Fiber-dependent amyloid formation as catalysis of an existing reaction pathway

Results

To define the processes governing the fibrous assembly of IAPP_20-29, we first determine the minimum number of nucleation pathways necessary to describe the kinetics of assembly. We then establish solution conditions for which alternative pathways are dominant. Then, for each pathway, we characterize the reaction order and enthalpy of the transition state barrier of the rate-limiting step.

Nucleation of IAPP_20-29 fibers occurs on surfaces. This is evident by comparing the kinetics of fiber formation reactions that differ only in the extent of filtration used to prepare reaction buffer. Fiber formation reactions are initiated by diluting a DMSO stock solution of IAPP_20-29 (10 mM) into aqueous buffer. The buffer is prepared by using a filtered (0.2 μm) 10× stock diluted with water that is either nominally free of particulates (Milli-Q; Millipore, Billerica, MA) or has had an additional 0.2-μm filtration step applied immediately before use. Kinetics are then assessed by either 90° light scattering or the change in fluorescence of an introduced dye, thioflavin T (ThT) (21). Under the former conditions, the kinetic profile of a reaction with 700 μM IAPP_20-29 is 50% complete (t₅₀) in 3,400 ± 700 sec (Fig. 1A). In marked contrast, additional filtration only to the water results in a t₅₀ of 32,000 ± 12,000 sec. This effect is not a consequence of the filter or the source of water [supporting information (SI) Fig. 8]. This finding suggests that fiber nucleation can be catalyzed by the surface of physical objects that can be eliminated by filtration.

The effects of surface can be deliberately exaggerated. Reaction t₅₀ are accelerated ≈10-fold by the presence of a water:dichloromethane (CH₂Cl₂) interface. CH₂Cl₂ has low solubility in water and forms a separate liquid phase below the aqueous buffer. Reactions were initiated by first assembling an aqueous reaction, as described above, and then layering it on top of CH₂Cl₂. A 700 μM reaction has a t₅₀ of 480 ± 170 sec in the presence and 3,400 ± 700 sec in the absence of this interface (Fig. 1A). Acceleration is attributable to this interface. Reactions conducted in the absence of an interface, but in the presence of buffer presaturated with CH₂Cl₂, have t₅₀ decreased by only a factor of 1.9 ± 0.2 (SI Fig. 9). Furthermore, the extent of acceleration depends on the size of the interface relative to reaction volume (SI Fig. 10). Fibers formed in the presence and absence of CH₂Cl₂ are indistinguishable by negative stain transmission electron microscopy (TEM) (Fig. 2 A and B) and atomic force microscopy (SI Fig. 11). Furthermore, they have a common intersheet spacing (8.5 Å) by x-ray fiber diffraction (Fig. 2C) and seed fiber formation with the same efficiency (Fig. 2D). This suggests that the structure of fibers formed in the presence and absence of the CH₂Cl₂:aqueous interface are the same.

In the presence of a CH₂Cl₂:aqueous interface, a single nucleation process is sufficient to describe the IAPP_20-29 kinetic profile. To interpret assembly profiles, we, like others (1, 3–5, 7), first assume that the initial assembly steps are governed by unfavorable equilibria. The nucleus is defined here as the highest energy, least populated intermediate on the reaction pathway. The nucleus, and all states involved in its formation, are in equilibrium with monomer. To validate this assumption for IAPP_20-29, we used ¹H NMR and ultraviolet circular dichroism to determine that the protein is monomeric and has a random-coil structure during the lag phase (SI Figs. 12 and 13). Second, we assume that later steps in assembly are essentially irreversible. The first of these steps, which we term here as nucleation, is rate-limiting in the assembly pathway because it has the nucleus as a reactant. With these assumptions, the initial reaction profile is quadratic ([F](t) ∝ t²) (1), where t is time and [F](t) is the amount of polymerized material in monomer units. The early profile of a 700 μM IAPP_20-29 reaction conducted in the presence of a CH₂Cl₂:aqueous interface fits clearly to this quadratic (Fig. 1B Inset). Furthermore, it is the interface that generates this curve shape; if CH₂Cl₂ is used only to saturate the aqueous buffer, then the initial time points are flat (SI Fig. 9). Actin is the canonical biopolymer that assembles via a single nucleation path (4). We note that the entire calculated profile of actin (Fig. 1B) is comparable to CH₂Cl₂-catalyzed assembly of 700 μM IAPP_20-29. This is not unique to this protein concentration; reactions from 300 μM to 2 mM IAPP_20-29 all have this time-renormalized profile (Fig. 1C and SI Fig. 14). Clearly, IAPP_20-29 fiber assembly can be described by a single, fiber-independent nucleation mechanism in the presence of a CH₂Cl₂:aqueous interface.

A fiber-dependent mechanism of nucleation is evident in the absence of a CH₂Cl₂:aqueous interface. The initial portion of the IAPP_20-29 reaction profile is flat and cannot be approximated by a quadratic (1) or higher order polynomial (3) (Fig. 1B). This property is evident when using detection methods that report on fiber growth [thioflavin T (ThT) and light scatter; SI Fig. 15] as well as methods sensitive to monomer loss (¹H NMR; Fig. 3). In the latter study, the ¹H NMR chemical shift dispersion is characteristic of random coil throughout the lag phase (SI Fig. 13). Furthermore, there are no time-dependent changes in chemical shift or linewidth that would be indicative of structure formation and/or oligomerization. Lastly, all of the protein is quantitatively present during the lag phase and diffuses as a single species (D = 3.0 ± 0.2 × 10⁻⁶ cm²/s) over an ≈10-fold range of concentration (SI Fig. 13). This is within error of calculated estimates of D for random coil monomer: 2.8 × 10⁻⁶ cm²/s (22) or 4.1 ± 1.7 × 10⁻⁶ cm²/s (23), respectively. A reaction profile with a flat lag phase can be generated by a reaction that proceeds through a series of irreversible steps (i.e., downhill polymerization) (1). A flat lag phase results if the detection method is only sensitive to downstream states. However, because intermediates are not detectably populated by ¹H NMR, such a mechanism is unlikely. In addition, a downhill polymerization model yields reaction kinetics that vary linearly with initial protein concentration (1). This is also not consistent with our observations reported below. A second possibility is that there are fiber-dependent nucleation processes. In this model, the probability that new fiber ends will form increases in proportion to fiber mass (8). Such a model is wholly consistent with our observations. Alone, this is not sufficient to describe the kinetic profile because fibers are not initially present in solution. Therefore, there must also be a contribution from a fiber-independent mechanism. Nevertheless, because the beginning of the reaction profile is completely flat, the vast majority of nucleation events must occur by the 2° mechanism. It is clear that both 1° and 2° nucleation are necessary to describe the entire reaction profile under wholly aqueous conditions.

Fiber formation can be indirectly detected during the lag phase. A 1 mM reaction was diluted to 800 μM during the lag phase and compared with a reaction initiated at 800 μM. If fibers have formed during the lag phase of the former, then the diluted reaction will convert faster than a reaction initiated at 800 μM. Alternatively, if the lag phase is a measure of the time taken until the first 1° event, then the distribution of reaction t₅₀ should be identical. Indeed, dilution to 800 μM at 150 sec gives t₅₀ that are 1.36 ± 0.04-fold shorter than a reaction initiated at 800 μM (Fig. 4). As a control, a reaction initiated at 800 μM was agitated in an identical fashion at 150 sec. This gives t₅₀ that are only 1.08 ± 0.09-fold accelerated. Importantly, the extent of acceleration depends on the time elapsed before dilution. Dilution at 300 sec gives t₅₀ that are 1.65 ± 0.02-fold accelerated. Furthermore, reaction t₅₀ show minimal (±7%) variation, indicating that stochastic occurrence of a 1° event is not governing the lag phase length (SI Fig. 16). Clearly, fiber formation has begun, albeit at low concentrations, during the lag phase.

Fiber-independent nucleation has a reaction order of 4. For reactions with only 1° nucleation, the rate of fiber end formation is proportional to [A₁]^m, where A₁ is free monomer and m is the reaction order. This gives t₅₀ = λ[A_tot]^−m/2, where A_tot is the total protein and λ is a constant (4, 6) (see SI Calculation 1A). Reactions with t₅₀ varying over more than a 10-fold range were measured by varying protein concentration in the presence of a CH₂Cl₂:aqueous interface. The reaction is strongly concentration-dependent with a reaction order of ≈4 (Fig. 5A). We note that in several analyses conducted on separate days, the reaction order was consistent but with varying λ, presumably because of a systematic error associated with variations in exogenous surface. We accommodated this observation by performing a global analysis of 61 kinetic profiles on 8 separate days (Fig. 5B). Simultaneous fitting to a common reaction order yielded 3.9 ± 0.1 for the fiber-independent nucleation process.

Fiber-dependent nucleation similarly has a reaction order of 4. The flat lag phase evident in profiles conducted in the absence of an interface suggests that 2° nucleation events predominate. Therefore, here but not in later analysis (see Discussion) we assume the rate of nucleus formation depends only on the amount of polymerized material, expressed as ([A_tot] − [A₁]). This gives a rate of fiber end formation proportional to [A₁]ⁿ([A_tot] − [A₁]), resulting in t₅₀ = λ[A_tot]^−(n+1)/2, where n is the reaction order of 2° nucleation (see SI Calculation 2A). The one in the exponent of the latter accounts for the contribution of fiber surface to the apparent concentration dependence of the reaction t₅₀. Any value of n ≥ 0 is allowable, with n = 0 corresponding to a fiber breakage mechanism. Reactions whose t₅₀ span an ≈100-fold range were measured by varying protein concentration (Fig. 5A). Above 3 mM, the t₅₀ become as fast or faster than the mixing time (<1 min). Reactions at and below 500 μM (t₅₀ > 2 h) show sufficient stochastic contributions that the data are not included in this analysis (SI Fig. 16). Global analysis of 112 reaction profiles collected over 13 separate days gives a reaction order of 4.0 ± 0.1 (Fig. 5B).

Elongation processes have a reaction order of 1. Fiber formation kinetics were conducted with 50 μM IAPP_20-29 preformed fibers and soluble peptide concentrations ranging from 100 μM to 1 mM (Fig. 5C). The rate of elongation, as measured by the rate of monomer depletion, was taken from the slope of a line fit to the first ≈400 sec of each reaction profile. If elongation of existing fiber ends occurs by addition of an oligomer of size l, then −d[A₁]/dt = k_e[E][A₁]^l, where E is fiber ends. Because the concentration of fiber ends is the same at the beginning of these reactions, a plot of log(d[A₁]/dt) vs. log([A_tot]) will have a slope of l. Analysis of three independent data sets give l = 0.90 ± 0.10, indicating that elongation proceeds via addition of monomer to fiber ends. Notably, this is distinct and smaller than the reaction orders obtained for nucleation shown above.

The enthalpic barrier to nucleation is the same in the presence and absence of a CH₂Cl₂:aqueous interface. This was assessed by measuring the temperature dependence of reaction t₅₀. The t₅₀ are exquisitely sensitive to temperature; for example, a 1 mM de novo reaction without a CH₂Cl₂:aqueous interface has a t₅₀ of 1,400 ± 180 sec at 23°C and 5,300 ± 400 sec at 36.5°C. By 39°C the reaction is not observed to convert (t₅₀ > 86,400 sec; data not shown). The Eyring equation enables us to relate the rate of nucleation to temperature, t₅₀ ∝ e^ΣΔH_i/2RT, where ΔH_i represents the enthalpic contribution from each of the barriers that determine the reaction t₅₀ (this includes but is not limited to oligomerization equilibria governing the nucleus population, surface binding, and the barriers to nucleation and elongation; see SI Calculation 1B and SI Calculation 2B). Fits to this relation give ΣΔH_i = −36 ± 6 kcal/mol (Fig. 6). Similar time scales were achieved in the presence of a CH₂Cl₂:aqueous interface at 350 μM protein (Fig. 6 Inset). Remarkably, this yields a closely similar ΣΔH_i = −39 ± 3 kcal/mol. The contributions of some of the individual ΔH_i can be inferred. For example, elongation reactions can be conducted at temperatures above 39°C, giving rates that differ by <2 between 25°C and 45°C (SI Fig. 17). Similarly, the near-identical ΣΔH_i suggests that surface binding makes a comparatively small contribution. Therefore, the sensitivity of de novo reactions to temperature can be attributed predominantly to changes to oligomerization preequilibria and/or nucleation. Although we cannot yet make precise determinations of the individual ΔH_i, the fact that the ΣΔH_i are similar under markedly different reaction conditions strongly suggest that the two reactions are mechanistically similar.

Discussion

IAPP_20-29 can form amyloid fibers by both a fiber-dependent and a fiber-independent nucleation mechanism. In the presence of a CH₂Cl₂:aqueous interface, fiber formation nucleates predominately by the 1° mechanism. Under wholly aqueous solution conditions, 1° nucleation is present but most nucleation occurs by the 2° mechanism. By making kinetic measurements under each of these solution conditions, we have shown that both nucleation processes can be described by a reaction order of 4 with net enthalpic contributions of approximately −37 kcal/mol to the apparent activation energy. Therefore, both 1° and 2° nucleation can be modeled as the same mechanism, differing only in the location of the event.

Global analysis of kinetics was used to verify our reaction orders without using our previous assumption that nucleation occurs by only a single mechanism under each solution condition (i.e., with or without the CH₂Cl₂:aqueous interface). Specifically, fiber formation kinetics were assessed for both conditions by using the following model:

where E represents fiber ends, A₁ represents free monomer, (A_tot − A₁) represents fiber in monomer units, m, n, and l represent the reaction orders, and k_m, k_n, and k_e are effective rate constants associated with 1° nucleation, 2° nucleation, and elongation, respectively. Note that the amount of external surface present is reflected by the magnitude of k_m (SI Calculation 1A). Rate constants were fitted by numerical methods for various integer values of m and n (at l = 1) by simultaneously analyzing reaction profiles collected in the presence and absence of CH₂Cl₂ (Fig. 7A). Evaluation of χ² as a function of m and n yields a best fit m = n = 4 (Fig. 7B). Thus, the same reaction orders are obtained whether or not we assume a single mechanism under each reaction condition. This does not represent a hidden property of the analysis, i.e., 1° does not mask 2° nucleation. To show this, Eqs. 1 and 2 were used to create synthetic data sets for alternative values of m and n. These were then subjected to the same global analysis and resulted in correct determination of m and n, for example m = 4, n = 2 (Fig. 7C). An important and generalizable observation (not shown) is that reaction profiles are concentration-dependent when m ≠ n. Experimentally, IAPP_20-29 shows no concentration dependence in its reaction profile (Fig. 1C and SI Fig. 14), consistent with m = n. Plainly, our global analysis faithfully extracts both 1° and 2° reaction orders.

Interrogation of our global analysis enables us to assert the relative contribution of 1° and 2° nucleation at each time point during fibrillogenesis (Fig. 7 D and E). For interface-free reactions, 2° nucleation is dominant at all but the earliest times (Fig. 7D). Similarly, for reactions in the presence of CH₂Cl₂, the rate of 1° nucleation is dominant at all times before the t₅₀ (Fig. 7E). This accounts for our ability to extract reaction order when assuming limiting conditions in the absence and presence of a CH₂Cl₂:aqueous interface (Fig. 5). However, the global analysis does not require the extremes of behavior provided by the interface. Alteration to the extent of 2° contributions provided, for example, by introduction of fiber as seed, would perturb the reaction profile and enable extraction of parameters. This should allow generalization of this approach, e.g., scission, as reported for Sup35 (13), is represented here by n = 0. Similarly, downhill polymerization, as reported for polyglutamine (7), is represented here by m = 1, k_n = 0.

Surface-catalyzed nucleation is consistent with the high entropic cost of assembly. For nucleation to be unfavorable, the entropic contribution at a given temperature must exceed the enthalpic contribution of approximately −37 kcal/mol (Fig. 6). There are several ways that a surface can reduce the entropic penalty of assembly. First, there may be a high local concentration of peptides bound to the interface. Second, peptides may bind to the surface in an ordered, specific way that favors assembly. This is particularly true for parallel assemblies of β-strands (24, 25). For IAPP_20-29, acceleration is specific to certain interfaces. For example, CH₂Cl₂, chloroform, and phospholipid bilayers accelerate fiber formation and result in an apparent loss of secondary nucleation processes (SI Fig. 18). In contrast, hexanes, n-butanol, and carboxylate derivatized polystyrene microspheres do not have the effects reported here. Finally, surface catalysis could represent the stabilization of a high-energy nucleus by binding to the surface. This is analogous to lateral nucleation suggested for polymerization of hemoglobin S (26).

The extreme sensitivity of the IAPP_20-29 fiber formation reaction to solution conditions can be explained if a surface, in addition to the protein itself, is required for nucleation. This result is not unique to IAPP_20-29, because surfaces have been shown to strongly influence fiber formation in a number of other systems. Aβ, full-length IAPP, and α-synuclein fiber formation reactions can be manipulated by lipid membranes (27–30) and halogenated organic solvents including chloroform (31). Tau aggregation can also be triggered by surfaces (32, 33). In some cases, e.g., Aβ, interfaces can give rise to alternative forms of fibrillar and nonfibrillar aggregates as determined by the nature of the interface (34). Finally, assembly of hydrophobins into functional amyloid-like rodlets occurs at an air–water interface (35). Thus, the choice of conditions is critical for understanding assembly. Furthermore, it is likely that surfaces are of importance to in vivo fiber formation, because there are many surfaces with a rich variety of properties with which cellular proteins can interact.

In this work, we have equated 1° nucleation with 2° nucleation on a growing fiber. The kinetic profiles of fiber formation by full-length IAPP, Aβ, insulin, and the mammalian prion show that fiber-dependent nucleation plays a prominent role (9, 10, 12, 14). Similarly, the stochastic reaction kinetics reported for insulin, Aβ, and huntingtin can be rationalized with 2° nucleation (10, 14, 36). Finally, we note that imaging of both insulin (37) and IAPP (38) fiber formation suggests an intrinsic capacity of amyloid fibers to laterally stabilize their precursors. Although it is always possible to invoke an additional process to account for fiber-dependent reaction profiles, we have demonstrated here that this process need not be distinct from 1° nucleation.

Materials and Methods

Supplementary Material