Models for Arrestin-1 and GRK1 Competition in Rhodopsin Inactivation


Arrestin Competition Influences the Kinetics and Variability of the Single-Photon Responses of Mammalian Rod Photoreceptors

T Doan, AW Azevedo, JB Hurley, and F Rieke. 2009. J Neurosci. 29(38):11867–11879.
Departments of Physiology and Biophysics and Biochemistry, and Howard Hughes Medical Institute, University of Washington, Seattle, Washington.


Background:
Rhodopsin absorbs a photon to activate G-protein transducin (Gt), that in turn closes cGMP-gated channels, thereby initiating an amplified electrical signal in rod photoreceptors. The signal generation is regulated at the level of rhodopsin by GPCR kinase 1 (GRK1) and arrestin-1. GRK1 bind to rhodopsin and phosphorylate at the C-terminal region; subsequent arrestin-1 binding to rhodopsin inactivates it. GRK1 and arrestin-1 share a portion of binding sites partially overlapping. Arrestin-1 binding affinity varies depending on phosphorylation status of the receptor.

Hypothesis:
Competition between arrestin-1 and GRK1 modulates rhodopsin activation by regulating GRK1 binding to rhodopsin.

Measured:
How alterations in the concentration of GRK1 and arrestin-1 affect the kinetics and variability of the single-photon responses of a rod.

Biological experiments:
They have recorded rod response by electrophysiology, and then isolated responses of each photon absorbed. In doing so, they have employed wild-type and mutant mice, the latter were homozygotes or heterozygotes knockout of arrestin-1 and/or GRK1. The expression of GRK1, arrestin-1, β-tublin, PDEs, RGSs were quantified.

Mathematical models:

Markov model for rhodopsin phosphorylation

Suppose the duration of rhodopsin phosphorylation depends on the competition of GRK1 and arrestin-1, and the time required for phosphorylation, a single phosphorylation step leading to rhodopsin inactivation can be treated as a Markov chain. The event was assumed to occur recurrently as dissociated GRK1 restarts the sequence presented in the figure below.


The first reaction (1) slows receptor inactivation, reactions (1-3) are repeated until sufficient number of phosphate groups are attached, and the receptor is inactive at 4.

Two determinants concerned in the events were:
How long rhodopsin binds to arrestin-1;
The time required for GRK1 binding relative to time spent for phosphorylation.

As the determinants are affected by four rate constants (α, β, γ, δ) as in the figure above, the model included differential equations to compute:
the ratio of β/α to find rate constants for arrestin-1association/dissociation; and
the ratio of γ/δ to find rate constants for GRK1 binding and phosphorylation catalysis.

The model assumed that β scaled linearly with the arrestin-1 concentration, and γ scaled linearly with the GRK1 concentration.

Four active receptor states were considered:
1. Arrestin-bound (R*Arr),
2. Unbound active (R*),
3. GRK1-bound (R*GRK),
4. Phosphorylated (R*Pn).

The mean phosphorylation time (between R* and R*Pn) was computed by iterating the probability of each state at time t with an updating transition matrix M containing relevant transition rates for given rate constants.

The model did not include:
Gt which also competes with arrestin-1 and GRK1 for rhodopsin binding. However, the effect of Gt was considered in the other model.

Stochastic transduction cascade model

The motivation of the model was to find how the time-dependent variance of the photon response depends on the relative inactivation rates of rhodopsin and Gt.

The model assumed that:
rhodopsin inactivates through a series of phosphorylations events by GRK1;
a rate constant of GRK1 binding (γ) is eight times larger than that of phosphorylation catalysis (δ) accordingly to the experimental results of this study;
each phosphorylation cycle controlled an equal fraction of the total rhodopsin activity, for multiple phosphorylation cycles contribute in inactivating the receptor (each phosphorylation step consistently contributed to receptor inactivation, so that the rate constant is decreased linearly with the number of phosphate group attached); and
the increased affinity of arrestin-1 by phosphorylation favour competing GRK1 for rhodopsin association.

The time course of a photon-activated rhodopsin was converted to a current change via either a linear or nonlinear approximation to the transduction cascade.

In the linear, the approximation was made with a Fourier transform by the formula including: the temporal frequency in radians per second (ω), dark [cGMP] (GD), the rate constant for PDE activity (ϕ), the rate constant for removal of calcium ions by cation exchange channels (θ), the dark PDE activity (PD). The inverse of ϕ gives a measure of average Gt activity. GD was determined from observed dark current (ID) as ID = kGD^3 where k = .0026 pA/μM^3.

In the non-linear, the response passed through a compressive linearity, to derive the current. A compression, which reduced sensitivity of observed current to variations in rhodopsin activity, could be caused by local saturation of the transduction cascade.

The relevant formulae are given in the method section of the original paper.

The model parameters were restricted by the essential properties of the observed single-photon responses, which are the low variability of rhodopsin, the late time-to-peak position and the symmetricity of the time-dependent variance.

Two of their models satisfied the above constrains:
1) In this model, each phosphorylation site contributed equally to rhodopsin inactivation.
On average, 5.6 phosphorylation cycles were completed before inactivation by arrestin. No compression was applied for this model.
2) Rhodopsin was inactivated through maximum of 4 phosphorylation cycles, with average value of 3.7 until arrestin binds. Compression was required to minimise response variability to meet experimental levels observed (saturation in the transduction cascade was needed to explain the low response variability). This model is a simplified versio of model introduced by Bisegna et al (2008).

The two models shared a common ground: rhodopsin inactivates more slowly than Gt.


Conclusions:

Competition between arrestin-1 and GRK1 modulates single-photon receptor kinetics.
The kinetic model (as in the diagram above) predicted that reducing [arrestin-1] 10-fold from physiological level would increase the period rhodopsin is available for GRK1 from ≈15 to ≈60%.

Competition between arrestin-1 and GRK1 reduces variability in rhodopsin inactivation. Decreasing [arrestin-1] and/or [GRK1] increased single-photon response variability.

The receptor active for a relatively long duration. The light-activated PDE action decreased when the arrestin-1 concentration was decreased. The changes in the kinetics with altered [arrestin-1] and/or [GRK1] relates with changes in GRK1 binding rates predicted by the model. They have demonstrated that the time-dependent variance of the single-photon responses can be explained by a long rhodopsin lifetime.


References

Doan T et al. 2009. Arrestin Competition Influences the Kinetics and Variability of the Single-Photon Responses of Mammalian Rod Photoreceptors. J Neurosci. 29(38):11867–11879.

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