Question

Answer all parts of the following question, showing all workings and reasonings/assumptions.

5. Antibodies immobilised on surfaces are often used to detect proteins or other antibodies that indicate disease, e.g., cancer, cardiovascular disease, infection etc. Antibodies are deposited on a plastic surface so that their concentration is 5x10-12 mol cm—2 (NOTE THE UNITS, THEY ARE 2-DIMENSIONAL, MOLES PER CENTIMENTRE SQUARED RATHER THAT MOLES PER CENTIMETRE CUBED AS YOU WOULD FIND IN SOLUTION!). The surface confined antibodies are to be labelled with metal nanoparticles.

i) Determine the maximum radius of the nanoparticles that will physically fit on the surface given the surface concentration of the antibodies and assuming that all antibodies are labelled with a single nanoparticle. (HINT! Work out area occupied by one antibodyyou are told the moles per centimetre squared so you can work out the number of antibody molecules per cm2 . Then work out the number of cm2 per antibody and convert to a radius assuming the area occupied is a disk.)

ii) The extinction coefficient of metal nanoparticles is described by the equation:  = 1.6x106 * r – 6.1x105 where  has units of M-1 cm-1 and r is in nm. Use this equation to predict the extinction coefficient of the nanoparticle using the radius obtained in part i. Comment on the significance of the intercept in the context of the Beer-Lambert Law.

iii) Reflectance absorbance spectroscopy can be used to measure the absorbance of ALL the nanoparticles immobilised on the plastic surface. Given that the lowest absorbance that can be accurately measured is 0.0001 AU, determine the area of the plastic surface needed to detect nanoparticles at a surface concentration of 5x10-12 mol cm—2 using reflectance absorbance spectroscopy.

Answer 1

The given data assumes antibodies to be two-dimensional entities. They have been immobilized on the surface with a surface concentration C_A = .

This implies that

Now we want one nanoparticle to bind to one antibody such that all antibodies are covered with nanoparticles. Assuming antibodies as discs, the maximum radius of the nanoparticle is the same as the radius of the antibody discs.

, where r is the radius of the nanoparticle.

Thus the maximum radius to ensure that one antibody is covered with one nanoparticle is 3.251nm.

Beer Lambert's law states that Absorbance is proportional to the concentration of the sample and to the path length. And the proportionality constant is given by the molar extinction coefficient () of the sample.

Now given that , where r is in nm.

Since Absorbance is highly instrument-specific and can vary due to various parameters across experiments, instead of reporting Absorbance values, people report the concentration values of the sample. To determine the concentration, a Beer-Lamber plot is constructed with Abosrbance as a function of the Concentration of known samples. Then a linear regression fits the plot and an unknown sample's concentration can be obtained by knowing the slope and the y-intercept of the plot. the y-intercept is basically the absorbance of a 0mM sample. That is just the solvent and no sample. This absorbance is the baseline that arises due to the absorption of light by the solvent and other instrumental errors.

Reflectance absorbance spectroscopy is based on Beer-Lambert's Law and determines the concentration of the sample. Here the pathlength is the diameter of the sample which absorbs the light. Therefore in our case, pathlength is 2r = 6.502nm.

Now Absorbance = Molar extinction coefficient * concentration of sample * pathlength. The minimum Absorbance that can be accurately measured is 0.0001AU. We have to determine the concentration of the sample that gives this absorbance.

Therefore the minimum concentration of nanoparticles required to get a signal is 66.99mM.

Now, therefore, the minimum area of sample required for the detector to collect sufficient absorbance can be obtained by solving

This is the minimum area of the sample required to be detected.

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