Chapter 6 – Forces  227

magnetic field. Beads can be chemically functionalized on their surface, using the same tech­

nology as for microspheres used for optical tweezers, to permit conjugation to a variety of

biomolecules, such as antibodies and short specific sequences of nucleic acid (see Chapter 7).

A suspension of magnetic beads is mixed with the target biological components.

Once bound to a specific biomolecule, then an applied magnetic field can pull the bead,

and the biomolecule and any other biological structures attached to that biomolecule (e.g., a

whole cell, in the case of the biomolecule attached to a cell membrane receptor protein) away

from a mix of heterogeneous biological components/​cells, and any unbound material can be

removed by aspiration/​washing, facilitating purification of that bound component. Magnetic

bead–​mediated separations result in comparatively low mechanical stress to the biological

components being isolated and are rapid, cheap, and high throughput.

Applications include purification of nucleic acids by using short nucleotide sequences (or

oligonucleotides, sometimes known simply as oligos) bound to the paramagnetic beads, which

are complementary to sequences in the specific target nucleic acid molecules. When coated

with specific antibodies, magnetic beads can also be used to purify proteins and to isolate

various specific cell types including eukaryotes such as human cells and bacteria, and also

smaller subcellular structures and viruses, subcellular organelles, and individual proteins.

6.4.2  MASS SPECTROMETRY

For a bulk ensemble average in vitro biophysical technique, mass spectrometry (often shorted

to mass spec) is one of the most quantitatively robust. Here, ~10⁻¹⁵ kg of sample (small,

but still equivalent to several millions of molecules) is injected into an ionizer. Ionization

generates fragments of molecules with different mass and charge. The simplest machine is

the sector mass spectrometer that accelerates ion fragments in a vacuum using an electric

field E and deflects them using a magnetic field sector oriented at right angles of magnitude

B to this so that the ions follow a roughly circular path. The circle radius r is a function of the

mass-​to-​charge ratio mq of particles in the beam, which can easily be derived by equating the

magnetic to the centripetal force:

(6.12)

r

Em

B

q

=

2

Different ionized molecule fragments are collected and analyzed depending upon the

detector position (often termed a velocity selector) in the circular ion path. This generates a

mass spectrum that can yield detailed data concerning the relative proportions of different

ionic species in the sample.

Variants of the basic mass spectrometer include ion trap (injected ions trapped in a cavity

using electric fields), Fourier transform (ions injected into a cyclotron cell and resonated into

orbit using an oscillating electric field generating a radio-​frequency signal that is detected and

subsequently Fourier transformed to yield mass spectrum), time of flight (an ion vapor pulse

is created using a high-​energy laser and high-​energy ions are accelerated using an electric field

with time taken to travel a given distance measured), and quadrupole (accelerated ion beam

passed between four metal rods to which direct current (DC) and alternating current (AC)

potentials are applied causing resonance to the ion beam such that only ions with a narrow

range of mq will pass through the rod cavity into the detector unit) mass spectrometers.

The state of the art for quantitative mass spectrometry includes matrix-​assisted laser

desorption ionization (MALDI, also known as MALDI imaging spectroscopy) and stable

isotopic labeling by amino acids in cell culture (SILAC) techniques. MALDI is an imaging

technique in which the sample, typically a thin section of biological tissue (which can be

applied both to animal and plant tissues), raster scans in 2D while the mass spectrum is

recorded using focused laser ablation of the biological material to generate ion fragments.

To enhance laser adsorption, a strongly laser-​absorbing chemical reagent matrix is nor­

mally sprayed onto the sample surface. MALDI can enable the imaging of the localization