**Tau filament length distributions.** The time-dependent evolution of length distribution was calculated for 1 μm tau from the parameters in in conjunction with Equations , , , , (*N* = 500) as described under “Experimental Procedures.” *A*, two-dimensional slices through resultant time courses at 0.5 (*red*), 1 (*orange*), 7 (*green*), and 24 h (*blue*) are plotted, where each line represents relative frequency of filament length in units of protomers. For a nucleation-dependent mechanism where *n* = 2, calculated length distributions predicted rapid formation of a stable peaked distribution followed by monotonously decreasing relative mode height as a function of time (*solid lines*). Adjusting *n* above or below a value of 2 greatly modified the simulation. For example, under isodesmic conditions (no nucleation ste*p, k*_{e-} = 0.019 s^{-1}, *k*_{e+} = 10^{6} m^{-1} s^{-1}), length distributions shifted toward shorter lengths, so that no filament exceeded a length of 100 protomers (*dotted lines*). In contrast, increasing *n* to 3 (while using nucleation and elongation constants from ) shifted the distribution so that all filaments aligned at the top limit of the calculated distribution range (*N* = 500), indicating that all filaments were at least 500 protomers in length at all time points between 0.5–24 h (shown as a single *dashed line*). The simulations predict that length distribution reflects aggregation mechanism. *B–E*, lengths of filaments >10 nm formed as function of time (*B*, 0.5 h; *C*, 1 h; *D*, 7 h; *E*, 24 h) from 1 μm tau were measured and segregated into 10-nm bins. The relative frequency of each bin relative to the total number of filaments in the sample was then calculated and superimposed on slices prepared from the calculated length distributions shown for *n* = 2 in *panel A* above. The calculated length distribution for this condition approximates experiment-derived mode and distribution skew.

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