Biological systems often fluctuate more noticeably than typical physical and chemical systems. This reflects the large size of many biological molecules and the small size of cells. The molecular nature of matter gives rise to fluctuations in every imaginable property. These fluctuations may or may not be easy to see, and size is a critical factor. In a system with N molecules, many measured quantities are proportional to N, but the fluctuations are proportional to N½. The fluctuations relative to the mean then decrease with the size of a system as N−½. When N is Avogadro's number, the task of observing these fluctuations in a conventional measurement becomes quite a challenge. Of course, there are some incredibly sensitive measurements that can be made. Signals arising from single molecules can be detected, and the fluctuations in these signals reflect the stochastic nature of molecular activity. But in many cases where the single-molecule signals are too small to see, the collective fluctuations may still be detectable. The special size scales found in biology generate a uniquely fluctuating world that merits special attention.

We have encountered fluctuations already in Chapter 3 in relation to conformations of macromolecules, and in Chapter 6 in relation to random walks. The probability of fluctuations can be calculated whenever statistical mechanics is used to develop a quantitative molecular description, and in many situations fluctuations contain important information. The study of fluctuations then becomes a powerful experimental approach by which models can be tested and molecular parameters estimated.