Wednesday, 18 April 2012

Photosynthesis is partly a quantum process

Photosynthesis is the process by which plants use energy from sunlight to convert carbon dioxide into organic compounds such as sugars. It is also the first biochemical process where the presence of quantum effects has been experimentally verified. 

Photosynthesis involves two kinds of reactions called light and dark reactions. 

Light reactions are the chemical processes where sunlight is needed. In particular, sunlight is absorbed by light-harvesting pigments such as chlorophyll, and substances within those pigments react with light and water to produce the standard energy-storage molecule ATP, oxygen and the co-enzyme NADPH. 

Dark reactions are processes that do not depend on light and part of what is known as the Calvin cycle, a series of biochemical processes which use NADPH and ATP from light reactions to turn carbon dioxide into sugar-phosphate molecules.      

The truly quantum effects, as far as we know, only appear in light reactions.

One of the most studied organisms for studying photosynthesis are green sulphur bacteria. In these bacteria, the basic structure of their light-harvesting apparatus is shown in the diagram below. 

Light is absorbed by an antenna region of densely packed pigments that converts light into chemical energy. This chemical energy is in the form of an excitation, which for our purposes can be thought of as an electron freed from one of the antenna molecules using energy from sunlight. (Technically speaking, the excitation is called a Frenkel exciton, which is a bound state of an electron and hole.)  

The excitation (or electron) gets transferred to any one of three proteins in what is called the Fenna-Matthews-Olson (FMO) complex.  The FMO complex is a structure composed three monomers (the 3 blue ovals) that function independently. Each FMO monomer consists of 7 major sites where chlorophyll molecules are found. These sites are arranged roughly in a circle (blue hexagons) with one in the middle, all of them surrounded by proteins (yellow bands) that act like a scaffold.  

The excitation moves from the antenna to the FMO protein into either site 1 or 6, jumps around the other sites, and then goes into the reaction center through site 3 or 4. The reaction center is where the dark reactions occur. 

So now we are ready to understand where quantum coherence plays a role. The thing to think about is how exactly does the excitation travel within the FMO complex? It is easy to imagine that maybe it jumps from one site to the next, for example, it might go from 1-7-2-3 or maybe 6-5-4. Which path it chooses might be random or it might depend on how the different sites are oriented and spaced at any particular time.

However, research studies using spectroscopy have determined that the transfer rates are incredibly fast, in the order of picoseconds, which is 0.000000000001 seconds. If it jumps from site to site in random fashion, that would take too much time. What it observed is that the excitation travels in a wave-like manner. It is not as though you can pinpoint specifically as being on one site or the other; rather, it scans the paths in simultaneous fashion.  

This is possible because the excitation is not in the state of being, for example, in site 1 or site 6 but it can be in a state that is both partly in site 1 and site 6. In quantum mechanics, this is called a superposition and it indicates quantum coherent behaviour. In fact, what the excitation does as it journeys through the FMO complex is to solve the problem of finding a most efficient path using a quantum walk. 

To gain some idea of what a quantum walk is, we can ask the following problem: suppose we have a “drunk” electron and as the electron walks, it is equally likely to go left or right from a position we will call x = 0. Suppose a left step counts as -1 and a right step counts as +1. After a total of 16 steps taken, where do you expect the electron to be on average? 

It might sound tough but if we are thinking of a random chance of going left and right, then on average you take the same number of steps to the left and steps to the right. That means we expect the electron to be at x = 0 after 16 steps. And that’s what a classical random walk would tell you.

Now since we have an electron, then instead of choosing to go left and right, it can also move in a superposition, where in some sense it partly moves in both directions. We can then ask, on average, where will the electron be after performing this quantum walk for 16 steps. It turns out the average will be roughly the square root of the total number of steps, so the electron will most likely be found either at x = -4 if it takes more left steps or x = +4 if it takes more right steps. 

Evidence for the fact that the excitation undergoes a quantum walk can also be obtained from analyzing the amount of quantum entanglement in the 7 chlorophyll sites in the FMO complex. In this case, the coherent transport of the electron through the FMO complex and the entanglement between chlorophyll states represent the same quantum phenomenon.

Quantum entanglement describes how parts of a quantum system can have properties that are strongly correlated, more so that what you would normally expect. A bit more precisely, entanglement has to do with the “state” you use to describe a system. It is a statement about how independent various parts of a system are from each other. If two systems are entangled then there is a state that provides good description of both systems together but a poor description of each system separately. 

Entanglement should strike you as quite weird: how can you know two systems well but not know them well individually? But we know such systems exist. There is even a standard procedure for creating entangled photons in the lab.

This suggests that the chlorophyll sites do not function independent of each other. It means that the FMO complex is more accurately described by an aggregate state rather than by 7 individual states. It has been shown in numerical models that entanglement between certain pairs of sites persists as long as the excitation has not reached the reaction center. The graph below shows the result for the amount of entanglement (concurrence) between some pairs of sites. For instance, the blue line corresponds to entanglement between sites 1 and 2. 

Why is presence of quantum coherence important in the study of photosynthetic systems? Since quantum coherence has been observed in a photosynthetic role, this might lead us to a further understanding of why pigments and proteins in the light-harvesting units of plants and bacteria are organized in the way they are. As is always the question with proteins, it might elucidate the relationship between structure and function in these pigment-protein complexes. In terms of physics, it opens avenues for research in quantum biology and perhaps organic systems can tell us more about how to use quantum effects in ways we have not yet imagined.


G. S. Engel, T. R. Calhoun, E. L. Read,T.-K. Ahn, T. ManĨal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems", Nature 446, (2007) 782-786.

M. Sarovar, A. Ishizaki, G. R. Fleming, and K. B. Whaley, "Quantum entanglement in photosynthetic light harvesting complexes", Nature Physics 6 (2010) 462.

M. Mohseni, P. Rebentrost, S. Lloyd, A. Aspuru-Guzik, "Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer", Journal of Chemical Physics 129 (2008) 174106.

M. Sarovar, "Quantum Mechanics of Photosynthetic Light Harvesting Machinery", Google Workshop on Quantum Biology (2010).

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