20-Bio-B10 Biomechanical Device Design & Human Factors · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, December 2017 — 04-Bio-B10 Analytical Biochemistry. Three hours, closed book, any non-communicating Casio/Sharp calculator. Six questions of equal value (20 marks each); five constitute a complete paper and only the first five appearing in the answer book are marked. All six are solved here, because this set is a study resource rather than an examination script. The paper is essay/descriptive throughout, with two embedded PCR copy-number sub-questions (Q2b, Q2c) that carry numeric content.
Reference texts (the books a candidate should have reviewed for this subject):
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
A Fourier Transform is a mathematical operation that converts a signal from one domain (typically time, or in an interferometer's case, mirror-displacement/optical path-length difference) into its equivalent representation in the frequency domain. It decomposes an arbitrarily complex signal — which may be a superposition of many sinusoidal components of different frequency, amplitude, and phase — into the individual sinusoidal (frequency) components that, summed together, reconstruct the original signal. The inverse Fourier Transform performs the reverse operation, reconstructing the time/spatial-domain signal from its frequency-domain components.
An FTIR spectrometer does not scan wavelength-by-wavelength as older dispersive IR instruments did. Instead, it uses a Michelson interferometer: broadband IR light is split, sent down a fixed and a moving mirror path, recombined, and passed through the sample, so the detector records a single time-domain signal — the interferogram — that is the sum of interference patterns from every wavelength in the source simultaneously, as a function of the moving mirror's path-length difference (this simultaneous, all-wavelengths-at-once acquisition is the multiplex/Fellgett advantage that gives FTIR its speed and sensitivity edge over dispersive instruments). The interferogram itself is not chemically interpretable by eye. The Fourier Transform is what converts that raw interferogram from its path-length/time-domain form into the familiar IR absorbance-or-transmittance-versus-wavenumber spectrum — i.e., it is the computational step that turns the instrument's raw multiplexed measurement into the actual chemical fingerprint the analyst reads.
FTIR is versatile across all three states of matter. Solids can be analyzed as a KBr pellet (finely ground sample diluted in dry potassium bromide and pressed into a transparent disc), as a Nujol mull (ground sample suspended in mineral oil between salt plates), or, most commonly today, directly via attenuated total reflectance (ATR), where the sample is simply pressed against a high-refractive-index crystal and the IR evanescent wave probes only the top few microns of the sample with no preparation needed. Liquids can be run as a thin film squeezed between IR-transparent salt plates (NaCl, KBr) or in a sealed liquid cell of fixed path length, and are equally amenable to ATR. Gases require a dedicated gas cell, typically with a long optical path length (multi-pass folded-mirror cells are common) because gas-phase samples are dilute and give inherently weaker absorbance than condensed-phase samples at the same pressure. This flexibility — essentially no state of matter is excluded — is part of why FTIR is such a broadly applied identification and characterization technique.
A representative biomedical/biochemical application is protein secondary-structure analysis via the Amide I band (roughly 1600–1700 cm−1, dominated by the C=O stretching vibration of the peptide backbone). The exact peak position and shape within this band are sensitive to the local hydrogen-bonding pattern of the peptide carbonyl, which differs systematically between secondary-structure elements: α-helix typically absorbs near ~1650–1658 cm−1, β-sheet nearer ~1620–1640 cm−1 (often with a companion high-frequency component near 1680–1695 cm−1 for antiparallel sheet), and random coil/unordered structure falls in between. By collecting the FTIR spectrum of a purified protein and mathematically deconvolving (second-derivative or curve-fitting analysis of) the composite Amide I envelope into its component sub-bands, an analyst can estimate the approximate percentage of α-helix, β-sheet, turn, and unordered content in the protein — without needing a crystal structure. This is routinely used to confirm that a purified or formulated therapeutic protein has retained its correctly folded secondary structure (a key quality-control check in biopharmaceutical development), or to monitor structural changes (e.g., unfolding, aggregation into β-sheet-rich amyloid) under stress conditions such as heat, pH shift, or agitation.
