## The package effect

The absorbance spectrum of a cell or colony suspension (in the case of unicellular algae) or of a segment of thallus or leaf (in the case of multicellular aquatic plants) will always differ noticeably from that of dispersed thylakoid fragments. The in vivo spectra (e.g. Euglena, Fig. 9.1) will be found to have peaks that are less pronounced with respect to the valleys, and to have, at all wavelengths, a lower specific absorption per unit pigment. These changes in the spectra are due to what we shall refer to as the package effect - sometimes, inappropriately, called the sieve effect. It is a consequence of the fact that the pigment molecules, instead of being uniformly distributed, are contained within discrete packages: within chloroplasts, within cells and within cell colonies. This, as one might intuitively suspect, lessens the effectiveness with which they collect light from the prevailing field - hence the lowered specific absorption. It is in the nature of the package effect to be proportionately greatest when absorption is strongest343 - hence the flattening of the peaks. The influence of the package effect on the absorption spectra of algal suspensions was first studied, experimentally and theoretically, by Duysens (1956), and its implications for the absorption of light by phytoplankton populations have been analysed by Kirk (1975a, b, 1976a) and Morel and Bricaud (1981).

To better understand the package effect, let us compare the absorption properties of a suspension of pigmented particles with those of the same amount of pigment uniformly dispersed - in effect, in solution. We shall for simplicity ignore the effects of scattering, and absorption by the medium. Consider a suspension containing N particles per m3, illuminated by a parallel beam of monochromatic light through a pathlength of 1.0 m. The jth particle in the light beam would, in the absence of the other particles, absorb a proportion sjAj of the light in unit area of beam, where sj is the projected area of the particle (m2) in the direction of the beam, and Aj is the particle absorptance - the fraction of the light incident on it which it absorbs. sjAj has the dimensions of area and is the absorption cross-section of the particle (see §4.1). The absorptance of unit area of the suspension due to the jth particle is thus sjAj, and so (from eqn 1.36) the absorption coefficient of the suspension due to the jth particle is ln 1/ (1- sjAj) which, since sjAj is small, is approximately equal to sjAj. Assuming that Beer's Law applies to a suspension of particles, i.e. that the absorb-ance (or absorption coefficient) of the suspension is equal to the sum of the absorbances (or absorption coefficients) due to all the individual particles, , then the absorption coefficient of the suspension is

Where sA is the mean value, for all the particles in the suspension, of the product of the projected area and the particle absorptance, i.e. the average absorption cross-section. The absorbance (0.434 ar, see §3.2) of the suspension for a 1.0 m pathlength, is given by

If the particles have an average volume of vm3, and the pigment concentration within the particle is C mgm~3, then if the pigment were to be uniformly dispersed throughout the medium, it would be present at a concentration of NCv mgm~3. If the specific absorption coefficient of the pigment (the absorption coefficient due to pigment at a concentration of 1 mgm~3) at the wavelength in question is gm2mg_1, then the absorption coefficient due to the dispersed pigment is given by aSoi = NCvg (9.3)

and the absorbance (1.0 m pathlength) by

The extent of the package effect can be characterized by the ratio of the absorption coefficient or absorbance of the suspension to that of the solution. From eqns 9.1 and 9.3, it follows that this ratio is given by asus _ Dsus _ sA (9 4)

aSol DSol Cvg '

It can be shown693 that for particles of any shape or orientation, asus/asol is always less than 1.0. However, it can also be shown695 that if the individual particles absorb only weakly, e.g. because they are small or because the pigment concentration within the particles is low, then sA « Cvg and so, for such particles asus « asol.

We shall now consider what happens if we make the particles absorb progressively more strongly. For simplicity we shall keep the size and shape of the particles constant, i.e. we shall keep s and v constant. Both C and g can be increased in value almost indefinitely by increasing the pigment concentration within the particles, and by changing to a more intensely absorbed wavelength, respectively: thus the denominator in eqn 9.4 can be increased in value many-fold. As C or g increases, so A in the numerator also increases, but since this is the fraction of the light incident on the particle which is absorbed, it can never exceed 1.0, and cannot increase in proportion to the increase in C or g. When A is very low (weakly absorbing particles) a doubling in C or g can bring about an almost commensurate increase in A, but the closer A gets to 1.0 the less leeway it has to increase in response to a given increase in C or g. This is why the package effect, the discrepancy between the spectrum of the particle suspension, and the corresponding solution, becomes more marked as absorption by the individual particles increases: this in turn explains why the peaks of the spectrum are affected more than the troughs. In short, it is the dependence of the absorption spectrum of a suspension on the fractional absorption per particle (particle absorptance) that accounts for the flattening of the spectrum and the lowered specific absorption per unit pigment concentration. A more extensive treatment of this phenomenon can be found elsewhere.693,694,695 It should be noted that the package effect still affects the absorption spectrum even in suspensions so dense that no photon can avoid traversing a chloroplast while passing through: this is one reason why the term 'sieve effect' is inappropriate.

In the special case of spherical cells or colonies, which present the same cross-section to the light, whatever their orientation, an explicit expression for the particle absorptance was derived by Duysens (1956)

where d is the diameter of the particle. Morel and Bricaud (1981) and Kirk (1975b) have used this relation to carry out an analysis of the package effect and its implications for light absorption for spherical phytoplankton cells.

It is apparent from eqn 9.4 that the extent to which the package effect influences absorbance depends only on the absorption properties of the individual particles. It is therefore just as true for a suspension of particles as it is for a solution, that the shape of the absorbance spectrum, and the specific absorbance per unit pigment, are independent of concentration. Measured spectra of suspensions of algal cells might sometimes seem not to conform to this rule: concentrated suspensions may have higher absor-bances than anticipated, even when spurious absorbance due to scattering of light away from the detector is eliminated. This is because there is a residual scattering artifact in dense suspensions that cannot be overcome by instrumental means; namely, that as a result of the multiple scattering that takes place within such suspensions, the pathlength of the photons and hence the number absorbed within the suspension is increased.

We noted at the beginning of this section that the package effect can be observed in the absorbance spectra of multicellular photosynthetic tissues as well as in those of suspensions. This is because within the tissue the pigments are also segregated into packages - the chloroplasts. However, since the chloroplasts are not randomly distributed in space and since, moreover, in many cases they change their position within the cells in response to changes in light intensity, no simple mathematical treatment of the light absorption properties of multicellular systems is possible.

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