Consistent Sets of Spectrophotometric Chlorophyll Equations for Acetone, Methanol and Ethanol Solvents

Abstract

A set of equations for determining chlorophyll a (Chl a) and accessory chlorophylls b, c ₂ , c ₁  + c ₂ and the special case of Acaryochloris marina, which uses Chl d as its primary photosynthetic pigment and also has Chl a, have been developed for 90% acetone, methanol and ethanol solvents. These equations for different solvents give chlorophyll assays that are consistent with each other. No algorithms for Chl c compounds (c ₂ , c ₁  + c ₂) in the presence of Chl a have previously been published for methanol or ethanol. The limits of detection (and inherent error, ± 95% confidence limit), for chlorophylls in all organisms tested, was generally less than 0.1 µg/ml. The Chl a and b algorithms for green algae and land plants have very small inherent errors (< 0.01 µg/ml). Chl a and d algorithms for Acaryochloris marina are consistent with each other, giving estimates of Chl d/a ratios which are consistent with previously published estimates using HPLC and a rarely used algorithm originally published for diethyl ether in 1955. The statistical error structure of chlorophyll algorithms is discussed. The relative error of measurements of chlorophylls increases hyperbolically in diluted chlorophyll extracts because the inherent errors of the chlorophyll algorithms are constants independent of the magnitude of absorbance readings. For safety reasons, efficient extraction of chlorophylls and the convenience of being able to use polystyrene cuvettes, the algorithms for ethanol are recommended for routine assays of chlorophylls. The methanol algorithms would be convenient for assays associated with HPLC work.

Appendices

Appendices

Appendix 1: Asymptotic errors

For a multiple linear equation of the form, $Z = Av + Bw + Cx + Dy{\hbox{,}}$ where, the absorbance coefficient constants A,B,C and D all have measurable errors ±A, ±B, ±C and ±D, the asymptotic error (±Z) is,

$$ \eqalign{ \pm Z^{{\hbox{2}}} \approx {\left( {\frac{{{\hbox{d}}Z}} {{{\hbox{d}}v}}} \right)}^{{\hbox{2}}} \pm A^{{\hbox{2}}} + {\left( {\frac{{{\hbox{d}}Z}} {{{\hbox{d}}w}}} \right)}^{{\hbox{2}}} \pm B^{{\hbox{2}}} + {\left( {\frac{{{\hbox{d}}Z}} {{{\hbox{d}}x}}} \right)}^{{\hbox{2}}} \cr \qquad\qquad\pm C^{{\hbox{2}}} + {\left( {\frac{{{\hbox{d}}Z}} {{{\hbox{d}}y}}} \right)}^{{\hbox{2}}} \pm D^{{\hbox{2}}}} $$

since $\frac{{{\hbox{d}}Z}} {{{\hbox{d}}v}}{\hbox{, }}\frac{{{\hbox{d}}Z}} {{{\hbox{d}}w}}{\hbox{, }}\frac{{{\hbox{d}}Z}} {{{\hbox{d}}x}}{\hbox{ \ }}\frac{{{\hbox{d}}Z}} {{{\hbox{d}}y}}{\hbox{ = 1,}}$ $<$> <$>\pm Z \approx {\sqrt { \pm A^{{\hbox{2}}} + \pm B^{{\hbox{2}}} + \pm C^{{\hbox{2}}} + \pm D^{{\hbox{2}}} } }$ (Note that the error is independent of absorbance readings v,w,x or y).

For example, for a spectrophotometric equation for Chl a using absorbancesat two wavelengths, A ₆₃₀ and A ₆₆₄ and calculated absorbance coefficients E ₆₃₀ and E ₆₆₄,

$$ \eqalign{ {\!\hbox{Chl }}a{\hbox{ (}}\mu {\hbox{g/ml)}} = A_{{{\hbox{630}}}} {\hbox{.}}E_{{{\hbox{630}}}} {\hbox{ + }}A_{{{\hbox{664}}}} {\hbox{.}}E_{{{\hbox{664}}}} {\hbox{,}} \cr \pm {\hbox{Chl }}a{\hbox{ (}}\mu {\hbox{g}}{\hbox{.ml)}} \approx {\sqrt { \pm E_{{{\hbox{630}}}} ^{{\hbox{2}}} {\hbox{ + }} \pm E_{{{\hbox{664}}}} ^{{\hbox{2}}} } }. \cr }<!endaligned> $$

The asymptotic error of a chlorophyll ratio can be calculated in a similar fashion.

For, $Z = \frac{B} {A}{\hbox{,}}$ where B and A have errors ± B and ± A, the error is approximately, $\pm Z \approx {\hbox{ }}{\sqrt {{\left( {\frac{{{\hbox{d}}Z}} {{{\hbox{d}}A}}} \right)}^{2} {\left( { \pm A} \right)}^{2} + {\left( {\frac{{{\hbox{d}}Z}} {{{\hbox{d}}B}}} \right)}^{2} {\left( { \pm B} \right)}^{2} } }{\hbox{,}}$ which simplifies to $\pm Z \approx Z{{\sqrt {{\left( {\frac{{ \pm{ A}}} {A}} \right)}^{{\hbox{2}}} + {\left( {\frac{{ \pm B}} {B}} \right)}^{{\hbox{2}}} } }}.$

A Chl b/a ratio can therefore be expressed as,

$$ \frac{{{\hbox{Chl }}b}} {{{\hbox{Chl }}a}} \pm {\left( {{\left( {\frac{{{\hbox{Chl }}b}} {{{\hbox{Chl }}a}}} \right)}{\sqrt {{\left( {\frac{{ \pm {\hbox{Chl }}a}} {{{\hbox{Chl }}a}}} \right)}^{{\hbox{2}}} + {\left( {\frac{{ \pm {\hbox{Chl }}b}} {{{\hbox{Chl }}b}}} \right)}^{{\hbox{2}}} } }} \right)}{\hbox{ }}. $$

Appendix 2: Matrix algebra

The example shown are for sets of spectrophotometric readings in acetone solvent where absorbances are measured at 630, 647, 664 and 691 nm which are the Q_y values are for Chl c ₂ and Chl c ₁  + c ₂, b, a and d respectively. It can be shown that all the chlorophyll equations have the same solution matrix. For a chlorophyll equation based on absorbance readings at two wavelengths, Chl = E ₆₄₇.A ₆₄₇ + E ₆₆₃.A ₆₆₄, for a chlorophyll equation requiring measurements at three wavelengths, Chl = E ₆₃₀.A ₆₃₀ + E ₆₄₇.A ₆₄₇ + E ₆₆₄.A ₆₆₄,

Appendix 3: Published chlorophyll formulae used in the present study

The equations of Smith and Benitez (1955) have been recalculated using the following extinction values: ε_{Chl a,663} = 101 l g⁻¹ A cm⁻¹, ε_{Chl a,688} = 1.848 l g⁻¹ A cm⁻¹, ε_{Chl d,663} = 12.83 l g⁻¹ A cm⁻¹, ε_{Chl d,663} = 110.23 l g⁻¹ A cm⁻¹). *Inherent errors calculated on the assumption that the relative errors of the absorbance coefficients were ± 1.0%. **Inherent errors quoted here are ± 2 × standard deviations of the extinction values found by Porra et al. (1989). The acetone equations for Chl a and b by Porra et al. (1989) are for 80% acetone and so have not been included in the present study.

Authority	Solvent	Chlorophyll	Formulae (µg ml−1)	Inherent error* (µg ml−1)
Humphrey and Jeffrey (1975)*	90% acetone	a	11.93 × A 664 − 1.93 × A 647	0.1209
		b	−5.5 × A 664 + 20.36 × A 647	0.2108
		a	11.43 × A 664 − 0.40 × A 630	0.1144
		c 2	−3.80 × A664 + 24.88 × A 630	0.2516
		a	11.47 × A 664 − 0.40 × A 630	0.1148
		c 1 + c 2	−3.73 × A 664 + 24.36 × A 630	0.2464
Porra et’al. (1989), Porra (1991, 2002)**	100% methanol	a	16.29 × A665–8.54 × A652	0.6056
		b	−13.58 × A 665 + 30.66 × A 652	1.1438
Rowan (1989)*	100% ethanol	a	13.70 × A665 − 5.76 × A649	0.1486
		b	−7.60 × A 665 + 25.8 × A 649	0.2690
Modified from Smith and Benitez (1955)*	100% diethyl ether	a	9.92 × A 663 − 1.15 × A 688	0.0999
		d	−0.166 × A 663 + 9.09 × A 688	0.0909