6. PHOTOTROPISM AND PHOTOTAXIS
287
but the intensity incident on unit 3 becomes Z 0 e~
(a+m) . Therefore in unit
3:
QA,Z = 7 0 e(a+w) (l - e-°)
The gradient of photochemical action in this system will simply be the
difference in the amounts of light absorption by A in units 1 and 3
(front and back). Thus:
AQA = QA.I - QA,Z = J 0 (l - e-*)[l - e-<«+->]
Since for maximum masking a must be small in comparison to m, the
expression simplifies to:
AQA = ha{\ - e--).
In this case increases in m evidently increase the gradient of photochemical action. In this sense the idea that the masking pigment "secures the necessary light absorption across the organ" is valid, and any
masking in such a system will always be in a positive sense. However,
inspection will show that when m is large, M will have relatively little
effect on the shape of the action spectrum. Thus, if m changes from 2 to
2.2 (10% increase), the fraction (1 — e~
m ) changes from 0.865 to 0.889,
which is less than a 3% increase. Therefore, the supposition that "the
phototropic action spectrum must be determined by the double-peaked
absorption curve of the carotene" requires careful quantitative study.
Differentiation of AQ A with respect to m (a constant), shows that
changes in m have a maximum effect on AQ A when m is small, i.e., when
the masking pigment is at a low absolute concentration (although still
present in much greater amount than A). The expression for the
gradient of light absorption by A then reduces to: AQ A = loam and the
action spectrum simply becomes the product of the two absorption
spectra. This represents the maximum possible masking effect of M in
this system. A 10% increase in m will now cause a 10% rise in the action
spectrum, providing a does not change in the same wavelength interval.
If the absorption spectrum of A were perfectly flat throughout the
range under consideration, the action spectrum would be completely
determined by the absorption spectrum of M.
In the phototropic system, however, the absorption of both a and m
changes with wavelength, and the gradient is therefore the product of
the absorption spectra. In Fig. 11 the product function (r X c) of a
riboflavin absorption spectrum and the absorption spectrum of a typical
carotenoid extract is plotted. The extract curve was used in this figure
because it gives a better estimate of the postulated masking pigments
in the plant than does the absorption spectrum of one particular
carotenoid. It is evident that the product curve bears little resemblance
to the observed action spectrum. Even the selection of a pure carotenoid
287
but the intensity incident on unit 3 becomes Z 0 e~
(a+m) . Therefore in unit
3:
QA,Z = 7 0 e(a+w) (l - e-°)
The gradient of photochemical action in this system will simply be the
difference in the amounts of light absorption by A in units 1 and 3
(front and back). Thus:
AQA = QA.I - QA,Z = J 0 (l - e-*)[l - e-<«+->]
Since for maximum masking a must be small in comparison to m, the
expression simplifies to:
AQA = ha{\ - e--).
In this case increases in m evidently increase the gradient of photochemical action. In this sense the idea that the masking pigment "secures the necessary light absorption across the organ" is valid, and any
masking in such a system will always be in a positive sense. However,
inspection will show that when m is large, M will have relatively little
effect on the shape of the action spectrum. Thus, if m changes from 2 to
2.2 (10% increase), the fraction (1 — e~
m ) changes from 0.865 to 0.889,
which is less than a 3% increase. Therefore, the supposition that "the
phototropic action spectrum must be determined by the double-peaked
absorption curve of the carotene" requires careful quantitative study.
Differentiation of AQ A with respect to m (a constant), shows that
changes in m have a maximum effect on AQ A when m is small, i.e., when
the masking pigment is at a low absolute concentration (although still
present in much greater amount than A). The expression for the
gradient of light absorption by A then reduces to: AQ A = loam and the
action spectrum simply becomes the product of the two absorption
spectra. This represents the maximum possible masking effect of M in
this system. A 10% increase in m will now cause a 10% rise in the action
spectrum, providing a does not change in the same wavelength interval.
If the absorption spectrum of A were perfectly flat throughout the
range under consideration, the action spectrum would be completely
determined by the absorption spectrum of M.
In the phototropic system, however, the absorption of both a and m
changes with wavelength, and the gradient is therefore the product of
the absorption spectra. In Fig. 11 the product function (r X c) of a
riboflavin absorption spectrum and the absorption spectrum of a typical
carotenoid extract is plotted. The extract curve was used in this figure
because it gives a better estimate of the postulated masking pigments
in the plant than does the absorption spectrum of one particular
carotenoid. It is evident that the product curve bears little resemblance
to the observed action spectrum. Even the selection of a pure carotenoid