Non-Markovian quantum dynamics in photosynthesis

Understanding how photosynthetic systems convert photons into separated charge is of fundamental scientific interest and relevant to the desire to develop efficient photovoltaic cells. Systematic studies could also provide a laboratory to test theories of quantum dynamics in complex environments, for reasons I will try and justify below. When I was at U. Washington earlier this year Bill Parson brought to my attention two very nice papers from the group of Neal Woodbury at Arizona State.

Protein Dynamics Control the Kinetics of Initial Electron Transfer in Photosynthesis

Unusual Temperature Dependence of Photosynthetic Electron Transfer due to Protein Dynamics

The Figures below are taken from the latter paper. I think the basic processes involved here are 

P + H_A + photon ->  P* + H_A -> P+ + H_A-

where a photon is absorbed by the P, producing the excited state P* which then decays non-radiatively by transfer of an electron to a neighbouring molecule H_A. The graphs below show the electron population on P as a function of time, for a range of different temperatures and with different mutants of the protein.  

The different mutants correspond to substituting amino acids which are located near the special pair. These change the relative free energy of the P+ state.
The simplest possible theory which might describe these experiments is Hush-Marcus theory. However, it predicts

* the decay should be exponential with a single decay constant
* the rate should decrease with decreasing temperature
* the activation energy for the rate should be smallest when the energy difference between the two charge states epsilon equals the environmental re-organisation energy.

The above two papers contained several important results which are inconsistent with the simplest version of Hush-Marcus theory:

• The population does not exhibit simple exponential decay, but rather there are several different times scales, suggesting that the dynamics is non-Markovian, and may be correlated with the dynamics of the protein environment.
• The temperature dependence: the rate increases with decreasing temperature.
• A quantitative description of the data could be given in terms of a modification of Hush-Marcus to include the slow dynamics of the protein environment. This allows extraction of epsilon for the different mutants.

Later I will present my perspective on this....