Researchers solve the equations governing the self-assembly of fibrils, such as beta-amyloid in Alzheimer's disease
UK researchers have solved the equations that govern the self-assembly of fibrils, such as beta-amyloid in Alzheimer’s disease and the prions associated with Creutzfeldt-Jakob disease. This allows them to test and predict the effects of different conditions on how the fibrils form, and should lead to a more rational approach to developing treatments for several diseases.
The team, led by Chris Dobson and Mark Welland from the University of Cambridge, UK, came up with a new approach to solving the set of ’master equations’ that describe the complex kinetics of fibril formation. ’Having this analytical solution,’ says Dobson, ’where you can make predictions by changing the parameters, rather than just numerically fitting experimental data into the equation, means that we can explore different mechanisms in detail.’
’Amyloid fibrils are associated with around 40 different diseases, including Parkinson’s and type II diabetes,’ says Dobson, ’and one of the important issues is understanding how soluble protein molecules assemble into these fibrillar states.’ He explains that being able to analyse the mechanism is key to designing drugs to treat the diseases - showing where and how we might intervene in the chemistry to achieve the best results.
One of the most surprising outcomes from the team’s analysis of experimental data is that it contradicts the classic explanation of fibril kinetics. The normal model, Dobson explains, is that there is a slow ’nucleation phase’ where small sections of fibril form and then - when there are sufficient of these nuclei, they grow rapidly by adding further protein molecules to either end. ’The picture that we’re getting,’ says Dobson, ’is that the real factor that determines proliferation is how fast the fibrils break - when a fibril breaks into two, then four, then eight, you get rapid proliferation.’
He explains that people already knew that breaking fibrils contributed to multiplying the number of growing fibrils, but most - including Dobson’s team - believed that nucleation was more important. By solving the equations the team could analyse which processes played the greatest part, and in most cases breakage turned out to be more important than nucleation. ’After realising that,’ adds Dobson, ’a lot of things make sense,’ and the new model fits very well with experimental observations that couldn’t easily be explained by the nucleation-growth mechanism.
Sheena Radford, who researches the mechanisms of protein folding and amyloid formation at the University of Leeds, UK, says that the development of this mathematical model really endorses recent work from several groups pointing to the importance of fibril fragmentation. ’It really makes us rethink the importance of nucleation in amyloid assembly.’
However, Radford points out that this is still a mathematical model and requires some simplifying assumptions to get to the solution. ’The question is whether those assumptions will hold, or is biology actually more complicated? Perhaps one challenge for the future will be to make these models more complex to capitulate more of the biology.’
The analytical method the team used to solve these equations could be applied to all sorts of other self-assembly processes to unpick the complex patterns of processes and work out which ones dominate the kinetics. ’It really is a case of the ideas of mathematics and physics helping us to understand chemistry and biology,’ says Dobson. He adds that understanding and controlling the kinetics could also allow scientists to make interesting new nanoscale materials using fibrillar proteins.
TPJ Knowles et al, Science, 2009, DOI:10.1126/science.1178250