The two-state model of Chapter 7 can be used as a basic building block for more complicated processes. When a system has more than two states, conversions between different pairs can occur, and then the kinetics reflects the aggregate behavior of those various transitions. The time course is no longer a simple exponential function, and in this chapter we will see how multi-state models lead to multi-exponential kinetics.

Much of Chapter 7 probed the fundamental physical processes that govern the speed of a transition. Now we will accept the basic phenomenon of a transition with a given rate, put some of these transitions together, and work out the dynamic behavior of these more complicated systems. The mathematical method for handling multi-state kinetics is very robust and powerful. With them one can develop quantitative descriptions for a general class of models. Aside from kinetic problems in biophysics, the mathematics introduced in this chapter has been applied to an extraordinarily wide range of fields from stochastic processes in physics to population dynamics in ecology.

Multi-state kinetics has considerable practical value, because most models for molecular mechanisms involve interconversions between a few distinct states. Kinetic behavior often provides the most direct experimental tool for testing the predictions of such a model.

The three-state model

Many important features of multi-state kinetics can be illustrated with this example.