Fundamental Limits on Wavelength, Efficiency and Yield of the Charge Separation Triad

In an attempt to optimize a high yield, high efficiency artificial photosynthetic protein we have discovered unique energy and spatial architecture limits which apply to all light-activated photosynthetic systems. We have generated an analytical solution for the time behavior of the core three cofactor charge separation element in photosynthesis, the photosynthetic cofactor triad, and explored the functional consequences of its makeup including its architecture, the reduction potentials of its components, and the absorption energy of the light absorbing primary-donor cofactor. Our primary findings are two: First, that a high efficiency, high yield triad will have an absorption frequency more than twice the reorganization energy of the first electron transfer, and second, that the relative distance of the acceptor and the donor from the primary-donor plays an important role in determining the yields, with the highest efficiency, highest yield architecture having the light absorbing cofactor closest to the acceptor. Surprisingly, despite the increased complexity found in natural solar energy conversion proteins, we find that the construction of this central triad in natural systems matches these predictions. Our analysis thus not only suggests explanations for some aspects of the makeup of natural photosynthetic systems, it also provides specific design criteria necessary to create high efficiency, high yield artificial protein-based triads

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Faculty Advisor: Dr. Lizbeth FinestackThis research was supported by the Undergraduate Research Opportunities Program (UROP)

The evolution of the charge separated state derived in eqn:ct.

<p> is normalized by , which we take to be unity. Rate constants are chosen as , and s. Relevant timescales are labeled on the upper axis and are marked by vertical lines (see eqn:kpm for definitions of ). A central quasi-steadystate (QSS) plateau region is formed when these timescales are well separated. We define the decay time of the QSS, , as the lifetime of the charge separated state. The horizontal line marks the yield, , defined as the value of <i>C</i> in QSS. Analytical expressions for and are derived in Equations 14 and 17, respectively.</p

(A) Orthogonality of the yield, , and the energy storage efficiency, , of QSS formation by the PCT.

<p>For each point, and are set to the values that maximizes within the limits set by and as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036065#pone-0036065-g005" target="_blank">Figure 5</a>. is strongly sensitive to the separation distance, , and is primarily sensitive to . (B) The decrease in the maximal values of with increasing plotted for different values of and . At large values of the optimized yield is primarily dependent on .</p

Structure and function of the photosynthetic triad.

<p>(A) Molecular detail of an idealized artificial charge separation construct, a self-assembling de novo designed protein. (B) Discrete steps in the formation of the charge separated state: The primary-donor molecule P in the ground state configuration DPA absorbs a photon of the correct frequency to form DA, where is the photoexcited state of P. The excited electron transfers to the acceptor cofactor, A, forming the intermediate state DP⁺A⁻. The donor cofactor, D, then transfers an electron into P, resulting in the charge separated state D⁺PA⁻. (C) Energy level diagram of the states in B. The <i>k</i>-variables denote the corresponding microscopic single-electron ET rates. In this scheme, the direct long range tunneling between D and A (i.e., ) and the ‘thermal back reaction’ <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036065#pone.0036065-Xu1" target="_blank">[33]</a> between P and A (i.e., ) are not considered. As explained in the main text, their magnitudes can be significantly suppressed without affecting the efficiency and yield.</p

The optimal range for and are shown on the Marcus curve.

<p>A high yield, high efficiency QSS formation in a triad requires that back electron transfer from A to P be so downhill as to be well into the Marcus inverted region. To see this, we substitute in Equation 27b so that , from which it immediately follows that the condition is satisfied if the mean value . The condition was derived in Equation 20 to be a necessary condition for the formation of a QSS.</p

Predicted long-wavelength limit or red-edge for efficient solar energy conversion.

<p>Photon energies smaller than cause a loss in either yield or energy storage efficiciency. For each point, the value of used maximizes within the constraints set by and as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036065#pone-0036065-g005" target="_blank">Figure 5</a>. The values are calculated as where and 0.4 eV. Wavelength limits of natural systems depicted above the axis are taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036065#pone.0036065-Kiang1" target="_blank">[34]</a>.</p