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Dynamics and Control of Peptide Self-Assembly and Aggregation

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Biological and Bio-inspired Nanomaterials

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 1174))

Abstract

The aggregation of proteins into fibrillar structures is a central process implicated in the onset and development of several devastating neuro-degenerative diseases, but can, in contrast to these pathological roles, also fulfil important biological functions. In both scenarios, an understanding of the mechanisms by which soluble proteins convert to their fibrillar forms represents a fundamental objective for molecular sciences. This chapter details the different classes of microscopic processes responsible for this conversion and discusses how they can be described by a mathematical formulation of the aggregation kinetics. We present easily accessible experimental quantities that allow the determination of the dominant pathways of aggregation, as well as a general strategy to obtain detailed solutions to the kinetic rate laws that yield the microscopic rate constants of the individual processes of nucleation and growth. This chapter discusses a framework for a structured approach to address key questions regarding the dynamics of protein aggregation and shows how the use of chemical kinetics to tackle complex biophysical systems can lead to a deeper understanding of the underlying physical and chemical principles.

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Notes

  1. 1.

    Dissociation ensures that fibril growth is reversible, in accordance with the principle of detailed balance, however, in most aggregation reactions which are performed at significant supersaturation this process does not have significant influence on the time course of the aggregate mass, which is the observable of main interest to our discussion (see Sect. 1.2.3, “Common Approximations”). It becomes relevant only at the very late stages of the aggregation process, when the aggregate mass has equilibrated and the aggregate length distribution tends towards an exponential distribution [27]. Equally the reverse of fragmentation is negligible and thus ignored.

  2. 2.

    When analysing the kinetics of aggregate formation, we simply fit rate laws and obtain rate constants and reaction orders, but we do not directly monitor the process. The microscopic mechanism is inferred by our interpretation of the fitted parameters. This leads to an interesting phenomenon: From a mathematical point of view, considering only the moment equations (1.8) and (1.9), fragmentation and secondary nucleation with n 2 = 0 (i.e. the rate determining step of secondary nucleation is monomer independent, see Sect. 1.3.2) are equivalent and hence indistinguishable in this kind of kinetic analysis. In order to distinguish between these two possibilities, experiments that yield information on the fibril distribution are necessary. This could constitute measurements of the full length distribution of fibrils, use trapping of fibrils in filters to test for seeding of monomer nucleation or employ the addition of specific labels to fibrils and monomer [43,44,45].

  3. 3.

    Note that the fixed-point operator takes the form of Eq. (1.10) as long as the equation for dM∕dt, Eq. (1.9) remains unchanged.

  4. 4.

    Note that for a simple serial reaction, without catalyst, the rate of formation of product depends on the rates of the individual reactions in a multiplicative fashion, so no saturation effects emerge and the overall monomer dependence will remain constant.

  5. 5.

    However, keep in mind that the rates and reaction orders of such coarse-grained processes are not as straightforward to interpret on a molecular level as in elementary reactions.

  6. 6.

    Fragmentation is a first order reaction, dependent only on fibril mass and could reasonably be expected to follow single-step kinetics. No kinetic evidence for its multi-step nature exists to date, so it is not discussed here.

  7. 7.

    As described in Sect. 1.2.3, “Common Approximations”, the mass produced by nucleation can be neglected relative to that generated through elongation.

  8. 8.

    This is a treatment of inhibition as a perturbation to the models for aggregation of pure protein and does not explicitly include reactions of the inhibitor with the various species in the aggregation reaction network. Therefore, it does not reproduce intricate effects, for example due to the kinetics of inhibitor binding, but it does to a very good approximation yield the same overall behaviour as the more complex approach and is thus sufficient for the purposes of illustrating the effect or establishing which species is targeted by the inhibitor.

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Acknowledgements

We would like to thank the Swiss National Science Foundation, Peterhouse College Cambridge, the European Research Council, the BBSRC, the EPSRC, the Newman Foundation and Sidney Sussex College Cambridge.

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Authors and Affiliations

  1. Department of Chemistry, University of Cambridge, Cambridge, UK

    Georg Meisl, Thomas C. T. Michaels, Michele Vendruscolo & Christopher M. Dobson

  2. Department of Chemistry and Applied Bioscience, ETH Zurich, Zurich, Switzerland

    Paolo Arosio

  3. Centre for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge, UK

    Tuomas P. J. Knowles

  4. Cavendish Laboratory, University of Cambridge, Cambridge, UK

    Tuomas P. J. Knowles

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  1. Georg Meisl
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Correspondence to Georg Meisl .

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Editors and Affiliations

  1. National Laboratory of Biomacromolecules, Institute of Biophysics Chinese Academy of Sciences, Beijing, China

    Sarah Perrett

  2. Department of Biotechnology and Biomedicine, Technical University of Denmark DTU, Lyngby, Denmark

    Alexander K. Buell

  3. Department of Chemistry, University of Cambridge, Cambridge, UK

    Tuomas P.J. Knowles

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Meisl, G., Michaels, T.C.T., Arosio, P., Vendruscolo, M., Dobson, C.M., Knowles, T.P.J. (2019). Dynamics and Control of Peptide Self-Assembly and Aggregation. In: Perrett, S., Buell, A., Knowles, T. (eds) Biological and Bio-inspired Nanomaterials. Advances in Experimental Medicine and Biology, vol 1174. Springer, Singapore. https://doi.org/10.1007/978-981-13-9791-2_1

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