To estimate the number of isomerizations (φ) produced by the stimuli, we followed previously described methods
29 30 31 and used the equation
\[{\theta}\ {=}\ L\ {\cdot}\ A\ {\cdot}\ t({\lambda})k({\lambda})(1\ {-}\ 10^{{-}D{\lambda}}){\gamma}.\]
In this equation,
L is the luminance of the stimulus (in candelas per square meter),
A is the area of the pupil, and
t(λ) the transmissivity of the ocular media. The constant
k(λ) includes the posterior nodal distance, the scotopic luminance efficiency (
V′
λ), the end-on collecting area of a single rod, and the wavelength of the stimulus (λ). The quantum efficiency of isomerization (γ) and the optical density of rhodopsin (
D λ) are the other terms in the equation. For the conversion, the end-on collecting area of the rod and quantum efficiency of isomerization are assumed to be the same in infants and adults. Further, the axial density of rhodopsin in the outer segment is taken to be proportional to the rhodopsin content of the retina,
3 and thus, the ratio of infant to adult isomerizations is proportional to (1–10
−D infant)/(1–10
−D adult).
From the human rhodopsin growth curve,
3 4-week-old infants have 46% and 10-week-olds 68% of the adult rhodopsin density of 0.4. Therefore, optical density is 0.18 at 4 weeks and 0.27 at 10 weeks, and the calculated ratio of (1–10
−D infant)/(1–10
−D adult) is 0.56 at 4 weeks and 0.77 at 10 weeks. Thus, 1 scot td · s isomerizes 4.8 molecules of rhodopsin in 4-week-olds, 6.6 molecules in 10-week-olds, and 8.5 molecules in adults.
The main parameters of the model are
S and
R mp3.
S is a sensitivity parameter related to the gain of activation. It is based on the time constants of the molecular processes involved in the activation of phototransduction.
4 5 The saturated amplitude of the response,
R mp3, represents the number of channels in the outer segment membrane that are available for closure by light.
4 5 In immature rat and human retina, both
S and
R mp3 are proportional to the rhodopsin content of the retina.
3 6 7