Analysis of protein aggregation kinetics.

Given a set of kinetic data, then, the preceding discussions suggest the following approach to its analysis. 1. For purposes of establishing the reaction, ignore the final stages and concentrate on the initial 10-20% of the reaction at first. A globally optimized model may be based on a faulty assumption for the initial steps. Thus, although the whole data set may look reasonably well fit, the reaction could be misrepresented, and thus the fit unhelpful if accuracy at the later stages has come at the expense of the initial phase of the reaction. 2. What is the time course of the initial reaction? (A) Is the reaction exponential? Exponential growth gives dramatic lag times (see Fig. 3), whereas nonexponential "lag times" have a visible signal from time 0 (i.e., Fig. 2). If the data set shows the abrupt appearance of signals after a period of quiescence, the chances are excellent that the time course is exponential. High sensitivity measurement of the signal at times during the lag phase should be used to confirm the exponential nature quantitatively. Exponential reactions mean a secondary pathway is operative. (a) A cascade (tn) can look similar to an exponential, but may proceed from a multistep single-path reaction. Thus the exponential needs to be ascertained with some accuracy. (b) It is possible that some or all of the lag results from a stochastic process, i.e., formation of a single nucleus being observed. This, however, is likely to be accompanied by a secondary process, as few techniques are sensitive enough to detect a single polymer at a time, and having one nucleus form many polymers is a hallmark of a secondary process. Thus, the reproducibility of the kinetics must be established to rule out stochastics. If data show wide variation, stochastic methods as described earlier may be employed. (c) Given a secondary process, one must separate the primary nucleation process from the secondary process (by stochastic means or by use of the product B2A, as described earlier). (B) If the reaction does not begin with an exponential, is it parabolic? If so, it falls in the general class of linear polymerizations. 3. What is the concentration dependence of the reaction(s)? This will separate nucleation processes from growth, and so on. 4. If the initial reaction is neither exponential nor parabolic, a reaction mechanism needs to be proposed and evaluated. Solving the resulting equations is best done by linearization, which has the best chance of giving equations whose solutions and their sensitivity to parameters are readily understood. If this proves fruitful, full numeric solutions may be useful. 5. At this point, the full reaction may be considered to completion. 6. The physical basis of the description (sizes of parameters and their dependencies) needs to be finally considered to ensure that the mathematical success of the description rests on tenable physical grounds.