1. Introduction to Spectroscopy
Electromagnetic Radiation · Wave-Particle Duality · Biological Energy Transitions
1. Introduction to Spectroscopy and Electromagnetic Radiation
Spectroscopy is the study of the physical interaction between electromagnetic radiation (light) and matter as a function of the wavelength (λ) or frequency (ν) of the radiation. When electromagnetic radiation is directed onto a biological or chemical sample, the light can be absorbed, emitted, scattered, reflected, or transmitted — and it is precisely this interaction, measured across the spectrum, that spectroscopic methods exploit to probe molecular structure.
1.1 Wave-Particle Duality and the Electromagnetic Wave
Electromagnetic radiation possesses both wave-like and particle-like properties. As a wave, it consists of an electric field vector (E) and a magnetic field vector (B) oscillating at right angles to one another and perpendicular to the direction of wave propagation.
Figure: The electromagnetic wave. The electric field (E, solid teal) and magnetic field (B, dashed orange) oscillate in phase, perpendicular to each other and to the direction of propagation. One full wave cycle spans the wavelength, λ, marked here as the distance between two successive crests.
A wave of electromagnetic radiation is characterized mathematically by three fundamental properties:
- Wavelength (λ): the linear distance between two consecutive wave peaks (crests) or troughs, measured in meters (m), nanometers (nm), or Ångstroms (Å).
- Frequency (ν): the number of complete wave cycles that pass a stationary point in one second, measured in hertz (Hz, or s−1).
- Wavenumber (ν): the reciprocal of the wavelength, representing the number of waves per unit distance, expressed in reciprocal centimeters (cm−1).
Wavelength and frequency are related through the constant speed of light in a vacuum (c = 2.998 × 108 m/s):
1.2 The Photon and the Planck-Einstein Relation
According to quantum mechanics, light is also composed of discrete, quantized packets of energy called photons. The energy (E) of a single photon is directly proportional to its frequency and inversely proportional to its wavelength, as expressed by the Planck-Einstein relation:
1.3 The Electromagnetic Spectrum and Biological Energy Transitions
The electromagnetic spectrum is divided into distinct regions based on wavelength and photon energy. When radiation interacts with biological molecules, the energy of the incident photon determines the specific type of physical or molecular transition that is induced:
| Region | Wavelength range | Photon energy | Molecular transition induced | Analytical / spectroscopic method |
|---|---|---|---|---|
| X-rays | 0.01–10 nm | Extremely high | Inner-shell electron ejection (ionization) | X-ray crystallography / diffraction |
| Ultraviolet (UV) | 100–400 nm | High | Valence electron excitation to unoccupied molecular orbitals | UV absorption spectroscopy |
| Visible (Vis) | 400–700 nm | Moderate | Valence electron excitation (electronic transitions) | Visible spectrophotometry / colorimetry |
| Microwaves | 1 mm–30 cm | Very low | Molecular rotation along an axis | Rotational spectroscopy |
| Radio waves | 0.5–10 m | Extremely low | Nuclear spin state inversion in a magnetic field | Nuclear magnetic resonance (NMR) |
Moving down the table from X-rays to radio waves, wavelength increases while photon energy falls off steeply — from energies capable of ejecting inner-shell electrons entirely, down to energies barely sufficient to flip a nuclear spin in an applied magnetic field. This energy gradient is why each region probes a physically distinct level of molecular structure, from electronic configuration down to nuclear spin state.
2. UV-Visible Absorption Spectroscopy
Electronic Transitions · Chromophores · The Beer-Lambert Law
2. UV-Visible Absorption Spectroscopy
Ultraviolet-Visible (UV-Vis) spectroscopy measures the absorption of light in the ultraviolet (200–400 nm) and visible (400–700 nm) regions of the spectrum. This absorption results in electronic transitions, where valence electrons are promoted from occupied, lower-energy molecular orbitals in the ground state to unoccupied, higher-energy molecular orbitals in the excited state.
2.1 Molecular Orbitals and Electronic Transitions
Molecules contain three primary types of electronic orbitals: bonding orbitals (σ and π) — low-energy orbitals holding shared electrons in covalent bonds; non-bonding orbitals (n) — intermediate-energy orbitals holding lone pairs not involved in bonding; and anti-bonding orbitals (σ* and π*) — high-energy orbitals that are unoccupied in the ground state.
Figure: Electronic molecular energy levels. The four possible UV-Vis electronic transitions, ordered here left to right from highest energy (shortest wavelength) to lowest energy (longest wavelength). Only transitions 3 and 4 fall within the practical UV-Vis range typically measured by benchtop spectrophotometers (≥ ~200 nm).
The four possible transitions, ordered from highest to lowest energy, are:
- σ → σ* transitions: promote an electron from a bonding σ orbital to an anti-bonding σ* orbital. Extremely high-energy, requiring deep vacuum-UV light (λ < 200 nm); occur in saturated hydrocarbons (methane, ethane) where only single C–C and C–H bonds are present.
- n → σ* transitions: promote a non-bonding lone-pair electron to an anti-bonding σ* orbital. Require moderate UV energy (λ ≈ 160–260 nm); occur in saturated compounds with heteroatom lone pairs, such as alcohols, amines, and alkyl halides.
- π → π* transitions: promote a bonding π electron to an anti-bonding π* orbital. Require lower energy (λ ≈ 200–500 nm); occur in unsaturated compounds with double or triple bonds (alkenes, alkynes, aromatics, carbonyls).
- n → π* transitions: promote a non-bonding lone-pair electron to an anti-bonding π* orbital. Require the lowest energy of all (λ ≈ 250–600 nm); occur in unsaturated compounds with heteroatoms, such as carbonyl (C=O) and nitro (N=O) groups.
2.2 Chromophores and the Conjugation Effect
A chromophore is any functional group or covalently unsaturated structural unit within a molecule that is directly responsible for the absorption of UV or visible light. Common biological chromophores include carbonyl groups (C=O), carbon-carbon double bonds (C=C), aromatic rings, and azo groups (N=N).
When multiple double bonds are separated by single bonds, their π orbitals overlap, creating a conjugated system where the π electrons are delocalized across the entire carbon framework:
- HOMO-LUMO gap narrowing: as the extent of conjugation increases, the energy gap between the Highest Occupied Molecular Orbital (HOMO, π) and the Lowest Unoccupied Molecular Orbital (LUMO, π*) progressively decreases.
- Bathochromic shift (red shift): because the HOMO-LUMO gap is smaller, less energetic photons are required to excite the electrons, so the absorption maximum (λmax) shifts toward longer wavelengths.
- Hyperchromic effect: the intensity of the absorption (the extinction coefficient, ε) also increases with extended conjugation.
Figure: Effect of conjugation on the HOMO-LUMO gap. Extending conjugation from ethylene's single π bond to 1,3-butadiene's two conjugated π bonds narrows the HOMO-LUMO gap, red-shifting the π→π* absorption maximum from ~171 nm to ~217 nm.
2.3 The Physics of Absorption: Lambert's and Beer's Laws
The physical process of light absorption through a solution is governed by two independent physical principles. Lambert's Law states that when monochromatic light passes through a homogeneous absorbing medium, the intensity of the light decreases exponentially as the physical thickness (path length) of the medium increases. Beer's Law states that when monochromatic light passes through a homogeneous solution, the intensity of the light decreases exponentially as the concentration of the absorbing solute increases.
Combining these two laws gives the unified Beer-Lambert Law, which relates the absorbance of light directly to concentration and path length:
Figure: The Beer-Lambert light path. A monochromatic beam of incident intensity I₀ enters a cuvette of path length l containing an absorbing solute at concentration c; the transmitted beam exiting the far side has a reduced intensity I.
2.4 Transmittance, Percent Transmittance, and Absorbance
The fraction of light passing through the sample is the transmittance (T), often expressed as percent transmittance (%T):
Because absorbance is the base-10 logarithm of the reciprocal of transmittance:
| Light absorbed | Transmittance (T) | %Transmittance | Absorbance (A) |
|---|---|---|---|
| 0% (none) | 1.0 | 100% | 0.0 |
| 90% | 0.1 | 10% | 1.0 |
| 99% | 0.01 | 1% | 2.0 |
| 99.9% | 0.001 | 0.1% | 3.0 |
2.5 Molar vs. Percent Extinction Coefficients
The physical unit of the extinction coefficient (ε) is set by the units used to express solute concentration:
- Molar extinction coefficient (εmolar): used when concentration is expressed in molarity (M). Units: M−1cm−1. Defined as the absorbance of a 1.00 M solution in a 1.00 cm cuvette.
- Percent extinction coefficient (εpercent, or E1%1cm): used in biochemistry when a protein or nucleic acid's molecular weight is unknown or variable. Concentration is expressed as %w/v (1% = 1 g/100 mL = 10 mg/mL). Units: (%w/v)−1cm−1.
- Specific absorption coefficient (εspecific): used when concentration is expressed in g/L or mg/mL.
To convert between a known percent extinction coefficient and its corresponding molar extinction coefficient, using the solute's molecular weight (MW):
2.6 Solved Quantitative Problems
Problem 1 — Concentrating a solution from transmittance data
A protein solution in a 1.00 cm cuvette transmits exactly 40.0% of the incident light at 280 nm. Its molar absorption coefficient (ε) at this wavelength is 6,000 M−1cm−1. Calculate the molar concentration.
- Convert %T to A: A = 2 − log10(40.0) = 2 − 1.6020 = 0.3980
- Apply Beer-Lambert: 0.3980 = (6,000 M−1cm−1) · c · (1.00 cm)
Problem 2 — Light attenuation through an extended path length
A 0.06 M solution in an 8.0 cm cuvette reduces light intensity to exactly one-fourth of its initial value (I₀/I = 4). Calculate the molar extinction coefficient.
- Determine A: A = log10(I₀/I) = log10(4) ≈ 0.6020
- Apply Beer-Lambert: 0.6020 = ε · (0.06 M) · (8.0 cm) = ε · (0.48 M·cm)
Problem 3 — Deconvolution of a two-component mixture (NAD+ / NADH)
A 1.00 cm cuvette holding a mixture of NAD+ and NADH reads A = 0.311 at 340 nm and A = 1.200 at 260 nm.
| Wavelength | ε(NAD+), M−1cm−1 | ε(NADH), M−1cm−1 |
|---|---|---|
| 340 nm | 0 | 6,220 |
| 260 nm | 18,000 | 15,000 |
Because absorbance is additive, the total absorbance at each wavelength is the sum of each species' individual absorbance.
- Solve NADH from the 340 nm data (NAD+ does not absorb here): cNADH = 0.311 / 6,220 = 5.00 × 10−5 M
- NADH's contribution at 260 nm: A = (15,000)(5.00 × 10−5)(1.00) = 0.750
- Remaining absorbance is NAD+'s: ANAD+,260 = 1.200 − 0.750 = 0.450
- Solve NAD+ concentration: cNAD+ = 0.450 / 18,000 = 2.50 × 10−5 M
3. Fluorescence and the Jablonski Diagram
Singlet & Triplet States · Radiative and Non-Radiative Decay · Stokes Shift
3. Fluorescence and the Jablonski Diagram
Fluorescence is a type of emission spectroscopy where a molecule absorbs electromagnetic radiation of a specific wavelength, transitions to an excited electronic state, and subsequently re-emits that energy as light of a different, longer wavelength.
3.1 Electronic Spin States: Singlet vs. Triplet Configurations
To understand energy transitions, we must define a molecule's electronic spin states based on multiplicity:
- Singlet ground state (S0): in the ground state of almost all organic molecules, the electrons in each occupied molecular orbital are paired with opposite spins (↑↓). The net spin quantum number (S) is 0, and the multiplicity (2S+1) is 1 — a singlet state.
- Excited singlet states (S1, S2): when an electron is promoted to a higher-energy orbital, its spin orientation remains unchanged, staying antiparallel to the spin of the electron left behind. The multiplicity remains 1.
- Excited triplet state (T1): under certain conditions, the spin of the promoted electron can undergo a spin-flip, becoming parallel to the spin of the electron in the ground orbital. The net spin (S) becomes 1, and the multiplicity (2S+1) becomes 3 — a triplet state.
3.2 Non-Radiative Decay Pathways
Once an electron is promoted to an excited singlet state (e.g., S2, or a high vibrational sub-level of S1), the molecule loses excess energy rapidly through three primary non-radiative (heat-generating) pathways:
- Vibrational relaxation (VR): extremely rapid (< 10−12 s). An excited molecule in a high vibrational sub-level collides with surrounding solvent molecules, shedding energy as thermal motion until it falls to the lowest vibrational sub-level of that same electronic state.
- Internal conversion (IC): a non-radiative transition between two electronic states of the same spin multiplicity (e.g., S2→S1). It occurs where the vibrational levels of the lower electronic state overlap with the ground vibrational level of the higher one.
- Intersystem crossing (ISC): a non-radiative transition between two electronic states of different spin multiplicities (e.g., S1→T1). This requires a spin-flip, which is quantum mechanically "forbidden" and occurs much more slowly than internal conversion. ISC is strongly promoted by heavy atoms (iodine, bromine) or paramagnetic species.
3.3 Radiative Decay: Fluorescence and Phosphorescence
A molecule at the lowest vibrational level of an excited state can return to the ground state by emitting a photon:
- Fluorescence (S1→S0): radiative transition from an excited singlet state to the ground singlet state. Because it requires no change in spin multiplicity, it is quantum mechanically allowed. Lifetime: 10−9 to 10−7 s — fluorescence stops almost instantly once the excitation source is turned off.
- Phosphorescence (T1→S0): radiative transition from an excited triplet state to the ground singlet state. Because it requires a spin-flip, it is quantum mechanically forbidden. Lifetime: 10−3 s to several minutes or hours — phosphorescing substances continue to "glow in the dark" long after the excitation source is removed.
3.4 The Jablonski Diagram
The physical relationships between all of these radiative and non-radiative energy transitions are illustrated standardly by a Jablonski diagram:
Figure: The Jablonski diagram. Solid arrows mark radiative transitions (Absorption, Fluorescence, Phosphorescence — the latter drawn dashed to indicate its spin-forbidden, low-probability nature); short wavy arrows and diagonal dashed arrows mark non-radiative transitions (VR, vibrational relaxation; IC, internal conversion; ISC, intersystem crossing). Note that T₁'s lowest vibrational level sits below S₁'s, consistent with Hund's rule, and that fluorescence and phosphorescence both originate from the lowest vibrational level of their respective excited states after vibrational relaxation.
3.5 The Physics of Stokes Shift
The Stokes shift is the difference (in wavelength or frequency units) between the absorption maximum (excitation) and the emission maximum (fluorescence) of the same electronic transition:
The wavelength of emitted fluorescence light is always longer (lower energy) than the wavelength of light absorbed to excite the molecule, because energy is lost through several rapid processes:
- Excitation to high vibrational levels: the molecule is initially excited to a high vibrational level of S1.
- Vibrational relaxation: before emitting light, the molecule rapidly relaxes, losing energy as heat to the surrounding solvent until it reaches the lowest vibrational level of S1.
- Decay to excited vibrational levels of S0: fluorescence emission lands the molecule in an excited vibrational level of the ground state, not the absolute ground vibrational state; another round of vibrational relaxation follows.
- Solvent reorganization: polar solvent molecules physically reorient around the newly created dipole of the excited fluorophore, lowering its excited-state energy further before emission.
Figure: Stokes shift. The emission (fluorescence) spectrum is shifted to longer wavelengths relative to the absorption (excitation) spectrum. The Stokes shift is measured as the separation between the two peak maxima.
4. Circular Dichroism (CD) Spectroscopy
Polarized Light · Chiral Chromophores · Protein Secondary Structure
4. Circular Dichroism (CD) Spectroscopy
Circular Dichroism (CD) is an absorption spectroscopy technique that utilizes circularly polarized light to analyze the structural asymmetry and conformations of optically active (chiral) biomolecules in solution.
4.1 Polarization Physics: Plane-Polarized and Circularly Polarized Light
Light is a transverse electromagnetic wave; the behavior of its electric field vector defines its state of polarization. In unpolarized light, the electric field oscillates in every possible plane perpendicular to propagation. In linearly (plane) polarized light, oscillations are restricted to a single plane. In circularly polarized light (CPL), the electric field vector rotates about the propagation axis with constant magnitude, completing one full rotation every wavelength.
Figure: Linear vs. circularly polarized light. Left: the electric field of linearly polarized light stays confined to one plane, its amplitude tracing a simple sine wave. Right: circularly polarized light is the sum of two perpendicular sine components (solid magenta, dashed teal) 90° out of phase — their combination sweeps the electric vector around the propagation axis, shown schematically by the dashed circle.
4.2 CD vs. Optical Rotatory Dispersion (ORD)
An optically active (chiral) substance contains molecules that lack a plane or center of symmetry (e.g., L-amino acids, D-sugars, α-helical polypeptide chains). When polarized light interacts with a chiral sample, two distinct phenomena occur:
- Optical Rotatory Dispersion (ORD): chiral molecules exhibit different refractive indices for L-CPL and R-CPL (nL ≠ nR). This differential speed causes a phase shift that rotates the plane of linearly polarized light — a scattering/refraction phenomenon.
- Circular Dichroism (CD): chiral molecules contain chromophores in asymmetric environments that absorb L-CPL and R-CPL to different extents (AL ≠ AR). CD is an absorption phenomenon, measured strictly within the absorption bands of the chiral chromophores.
4.3 The Beer-Lambert Formulation in CD
The quantitative measure of CD is the difference in absorbance between left- and right-circularly polarized light:
Applying the Beer-Lambert law to both components expresses CD in terms of the differential molar extinction coefficient (Δε):
4.4 Ellipticity and the Elliptic Path of Light
When L-CPL and R-CPL of equal amplitude are superimposed, they form plane-polarized light. But after passing through a circularly dichroic medium (AL ≠ AR), the two rotating vectors are unequal, and their superposition traces an ellipse rather than a straight line — elliptically polarized light. The degree of ellipticity (θ) is the ratio of the ellipse's minor to major axis, and is directly proportional to the differential absorbance:
4.5 CD Units: Molar and Mean Residue Ellipticity
To standardize CD data across instruments, concentrations, and path lengths, raw ellipticity (θλ) is converted into normalized molar quantities:
- Molar ellipticity ([θ]molar): used for small molecules of known molecular weight. [θ]molar = 100 × θλ / (c · l), expressed in degrees·cm2·decimol−1.
- Mean Residue Ellipticity ([θ]MRE): used for proteins/polypeptides, since the chromophore of interest is the repeating peptide backbone. Normalizing by residue count allows comparing secondary structure independent of overall molecular weight: [θ]MRE = (MRW × θλ) / (10 × l × cg/mL).
4.6 Mapping Far-UV CD Spectra to Protein Secondary Structures
Far-UV CD (190–250 nm) measures circular dichroism of the peptide bond backbone, giving sensitive qualitative and quantitative estimates of secondary structure. Each conformation has a characteristic spectral signature:
Figure: Far-UV CD spectral signatures. α-Helix (magenta) shows a positive peak near 192 nm and a double minimum at 208/222 nm. β-Sheet (teal) shows a smaller positive peak near 198 nm and a single minimum around 216–218 nm. Random coil (orange) shows a strong single negative minimum near 195–200 nm and near-zero ellipticity from 210–220 nm. A raw spectrum from an unknown protein can be fitted as a linear combination of these three reference curves to estimate secondary-structure percentages.
- α-Helix: strong positive peak at 191–193 nm; prominent double minimum at 208 nm and 222 nm. The 222 nm band is the n→π* transition of peptide carbonyls; the 208/192 nm peaks arise from excitonic splitting of the π→π* transition.
- β-Sheet: less intense spectrum with a positive peak at 195–200 nm and a single negative minimum at 216–218 nm (n→π* transition).
- Random coil: strong negative minimum near 195–200 nm and ellipticity near zero in the 210–220 nm region.
4.7 Near-UV CD as a Reporter for Tertiary Structure
Near-UV CD (260–320 nm) measures the circular dichroism of aromatic side chains and disulfide bonds: phenylalanine (255–270 nm), tyrosine (275–285 nm), and tryptophan (290–305 nm) absorb in this region, with disulfide bonds contributing a broad, weak signal across the whole range.
5. Nuclear Magnetic Resonance (NMR)
Nuclear Spin · Chemical Shielding · Chemical Shift · Spin-Spin Splitting
5. Nuclear Magnetic Resonance (NMR) Spectroscopy
Nuclear Magnetic Resonance (NMR) is a high-resolution spectroscopic technique that exploits the magnetic properties of certain atomic nuclei to determine the 3D chemical structure, connectivity, and molecular dynamics of biological macromolecules in solution.
5.1 Nuclear Spin Properties and Selection Rules
Atomic nuclei consist of protons and neutrons. Some possess an intrinsic property called nuclear spin, quantified by the spin quantum number (I). The selection rules for nuclear spin are:
- NMR-inactive (I = 0): if both the proton count and neutron count are even, their spins pair up completely and the net nuclear spin is zero. These nuclei are invisible to NMR (e.g., 12C, 16O).
- Integer spin (I = 1, 2, 3…): if both the proton and neutron counts are odd, the nucleus has an integer spin (e.g., 14N has I = 1).
- Half-integer spin (I = 1/2, 3/2, 5/2…): if the mass number (protons + neutrons) is odd, the nucleus has a half-integer spin — the most favorable nuclei for high-resolution biological NMR.
5.2 Spin States in an External Magnetic Field (B0)
A nucleus with spin quantum number I can adopt exactly 2I + 1 spin states. For I = 1/2 (such as 1H), there are exactly two allowed states. With no external field, the nuclear dipoles point randomly and all spin states are degenerate (identical energy). In an applied field B0, this degeneracy is broken, splitting the population into two distinct energy states:
Figure: Nuclear spin splitting in field B₀. With no applied field, all nuclear spin orientations are degenerate. Once an external field B₀ is applied, the degeneracy breaks into two states: the α state (nuclear dipole aligned parallel/with the field) at lower energy, and the β state (aligned antiparallel/against the field) at higher energy, separated by ΔE = h·ν.
5.3 The Energy Gap and the Gyromagnetic Ratio (γ)
The energy difference (ΔE) between the α and β states is directly proportional to the local magnetic field strength felt by the nucleus (Bp):
5.4 Resonance and Spin Flipping
At thermal equilibrium, the population in the lower-energy α state slightly exceeds the population in the higher-energy β state, per the Boltzmann distribution. If this population is irradiated with radiofrequency (RF) radiation matching the energy gap exactly (ΔE = h·ν), α-state nuclei absorb the photon and "flip" into the β state — this condition is called resonance. The resonance frequency required is:
5.5 Chemical Shielding and Induced Diamagnetic Currents
If every proton in a molecule experienced the exact same external field B0, they would all resonate at one identical frequency — a single, uninformative peak. But different protons sit in different local densities of valence electrons:
- Induced diamagnetic currents: in field B0, the surrounding valence-electron cloud is forced to circulate, generating a small local induced field that opposes B0 (Lenz's Law).
- Shielding: this induced field shields the nucleus from the full external field. The effective field felt is Bp = B0(1 − σ), where σ is the chemical shielding constant.
5.6 Chemical Shift (δ, ppm) and the TMS Reference
Because absolute resonance frequency scales with the spectrometer's magnet strength (e.g., a proton resonates at 400 MHz on a 9.4 T magnet but 800 MHz on an 18.8 T magnet), absolute frequencies can't be compared between labs. Instead, all shifts are measured relative to tetramethylsilane (TMS, Si(CH3)4): its 12 equivalent protons are exceptionally highly shielded (silicon is electropositive, pushing electron density toward the methyl carbons), producing a single sharp peak upfield of almost all other organic signals, defined as exactly 0.00 ppm.
5.7 Information Extracted from ¹H NMR Spectra
A standard 1H NMR spectrum yields four distinct types of structural information, illustrated here for dimethoxymethane (CH3O–CH2–OCH3):
Figure: ¹H NMR spectrum of dimethoxymethane. Peak a (the two equivalent –OCH₃ methyl groups, 6H) appears at δ ≈ 3.35 ppm; peak b (the central –CH₂– methylene, 2H, flanked by two oxygens) is more deshielded and appears downfield at δ ≈ 4.56 ppm. The TMS reference peak defines 0.00 ppm. Peak areas are drawn proportional to proton count (a:b = 6:2 = 3:1).
- Number of signals: the count of chemically non-equivalent proton sets. Dimethoxymethane has two sets — the outer –OCH3 groups (a) and the central –CH2– (b) — yielding exactly two signals.
- Chemical shift (δ): pinpoints each set's electronic environment. Protons a sit next to one oxygen (δ ≈ 3.35 ppm); protons b sit between two oxygens, doubling the deshielding effect and shifting downfield to δ ≈ 4.56 ppm.
- Peak integration: the area under each peak is proportional to the number of contributing protons. For dimethoxymethane, a:b = 6:2 = 3:1, matching the structure.
- Spin-spin splitting (multiplicity): the field sensed by a proton is perturbed by neighboring protons on adjacent carbons. Under the N+1 Rule (for I = 1/2 nuclei), a signal splits into N+1 peaks, where N is the number of equivalent neighboring protons.
| Multiplicity | N (neighboring H) | Peaks | Intensity ratio |
|---|---|---|---|
| Singlet | 0 | 1 | 1 |
| Doublet | 1 | 2 | 1:1 |
| Triplet | 2 | 3 | 1:2:1 |
| Quartet | 3 | 4 | 1:3:3:1 |
6. Mass Spectrometry (MS)
Ionization · MALDI & ESI · Time-of-Flight Analysis
6. Mass Spectrometry (MS)
Mass spectrometry is an analytical technique that determines the molecular mass of a chemical or biological compound by measuring the mass-to-charge (m/z) ratio of its gas-phase ionized species. Unlike UV-Vis, CD, or NMR, mass spectrometry is not an absorption or emission spectroscopy technique — it does not involve transitions between quantum energy levels induced by light absorption.
6.1 The Four-Stage Architecture of Mass Spectrometry Systems
Every mass spectrometer consists of four core components operating under high vacuum, to prevent ion collisions with background air molecules:
Figure: The mass spectrometry instrument flow. Neutral analyte molecules are ionized, accelerated to uniform kinetic energy, separated by their mass-to-charge ratio, and finally counted at the detector, producing a mass spectrum of relative abundance vs. m/z. All four stages sit inside one continuous vacuum system.
6.2 Hard vs. Soft Ionization
Ionization techniques fall into two classes based on how much energy is transferred to the analyte:
- Hard ionization: transfers high excess energy, causing extensive bond breakage and fragmentation (e.g., Electron Ionization, EI). Excellent for identifying small organic molecules by matching fragmentation "fingerprints" to databases.
- Soft ionization: transfers minimal energy, converting the analyte into a gas-phase ion with little fragmentation. Essential for analyzing large, intact biomolecules (proteins, glycoproteins, intact nucleic acids) that would otherwise disintegrate.
6.3 Matrix-Assisted Laser Desorption/Ionization (MALDI)
MALDI is a highly effective soft ionization technique.
Figure: The MALDI ionization process. Analyte is co-crystallized with a large molar excess of a light-absorbing matrix on a metal target plate. A UV laser pulse (e.g., 337 nm nitrogen laser) is absorbed intensely by the matrix, rapidly heating and vaporizing it and carrying the embedded analyte molecules into the gas phase as a desorbed plume, where proton transfer from excited matrix molecules generates singly-charged [M+H]⁺ ions.
- Co-crystallization: analyte is mixed with a massive molar excess (typically 10,000-fold) of a small, light-absorbing organic acid, the matrix (e.g., α-cyano-4-hydroxycinnamic acid for small proteins/peptides; sinapinic acid for large proteins).
- Solid target: the mixture is spotted onto a metal target plate and dried, forming a co-crystalline solid.
- Laser pulse: the target, in the vacuum chamber, is irradiated with a short UV laser pulse.
- Desorption: matrix molecules absorb the laser energy intensely, rapidly heating and vaporizing, carrying the embedded non-volatile analyte into the gas phase in a desorbed plume.
- Proton transfer: excited matrix molecules transfer protons (H+) to analyte molecules in the dense gas plume, producing predominantly singly-charged intact ions: M + H+ → [M+H]+.
6.4 Electrospray Ionization (ESI)
ESI is a highly effective soft ionization technique.
Figure: The ESI capillary spray. Liquid analyte is pumped through a silica capillary held at 3–4 kV. The electric field forms a Taylor cone that disperses into highly charged droplets; as a warm nitrogen counter-flow evaporates solvent, each droplet shrinks until its surface charge density reaches the Rayleigh limit, triggering a Coulombic explosion into smaller droplets. This evaporation-explosion cycle repeats until bare, gas-phase, multiply-charged analyte ions remain.
- Charged spray: liquid analyte (usually from an HPLC column) is pumped through a narrow silica capillary held at high positive voltage (3–4 kV).
- Taylor cone: the strong electric field forces the emerging liquid into a sharp cone, dispersing it into a fine aerosol of highly charged droplets.
- Solvent evaporation: a counter-flow of warm nitrogen gas evaporates solvent from the migrating droplets, shrinking them.
- Rayleigh limit and Coulombic explosion: as a droplet shrinks, its surface charge density increases until electrostatic repulsion overcomes surface tension, and the droplet bursts into smaller droplets.
- Ion release: this evaporation-explosion cycle repeats until all solvent is gone, releasing free, gas-phase analyte ions.
6.5 Physics of Time-of-Flight (TOF) Mass Analyzers
The TOF analyzer separates ions in time based on how long they take to travel down a field-free drift tube of known length (L).
Figure: The time-of-flight (TOF) tube. Ions accelerated through the same potential V carry identical kinetic energy but different velocities; lighter ions travel faster and arrive at the detector first, heavier ions arrive last.
Derivation: an ion of mass m carrying charge z·e is accelerated from rest through potential V, so its potential energy converts entirely to kinetic energy in the flight tube:
Inside the field-free tube the ion travels at constant velocity v = L/t. Substituting and solving for m/z:
7. Tandem MS/MS & Peptide Sequencing
Collision-Induced Dissociation · b/y Ions · De Novo Sequencing · Glycoproteomics
7. Tandem Mass Spectrometry (MS/MS) and Peptide Sequencing
Tandem mass spectrometry (MS/MS) couples two distinct mass spectrometers in series, separated by a collision chamber, to determine the exact primary amino acid sequence of a polypeptide.
7.1 System Design: MS-1, Collision Cell (CID), and MS-2
Figure: The tandem MS/MS workflow. A complex peptide mixture (from protease digestion) is ionized by ESI. MS-1 acts as a mass filter, isolating one precursor peptide ion by m/z and discarding the rest. The precursor collides with an inert gas in the collision cell, fracturing along the backbone (Collision-Induced Dissociation, CID). MS-2 then analyzes the resulting fragment ions to produce a fragmentation spectrum.
- First stage (MS-1): a complex peptide mixture (from digesting a protein with a protease like trypsin) is ionized by ESI and directed into MS-1, which selects a single precursor peptide ion by its m/z ratio, discarding all others.
- Second stage (Collision Cell): the selected precursor is focused into a collision cell filled with a low pressure of inert gas (He or Ar). Collisions convert kinetic energy into internal vibrational energy, fracturing the peptide backbone — Collision-Induced Dissociation (CID).
- Third stage (MS-2): the resulting fragment ions are directed into MS-2, which analyzes their m/z values to produce a fragmentation spectrum.
7.2 Peptide Backbone Fragmentation (a/x, b/y, c/z Cleavage)
A peptide backbone is a repeating chain of N–Cα–C(=O) units. Under CID, three different backbone bonds can break:
Figure: Peptide backbone fragmentation sites. Three distinct bonds along the repeating N–Cα–C(=O) backbone can cleave under CID. N-terminal fragments are labeled a/b/c (top); the complementary C-terminal fragments are labeled x/y/z (bottom), numbered from their respective termini.
- Cα–CO bond: cleavage yields a-type ions (charge on N-terminal fragment) and x-type ions (charge on C-terminal fragment).
- CO–NH bond (the peptide bond): cleavage yields b-type ions (N-terminal charge) and y-type ions (C-terminal charge). This is the most common and analytically useful pathway under low-energy CID.
- NH–Cα bond: cleavage yields c-type ions (N-terminal charge) and z-type ions (C-terminal charge).
7.3 b-ion and y-ion Nomenclature
When the peptide bond (CO–NH) is cleaved, a complementary pair of a b-ion and a y-ion is produced. b-ions extend from the N-terminus and are numbered sequentially (b1 = first residue, b2 = first two, etc.). y-ions extend from the C-terminus, numbered sequentially from that end. For a peptide of n residues, a cleavage produces a bi ion and a yn−i ion whose masses sum to the mass of the intact protonated peptide plus water.
Figure: b-ion and y-ion generation. Cleaving the Gly–Cys peptide bond of Ala-Val-Gly-Cys-Arg produces a b₃ ion (Ala-Val-Gly, N-terminal, charge retained as an acylium-like C-terminus) and a complementary y₂ ion (Cys-Arg, C-terminal, protonated free amine).
7.4 De Novo Sequencing from MS/MS Fragmentation Spectra
To sequence a peptide de novo (without a genomic database match), the sequential peaks of a continuous y-ion (or b-ion) series are analyzed:
- Calculate peak differences: in a continuous y-ion (or b-ion) series, adjacent peaks differ by exactly one residue.
- Determine residue mass: Δm = m/z(yk) − m/z(yk−1).
- Identify the amino acid: the mass difference matches a specific residue's monoisotopic mass — e.g., 71.04 Da = Alanine; 57.02 Da = Glycine; 113.08 Da = Leucine/Isoleucine (indistinguishable by low-energy CID); 128.09 Da = Lysine/Glutamine (isobaric on low-resolution instruments).
Figure: MS/MS fragmentation peaks. A continuous y-ion series (y3 → y6) differs by a mass gap of 231 Da, matching the combined residue masses of Gly and Cys — identifying those two residues in the sequence between the two fragment sizes. Reading consecutive gaps across the full y-ion (or b-ion) series maps the complete primary sequence from N- to C-terminus.
7.5 Glycan Mass and Glycoprotein Structures
Many proteins are modified by carbohydrates (glycans), playing roles in cellular signaling, structural stability, and immunology. Mass spectrometry characterizes these modifications through two disciplines:
Figure: The two glycoprotein analysis disciplines. Glycomics (left) enzymatically or chemically releases glycans from the protein backbone, separates and derivatizes them, then determines their mass, branching structure, linkage chemistry, and anomeric configuration by MS. Glycoproteomics (right) instead digests the intact glycoprotein into glycopeptides, then uses MS/MS — diagnostic oxonium ions (e.g., hexose at m/z≈163, HexNAc at m/z≈204) signal a glycopeptide at low energy, while higher energy fragments the peptide backbone — simultaneously mapping peptide sequence, glycosylation site, and glycan composition.
LessonStep 10 of 14
