Chlorophyll Absorption Spectrum
2.1 The Beer–Lambert law #
2.1.1 The equation #
Absorbance is defined from the incident intensity I₀ and the transmitted intensity I:
A = log₁₀(I₀ / I) = ε c l
c is molar concentration, l is path length, and ε is the molar absorption coefficient. With c in mol L⁻¹ and l in centimetres, ε has units L mol⁻¹ cm⁻¹. Transmittance is T = I/I₀, so A = −log₁₀ T. Doubling c or l doubles A only while ε stays constant and the instrument is truly measuring I. ε belongs to a stated chromophore in a stated solvent, pH, and temperature. Protonation, ligation of a haem, or melting of a DNA duplex changes it. A concentration calculated with the wrong ε is wrong by that factor.
At 280 nm tryptophan contributes about 5500 L mol⁻¹ cm⁻¹, tyrosine about 1490, and a cystine disulphide about 125. Phenylalanine is weaker and usually ignored there. The peptide bond is almost silent at 280 nm; it absorbs in the far-ultraviolet. A protein with no tryptophan and no tyrosine has an ε₂₈₀ near zero. The rule of thumb that 1 mg mL⁻¹ gives A₂₈₀ about 1 is only an average and can be wrong several-fold once the sequence is known.
2.1.2 When the law fails #
Stray light flattens the calibration at high absorbance. A = 2 means only 1% of the light is transmitted. Stray light equal to 0.1% of I₀ is then a tenth of the true signal and the reading is already low. A spectrum that flattens above an absorbance of about 1–2 is not a saturated chromophore. Dilute the sample or shorten the path.
Scattering removes photons by redirection, and the detector records the loss as absorption. Aggregates therefore inflate A₂₈₀. Rayleigh scatter from particles much smaller than λ falls off roughly as λ⁻⁴, so a scatter baseline rises smoothly toward the ultraviolet and lacks tryptophan’s peaks. Extrapolating a baseline is better than nothing and is not exact. The cure is to remove the particles.
Association into a second species with a different ε, fluorescence reaching the detector, and a monochromator bandwidth wider than a sharp peak all bend the law as well. Bubbles, fingerprints, and a cuvette not square to the beam change I without changing c. The law holds for a clear solution of one chromophore, at an absorbance the instrument can still distinguish from stray light, with ε taken from that chromophore’s actual state.
2.1.3 What the spectrophotometer compares #
A bench instrument sends light from a deuterium source (ultraviolet) or a tungsten-type lamp (visible) through a monochromator or filter, through the sample, and onto a detector. A double-beam machine compares a reference cuvette of solvent at the same wavelength. A single-beam machine needs a separate blank. Either way the blank is part of the result: a buffer that absorbs at the working wavelength is attributed to the sample if it is not subtracted. Glass and many plastics are useless below about 320 nm; quartz is required at 260 and 280 nm. Path length is usually 1 cm and must be the value used in εcl. The instrument does not know the path.
2.2 Proteins, nucleic acids, and colour assays #
2.2.1 Absorbance at 280 and at 260 nm #
Protein concentration from A₂₈₀ uses the sequence-based ε after the blank. Folding shifts ε by only a small fraction for most proteins. Nucleic acid and scatter both push the estimate up. A cloudy solution does not have a trustworthy A₂₈₀.
Nucleic acids absorb at 260 nm because the bases are conjugated. For double-stranded DNA of ordinary base composition, A₂₆₀ = 1 in a 1 cm cell corresponds to about 50 µg mL⁻¹. The rough companions are about 40 µg mL⁻¹ for RNA and about 33 µg mL⁻¹ for single-stranded DNA. Base composition changes them. So does hypochromism: stacked bases in a duplex absorb less than free bases, and A₂₆₀ rises, often by roughly a third to two-fifths, when the duplex melts. A melting curve at 260 nm measures stacking, not how much DNA was weighed in. The duplex conversion is wrong if the sample was already denatured.
2.2.2 The 260/280 ratio and its limits #
A₂₆₀/A₂₈₀ is a purity indicator because the two polymers have different spectral shapes. Pure DNA gives a ratio near 1.8, pure RNA near 2.0, and a typical protein near 0.6. Protein pulls a nucleic-acid ratio down; nucleic acid pushes a protein ratio up. The Warburg–Christian correction estimates protein in the presence of nucleic acid from the two readings and assumes average extinction coefficients for both.
A ratio of 1.8 does not prove that only DNA is present. Salt, ethanol, and many carbohydrates absorb at neither wavelength. Phenol, left from an extraction, absorbs near 270 nm and distorts both the ratio and the concentration. Scatter raises both readings. A protein with no tryptophan can look “nucleic-acid-like” while containing none. The ratio is not a concentration. A₂₆₀/A₂₃₀ is sometimes used because many organic contaminants absorb near 230 nm; it has the same status. It is a warning, not an assay.
2.2.3 Colorimetric assays #
Biuret, Lowry, bicinchoninic-acid, and Bradford assays produce a visible colour from protein plus a reagent. Biuret coordinates copper to peptide bonds and is the least sensitive. Lowry and BCA couple copper reduction to a colour. Bradford dye binding depends strongly on arginine and other basic and aromatic residues. Two proteins at the same mass concentration need not give the same absorbance.
A standard curve of a known protein, often bovine serum albumin, is required, and the standard is not the analyte. The assay reports equivalence to the standard under those conditions. It is appropriate for a crude mixture whose ε₂₈₀ is meaningless, and inappropriate for the molarity of a pure, sequenced protein. These notes give no reagent recipes. The principle is comparative colour, not Beer’s law applied to the protein’s own chromophores.
2.3 Circular dichroism #
2.3.1 Ellipticity and secondary structure #
Circular dichroism is the difference in absorption of left and right circularly polarised light, ΔA = A_L − A_R. An achiral chromophore in an achiral solvent gives ΔA = 0 even if it absorbs strongly. Instruments often report ellipticity. Molar ellipticity in deg cm² dmol⁻¹ is about 3300 times Δε in L mol⁻¹ cm⁻¹. Mean residue ellipticity divides by the number of residues so that proteins of different length can be compared. An error in concentration or path length scales the whole curve and therefore the apparent helix content.
In the far-ultraviolet the chromophore is the peptide bond. An α-helix typically shows negative bands near 222 and 208 nm and a positive band near 193 nm. A β-sheet is typically negative near 215–218 nm and positive near 195 nm. A disordered chain is strongly negative near 200 nm. These are guides. Real spectra are overlapping sums.
2.3.2 Far-UV and near-UV #
Far-ultraviolet CD, about 180–250 nm, reports backbone conformation. A percentage such as “about 40% helix” comes from fitting the curve to spectra of proteins of known structure, or to model peptides. Errors of several percentage points are ordinary, and β-sheet content is less secure than helix content because sheet spectra vary with twist and strand length. Chloride, imidazole, reducing agents, and many organic buffers absorb in this region; phosphate is more transparent. High absorbance forces a short path, often well below 1 mm. A spectrum that dies below 200 nm in noise is usually the solvent, not a sudden loss of structure.
Near-ultraviolet CD, about 250–320 nm, belongs to tryptophan, tyrosine, and disulphides held in asymmetric environments by the tertiary fold. A molten globule often keeps the far-ultraviolet spectrum and loses the near-ultraviolet signal: the backbone is still ordered and the side chains are not packed. The two regions should not be collapsed into “the CD looks native”.
2.3.3 What a CD spectrum cannot give #
CD cannot give a unique atomic structure. The spectrum contains far fewer independent numbers than a protein contains residues, and it assigns nothing to a particular residue. Atomic models are the business of Structural Biology. CD is the solution check that a fold is present, or that a ligand, a mutation, or a temperature change has altered it.
Aggregates can scatter the two circular polarisations differently and distort the short-wavelength end. A buffer that does not match the blank is interpreted by fitting software as secondary structure. A thermal midpoint watched by CD is a thermodynamic melting temperature only if the transition is reversible and two-state. Irreversible aggregation looks like a melt and is not an equilibrium. The heat of the transition, and the two-state test, belong to scanning calorimetry in Chapter 7.
2.4 Key terms, summary, and self-check #
Key terms. Absorbance; molar absorption coefficient; stray light; hypochromism; 260/280 ratio; mean residue ellipticity; far-ultraviolet CD; near-ultraviolet CD; molten globule.
Summary. Absorbance reports concentration only when Beer’s law holds: a clear solution, a known ε, and an instrument not dominated by stray light. A₂₈₀ and A₂₆₀ exploit particular chromophores, and the 260/280 ratio is a purity warning with defined blind spots. Circular dichroism reports chiral structure, backbone in the far-ultraviolet and side-chain packing in the near-ultraviolet, and it does not determine a unique structure.
Self-check.
1. A solution in a 1 cm cell has A = 1.0 and ε = 20 000 L mol⁻¹ cm⁻¹. What is c, and why is a reading of A = 3 on the same instrument less trustworthy?
2. Why is the calculated concentration suspect for a cloudy sample whose apparent absorbance rises smoothly toward shorter wavelengths?
3. Why does a DNA 260/280 ratio of 1.8 not prove the sample is free of salt?
4. A mild treatment leaves the far-ultraviolet CD unchanged and abolishes the near-ultraviolet CD. What levels of structure are implicated?
5. Why can two different mixes of helix and sheet give similar far-ultraviolet CD spectra?
