Rhodopsin Inactivation Mechanism II

Kinetics of Rhodopsin Deactivation and Its Role in Regulating Recovery and Reproducibility of Rod Photoresponse
G Caruso, P Bisegna, L Lenoci, D Andreucci, VV Gurevich, HE Hamm, E DiBenedetto. 2010. PLoS Comput Biol 6(12): e1001031.
Construction Technologies Institute, National Research Council, Rome, Italy, Department of Civil Engineering, University of Rome Tor Vergata, Rome, Italy, Department of Pharmacology, Vanderbilt University Medical Center, Tennessee, USA, Department of Mathematical Methods and Models, University of Rome La Sapienza, Rome, Italy, Department of Mathematics, Vanderbilt University, Tennessee, USA.

Aims of the study:
In photo-transduction, a single photon response (SPR) via rhodopsin occurs typically with a low variability, regardless of the dynamic nature of the receptor activation. The kinetics of rhodopsin inactivation was investigated to find what contribute to the variability most.

A query:
What does lead to the known variability: a random number of turnoff steps, sojourn period between steps, or both?

Model method:
Continuous Time Markov Chain (CTMC) of receptor actions, interfaced with a spatio-temporal model of photo-transduction.

Results:
The randomness of the period at which receptor stays in each phosphorylation state contribute to coefficient of variation (CV: standard deviation/mean). The randomness of the number of receptor turnoff steps has a negligible effect.

Their conclusion:
A randomness of sojourn time in number of phosphorylation steps for receptor shutoff is responsible for variability of the photo-transduction. The diffusion of the second messengers acts as a variability suppressor. The geometry of the rod outer segment might also contribute.


Model

The model was aimed to assess the effect of parameters on rhodopsin deactivation reaction.

Key components of the model in a sequence of Bernoulli trials:
The phosphorylation status of rhodopsin at active state (R*), acquiring i − 1 phosphate;
The rate of GRK phosphorylation (λi);
The rate of phosphorylation quenching by arrestin (μi);
The G-protein activation by R* (νi);
The sojourn time for R* phosphorylated (si), of mean (τi).

The WT responses alone were not sufficient to identify the parameters, and so they sought them along with other experimental observations in mutant mice (Hanson et al. 2006; 2007; Raman et al. 2005; Vishnivetskiy et al. 2007).

With the parameters identified, the R* deactivation cascade was translated by CTMC into the probabilities Pi(t) for receptor to be in the i-th state at time t. The output measured for activated effector (E*) was used as input in the spatio-temporal model (Andreucci et al. 2003; Bisegna et al. 2008; Caruso et al. 2005; 2006), which describes the dynamic behaviours of cGMP and calcium ions in the cytoplasm and the generation of current jtot(t) which flows through the cell membrane as a function of time t.

The variability of the effector E*:
E*(t) --- n. of E* at time t;
E*int (t) = ∫ E*(s)ds --- activity of E* up to time t;
E*area = ∫ E* (t)dt --- activity of E* over the whole lifetime;
E*(t*peak) --- Peak value of E*(t)

The natural variable functionals of the current:
I(t) = 1− (jtot(t) / jdark) --- current suppression at time t;
Iint (t) = ∫ I(s)ds --- charge suppression up to time t;
Iarea = ∫ I(t)dt --- chage suppression over the time course;
I (tpeak) --- peak value of I(t).

See their original paper for the figures of CV (linked above).

The CTMC model enables independent assessment of the effects by the random components on the variability. The effect such as the randomness of sojourn period can be isolated from the randomness due to variable numbers of receptor shutoff steps, as follows.

Three sets of simulations performed:

A. In the first case, the number of steps to R* shutoff was fixed to integer closest to mean N. A random sojourn time was applied to R*: si was generated according to their exponential distribution with τi, which is the inverse of (λi + μi);

B. In the second, the si of R* at their τi was fixed, and the R* was left to shutoff in k random steps. The value of k was generated by a series of Bernoulli trails wherein the probability of phosphorylation is λi / (λi + μi) and the probability of arrestin binding is μi / (λi+ μi);

C. Third case left both si and k remain being at random.

After about 5000 simulations up to 3 s, mean, SD and CV are computed for effector and the normalised current suppression (described in the original document).

Findings:
The CV for B was negligible, but it was produced by A similarly as in C; hence it is the randomness in the sojourn time that contribute to CV of E*. Their simulation showed a similar pattern for variability of the current. The single-photon response generated by unphosphorylated R* were highly reproducible within about 10 s. The average number of steps for receptor shutoff was estimated to be 4 steps.


Estimations:

k
The estimation of k was made based on the experiments by Wilden (1995): G-proteins, PDE and cGMP were mixed in a pool with a sufficient quantity of rhodopsin Ri, which can have up to 6 phosphate groups; Ri was activated by a flash of light to isomerise, and the rate of cGMP depletion was recorded. Form Wilden’s data they assumed the catalytic activity of R* as:

νi = vRGe^(−kv(i−1)) i = 1,…,n. ^ : to the power of ()

where νi = vRG indicates R* in initial unphosphorylated state.

Further derived was an equation based on experimental observations:

1 = [cGMP]’7/[cGMP]’1 ≈ (khydv7ϕ7[cGMP])/(khydv1ϕ1[cGMP]) = 10ν7/νRG

where ϕ denotes number of receptor isomerisation and [cGMP]i indicates [cGMP] at i-th phosphorylation state of R* and [cGMP]’ at a saturating light levels. At the limiting rates, [cGMP]i are almost the same for all i due to hydrolysation by [E*]sat. The rate of depletion [cGMP]’1 applied for an experiment with rhodopsin R1 (no phosphate) with activity ν1~νRG, and ϕ1 can be obtained from an experiment with rhodopsin R7 (6 phosphates) and ν7, provided that the ϕ7 is 10-fold larger than ϕ1. Then, 10 = e^(kv6), kv was approximated to be ≈ 0.38 thereby. ^ : to the power of

Arresitin binding rate and its affinity for R
They took the binding as if an irreversible act for deactivating R*, and counted only the high enough affinities which make the R*-Arr half-life significantly greater than the time-course of the single-photon response. Arrestin-binding was reported to be equivalently low for unphosphorylated and mono-phosphorylated R*, and three phosphate groups are required for a full association to occur (Vishnivetskiy et al. 2007); based on the data obtained by Vishnivetskiy et al., they have set the sequence for arresting binding rate accordingly to the phosphorylation level as

μ1 = μ2 = μ3 = 0, μi = μ0, i = 4,…,n.

where μ0 is the arrestin binding rate at maximum affinity after sufficient phosphorylation; n in the model gives arresting binding that terminates transducin (Gt) activation.
NB: i − 1 number of phosphates attached to R* at each step.


References

Andreucci D et al. 2003. Mathematical model of the spatio-temporal dynamics of second messengers in visual transduction. Biophys J 85: 1358–1376.

Bisegna P et al. 2008. Diffusion of the second messengers in the cytoplasm acts as a variability suppressor of the single photon response in vertebrate phototransduction. Biophys J 94: 3363–3383.

Caruso G et al. 2005. Mathematical and computational modeling of spatio-temporal signaling in rod phototransduction. IEE Proc Syst Biol 152: 119–137.

Caruso G et al. 2006. Modeling the role of incisures in vertebrate phototransduction. Biophys J 91: 1192–1212.

Hanson SM et al. 2006. Visual arrestin binding to microtubules involves a distinct conformational change. J Biol Chem 281: 9765–9772.

Hanson SM et al. 2007. Each rhodopsin molecule binds its own arrestin. Proc Natl Acad Sci USA 104: 3125–3128.

Raman D et al. 2005. Threshold mechanism of arrestin activation: two rhodopsin-attached phosphates are necessary and sufficient for high-affinity arrestin binding. In: Association for Research in Vision and Ophthalmology Annual Meeting; 1-4 May 2005; Fort Lauderdale, Florida, USA.

Vishnivetskiy SA et al. 2007. Regulation of arrestin binding by rhodopsin phosphorylation level. J Biol Chem 282: 32075–32083.

Wilden U. 1995. Duration and amplitude of the light-induced cGMP hydrolysis in vertebrate photoreceptors are regulated by multiple phosphorylation of rhodopsin and by arrestin binding. Biochemistry 34: 1446–1454.