This model is similar to those developed previously by other groups (e.g., Hamer et al., 2003; Caruso et al., 2010). However, unlike previous simulations, we Obeticholic Acid in vitro included no initial delay before phosphorylation (Caruso et al., 2010) nor did our scheme make any assumptions about competition between G protein, Grk1, and arrestin, or incorporate any mechanism for feedback via recoverin (Hamer et al., 2003). We emphasize that the details

of the multistep scheme were not selected in order to make any novel claim about the actual mechanism of rhodopsin deactivation or its actual degree of reproducibility; instead, it was used to test whether transduction operating with variable rhodopsin lifetimes (c.v. ∼0.5) could generate reproducible single-photon responses, and whether the degree of reproducibility was improved with GCAPs-mediated feedback. We also found that this multistep model provided a better account of the rising phase of the response than the single exponential decay function for R∗ deactivation (Figure S2). In this scheme, it is assumed that R∗ reaches maximal catalytic efficiency within the first millisecond following isomerization, and that as long as it remains unphosphorylated, its affinities for the PCI-32765 price G protein and the kinase (GRK1) are maximal, while its affinity for arrestin is negligible (Gibson et al., 2000; Vishnivetskiy

et al., 2007). Sequential phosphorylations of rhodopsin by GRK1 decrease the rate of subsequent phosphorylation (Kennedy et al., 2001), while increasing the rate of irreversible Arr1 binding sharply after three phosphorylations (Vishnivetskiy et al., 2007). These biochemical features are embodied in the phosphorylation dependence of the rate constants for transitions between phosphorylation states and the arrestin-bound state: equation(9) kph(p)=kphmaxe−p equation(10) karr(p)=karrmax1+ep0−pθ Here kph(p)kph(p) is the transition rate constant

(s−1) of R∗ from the state with p   to that with p  +1 phosphates (p = 0, 1, …, 6), kphmax the maximum phosphorylation rate (which applies when R∗ is not yet nearly phosphorylated, p = 0), karr(p)karr(p) is the rate constant for arrestin binding, and karrmax its maximum ( Figure S2). According to Equation 10, the rate of arrestin quench is a sigmoidal function of phosphorylation state p with midpoint at p0 = 2.9 and a steepness factor θ = 0.1. As implemented, this sigmoid approximates a step function ( Figure S2B), a feature consistent with previous conclusions ( Vishnivetskiy et al., 2007), and employed in previous models that incorporate stochastic R∗ deactivation (e.g., Hamer et al., 2003, 2005; Bisegna et al., 2008; Caruso et al., 2010, 2011). The transition rates defined in Equations 9 and 10 correspond to a continuous-time Markov process for the decay of R∗ activity and determine the probability Prp   that an R∗ molecule has p   phosphates or has been quenched by arrestin at time t   after photoisomerization.