Photoactivated biological processes as quantum measurements

We outline a framework for describing photoactivated biological reactions as generalized quantum measurements of external fields, for which the biological system takes on the role of a quantum meter. By using general arguments regarding the Hamiltonian that describes the measurement interaction, we identify the cases where it is essential for a complex chemical or biological system to exhibit nonequilibrium quantum coherent dynamics in order to achieve the requisite functionality. We illustrate the analysis by considering measurement of the solar radiation field in photosynthesis and measurement of the earth's magnetic field in avian magnetoreception.

Figure 1

(a) Schematic of optical pumping for light harvesting. The rate constants for this optical pumping scheme are as follows: ${\Gamma }_{31},{\Gamma }_{21}\sim {\left(\text{15}\text{ns}\right)}^{-1}$ [9], ${\Gamma }_{2X}\sim {\left(\text{200–700}\text{ps}\right)}^{-1}$ [10], ${\Gamma }_{32}\sim {\left(\text{5–70}\text{ps}\right)}^{-1}$ [11]. (b) Optical pumping scheme corresponding to photon-absorption induced dynamics of rhodopsin. The magnitude of the key decay rates are ${\Gamma }_{32}\sim {\left(80\text{fs}\right)}^{-1}$ [12], ${\Gamma }_{2t}\sim {\left(140\text{fs}\right)}^{-1}$ [13], ${\Gamma }_{2c}\sim {\left(280\text{ps}\right)}^{-1}$ [14], while the remaining rate constants are ${\Gamma }_{31}\sim {\left(20\text{ps}\right)}^{-1}$ [15] and ${\Gamma }_{tX}\sim {\left(1\text{ps}\right)}^{-1}$ [13].

Figure 2

(a) Schematic of energy levels relevant to magnetoreception in cryptochrome, within the simplified radical pair model of two electron spins $S^F$ at FAD and $S^T$ at tryptophan (single up/down arrows) with a single nuclear spin $I^F$ (double up/down arrows) interacting with the FAD electron spin. With an anisotropic hyperfine tensor $A\equiv A_z$, a weak external field $B_e\parallel \widehat{z}$ just shifts the energy levels (vertical bars), while $B_e\perp \widehat{z}$ induces transitions between spin levels with different $z$ projection of $S=S^F+S^T$ (double headed arrows). For $A_z\gg B_e$, the resulting eight total spin levels are divided into two groups separated by a gap of order $A_z$. (b) Schematic of the resulting external magnetic field modified singlet-triplet conversion in optically excited cryptochrome for $B_e\perp \widehat{z}$. Upon optical excitation and the subsequent fast relaxation leading to radical pair formation, the protein-chromophore complex is prepared in a coherent superposition of its electronic eigenstates $|\uparrow \downarrow \rangle$ and $|\downarrow \uparrow \rangle$, i.e., of $|s\rangle$ and $|t_0\rangle$. While the hyperfine interaction modifies the relative phase accumulated by $|\uparrow \downarrow \rangle$ and $|\downarrow \uparrow \rangle$, $B_e\perp A_z$ leads to coherent excitation of the other two triplet states $|t_{+}\rangle =|\uparrow \uparrow \rangle$ and $|t_{-}\rangle =|\downarrow \downarrow \rangle$, thereby modifying the probability that the molecule ends up in the protonated state.