Quantification of Light Absorption If light with wavelength λ and intensity I0 passes through a sample with appropriate transparency and path length (thickness) d , the intensity I drops along the pathway in an exponential manner (Figure 1). I is the number of photons by unit of surface and by unit of time.
Fig1. When light is absorbed by a sample of thickness d , the intensity I decreases in an exponential fashion along the path.
The chance of a photon being absorbed by matter is given by an extinction coefficient, which itself is dependent on the wavelength λ of the photon. The characteristic absorption parameter for the sample is the extinction coefficient α, yielding the correlation
The ratio T = I / I0 is called the transmission.
Biochemical samples usually comprise aqueous solutions, where the substance of interest is present at a molar concentration c. Algebraic transformation of the exponential correlation into an expression based on the decadic logarithm yields the Beer– Lambert law:
where [ d ] = 1 cm, [ c ] = 1 mol dm−3 and [ε] = 1 dm 3 mol−1 cm−1. ε is the molar absorption coefficient (also molar extinction coefficient ). Due to the change of base from e to 10, the extinction coefficient α is related to the molar absorption coefficient ε as α = 2.303 × ε. A is the absorbance of the sample, which is displayed on the spectrophotometer.
The Lambert–Beer law is valid for low concentrations only. Higher concentrations might lead to association of molecules and therefore cause deviations from ideal behaviour. Absorbance and extinction coefficients are additive parameters, which complicates determination of concentrations in samples with more than one absorbing species. Note that in dispersive samples or suspensions, scattering effects increase the absorbance, since the scattered light is not reaching the detector for readout. The absorbance recorded by the spectrophotometer is thus overestimated and needs to be corrected ( Figure 2).
Fig2. The presence of larger aggregates in biological samples gives rise to Rayleigh scatter visible by a considerable slope in the region from 500 to 350 nm. The dashed line shows the correction to be applied to spectra with Rayleigh scatter, which increases with λ −4 . Practically, linear extrapolation of the region from 500 to 350 nm is often performed to correct for the scatter. The corrected absorbance is indicated by the double arrow.
Deviations from the Beer–Lambert Law
According to the Beer–Lambert law, absorbance is linearly proportional to the con centration of chromophores. This might not be the case in samples with high absorbance. Every spectrophotometer has a certain amount of stray light, which is light received at the detector, but not anticipated in the spectral band isolated by the mono chromator. In order to obtain reasonable signal-to-noise ratios, the intensity of light at the chosen wavelength ( I λ ) should be 10 times higher than the intensity of the stray light ( I stray ). If the stray light gains in intensity, the effects measured at the detector have nothing or little to do with chromophore concentration. Secondly, molecular events might lead to deviations from the Beer–Lambert law. For instance, chromophores might dimerise at high concentrations and, as a result, might possess different spectroscopic parameter.
Absorption or Light Scattering: Optical Density
In some applications, for example measurement of turbidity of cell cultures (determination of biomass concentration), it is not the absorption but the scattering of light that is actually measured with a spectrophotometer. Extremely turbid samples like bacterial cultures do not absorb the incoming light. Instead, the light is scattered and thus, the spectrometer will record an apparent absorbance (sometimes also called attenuance ). In this case, the observed parameter is called optical density (OD). Instruments specifically designed to measure turbid samples are nephelometers or Klett meters; however, most biochemical laboratories use the general UV/vis spectrometer for determination of optical densities of cell cultures.
Factors Affecting UV/Vis Absorption
Biochemical samples are usually buffered aqueous solutions, which have two major advantages. First, proteins and peptides are comfortable in water as a solvent, which is also the ‘native’ solvent. Second, in the wavelength interval of UV/vis (700–200 nm) the water spectrum does not show any absorption bands and thus acts as a silent component of the sample.
The absorption spectrum of a chromophore is only partly determined by its chemical structure. The environment also affects the observed spectrum, which can be described by three main parameters:
• protonation/deprotonation (pH, redox)
• solvent polarity (dielectric constant of the solvent)
• orientation effects.
Vice versa, the immediate environment of chromophores can be probed by assessing their absorption, which makes chromophores ideal reporter molecules for environ mental factors. Four effects, two each for wavelength and absorption changes, have to be considered:
• a wavelength shift to higher values is called a red shift or bathochromic effect
• similarly, a shift to lower wavelengths is called a blue shift or hypsochromic effect
• an increase in absorption is called hyperchromicity (‘more colour’)
• a decrease in absorption is called hypochromicity (‘less colour’).
Protonation / deprotonation arises either from changes in pH or oxidation / reduction reactions, which makes chromophores pH- and redox-sensitive reporters. As a rule of thumb, λ max and ε increase, i.e. the sample displays a batho- and hyperchromic shift, if a titratable group becomes charged.
Furthermore, solvent polarity affects the difference between ground and excited states. Generally, when shifting to a less polar environment one observes a batho- and hyperchromic effect. Conversely, a solvent with higher polarity elicits a hypso- and hypochromic effect.
Lastly, orientation effects, such as an increase in order of nucleic acids from sin gle-stranded to double-stranded DNA, lead to different absorption behaviour. A sample of free nucleotides exhibits a higher absorption than a sample with identical amounts of nucleotides, but assembled into a single-stranded polynucleotide. Accordingly, double-stranded polynucleotides exhibit an even smaller absorption than two single-stranded polynucleotides. This phenomenon is known as the hypochromicity of polynucleotides. The increased exposure (and thus stronger absorption) of the individual nucleotides in the less ordered states provides a simplified explanation for this behaviour.
