PVisionRes., Vol. 36, No. 16, pp. 2609–2621,1996

Copyright01996 ElsevierScience Ltd. All rights reserved0042-6989(95)00327-4 Printed in Great Britain

0042-6989/96$15.00 + 0.00

An Alternative Phototransduction Model forHuman Rod and Cone ERG a-waves: NormalParameters and Variation with Age

G

Received 25 January1995; in revisedform 20 June 1995; injinal form 1 December 1995

A quantitative description of the activation reactions in the cGMP phototransduction cascade hasbeen recently developed [Lamb & Pugh (1992).Journalo~Physiobgy, 449, 719-758]. When appliedto the human electroretinogram a-wave, the widely used simplified form of this model provides agood description of all waveforms except those elicited with very high energy stimuli. The basis forthese misfits at high energies is explored in the current study and an alternative model ofphototransduction is derived that retains the quantitative aspects but avoids certain simplifyingassumptions previously made. The new model describes well both rod- and cone-isolated a-wavesover a large range of stimulus energies extending up to those that cause significant bleaching. Tofacilitate clinical application of this methodology, a short test protocol is developed and normal datafor rod and cone transduction parameters are provided over a wide age range. In the sample ofnormal subjects studied, maximum amplitude of rod and cone a-waves and sensitivity of the cone a-wave do not change with age. An age-related decline in rod a-wave sensitivity is present and it isgreater than that expected from pre-retinal absorptionalone. Copyright @ 1996 Elsevier ScienceLtd.

INTRODUCTION

a-

&

o

&

o

al.,o

ao

& &

io oF

5

t a ao o

ao

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o o& &

& e al.,e al., &

e al., i oo

tt

tb t

a bo o

A V S G

to

a

a

i

t

u tI

oo

METHODS

Subjects

The 17

o 1

ti

o

Recording technique

a a

a2 a

a &a

ao

J a ot c 5 a

I tJ

= c t

o t o= n

= n i at

o ta

t a te al., &

I ob

o& t a o

u t 2 ti

4

t( m

i 1 a ta

i a i

t t to

bo a

i

o a c

o i i tt

t 1 ao 3

t

Mathematical analysis

o at o

ba

o

~.g3

-300E0 -400aJ>0

–500

(b) ;u o0

Iuo -200E

-300

-400

-500

, 1

1

, 1

1 1

2

1 1

2 4 6 8

o

a1 o t

tb

= u = =R~,x=

7 = 12

&

a

t

a i t

aa

o 1

a

ao

bo

o

a

ot

i a

Rod phototransduction model

1 o aa

b o1 t

oi i t b

t a-

R(ZW,t) =

R max[(1 – – 1 – teff)2 t teff

R(l,C,t) is io i

t t iRmax> i

o i ai 1

~ aR max = ~ 5 = +

= ~+

o o 1 ta

1o

a a I

a aa i b

oet al., et al.,

a b to a

b bo o

t 1I

t oo

i t bt

b u at o

oo

to o w

a

A V S G

u

GE;z

1

a v ob

= i b

R~.x

o2

a

i 1

ob

i

=

Rmax[(1 – – – +

+ + *

1a o

t

~ G t –d

iA

1 21 –

2 t

+ Rrn.. =+ = +

= ~ i

I b o= i t

o o2 t b

a Rm,x tb t

t oRm.x

~ p t ~A i i 1 2 o

12 o

a o a Ao 2 i b

12 i

a a o i

= t io b

(Rm,x, a,., 12 t

b(Rmax) a

o @ t i t2

1 b ai

2 b 1b 2

32 t 1

i i 2a i 1

o iI o 2

oi

1

it

oo 1

o 2 i ob a

ob a o

I to

bo i 3

o R~,xa o a

o oa

(a)

/

(b)

Inar.-L0W

: 1.5003Io3

* 1,25

I 1 1 I

400 500 600Six–wave series

=

I 1 I 1

1.25 1.75

Six–wave series

J

2

a

o—

y

Cone phototransduction model

2t

t b

&o 2

~.

0$3

. -20EE0 -40al>0s

0

a

Ev

r 1

1 !

2 4 6 .9

4 o o ab

o 2 o ti o t

b == ] =

tZ *

4a o

2 i~ a

Rm.x = + ~ = ~= i d

at t

io

at

~ U t~ o

i bo 2

Rod phototransduction with high energy stimuli

A i o a-a

1 et al., I i ti o b bo

o

t t aa

ib

o 2 t

= 76 a

o t

= p = r = c =

A V S G

2468 2468

c 0.50 ~

2

; 2 3 4 5 6

i ti

t

12

b1 a

b2 a

5

12

Rrn~x

1 =a

2 =

a1

21 2

1

~ :--.....Q.

~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~ o. n o:

03.z~ -

<

u

~.. . . . . .. . . . . . . . .. . . . . . . . .

. .. . . .. . . . .I>

.

:< 0.5 u,,

:a, 0.0

I I

4

t i

H

o

u p

G 20 40 60 80 ““- 20 40 60 80

[years]

6 (R~,x) oo o 2 a a

o to

a

i t - 1i ]

4.0 t ot i t

2 tb t d

a

o a at

i i t 1o i

a at i

2 tb o a

it 2 t

4 t a o1

2 A4 t

t 1 o2

i1 a b a o

o o ao a

Normal variation of rod and cone transductionparameters

6

G , 1;c

“F-. predicted

~ ?4.6 ‘-... . /

u.

predicted from . .

~ u

‘x-.”

10 20 30 40 50 60 70 B

oo

oi

i

o ao y

o2 a a o

a =d = =

Oph tO Vary in a

Sewrt-waw = 6 ==

—o p

R~,,lines for cones had slopes of

~ph,

RmaxR~.,a

&

o

oal., 7

o

&t

7

a et al.,i

t b 3 yi o i

7i t

t b a o

oa o o t i

o

DISCUSSION

I w ao o

ot

b Io

b a ot

i 1 i w

o

ab

a

Rod phototransduction with high energy stimuli

The o oo

t &et al.,

oi &

i &

io I

o ib

i&

oi

b t

1 o aa o

i i1 o b ao a a1 i

A V S G

1 b

2a

a

1 o

ob

aa

2 a

Routine recording and modeling of photoreceptorjhnction

oo

&

oa

aet al., A

ab

aa-

a

2 i ba

i t

bbt

a i

= = = t Ba

iet al.,

Cone phototransduction

I ai t &

e al.,o et al.,

et al.,o t io & i b

o oi t o

o1

&

i a a ii

t at o

aa

et al., &t

t a aa a o

& &

oo a t 1

&i

ao

Amplification in rod and cone transduction

i& o i

ib i o

it

et al., 1t &

oS Oph>

1t o 1 &

et al., Id

i &i

io

aa

Delay of rod and cone activation

12

bo

= a a= a o

bi

a a

&o

I i

i it o

& et al., et al.,& et al., A

a1

o

Aging and phototransduction

et al.,& i

oo o

ao

&a o

&

n oi

i ao ni

w n i

oi a o

ob

t i i a-

t oa

i i

a o wo i

oo i t

oa

i

i io o

o&

ote al., &

o io

&et al., &

et al., o ni

i iI i o t t

tI w

1

2

3

t

d

n i oo

b tt o

i

A V S G

et al. n

a

(

a

REFERENCES

& F Ao

ClinicalVisionSciences,5,353-362.

&o Macaca

fascicularis. Journal of Physiology, 357,575-607.&

Archives of Ophthalmology, 110, 1571–1576.&

Investigative Ophthalmology and Visual Science, ARVO Abstracts,

&

Journal of Biological Chemistry, 265,20727-20730.& o

iDocumenta Ophthalmologic, 79, 337–361.& i a

oInvestigative Ophthalmology and Visual

Science, 36, S924.D & E N

i oInvestigative Ophthalmol-

ogy and Visual Science, 35, 295–309.& A i

Investigative Ophthalmology andVisual Science, 35, 635-645.

&Investigative Ophthalmology and

Visual Science, 34, 3253–3263.& N

o Nature,317,6446.

oo

Ambystoma tigrinum. Journal of Physiology, 394,529-572.A & R E

Investigative Ophthalmologyand Visual Science, 34, 3278-3296.

i I& Progress in retinal research

& B oi

Investigative Ophthalmology and Visual Science, 36, 1019-1026.& o

Archives of Ophthalmology, 111,1479-1481.

& o

oInvestigative Ophthalmology and Visual

R o it i

Journal of Physiology, 77,207-239.L W &

i o Nature,317, 61-64.

D C & D G A oo

Visual Neuroscience, 5, 379–387.D C & D G o

o oVision Research, 33, 1605–1618.

D C & D Go o

Neuroscience, 10, 857-871.D C & D G i

oInvestigative Ophthalmology and Visual

Science, 35, 2948-2961.D C & D G i

o Vision Research, 35,2801-2819.

D C & D G oi Vision Research, 36, 1699–1709.

D A A J & S GS a

o S Vision Research, 35, 1473–1481.R A M L & J A

i oJournal of Biological Chemistry, 260, 56%573.

S C A J& J o

InvestigativeOphthalmology and Visual Science, 35, 2521-2534.

T D o i Go Biophysical Journal, 67,

1439-1454.T D & E N A o

i iJournal of Physiology, 449, 719–758.

M G S E G & EArchives of

Ophthalmology, 107, 816-819.D & D S

oScience, 232, 193-202.

J A & R AComputer Journal, 7, 308–313.

K Io

Investigative Ophthalmology and Visual Science, 35,3577-3581.R D & W A

o Nature, 223,201-205.

R D & W A o oBiophysical Journal, 12, 1073-1096.

E N J & W H iA o

Vision Research, 26, 1613–1643.E N J & T D o

i Biochimica et BiophysicsActa, 1141, 111–149.

M S & E Li a

Investigative Ophthalmol-ogy and Visual Science, 31, 2283-2287.

G G & A Ji o Clinical

Sciences, 8

& FA

VisualNeuroscience, 11, 519–532.

&

oInvestigative Ophthalmology and

Visual Science, 22, 392–399.& Color science

& Sons.

b

C N

APPENDIX

Derivation of the Alternative Model of PhototransductionThe i

a aa i

ooo i

&

= @ m k

PDE”(t) is aisomerizations a o a

by = O t <0 y = t t = O; k,

o

t

a o G

io

a&

PDE* (t) = @ VSp –

at

o o&

a t n

PDE*o(t) = PDE”(t)/0.

i&

- f m

—

o

E

I a

AN’ 0.0IL‘

0.0 0.5 1.0 1.5 2.0

. . . . . . . . . . . . . . ,. . . . . . .

I J

40

i oi i t a

i io b o

io t a

b i i

t i o1 i i i o

aT i

1 o b2 o b3 o t

o

ii o

i t b a ii # i i

t oo

approximations && w o

1 i a t a

2 o i

3 i a

o

A bo o

wo a

A V S G

I , , , , , , ( , , 1

1

a c 3 I b ot a o

ib b a

2

I 1 I , , , , , , , I

I, , , , I r

I

I

2

I , , , 1 1 , , t , I, , , I I r I I

1

2

I , , , , , I , , i

o 4 8 12 16 20

o 12

1 6 1o

o 21 a a

o bo

1 2 oo d b t

I(O, t) =

t t’” t“

(1 – –k@ Aq,(t’)dt’dt’’dt’”

}

k t))

(M)

0 ot i k, a

i bi a

t oa o

A

8 a 2 I a1 A

i a 1

t /“ f“

} - t6 i a i o

oa i i Ao 6 i I i t

i a i #w o o a

o ai

i ao

i it b

oo o i

1 o2 o b a3 o

I a ii t b c &

o i t&

oi o i

i a &o i i

i i i it b &

t io i i t a

o same time constant...The impulse

‘2 (;) (A7)w T T t = ~~p –

t i o t bo

i

t =

(–~k. @ (C2– + – + +

}

e = t– i I i t6 i a i i a

bb b a i

b oi t a a

approxhnatdy to a constant time delayo i H

b ot b i

6 i t tt

b bi

i io

it b

b ba

i a

1 &

o

o

a t9

i i i

o a t 1o

2 I ou t 4 t a

o b1 1 o a

to i

b a a u t c5 t a i

t wi

o

a