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Linearization of the Bradford Protein Assay Increases Its Sensitivity ...

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304<br />

ZOR AND SELINGER<br />

K Å<br />

[DP]<br />

[nP] 1 [D] 1 f b<br />

[2]<br />

compatible with <strong>the</strong> microplate autoreader instrument.<br />

It should be pointed out that e D , at both 590 and 450<br />

nm, is a weighted average <strong>of</strong> <strong>the</strong> molar absorption coefficients<br />

<strong>of</strong> <strong>the</strong> three dye forms. The addition <strong>of</strong> protein<br />

does not change <strong>the</strong> combined e D since <strong>the</strong> fraction <strong>of</strong><br />

each dye form depends only on pH and not on total<br />

concentration or consumption <strong>of</strong> one dye form. The substitution<br />

<strong>of</strong> Eq. [7] into Eq. [6] results in<br />

where f b , <strong>the</strong> fraction <strong>of</strong> <strong>the</strong> reactive blue dye form,<br />

equals 0.053 under assay conditions (6) and n is <strong>the</strong><br />

number <strong>of</strong> binding sites on a protein molecule, being<br />

primarily arginine residues (8). For simplicity <strong>the</strong> bind-<br />

ing sites are assumed to be homogeneous and noninteracting,<br />

although binding has some unclear dependence<br />

on macromolecular structure (8). Substituting <strong>the</strong> conservation<br />

equation <strong>of</strong> protein binding sites, [nP] t Å [nP]<br />

/ [DP], where t indicates total, into Eq. [2] and rearrangement<br />

yields<br />

[DP] Å<br />

K 1 f b 1 [D]<br />

1 / K 1 f b 1 [D] 1 [nP] t. [3]<br />

Fur<strong>the</strong>r rearrangement gives <strong>the</strong> following expression<br />

for <strong>the</strong> complex concentration:<br />

[DP] Å<br />

1<br />

<br />

1<br />

K 1 f b 1 [D] / 1 1 [nP] t. [4]<br />

A 590 Å e DP<br />

590 1 l 1 [DP] / e D 590 1 l 1 [D], [5]<br />

where <strong>the</strong> superscript <strong>of</strong> e defines <strong>the</strong> compound and<br />

<strong>the</strong> subscript refers to <strong>the</strong> wavelength.<br />

Substitution <strong>of</strong> Eq. [4] into Eq. [5] leads to<br />

A 590 Å<br />

A 590 Å<br />

e DP<br />

590 1 l<br />

<br />

e D 450 1 l<br />

K 1 f b 1 A 450<br />

/ 1<br />

which is rearranged to become<br />

A 590<br />

A 450<br />

Å<br />

e DP<br />

1 [nP] t / e D 590 1 l<br />

e D 450 1 l 1 A 450 [8]<br />

590 1 l<br />

<br />

D<br />

e 450 1 l<br />

/ A<br />

K 1 f b<br />

450 1 [nP] t / e 590<br />

D . [9]<br />

e 450<br />

D<br />

The absorbance at 590 nm, composed <strong>of</strong> <strong>the</strong> indepen-<br />

dent absorbances <strong>of</strong> both <strong>the</strong> dye–protein complex and<br />

<strong>the</strong> free dye, is given by<br />

To reach a linear equation, in which protein concentration<br />

is <strong>the</strong> X variable, <strong>the</strong> following assumption is<br />

made<br />

e D 450 1 l<br />

K 1 f b<br />

A 450 . [10]<br />

Substitution <strong>of</strong> Eqs. [2] and [7] into Expression [10]<br />

and rearrangement gives<br />

[nP]<br />

1. [11]<br />

[DP]<br />

e DP<br />

590 1 l<br />

<br />

1<br />

K 1 f b 1 [D] / 1 The critical assumption given by Expressions [10]<br />

and [11] was verified by <strong>the</strong> elegant experiments <strong>of</strong><br />

Splittgerber and colleagues (6, 9). According to <strong>the</strong>se<br />

1 [nP] t / e D 590 1 l 1 [D]. [6] experiments, <strong>the</strong> ratio [nP]/[DP] equals approximately<br />

4 when considering only high-affinity binding sites. In<br />

this case, <strong>the</strong> value <strong>of</strong> <strong>the</strong> expression preceding [nP] t<br />

in Eq. [9] changes by less than 5% over <strong>the</strong> protein<br />

concentrations range assayed. Fur<strong>the</strong>rmore, when con-<br />

sidering low-affinity binding sites, <strong>the</strong> ratio [nP]/[DP]<br />

is indeed far larger than 1 as assumed in Expression<br />

[11] and <strong>the</strong> value <strong>of</strong> <strong>the</strong> expression preceding [nP] t<br />

in Eq. [9] is practically constant. Since under assay<br />

conditions a substantial part <strong>of</strong> <strong>the</strong> absorbance is contributed<br />

by low-affinity binding sites (9), it can be con-<br />

A 450 Å e 450 D 1 l 1 [D]. [7] cluded that <strong>the</strong> assumption given by Expressions [10]<br />

and [11] is fully justified.<br />

According to Eq. [6], both components <strong>of</strong> A 590 depend<br />

upon free dye concentration. Thus <strong>the</strong> correction for<br />

<strong>the</strong> absorbance <strong>of</strong> <strong>the</strong> free dye alone will not lead to<br />

linear dependence between A 590 and protein concentration.<br />

Because <strong>the</strong> dye–protein complex has no contribution<br />

to <strong>the</strong> absorbance at 450 nm, [D] can be calculated<br />

as follows:<br />

This wavelength, like 590 nm, was chosen ra<strong>the</strong>r Therefore, when assuming relationship [10], Expresthan<br />

<strong>the</strong> l max (466 and 594 nm) to make <strong>the</strong> assay sion [9] becomes

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