It is possible to combine the summation with the connectivity theorems to obtain closed expressions that relate the control coefficients to the elasticity coefficients. For example, consider the simplest non-trivial pathway:
We assume that  and  are fixed boundary species so that the pathway can reach a steady state. Let the first step have a rate  and the second step . Focusing on the flux control coefficients, we can write one summation and one connectivity theorem for this simple pathway:
Using these two equations we can solve for the flux control coefficients to yield
Using these equations we can look at some simple extreme behaviors. For example, let us assume that the first step is completely insensitive to its product (i.e. not reacting with it), S, then . In this case, the control coefficients reduce to
That is all the control (or sensitivity) is on the first step. This situation represents the classic rate-limiting step that is frequently mentioned in textbooks. The flux through the pathway is completely dependent on the first step. Under these conditions, no other step in the pathway can affect the flux. The effect is however dependent on the complete insensitivity of the first step to its product. Such a situation is likely to be rare in real pathways. In fact the classic rate limiting step has almost never been observed experimentally. Instead, a range of limitingness is observed, with some steps having more limitingness (control) than others.
We can also derive the concentration control coefficients for the simple two step pathway: