Chapter 9

Cooperative transitions in

macromolecules

Hooke gave in 1678 the famous law of proportionality of stress

and strain which bears his name, in the words ‘Ut tensio sic

vis’....This law he discovered in 1660, but did not publish until

1676, and then only under the form of an anagram, “ceiiinossst-

tuu.” – A. Love,ATreatise on the Mathematical Theory of

Elasticity

The preceding chapters may have shed some light on particular molecular forces and processes,
but they also leave us with a deeper sense of dissonance. On one hand, we have seen that the activity
of individual small molecules is chaotic, leading to phenomena like Brownian motion. We have come
to expect predictable, effectively deterministic behavior only when dealing with vast numbers of
molecules, for example the diffusion of a drop of ink, or the pressure of air in a bicycle tire. On the
other hand, Chapter 2 showed a gallery of exquisitely structuredindividualmacromolecules, each
engineered to do specific jobs reliably. So which image is right—should we think of macromolecules
as being like gas molecules, or like tables and chairs?
More precisely, we’d like to know how individual molecules, held together by weak interactions,
nevertheless retain their structural integrity in the face of thermal motion, and indeed can perform
specific functions. The key to this puzzle is the phenomenon of cooperativity.
Chapter 8 already introduced cooperativity, showing that it makes the micelle transition sharper
than we would otherwise expect it to be. This chapter will extend the analysis, and also deepen
our understanding of macromolecules as brokers at the interface between the worlds of mechanical
and chemical forces. Section 9.1 begins by studying how an external force affects the conformation
of a macromolecule, first in a very simplified model and then adding the cooperative tendency
of each monomer to do what its nearest neighbors are doing. The ideas of Chapter 6, and the
partition function method for calculating entropic forces (from Section 7.1), will be very useful
here. Next, Section 9.5 will extend the discussion to transitions induced by changes in thechemical
environment. The final sections argue briefly that the lessons learned from simple model systems

©c2000 Philip C. Nelson

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