Chapter 9 – Emerging Biophysics Techniques  423

would imply a kinetic energy for the electron during the transition equivalent to ca. −0.6 eV,

which is negative and thus forbidden.

However, experimentally it is known that electrons undergo these transitions (you are

alive while reading this book, for example… one hopes…), and one explanation for these

observations is that the electrons undergo quantum tunneling between the donor and

acceptor sites, over a rapid time scale predicted to be ~10 fs (i.e., ~10⁻¹⁴ s). Quantum tun­

neling is also predicted to occur over longer length scales between secondary donor/​acceptor

sites; however, even though the time scale of tunneling transitions is within reach of the tem­

poral resolution of electron spectroscopy measurements, no definitive experiments, at the

time of writing of this book, have yet directly reported individual quantum tunneling events

between electron transport carrier proteins in OXPHOS.

In a vacuum, quantum tunneling over such long distances would be highly improbable.

However, in proteins, such as the electron transport carriers used in OXPHOS, the inter­

vening soft-​matter medium facilitates quantum tunneling by providing lower-​energy virtual

quantum states, which in effect reduce the overall height of the tunneling energy barrier,

significantly increasing the physiological tunneling rates. The question is then not whether

quantum tunneling is a component of the electron transport mechanism—​it clearly is. Rather,

it is whether these proteins evolved to utilize quantum tunneling as a selective advantage to

the survival of their cell/​organism host from the outset (see Chapter 2), or if the drivers of

evolution were initially more aligned with classical physics with later tunneling capability

providing a significant advantage. In several ways, one could argue that it is remarkable that

the entire biological energy transduction machinery appears to be based on this quantum

mechanical phenomenon of tunneling, given that much of biology does not require quantum

mechanics at all.

A second interesting biological phenomenon, which is difficult to explain using classical

physics, is the fundamental process by which plants covert the energy from sunlight into

trapped chemical potential energy embedded in sugar molecules, the process of photosyn­

thesis (see Chapter 2). Photosynthesis utilizes the absorption of photons of visible light by

light-​harvesting complexes, which are an array of protein and chlorophyll molecules typ­

ically embedded into organelles inside plant cells called “chloroplasts,” expressed in high

numbers to maximize the effective total photon absorption cross-​sectional area. Since the

early twenty-​first century, there has been experimental evidence for coherent oscillatory

electronic dynamics in these light-​harvesting complexes, that is, light-​harvesting complexes

in an extended array, which are all in phase with regard to molecular electronic resonance.

When initially observed, it was tempting to assign this phenomenon to quantum coher­

ence, a definitive and nontrivial quantum mechanical phenomenon by which the relative

phases of the wave functions of particles, electrons in this case, are kept constant. However,

these oscillation patterns alone are not sufficient evidence to indicate quantum mechanical

effects. For example, the effect can be modeled by classical physics as one of excitonic coup­

ling to generate the appearance of coherence beating of the electronic excitation states across

an array of light-​harvesting complexes.

KEY POINT 9.5

An exciton is a classical state describing a bound electron and electron hole that are

coupled through the attractive electrostatic Coulomb force that has overall net zero

electrical charge but can be considered as a quasiparticle, usually in insulators and

semiconductors, which has a typical lifetime of around a microsecond.

It is only relatively recently that more promising evidence has emerged for room tempera­

ture quantum coherence effects in photosynthesis (O’Reilly and Olaya-​Castro, 2014). When

the vibrations of neighboring chlorophyll molecules match the energy difference between

their electronic transitions, then a resonance effect can occur, with a by-​product of a very

efficient energy exchange between these electronic and vibrational modes. If the vibrational