Chapter 1 – Introduction  5

tools can now address exquisitely well. The wind’s direction is already beginning to change

with a greater investment in functional imaging tools of novel techniques of light microscopy

in particular, some of which may indeed develop into new methods of dynamic structural

biology themselves.

The benefits of providing new insight into life through the bridging of physics and

biology are substantial. Robust quantitation through physical science offers a precise route

into reductionist inference of life, namely, being able to address questions concerning the

real underlying mechanisms of natural processes, how tissues are made up of cells and the

cells from molecules, and how these all work together to bring about something we call a

living organism. The absence of quantifying the components of life precisely, both in space

and in time, makes the process of reducing biological phenomena to core processes that

we can understand quite challenging, especially in light of the complexity of even the sim­

plest organism. And quantifying physical parameters precisely is one thing in particular that

physics does very well.

One of the most cited achievements of biophysics is that of the determination of the struc­

ture of the biological molecule called “deoxyribonucleic acid” (DNA), which in the 1950s

was resolved through an exquisite combination of biology and physics expertise, in that it

required challenging biochemical techniques to purify DNA and then form near-​perfect

crystalline fibers, and then applying innovative physical science x-​ray crystallography tools

on these DNA fibers followed by a bespoke physical science analysis to infer the double-​

helical structure of DNA. But there are also lesser known but equally important examples in

which physical science tools that initially had no intended application in the life sciences were

eventually utilized for such and which today are very tightly coupled with biology research

but decoupled from their original invention.

For example, there is small-​angle x-​ray scattering (SAXS). SAXS was a physical science

tool developed in the 1980s for the investigation of material properties of, originally, non­

biological composites at the nanometer length scale, in which a sample’s elastic scattering

of x-​rays is recorded at very low angles (typically ≲10°). However, this technique found later

application in the investigation of some natural polymers that are made by living cells, for

example, the large sugar molecule, starch, that is made by plants. These days, SAXS has grown

into a very powerful tool for investigating the mesoscopic periodic length scale features over

a range of typically ∼5–​150 nm (a “nm” or nanometer is 1000 million times smaller than a

meter) of several different biological filamentous/​polymeric structures and in fact is largely

viewed now as being primarily a biophysical technique.

Worked Case Example 1.1—​Biomolecular Springs

As you will discover in Chapter 2, DNA molecules are an essential and special type of bio­

polymer which carry the genetic code, and you would already be aware that they often

adopt an intriguing double-​helical structure. What you may be less familiar with is that

they also act as a tiny spring when you stretch them…

Stretch experiments were performed on a type of DNA called lambda DNA (a type of

DNA produced by a virus that infects bacteria… but it is commonly used in biophysics

experiments on DNA) at room temperature by tethering opposite ends of one or more DNA

molecule in parallel between two tiny plastic beads around three thousandths of a milli­

meter in diameter using a tool called “optical tweezers,” also known as an “optical trap”

(see Chapter 6). Assume that DNA acts as a Hookean spring, and that the optical twee­

zers work by producing an attractive force on a bead toward the center of a focused near

infrared laser beam of wavelength one thousandth of a millimeter, which is proportional

to the displacement of the bead from the center of the laser focus whose constant of pro­

portionality is known as the trap stiffness, k.

a

If the maximum extent of this optical trap is “diffraction-​limited,” which you can

assume here is symmetrical, so roughly the same diameter as the wavelength of

the laser, write down an expression for the maximum force that can be exerted on a