True and apparent inhibition of amyloid fibril formation

Abstract

A possible therapeutic strategy for amyloid diseases involves the use of small molecule compounds to inhibit protein assembly into insoluble aggregates. According to the recently proposed Crystallization-Like Model, the kinetics of amyloid fibrillization can be retarded by decreasing the frequency of new fibril formation or by decreasing the elongation rate of existing fibrils. To the compounds that affect the nucleation and/or the growth steps we call true inhibitors. An apparent inhibition mechanism may however result from the alteration of thermodynamic properties such as the solubility of the amyloidogenic protein. Apparent inhibitors markedly influence protein aggregation kinetics measured in vitro, yet they are likely to lead to disappointing results when tested in vivo. This is because cells and tissues media are in general much more buffered against small variations in composition than the solutions prepared in lab. Here we show how to discriminate between true and apparent inhibition mechanisms from experimental data on protein aggregation kinetics. The goal is to be able to identify false positives much earlier during the drug development process.

Keywords: :

• amyloid
• aggregation
• inhibitors
• kinetics
• modeling

This article refers to:

Perturbations in the folding homeostasis trigger the aggregation of proteins into insoluble ordered structures called amyloid fibrils.^1,2 These structures share a common cross β-sheet conformation with parallel strands running perpendicularly to the long fibril axis.^1,3,4 Their accumulation in intra- and extracellular inclusions is closely associated to a series of amyloid diseases that include neurodegenerative disorders and prionopathies.^1,3 Several methods have been employed to measure amyloid fibrillization kinetics in terms of the amount of protein aggregates over time.^5,6 The effect of external factors such as inhibitors,^7,8 surfactants,^9,10 ionic strength,^11-13 molecular crowding^14,15 or external fields^16,17 are investigated by quantifying their impact on the (1) duration of the initial lag phase, (2) maximum aggregation rate and (3) end plateau level of aggregation. The recently proposed Crystallization-Like Model (CLM) ascribes these effects to either kinetic or thermodynamic reasons.¹⁸ The first category is characterized by altered rate constants for the nucleation and growth (or elongation) steps, while the second category represents the cases of altered thermodynamic driving force for fibrillization. By preventing protein misfolding, kinetic stabilizers also decrease the nucleation rates and the amount of amyloid fibrils produced.¹⁹ Similarly, by promoting correct protein folding, molecular chaperones may prevent the pathogenic cascade to take place.^1,20 This early disruption of the kinetic pathways of amyloid aggregation is particularly advantageous when oligomers and protofibrils are the most neurotoxic species.^21,22 On the other hand, drugs that block the subsequent fibril elongation step are more suitable for amyloidogenic proteins lacking fully ordered native structures²³ being also expected to require lower clinical doses to be effective.²⁴ Independently of the kinetic step involved, some sort of binding affinity is required between the inhibitor and either the folded protein or the amyloid fibril. Contrarily to true inhibitors, other compounds and external factors do not necessarily require specific chemical affinity to produce marked effects on amyloid fibril formation. For example, the existence of a critical balance of electrostatic interactions has been demonstrated for β₂-microglobulin,²⁵ α-synuclein¹² and yeast prion protein²⁶ in the presence of different concentrations of salt ions. Besides being influenced by the composition of solution, the electrostatic equilibrium is also disturbed in the solid-liquid and gas-liquid interfaces. This provides a possible explanation for the in vitro effects of reaction volume,²⁷ hydrophobic interfaces²⁸ and type of agitation²⁸ based on altered “effective” concentration of protein on the interfaces. We will return to one of such examples to illustrate how they can be identified. Drug candidates that only show thermodynamic effects in laboratory tests are likely to be dismissed in later phases of the drug development process given that cellular proteostasis would be able to regulate the non-specific disturbances. To these compounds we call “apparent inhibitors.”

In the CLM formalism, the thermodynamic driving force for amyloid fibril formation is supersaturation σ defined as¹⁸

(1) $$\sigma =\frac{C-C^{*}}{C^{*}}$$(1)

where C and C* are the protein concentration and the protein solubility in mass per solution volume units. Being an equilibrium concentration, C* also corresponds to the concentration of protein at the end of the amyloid fibrillization assay. Supersaturation drives the formation of critical-sized amyloid nuclei (nucleation step) and the elongation of preformed fibrils (growth step).²⁹ The obtained CLM expression for the time-dependent amyloid conversion during unseeded reactions was¹⁸

(2) $$\frac{\Delta m}{\Delta m_T}=1-\frac{1}{k_{\text{b}}\left[\exp \right(k_{\text{a}}t)-1]+1}$$(2)

Amyloid conversion is expressed as the quotient of the fibril mass increase Δm at a given instant divided by the total mass of fibrils formed at the end of the assay Δm_T. The growth and nucleation-to-growth rate constants (k_a and k_b, respectively) are the ones reflecting the action of true inhibitors. Figure 1 shows numerical examples of the amyloid fibrillization inhibition provoked by decreasing the values of k_a (red curves) and k_b (blue curves). Sigmoid and hyperbolic shaped protein aggregation kinetics have different responses to equivalent variations of k_a and k_b. For example, the inhibition of the elongation step (red curves) has a more marked effect on sigmoidal aggregation kinetics (Fig. 1A). Conversely, hyperbolic aggregation kinetics (Fig. 1B) is more effectively affected by inhibiting the nucleation step (blue curves). While these effects are not thermodynamic, the overall mass of fibrils formed at the end of the reactions remains unchanged. Apparent inhibitors, on the contrary, may change the value of Δm_T as the result of altered values of the equilibrium concentration. Consider the case of an electrolyte that is added to an amyloidogenic solution; the electrostatic interactions between the electrolyte and the protein may change the availability of water molecules, thus changing the thermodynamic activity of the protein. So, the effective protein concentration C is altered by a factor γ that resembles the activity coefficient. The green curves represented in Figure 1 are computed assuming that the coefficient γ remains constant during the reaction time. This means that the initial supersaturation σ₀ is not altered by the presence of the apparent inhibitor (see Eqn. 1(1) $$\sigma =\frac{C-C^{*}}{C^{*}}$$(1) ), while the final amount of fibrils, given by mass balance, will change in the direct proportion of factor γ:

Figure 1. The inhibition of amyloid fibrillization as predicted by the CLM for (A) sigmoidal and (B) hyperbolic aggregation kinetics. Black curves represent the normalized fibril mass increase as a function of time calculated using Equations 2(2) $$\frac{\Delta m}{\Delta m_T}=1-\frac{1}{k_{\text{b}}\left[\exp \right(k_{\text{a}}t)-1]+1}$$(2) and 3(3) $$\Delta m_T={\sigma }_{0}V{C}^{\ast }\gamma$$(3) , and using reference values of parameters k_a, k_b and γ: in (A) k_a = 1 (units of time)^–1, k_b = 1 × 10–3 and γ = 1, and in (B) k_a = 0.1 (units of time)^–1, k_b = 10 and γ = 1. Blue and red curves represent the inhibition of the nucleation and growth steps, respectively; green curves represent the apparent inhibition that results from changing the solution activity of the protein. The variation of parameters k_a, k_b and γ relatively to the reference values is indicated by the text next to the curves.

(3) $$\Delta m_T={\sigma }_{0}V{C}^{\ast }\gamma$$(3)

where V is the reaction volume. Based on the molecular-level description of k_a and k_b, this change of the effective protein concentration should not affect any of the two rate constants. Although k_b has an apparent first-order dependence on the reciprocal of the protein solubility,¹⁸ this relationship is cancelled by the kinetic factor for nucleation A, which is expected to directly increase with the protein solubility.³⁰ Impressive as they may seem, inhibition results such as those represented by green curves in Figure 1 should be taken cautiously as they result from non-specific, thermodynamic effects.

More than a conceptual possibility arising from the CLM, apparent inhibition is able to be tested against experimental data. To illustrate this, α-Synuclein (αSyn) fibrillization data measured by Pronchik et al.²⁸ will be used. In the example of Figure 2A, the supposed thermodynamic effect involves the promotion of amyloid fibril formation (rather than its inhibition), and is achieved by increasing the number of polytetrafluoroethylene (PTFE) balls in solution (rather than by adding a chemical compound). Even though PTFE balls increase mass transfer, fibril fragmentation and the hydrophobic surface area, only the last effect is capable to explain the observed accelerated aggregation.²⁸ As the authors anticipated, a catalytic mechanism induced by the hydrophobic interface is not sufficient to explain the different endpoint signals of thioflavin T fluorescence shown in Figure 2A; catalytic surfaces are expected to increase the reaction rate but not the reaction extension.²⁸ According to the CLM's thermodynamic hypothesis, such variation in the reaction extent is due to different solution activities of αSyn in the presence of PTFE. Protein molecules accumulate at the hydrophobic surface and build up the concentration needed for the fibrillization reaction to take place. As more PTFE balls are added, more protein molecules will participate on the aggregation process and more amyloid fibrils will be formed. It follows from Eqn. 3 that the reaction extent Δm_T increases in the same proportion as it does the effective concentration, i.e., by a factor of γ. After identifying the thermodynamic effect, we want to know whether the nucleation and growth kinetics were also affected. This will determine if PTFE materials can be considered true aggregation promoters of αSyn. Figure 2B shows the time-dependent amyloid conversion normalized by the fluorescence signal at the end of each experiment. This type of data processing permits Eqn. 2 to be directly used to determine the kinetic parameters k_a and k_b without having to enter into thermodynamic considerations. Moreover, the drastic effect of the hydrophobic interface area evident from Figure 2A becomes hardly visible in the normalized representation of Figure 2B. The promotion of amyloid fibrillization of αSyn by PTFE materials is therefore purely thermodynamic and not related with the nucleation and growth steps. Although important for a better understanding of amyloid fibrillization, the use of hydrophobic surfaces during αSyn aggregation was not intended for physiological applications.²⁸ Nevertheless, this example helped us to illustrate how to discriminate the action of external factors between thermodynamic and kinetic, with the latter being the most promising mechanism for the development of new therapeutic alternatives.

Figure 2. The thermodynamic effect provoked by the presence of PTFE balls during amyloidogenic incubation of αSyn. (A) The evolution of the thioflavin T fluorescence signal measured by Pronchik et al.²⁸ and digitized by us shows increasing reaction extents as the number of PTFE balls increases from 10 (▲) to 20 (□) to 50 (●). Reprinted with permission from Pronchik et al.²⁸ Copyright 2012 American Chemical Society. (B) By normalizing the results shown in (A) by the final fluorescence signal of each experiment the differences between kinetics become hardly visible; Equation 2(2) $$\frac{\Delta m}{\Delta m_T}=1-\frac{1}{k_{\text{b}}\left[\exp \right(k_{\text{a}}t)-1]+1}$$(2) was fitted to the normalized results obtained with 10 PTFE balls (solid line) to obtain k_a = 0.121 h^–1 and k_b = 0.253.

Conclusions

The effect of external factors during amyloid fibril formation can be thermodynamic or kinetic. Thermodynamic effects are not likely to work in vivo as they do in vitro, being this the reason why they are considered “apparent.” Changing the solution activity of the protein by the addition of salts is a simple example of such effects. “True” inhibitors on the contrary have some kind of specific activity that retards the kinetics of nucleation and/or growth of amyloid fibrils. The CLM provides the tools to discriminate between apparent and true inhibitors in the early phases of the drug development process. Chemical compounds having a thermodynamic effect induce different reaction extents in the direct proportion of factor γ in Eqn. 3(3) $$\Delta m_T={\sigma }_{0}V{C}^{\ast }\gamma$$(3) . To be considered true inhibitors, slower amyloid fibrillization rates should be the result of altered k_a and/or k_b parameters in Eqn. 2(2) $$\frac{\Delta m}{\Delta m_T}=1-\frac{1}{k_{\text{b}}\left[\exp \right(k_{\text{a}}t)-1]+1}$$(2) . According to this equation, amyloid conversion normalized by the final reaction extent is insensitive to thermodynamic factors. This type of representation should therefore be used in order to identify true inhibitors.

Disclosure of Potential Conflicts of Interest

No potential conflicts of interest were disclosed.

Acknowledgments

I thank Rosa Crespo, Ana M. Damas and Fernando A. Rocha for helpful discussions. This work is funded by FEDER Funds through the Operational Competitiveness Programme, COMPETE and by National Funds through FCT, Fundação para a Ciência e a Tecnologia under the project FCOMP-01–0124-FEDER-009037 (PTDC/BIA-PRO/101260/2008).