Stop-and-go kinetics in amyloid fibrillation

Many human diseases are associated with protein aggregation and fibrillation. We present experiments on in vitro glucagon fibrillation using total internal reflection fluorescence microscopy, providing real-time measurements of single-fibril growth. We find that amyloid fibrils grow in an intermittent fashion, with periods of growth followed by long pauses. The observed exponential distributions of stop and growth times support a Markovian model, in which fibrils shift between the two states with specific rates. Even if the individual rates vary considerably, we observe that the probability of being in the growing (stopping) state is very close to 1/4 (3/4) in all experiments.

Figure 1

(Color) TIRFM images of glucacon fibril growth with initial glucagon concentration of $\rho =0.25\text{mg}/\text{ml}$ in aqueous buffer (50 mM glycine HCl, $p\text{H}$ 2.5) at three consecutive times after the initiation of the aggregation. Red lines in the last picture mark examples of fibrils which are tracked during the growth process.

Figure 2

(Color) Length as a function of time for 16 fibrils tracked from the images shown in Fig. 1. Note the long plateaus, corresponding to the stop states, followed by shorter (on average) growing periods. The average growth is indicated with a dotted blue line. The sampling time between each image can be seen from the time separation between each point.

Figure 3

(Color) (a) Growth $f_g\left(t\right)$ and (b) stop $f_s\left(t\right)$ times distributions on semilogarithmic scales. Blue lines are data and yellow straight lines are the exponential fit. Both for data and fits, continuous lines are the lower estimates and dashed lines are the upper estimates (see text). All fits are of extremely good quality as indicated by the large $R$ value, $R^2>0.98$.

Figure 4

(Color) (a) The simplest two-state model of fibril growth. The fibril is assumed to be in one of two states with intrinsic transition rates of $k_{+}$ and $k_{-}$. In the growing state, monomer attachment occurs with the rate $g$. (b) The iso-energetic four state model where a fixed transition rate, $k^{\ast }=k_{+}=k_{-}/3$, between growth and stop states is assumed. The intrinsic rates between the different stop states (red arrows) are irrelevant to the observed kinetics.