On the lag phase in amyloid fibril formation

Abstract

The formation of nanoscale amyloid fibrils from normally soluble peptides and proteins is a common form of self-assembly phenomenon that has fundamental connections with biological functions and human diseases. The kinetics of this process has been widely studied and exhibits on a macroscopic level three characteristic stages: a lag phase, a growth phase and a final plateau regime. The question of which molecular events take place during each one of these phases has been a central element in the quest for a mechanism of amyloid formation. In this review, we discuss the nature and molecular origin of the lag-phase in amyloid formation by making use of tools and concepts from physical chemistry, in particular from chemical reaction kinetics. We discuss how, in macroscopic samples, it has become apparent that the lag-phase is not a waiting time for nuclei to form. Rather, multiple parallel processes exist and typically millions of primary nuclei form during the lag phase from monomers in solution. Thus, the lag-time represents a time that is required for the nuclei that are formed early on in the reaction to grow and proliferate in order to reach an aggregate concentration that is readily detected in bulk assays. In many cases, this proliferation takes place through secondary nucleation, where fibrils may present a catalytic surface for the formation of new aggregates. Fibrils may also break (fragmentation) and thereby provide new ends for elongation. Thus, at least two - primary nucleation and elongation - and in many systems at least four - primary nucleation, elongation, secondary nucleation and fragmentation - microscopic processes occur during the lag phase. Moreover, these same processes occur during all three phases of the macroscopic aggregation process, albeit at different rates as governed by rate constants and by the concentration of reacting species at each point in time.

Fig. 1. Sketches of amyloid forming proteins associated to several human diseases.

Fig. 2. Free energy diagram of amyloid fibril formation. The nucleus is the state with the highest free energy. Fibrils and monomers may have similar free energy, and the total concentration of monomer governs which state dominates at equilibrium.

Fig. 3. (a) A characteristic macroscopic aggregation curve for amyloid fibril formation is displayed in terms of aggregate concentration (in monomer equivalents, % of total monomer) versus time. The curve is typically divided into a lag phase, a growth phase and a final plateau; (b) definition of t _1/2, and two alternative definitions of the lag time. Here t _lag is obtained by extrapolating the maximum derivative down to the intercept with the pre-transition base-line; while t _lag′ and t _1/2 are defined as the point in time where the signal relative to the pre-transition base line has reached 10% and 50% of the amplitude of the transition, respectively.

Fig. 4. CD spectra acquired during an ongoing reaction (left). The first spectrum (red) shows the unfolded monomer and the last spectrum (blue) the β-sheet fibril. The monomer and fibril concentration as a function of time (right) can be extracted by fitting superpositions of the start and end spectra to the experimental data acquired at different time points.

Fig. 5. NMR spectra acquired during an ongoing reaction (left). The monomer concentration as a function of time (right) is extracted from the peak intensities.

Fig. 6. (a) Structure of the ThT dye and (b) change in the emission fluorescence spectrum upon binding to amyloid fibrils. Typical excitation wavelength is 440 nm; (c) the fibril formation process is monitored by recording the relative changes in the fluorescence intensity during time with respect to the situation at time zero.

Fig. 7. An example of post-reaction analysis of monomer and aggregate concentration ex situ. Samples are withdrawn from an ongoing reaction, separated into monomers and fibrils by centrifugation, and quantified using immunoblots, UV absorbance or ELISA assay.

Fig. 8. An amyloid chain amplification method. Samples are withdrawn from an ongoing reaction and separated on 200 nm filters (a). The retentates are added to fresh monomer and the aggregation kinetics, monitored through ThT fluorescence (b), are compared to reactions seeded with controlled amounts of fibrils at the same monomer concentration (c).

Fig. 9. Microscopic processes underlying amyloid formation and associated rate constants and reaction rates: primary nucleation from monomers in solution (a), elongation (growth) by monomers addition to existing aggregates (b), surface catalyzed secondary nucleation from monomers on fibril surface (c) and fragmentation (d). In the expressions of the reaction rates in the last row, [m] refers to the free monomer concentration, [M] to the total fibril mass concentration and [f _i] to the fibril number concentration, while the rate constants are defined in the middle row.

Fig. 10. We are used to think in small numbers in a linear fashion. This vision may induce the misleading interpretation of the lag phase as a waiting time for fibrils to appear from a small number of oligomers. However, typical samples used in amyloid studies contain billions of monomers or more, and millions of primary nuclei may form during the lag phase. Adapted from ref. 51.

Fig. 11. Model predictions of the aggregation reaction of a 4 μM solution of Aβ42 using the rate constants as determined from kinetic analysis of a large body of data;^, (a and b) microscopic reaction rates: the maximum elongation (green line) and secondary nucleation rate (red line) occurs close to the half-time, while primary nucleation rate (blue line) is constant during the lag phase and decreases as monomers concentration is reduced. The reaction rates are shown with logarithmic y-axis in (a) and with linear y-axis in (b). The macroscopic aggregation curve is shown as a dashed grey line with linear y-axis in both panels.

Fig. 12. Effect of individual rate constants on macroscopic aggregation growth curves. In each panel the black curve represents the simulated time evolution of the fibril mass versus time for a 4 μM solution of Aβ42 in 20 mM phosphate buffer, 0.2 mM EDTA, 0.02% NaN₃ at pH 8.0 under quiescent conditions according to the following rate constants: k _n k ₊ = 900 M^–2 s^–2; k ₂ k ₊ = 4 × 10¹⁰ M^–3 s^–2, and nucleus size n _C = n ₂ = 2. (a) The original calculated curve (black) and curves generated by increasing (k _n k ₊ = 9 × 10³ M^–2 s^–2; orange and k _n k ₊ = 9 × 10⁴ M^–2 s^–2; red) or decreasing (k _n k ₊ = 90 M^–2 s^–2, green; k _n k ₊ = 9 M^–2 s^–2, blue) the rate constant for primary nucleation by a factor of 10 or 100. (b) The original curve (black) and curves generated by increasing (k ₂ k ₊ = 4 × 10¹¹ M^–3 s^–2 orange; k ₂ k ₊ = 4 × 10¹² M^–3 s^–2 red) or decreasing (k ₂ k ₊ = 4 × 10⁹ M^–3 s^–2 green; k ₂ k ₊ = 4 × 10⁸ M^–3 s^–2 blue) the rate constant for secondary nucleation by a factor of 10 or 100. (c) The original curve (black) and curves generated by increasing (k _n k ₊ = 9 × 10³ M^–2 s^–2 and k ₂ k ₊ = 4 × 10¹¹ M^–3 s^–2 orange; k _n k ₊ = 9 × 10⁴ M^–2 s^–2 and k ₂ k ₊ = 4 × 10¹² M^–3 s^–2 red) or decreasing (k _n k ₊ = 90 M^–2 s^–2, k ₂ k ₊ = 4 × 10⁹ M^–3 s^–2, green; k _n k ₊ = 9 M^–2 s^–2, 4 × 10⁸ M^–3 s^–2, k ₂ k ₊ = 4 × 10⁸ M^–3 s^–2, blue) the rate constant for elongation by a factor of 10 or 100.

Paolo Arosio

Tuomas P. J. Knowles

Sara LinsePhoto by Gunnar Menander.