Thursday, April 2, 2009

Survival of the fittest quantum noise?

A series of recent theoretical papers from groups at Harvard and Imperial college have raised the possibility that biological systems may use the sensitivity of quantum systems to noise to optimise energy transport.
(I thank Drew Ringsmuth and Gerard Milburn for bringing these papers to my attention).
These papers were inspired by experiments at Berkeley which found that in a particular photosynthetic complex at a temperature of 77K (n.b., not room temperature) there was evidence for quantum coherence of excitons for time scales of the order of a few hundred femtoseconds. Furthermore, it was claimed that the protein is actually designed to protect this coherence.

These new theoretical papers perform calculations on several model systems and make the general observation that there is an optimum non-zero coupling to the environment for maximum efficiency and rate of transport. This goes against ones simple intuition that one might think that noise will aways reduce efficiency and rate of energy transfer. This is interesting and I think it is worth pointing out a much simpler (and older) example that illustrates this principle: a classic result of Marcus-Hush electron transport theory.

Following Weiss’ (useful, encyclopedic, but unfortunately opaque)
book on Quantum Dissipative Systems (see especially Section 20.1) this observation can be framed in the following terms: consider a spin boson model with bias epsilon and coupling matrix element Delta between two quantum states, denoted 1 and 2.

The reorganisation energy lambda is a measure of the strength of the coupling of the environment to the two quantum states. At temperatures larger than Delta and the characteristic frequency of the boson (environment) bath and for Delta small enough that the “non-adiabatic” limit holds. The rate of transfer from state 1 to state 2 is given by equation (5) in Marcus’ Nobel lecture.

The rate is a maximum when the reorganisation energy equals the bias. See Figures 7 and 8 in Marcus’ Nobel lecture. Hence, for a fixed bias epsilon there is an optimal (non-zero) value for the coupling to the environment.

Thus, this is another example of how the optimum rate occurs for a non-zero coupling to the environment.

Although Marcus and Hush were concerned with electron transfer, Joel Gilmore and I showed the mathematics is identical for Forster resonant energy transfer between chromophores.

Have biomolecules evolved to optimise energy transfer, as claimed by some? I doubt it.

A recent article claims that for electron transfer in proteins it appears that the reorganisation energy is NOT particularly selected by nature to optimise the rate.

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