The formation of filaments from naturally occurring protein molecules is a process at the core of a range of functional and aberrant biological phenomena, such as the assembly of the cytoskeleton or the appearance of aggregates in Alzheimer's disease. The macroscopic behaviour associated with such processes is remarkably diverse, ranging from simple nucleated growth to highly cooperative processes with a well-defined lagtime. Thus, conventionally, different molecular mechanisms have been used to explain the self-assembly of different proteins. Here we show that this range of behaviour can be quantitatively captured by a single unifying Petri net that describes filamentous growth in terms of aggregate number and aggregate mass concentrations. By considering general features associated with a particular network connectivity, we are able to establish directly the rate-determining steps of the overall aggregation reaction from the system's scaling behaviour. We illustrate the power of this framework on a range of different experimental and simulated aggregating systems. The approach is general and will be applicable to any future extensions of the reaction network of filamentous self-assembly.
The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) through the ERC grant PhysProt (agreement no. 337969) (SL, TPJK), Sidney Sussex College Cambridge (GM), the Frances and Augusta Newman Foundation (TPJK), the Biotechnology and Biological Science Research Council (TPJK), the Swedish Research Council (SL), the Academy of Medical Sciences (AŠ), Wellcome Trust (AŠ), and the Cambridge Centre for Misfolding Diseases (CMD, TPJK, MV).
Meisl G, Rajah L, Cohen SAI, et al. Scaling behaviour and rate-determining steps in filamentous self-assembly. Chemical Science. 2017;8(10):7087-7097. doi:10.1039/c7sc01965c
Meisl, G., Rajah, L., Cohen, S. A. I., Pfammatter, M., Šarić, A., Hellstrand, E., … Knowles, T. P. J. (2017). Scaling behaviour and rate-determining steps in filamentous self-assembly. Chemical Science. Royal Society of Chemistry. https://doi.org/10.1039/c7sc01965c
Meisl, Georg, Luke Rajah, Samuel A. I. Cohen, Manuela Pfammatter, Anđela Šarić, Erik Hellstrand, Alexander K. Buell, et al. “Scaling Behaviour and Rate-Determining Steps in Filamentous Self-Assembly.” Chemical Science. Royal Society of Chemistry, 2017. https://doi.org/10.1039/c7sc01965c.
G. Meisl et al., “Scaling behaviour and rate-determining steps in filamentous self-assembly,” Chemical Science, vol. 8, no. 10. Royal Society of Chemistry, pp. 7087–7097, 2017.
Meisl G, Rajah L, Cohen SAI, Pfammatter M, Šarić A, Hellstrand E, Buell AK, Aguzzi A, Linse S, Vendruscolo M, Dobson CM, Knowles TPJ. 2017. Scaling behaviour and rate-determining steps in filamentous self-assembly. Chemical Science. 8(10), 7087–7097.
Meisl, Georg, et al. “Scaling Behaviour and Rate-Determining Steps in Filamentous Self-Assembly.” Chemical Science, vol. 8, no. 10, Royal Society of Chemistry, 2017, pp. 7087–97, doi:10.1039/c7sc01965c.
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