Unearthing the transition rates between photoreceptor conformers

Obtaining accurate estimates of biological or enzymatic reaction rates is critical in understanding the design principles of a network and how biological processes can be experimentally manipulated on demand. In many cases experimental limitations mean that some enzymatic rates cannot be measured directly, requiring mathematical algorithms to estimate them. Here, we describe a methodology that calculates rates at which light-regulated proteins switch between conformational states. We focus our analysis on the phytochrome family of photoreceptors found in cyanobacteria, plants and many optogenetic tools. Phytochrome proteins change between active (P _A ) and inactive (P _I ) states at rates that are proportional to photoconversion cross-sections and influenced by light quality, light intensity, thermal reactions and dimerisation. This work presents a method that can accurately calculate these photoconversion cross-sections in the presence of multiple non-light regulated reactions.

Our approach to calculating the photoconversion cross-sections comprises three steps: i) calculate the thermal reversion reaction rate(s); ii) develop search spaces from which all possible sets of photoconversion cross-sections exist, and; iii) estimate extinction coefficients that describe our absorption spectra. We confirm that the presented approach yields accurate results through the use of simulated test cases. Our test cases were further expanded to more realistic scenarios where noise, multiple thermal reactions and dimerisation are considered. Finally, we present the photoconversion cross-sections of an Arabidopsis phyB N-terminal fragment commonly used in optogenetic tools.

The calculation of photoconversion cross-sections has implications for both photoreceptor and synthetic biologists. Our method allows, for the first time, direct comparisons of photoconversion cross-sections and response speeds of photoreceptors in different cellular environments and synthetic tools. Due to the generality of our procedure, as shown by the application to multiple test cases, the photoconversion cross-sections and quantum yields of any photoreceptor might now, in principle, be obtained.