Axonal elongation as a stochastic walk.

A new formula calculates rates of directed axonal growth (elongation or retraction) using measurements of growth cone movements. By explicitly separating changes in axonal length from other nonelongational growth cone movements, the calculated rates reflect the detailed cellular growth mechanisms more directly than previous growth measures. In addition, the formula produces three distinct parameters of axonal elongation: n, a growth step rate; s, a growth step size; and P, a probability that a growth step leads to axonal elongation. For normal and regenerating individual chick and frog axons in culture, the formula has quantitated the following differences: the axon itself can elongate more rapidly in the chick, and the axon elongates in smaller steps in the chick. The underlying dynamics of growth of regenerating axons are quite similar to normal axons, but, in the short term, regenerating axons elongate in larger steps and at a slower rate. The distribution of these new rate measurements suggests that the elongation of axons can be usefully modelled as a one-dimensional stochastic walk.