perturbation of the environment by the system and a back-action of the very same environment on the system initiating as a result a dynamical exchange between system and environment.”

In the paper

“It will become crucial that far from being passive scaffolds whose mere purpose is to hold other molecules in their place, the primary, secondary and especially the tertiary structure of proteins play a much broader and active role for the emergence of quantum effects in biology.”

In the paper

“It must be stressed however that the study of quantum effects in biology is an endeavour in which theory alone cannot succeed and has to proceed hand-in-hand with experiment.”

In the paper

“Biological environments are not featureless sources of white noise nor do they represent merely weak perturbations.”

In the paper

“Excitation by incoherent sunlight as well as ensemble averages may suppress the observed coherence and have tempted some researchers to reach the conclusion that coherence may be of no relevance in these systems under natural conditions.”

In the paper

“the coherence and entanglement [63, 64] properties of states [62, 65] and, more importantly, the dynamics of the system [66] which demonstrate quite clearly that on shorter lengthand timescales quantum coherence is present in the systems while for longer distances and times classical properties dominate.”

What the sources say

• Not checked yetcites [62]
• Not checked yetcites [65]
• Not checked yetcites [66]

In the paper

“We will later see that there are a number of additional mechanisms in which noise and coherent dynamics coexist to lead to similar conclusions [62, 79].”

What the sources say

• Not checked yetcites [62]
• Not checked yetcites [79]

In the paper

“Note, that H I describes a purely dephasing interaction because the vibrational degrees of freedom have energies that are at least 10 -100 times smaller than the excitation energies of the excitons thus suppressing direct exciton-phonon interconversion.”

In the paper

“More importantly, this principle is sufficiently general to provide a mechanism that can support the surprisingly long-lasting oscillatory features observed in recent ultra-fast laser spectroscopy experiments [11-14] and explain key aspects of the dynamics that may underlie the process olfaction.”

What the sources say

• Not checked yetcites [11]
• Not checked yetcites [12]
• Not checked yetcites [13] source
• Not checked yetcites [14] source

In the paper

“Indeed, if the environmental noise is too weak, then the formation of dressed states will present little benefit for transport. On the other hand if dephasing noise is very strong then it will suppress the formation of the dressed states and thus of the phonon antenna effect in the first place.”

In the paper

“Needless to say, these dynamical equations describing the full state of system and vibrational environment are generally too complex to be solved exactly.”

In the paper

“Observing these two points alone, that is inducing strong coherent coupling to move to a dressed basis and tuning the coupling such that it matches the maximum of the spectral density of the environmental fluctuations, one already comes close to the numerically obtained solution of the above optimization problem and can thus optimize excitation energy transport.”

In the paper

“In the presence of a long-lived vibrational mode the phonon antenna principle remains the same but, crucially, the nature of the interaction changes as the interaction between a single vibrational mode and the electronic degrees of freedom is coherent, at least for as long as the mode itself remains coherent.”

In the paper

“It is the equations of motion that determine the performance of each individual system and are unaffected by the nature of the initial preparation or ensemble averages that may obscure the observed coherence”

In the paper

“Crucially however we will see shortly that the structure of the environment does play an important role and thus the development of methods that can capture these features will be of considerable importance for quantitative studies of such systems.”

In the paper

“We will contend that nature can construct and optimize pigment-protein complexes, for example the FMO complex, to create transport networks that exploit both the quantum dynamics of its electronic degrees of freedom and their interaction with a structured vibrational environment.”

In the paper

“Needless to say, not all biological systems will possess long-lived vibrational modes that are strongly coupled to electronic degrees of freedom and can therefore play a role in the dynamics of the system.”

In the paper

“Pigment-protein complexes consist of a number of sites, schematically depicted in Fig. 3, whose excitation energies generally exhibit a certain degree of static disorder, that is, their on-site energies will differ from site to site and also from one pigment-protein complexes to another.”

In the paper

“As is well-known in quantum optics a mode in a coherent state acts on a two-level system essentially like a time-dependent classical driving field resulting in coherent Rabi-like oscillations following approximately the Hamiltonian”

In the paper

“Remarkably, it was well before the advent of the lock-and-key principle that Dyson in 1938 proposed [93] that the smell of a molecule may be determined by its vibrational spectrum and that hence the olfactory system effectively operates as a vibrational spectrometer”

What the sources say

• Not checked yetcites [93]

In the paper

“As a result we will observe coherent transitions between dissipative excitonic states and thus coherences that will last for the coherence time of the vibrational mode an expectation that can be corroborated by more sophisticated numerical treatments employing methods described in [28, 87-89].”

What the sources say

• Not checked yetcites [28]
• Not checked yetcites [87] source
• Not checked yetcites [88] source
• Not checked yetcites [89]

In the paper

“This electron-vibrational coupling regenerates electronic coherences in the system to replace those that are continuously damped out by the fluctuations of the smooth background environment and may even lead to stationary entanglement [90].”

What the sources say

• Not checked yetcites [90]

In the paper

“Secondly, we note that the sudden displacement of this mode implies that it is now found to be in a displaced thermal state which will be close to a coherent state if the frequency of the mode is such that its thermal occupation number is low.”

In the paper

“The initial (fast) injection of an exciton, either coherently or incoherently, populates one of the exciton states of the system (raised black dot in Fig. 7b) and creates a sudden force on the electrons and nuclei and thus change their equilibrium positions (compressed spring in Fig. 7b).”

In the paper

“What is present in all biological systems however are thermal fluctuations of the molecular and protein structures as well as the surrounding solvents, water etc.”

In the paper

“This resonance condition ensures increased transport efficiency and thus leads to a detectable effect at the physiological level (delivery of an electronic excitation to the reaction center or electron transfer which stimulates a subsequent response of a receptor).”

In the paper

“In that case tunneling is suppressed in the absence of the odorant because of the impossibility to satisfy energy conservation.”

In the paper

“Despite considerable progress concerning the understanding of the structure of olfactory receptors that involved in the early stages of the olfactory process, the detailed mechanisms by which we are able to discriminate between the vast number of odorants are not yet fully understood [91].”

What the sources say

• Not checked yetcites [91]

In the paper

“They realised that these anomalies arose for certain voltages such that the energy difference of the electrons on both sides of the tunneling barrier would match a vibrational quantum of energy of the adsorbed molecules and went on to demonstrate that this mechanism, inelastic electron tunneling spectroscopy, allows them to identify vibrational spectra of molecules”

What the sources say

• Not checked yetcites [97]
• Not checked yetcites [98]

In the paper

“What we would like to stress here though is the very close resemblance of the above mechanism to the phonon antenna principle and thus the importance of electronvibrational coupling.”

In the paper

“As a consequence we expect again that an intermediate noise level will be optimal, too low it will not suppress destructive interference efficiently and too high it will suppress all transport.”

In the paper

“The effects of weak magnetic field on the growth of plants as well as the remarkable orientation and navigation abilities of birds, mammals, reptiles, amphibians, fish, crustaceans and insects are well documented [123].”

What the sources say

• Not checked yetcites [123]

In the paper

“In this case, neither variations of the fine details of the spectral density nor variations of the electronic structure of the transport network have a significant effect.”

What the sources say

• Not checked yetcites [62]
• Not checked yetcites [122]

In the paper

“Thanks to constructive interference a symmetric superposition experiences a coherently enhanced coupling to the site 3 to which it will then propagate rapidly, and from there into the reaction center, while the antisymmetric part will not evolve at all.”

In the paper

“At this stage no magnetic field sensitivity can be expected as the spin singlet state is rotationally symmetric and hence insensitive to the orientation and magnitude of the external magnetic field.”

In the paper

“In such a case dephasing may be useful to reduce the effective transition rate to such sites and thus block unfavorable transfer paths from being followed [74, 106].”

What the sources say

• Not checked yetcites [74]
• Not checked yetcites [106]

In the paper

“As a consequence this excitation will remain localized and does not propagate through the system.”

In the paper

“The mechanism by which this magnetic field sense is achieved, however, is less well understood and at least two alternative ideas are being considered, one that exploits the forces exerted on ferrimagnetic iron oxide particles embedded in the body, essentially a classical effect, and another that is based on magnetically sensitive free radical reactions [17, 18, 124].”

What the sources say

• Not checked yetcites [17]
• Not checked yetcites [18]
• Not checked yetcites [124]

In the paper

“Indeed, a low level of fluctuations will not bring the site energies sufficiently close and transport remains suppressed, while excessive fluctuations of the site energies will reduce the time intervals in which the sites are energetically sufficiently close to allow for efficient energy transfer.”

In the paper

“It should also be noted that an energy mismatch and the resulting time-evolution of the relative phase between the two sites 1 and 2 also leads to transitions between symmetric and anti-symmetric state and can thus assists transport [16, 62, 121].”

What the sources say

• Not checked yetcites [16] source
• Not checked yetcites [62]
• Not checked yetcites [121]

In the paper

“which achieves a maximum for ∆ G 0 = λ .”

What the sources say

• Not checked yetcites [105]

In the paper

“Eventually the finite lifetime of the excitation implies that it will be lost to the general environment due to a spontaneous annihilation process, an event that is not in the interest of a transport network.”

In the paper

“Hence, the presence of dephasing noise inhibits both constructive and destructive interference and therefore slows the propagation of an excitation in a system initiated in the symmetric state and accelerates the propagation of an excitation in a system initiated in the antisymmetric state.”

In the paper

“Behavioral experiments with birds such as the European robin to study avian magneto-reception [125] have led to the observation that the process of avian magnetoreception depends on the wavelength of the ambient light [126] and can be disrupted by very weak external oscillating magnetic fields [19, 127].”

What the sources say

• Not checked yetcites [125]
• Not checked yetcites [126]
• Not checked yetcites [19]
• Not checked yetcites [127]

In the paper

“Such a stability can be an attractive feature to ensure robustness in an organism that is subject to changes in its environment.”

In the paper

“While in many respects it appears easier to achieve considerable changes in the electronic structure as compared to the vibrational environment it is likely that both will have been subject to evolutionary adaptation.”

In the paper

“Hence it is only when studying the properties of system and environment that we can gain and understanding of the chemical compass and an opportunity to predict optimal designs [138].”

What the sources say

• Not checked yetcites [138]

In the paper

“The fact that local interactions between electron spins and their nuclear environment lead to a breaking of the symmetry of the electronic spin state gives a first indication of the importance of the presence of local environments.”

In the paper

“Furthermore, it has become clear that the optimal operating regime for quantum bio dynamics tends to favour parameter ranges in which the interaction between system components is comparable to the interaction of these system components and their environment.”

In the paper

“The spectral function thus describes the overall strength of the interaction of the system with the reservoir modes of frequency ω .”

In the paper

“On the other hand it may on occasion be beneficial to increase the level of noise by arranging easily movable charges close to a site which will respond strongly to vibrations and thus create significant changes in the excitation energy of the site.”

In the paper

“This approach is non-perturbative and is capable of interpolating, for example, between the Bloch-Redfield and the F¨ orster regimes [152, 154].”

What the sources say

• Not checked yetcites [152]
• Not checked yetcites [154]

In the paper

“For spin environments, e.g. the nuclear spin environment in magneto-reception, the structure of the relevant molecule and the form of the electronic wavefunction determines the strength and anisotropy of the hyperfine interaction.”

In the paper

“We begin by presenting an approach to the systemenvironment interaction that preserves the full information about the environment state, is able to treat arbitrary spectral densities and coupling strengths within a single unified framework with known and controllable error and is computationally efficient in the size of the environment.”

In the paper

“In this way, it is conceivable that similar to a PC card the insertion of a specific molecule may allow for certain functionality to be achieved.”

In the paper

“A translationally invariant harmonic chain with this ratio ω n /t n has a gapless dispersion and excitations can escape down the chain without being scattered back towards the system (see Fig. 13 for illustration).”

In the paper

“We have also explained that it is likely that nature has optimized both the properties of its quantum networks and the structure of the environment to achieve optimal performance.”

In the paper

“The principles expounded here are more general though and apply to any quantum network whose task may include for example transport or sensing and that is in contact with an environment of charges, spins or vibrations.”

In the paper

“Thus the buildup of excitations in any region of the chain is limited over time, and correlations can be expected to be bounded.”

In the paper

“As it can be proven for a wide variety of spectral densities, in the large n limit the chain parameters ω n to t n converge and their ratio approaches ω n /t n → 2.”

In the paper

“In this model the quantum system interacts with a macroscopic number of environmental degrees of freedom and the total system and environment state evolves under a purely unitary dynamics.”

In the paper

“This suggests that indeed nature has at its hand a wide variety of possibilities for tuning quantum networks and their environments to achieve robust and efficient devices.”

In the paper

“There are two principal aspects that can be controlled, the electronic network and its environment.”

In the paper

“A donor acceptor pair in the singlet state may either recombine to reach the groundstate or lead to a reaction product at rate k S . Spins in the triplet state cannot recombine to reach the ground state but may lead to different reaction products at rate k T .”

In the paper

“It is this process for example that couples the vibrational motion of proteins and molecules to their electronic energies and is thus the cause of both dephasing and the interaction of long-lived vibrational modes with electronic degrees of freedom.”

In the paper

“Likewise the phonon assisted tunneling process in olfaction suggests that this process may be used to recognise molecules and to initiate charge transfer processes.”

In the paper

“Certainly, strong featureless noise can affect the ability to act and react specifically to external input.”

In the paper

“It should be noted however that, in contrast to some other methods, it becomes computationally less efficient with increasing temperature.”

In the paper

“Dissipation and decoherence appear when the system is observed without any knowledge of the state of its environment, leading to a non-unitary effective dynamics for the sub-system's reduced density matrix.”

In the paper

“Hence, in various circumstances it may be essential to reduce the level of noise for example by protecting a molecule inside a protein structure or a hydrophobic binding pocket.”

In the paper

“From this viewpoint the chemical compass can be seen as an environment assisted quantum interferometer thus affirming avian magneto-reception as an example of quantum biology that benefits from an interplay of system-environment interaction [138].”

What the sources say

• Not checked yetcites [138]

In the paper

“These changes can be significant and can reach the range of 100 ′ s of wavenumbers or more even for very small distance changes in the environment. For larger structural changes of the protein scaffold, e.g. due to variations in pH-value or other more drastic changes the shift in wavelength can even reach dozens of nanometers.”

In the paper

“Despite the relative simplicity of this model its dynamics is not exactly solvable and one has to resort to numerical methods. This is particularly so, when the environmental spectral density does exhibit considerable structure or when the coupling strength between system and environment lies in the non-perturbative regime.”

In the paper

“Indeed, a large amount of initial coherence in this picture correlates strongly with high sensitivity of the chemical compass and the impact of different types of decoherence can be predicted from it.”

What the sources say

• Not checked yetcites [138]

In the paper

“For highly structured environments in which for example both narrow and broad features are combined these methods find challenges.”

In the paper

“Temperatures not too far below the typical system frequencies appear to be accessible [169].”

What the sources say

• Not checked yetcites [169] M. Thorwart, P. Reimann and P. H¨ anggi, Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator , Phys. Rev. E 62 (2000) pp. 5808 - 5817.

In the paper

“Path integral methods have been applied mostly to dimers (see e.g.[166]) and their scaling to larger systems, just as for the transformation approach to be discussed below, remains to be demonstrated.”

What the sources say

• Not checked yetcites [166] M. Thorwart, J. Eckel, J.H. Reina, P. Nalbach, and S. Weiss, Enhanced quantum entanglement in the nonMarkovian dynamics of biomolecular excitons , Chem. Phys. Lett. 478 (2009), pp. 234 - 237.

In the paper

“The importance of these design principles goes beyond merely understanding what has been created already but also paves the way by which these principles, when spelled out and made quantitative, can allow for the rational design of optimal structures as well as the execution of optimized experiments by which to amplify and verify quantum effects in biology.”

In the paper

“With decreasing temperatures and thus increasing correlation time the computational effort grows rapidly.”

In the paper

“It can be understood from simple and generalizable principles that we have identified in our discussions to explain that too much or too little coherence can be detrimental and that it is in fact natural to expect that there is an intermediate regime that is optimal.”

In the paper

“The depth of this hierarchy and the structure of its coefficients depend on the correlation time of the bath and its spectral density.”

In the paper

“Nevertheless, it should be noted, that the hierarchy method has been applied successfully to a dimer [152, 154] as well as the seven-site FMO complex [154, 159, 160] with a Brownian harmonic oscillator spectral density of the environment.”

What the sources say

• Not checked yetcites [152]
• Not checked yetcites [154]
• Not checked yetcites [159] A.G. Dykstra and Y. Tanimura, The role of the environment time scale in light-harvesting efficiency and coherent oscillations , New J. Phys. 14 (2012), 073027.
• Not checked yetcites [160] Ch. Kreisbeck, T. Kramer, M. Rodriguez, and B. Hein, High-performance solution of hierarchical equations of motions for studying energy-transfer in light-harvesting complexes , J. Chem. Theo. Comp. 7 (2011), pp. 2166 2174.

In the paper

“For specific choices of the bath spectral density, namely the Brownian harmonic oscillator and/or high temperatures the temporal bath correlations decay exponentially so that the hierarchy can be terminated early with small but uncontrolled error and one obtains a manageable structure of the hierarchy.”

In the paper

“A nonexponential decay of the temporal bath correlations also leads one to estimate an exponential growth of the number of operators in the hierarchy.”

In the paper

“More complex spectral densities will lead to considerably more demanding evaluations of the coefficients of the hierarchy.”

In the paper

“Indeed, by the use of protein structure to arrange molecules and their local environment they are capable of tuning the properties of transport or sensory networks and, at the same time, adjust the environment of these networks by providing isolation or for example by inserting specific molecules with desirable vibrational or spin properties to fashion an environment.”

In the paper

“These procedures are expected to give good results in the high temperature limit and hence short correlation time of the environments.”