Some quantum weirdness in physiology

Quantum mechanics seems alien to physiology. Alarm bells go off in our heads when we hear even people of such genius as Sir Roger Penrose (1) invoke the weird coherence of quantum mechanical wave functions to explain biological function. Of course, it is only some of the “weirder” parts of quantum mechanics that bother us. Structural biochemistry is founded on the rigid geometrical relationships involved in chemical bonding that arise from quantum mechanics; the α-helix could only have been discovered by Pauling by acknowledging the power of quantum mechanical resonance to flatten the peptide bonding unit (2). Nevertheless, most modern biomolecular scientists view quantum mechanics much as deists view their God; it merely sets the stage for action and then classically understandable, largely deterministic, pictures take over. In this issue of PNAS Ishizaki and Fleming (3), by combining experimental and theoretical investigations, demonstrate that quantum coherence effects play a big role in light energy transport in photosynthetic green sulfur bacteria under physiological conditions. Quantum coherence allows a nonclassical simultaneous exploration of many paths of energy flow through the many chromophores of a light-harvesting complex, thereby significantly increasing the efficiency of the energy capture process, presumably helping the bacteria to survive in low light.

Classicism, Interrupted

Why do we so often ignore quantum dynamics in studying biomolecular function? When this question is asked by impertinent students, many of those who do computer simulations give the glib answer that most of the atoms in bio molecules are heavy, and so they have a small wavelength, thus they act merely as points in their motion. The simulation experts might also say quantum effects such as tunneling are seen but only in low-temperature cryogenic experiments (4), where owing to the lower velocity of atomic motion the thermal de Broglie wavelengths are larger.

When pressed further, this glib answer might be amplified by acknowledging that, yes, proton transfer reactions (5) and electron transfer reactions (6) are important at physiological temperatures throughout the cell and that these processes involve quantum effects but, again, these random transfer events only occur once the ponderous motions of the heavy atoms of the proteins have tuned the energetics of the reacting moieties to allow such intrinsic quantum processes to occur near a resonance between two alternatives (7).

Before and after these quantum transfer events, classical pictures are argued to take over. Perhaps so, but, in fact, mere heaviness of a biomolecule's atoms cannot completely justify the validity of such a stochastically interrupted but mostly classical picture. Rather, one must seek the justification of this picture in the complexity of most biomolecular motions. The argument goes like this: After a quantum mechanical choice has been presented to the system (i.e., the proton, the electron or in the present case involving photosynthesis, the electronic excitation, attempts a transfer), depending on the virtual outcome, the possible trajectories of the heavy atoms are sufficiently different from each other that the quantum mechanical phases of the different paths differ by large amounts (8). Thus, quantum mechanical addition of the wave function amplitudes for the different paths may be constructive or destructive, more or less at random because the phases involve large multiples of π. If many such choices occur, then it would seem the weird coherent interference relationships of quantum mechanics should average out and thus can safely be ignored.

Quantum coherence effects play a big role in light energy transport in photosynthetic green sulfur bacteria.

If, on the other hand, the heavy protein atoms repetitively carry out nearly the same motions like a clock, while the quantum choices are being made, the phases of the paths will add in some consistent fashion, perhaps destructively or perhaps constructively. How consistent the protein motions can be depends on the nature of the motions and the structure of the molecule. Motions of high frequency, which are sparse in number, have little chance to share energy with other modes, so often these modes of motion are quite repetitive and consistent: they give clear peaks in vibrational spectra. Lower-frequency motions can share energy in many ways, so they are often quite mixed up and appear to lose coherence rapidly (9). Several experiments suggest the most relevant coupled protein motions in the photosynthetic system actually retain their coherence for sufficient times to affect excitation transfer. Hints of this phase coherence came from observations of quantum beats in the spectroscopy of the Fenna-Matthews-Olson (FMO) complex as far back as the 1990s (10) but definitive evidence only recently emerged by using the 2D nonlinear spectroscopies developed in Fleming's group (11). These measurements were made at cryogenic temperatures, however, so one needs to extrapolate to room temperature conditions to see whether quantum coherence is physiologically significant.

Facing the Quantum Challenge

The simplest theoretical ideas to aid in extrapolation (12) would suggest the coherence effects may not be huge because the coherence enhancements depend on the quality of the quantum clocks: if completely constructive interference applies, the effective rate of transfer goes up roughly by the “quality factor” Q of the resonance, essentially how many times the relevant vibrational motion is repeated without significant interruption. The Q factor for the FMO complex, a somewhat imprecise notion for this multimode system, estimated from the experiment seems to be somewhere between 3 and 10. So the coherence effects probably are not huge. Such a modest quality factor, however, may be just what is needed when the heterogeneity of the energies of the interacting donor and acceptor chlorophylls is taken into account, because although high quality factors would accelerate precisely resonant processes they equally well can suppress transport if the levels happen to have been originally tuned out of resonance. This idea is the basis of Anderson localization in disordered low-temperature solids (13). In such a case a modest, critical rate of coherence loss optimizes transport (14).

Rebentrost et al. (15) have used an approximate theory of this dephasing effect on transport to suggest the loss of phase coherence in the FMO complex indeed is close to the optimal value that gives nearly 100% efficiency in the quantum transport process through the harvesting complex to the photosynthetic reaction center where a completely coherent process would be only 80% efficient. Similar arguments have been made by Plenio and Huelga (16). Clearly, though, in Carl Sagan's words, extraordinary claims require extraordinary evidence: either direct experimental confirmation of coherent transfer at physiological temperatures or numerical results from as conservative and reliable a theory as possible would be needed to believe in the physiological relevance of these weird quantum interference effects. Such a reliable calculation has been developed by Ishizaki and Fleming (3) and is used to substantiate the role of quantum coherence in this system under physiological conditions.

Why has a reliable computational framework been difficult to develop? The problem is that none of the simpler mathematical approaches are formally valid for this system: the couplings of excitations are neither very strong nor very weak, instead they seem, in a Goldilocks sense, to be “just right” for biology but therefore “just wrong” for perturbation theories. Quantum transport in this regime appears to be a general time-dependent quantum problem. Computer studies of many body quantum dynamics suffer from the “sign” problem of accounting for numerous destructively interfering paths (17); pure random sampling methods fail to sample a balancing number of positive and negative paths, making the averaging exponentially difficult when there are many interfering paths. The framework used by Ishizaki and Fleming (3), instead of sampling quantum trajectories, builds on a general approach to condensed-phase quantum dynamics developed extensively in the chemical context by Tanimura (18) in which a finite hierarchy of levels of excitations in each of the modes of motion are coupled together and accounted for completely. Then the dynamics in this large, but finite, quantum space is exhaustively probed. In the present system, convergence seems to be reached with 12 excitations. A very different-appearing, but actually deeply related, path integration scheme has been applied by Ray and Makri (19) to energy transport in a different photosynthetic complex, where, unfortunately, the experiments are less complete.

Will the weirdness of quantum coherence surface elsewhere in physiology? There are signs of it in the initial events of vision (20). Is there an evolutionary drive here, too, for quantum effects to be as fully exploited as possible? The quantum effects may be simply a relic of the fact that the molecular ancestors of the visual chromophore once were and still are used for photosynthetic energy capture by archaebacteria. Yet, seeing tigers even a little better could have helped survival over the eons. Perhaps some of the quantum coherent advantages of information processing and sensing are exploited in vision, but my internal alarm bells go off when I consider such a prospect. Should they?