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Labeling with Gold Nanoparticles:
Advanced Labeling Calculation Method
for proteins with significant absorption in the visible range


 

Once you have isolated your gold nanoparticle conjugate, the extent of labeling (the number of gold nanoparticles per biomolecule) can be calculated using the UV/visible spectra of the nanoparticle and the conjugate.

 

In this section:

Advanced Labeling Calculation Method

Examples

 

Simplified Calculation of Gold Nanoparticle Labeling
for proteins with no absorption in the visible range

 


 

Calculation of Labeling with Nanogold® and Undecagold

Assumptions in calculations:

  1. We assume that conjugation does not change the UV/visible absorbance spectrum of either the gold nanoparticle or the protein; and
  2. We assume that the absorbtion of the gold nanoparticle and the protein are strictly additive: the absorbance at all wavelengths for each component is identical to what it would be if the other were not present. For example, even though the gold nanoparticles absorb strongly at 280 nm, the absorbsnce of the protein at 280 nm is unchanged from the value observed for a solution of the same protein without the gold.

 

Extinction coefficients of gold nanoparticle labels, IgG and Fab'

The extinction coefficients for the undecagold and Nanogold® nanoparticles have been determined at 280 nm and 420 nm. These values are shown below, and also the values for IgG molecules and Fab' fragments.

Extinction coefficients (3k)

 

Calculation of extinction coefficients from optical densities

Note: The actual value for the extinction coefficient of Nanogold at 280 nm varies slightly from lot to lot. The most accurate value for the lot you are using will be given in the product specification sheet supplied with your product: use this value for the most accurate labeling calculation.

Absorbances of proteins are often given as optical densities (ODs), which expresses absorbance as a funtion of the mass of protein dissolved per unit volume. Usually the literature values (E1%) are for 1 % solutions, (10 mg/mL, or 10 g/L). In order to calculate rates of gold labeling, these must be converted to molar extinction coefficients, epsilon:

Derivation and calculation of epsilon (4k)

 


 

Calculation of gold nanoparticle labeling

Where both the protein and the gold nanoparticle absorb at 280 nm and 420 nm, the observed absorbance at each wavelength is expressed as a pair of simultaneous equations:

Simultaneous equations (1k)

Where:

c1 = measured absorbance at lambda = 280 nm
c2 = measured absorbance at lambda = 420 nm
a1 = extinction coefficient of protein at lambda = 280 nm
a2 = extinction coefficient of protein at lambda = 420 nm
x = concentration of protein (moles/liter)
b1 = extinction coefiicient of gold nanoparticle label at lambda = 280 nm
b2 = extinction coefficient of gold nanoparticle label at lambda = 420 nm
y = concentration of gold nanoparticle label (moles/liter)

Applying Cramer's Rule and solving for x and y in terms of a, b, and c gives:

Solution of simultaneous equations (2k)

This gives the general solution shown below.

General solution

General Solution (4k)

 

Labeling of IgG and Fab'

With antibody labeling, the calculation is simplified because these proteins do not absorb at 420 nm; therefore, a2 = 0. This gives the simplified solution below:

Simplified Solution

Simplified Solution (3k)

 


 

Examples

(i) Fab' labeled with Nanogold®

The following values were measured for UV/visible absorbtion:

280 nm: 0.6524
420 nm: 0.2012

Sample volume: 3.2 mL.

For this sample, the values of the constant terms are:

c1 = 0.6524 (measured absorbance at lambda = 280 nm)
c2 = 0.2012 (measured absorbance at lambda = 420 nm)
a1 = 7.5 X 104 (extinction coefficient of Fab' at lambda = 280 nm)
a2 = 0 (extinction coefficient of Fab' at lambda = 420 nm)
x = concentration of protein (moles/liter)
b1 = 4.12 X 105 (extinction coefiicient of Nanogold® at lambda = 280 nm)
b2 = 1.56 X 105 (extinction coefficient of Nanogold® at lambda = 420 nm)

Nanogold-Fab' calculation (3k)

 

(ii) Hemoprotein labeled with undecagold:

A hypothetical heme-containing protein with a moleular weight of 65,000 and extinction coefficients of 37,400 at 280 nm and 27,900 at 420 nm is labeled with mono-Sulfo-NHS-undecagold. 2.0 mL of labeled conjugate solution is isolated and absorbances were measured:

280 nm: 0.8705
420 nm: 0.4560

Values for the constants are:

c1 = 0.8705 (measured absorbance at lambda = 280 nm)
c2 = 0.4560 (measured absorbance at lambda = 420 nm)
a1 = 3.74 X 104 (extinction coefficient of protein at lambda = 280 nm)
a2 = 2.79 X 104 (extinction coefficient of protein at lambda = 420 nm)
x = concentration of protein (moles/liter)
b1 = 1.68 X 105 (extinction coefiicient of undecagold at lambda = 280 nm)
b2 = 4.71 X 104 (extinction coefficient of undecagold at lambda = 420 nm)

Undecagold-haem calculation (4k)

These results show 1 undecagold nanoparticle for every 5 heme-proteins; this labeling might indicate that the protein forms pentamers, each of which accomodates one gold label - STEM can then be used to investigate further.

 


 

See also:
Simple Method of Labeling Calculation

for proteins with no absorption in the visible range

 

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