Proctor et al., (2012). Aggregation, impaired degradation and immunization targeting of amyloid-beta dimers in Alzheimer's disease: a stochastic modelling approach.
May 2014, model of the month by Massimo Lai
Original model: BIOMD0000000462
Alzheimer's disease (AD) is a neurodegenerative disorder that is the most frequent cause of dementia, with incidence increasing dramatically in individuals beyond the age of 70. It is characterised by a progressive loss of neurons and synapses in the brain, causing atrophy of brain regions such as the cortex and the hippocampus. AD is currently not treatable, and leads to gradual destruction of the patient's memory and cognitive functions, and ultimately to death. The care of later-stage AD patients is emotionally and materially extremely burdensome and the growing impact of AD is of concern in an ageing society such as ours. The precise mechanism behind the onset and progression of AD is still not clearly elucidated, but one of the leading hypothesis is that the formation of amyloid plaques may be the molecular cause underlying the disease. Amyloid plaques are extracellular aggregates of amyloid β-peptide (Aβ), short peptide sequences naturally present in neuronal cells, produced by cleavage of amyloid precursor protein (APP) whose function is unclear. Impaired proteolysis of APP leads to increased production of the longest 42-residue Aβ peptide (Aβ42) which has the highest tendency to self-association, thus promoting the formation of the neurotoxic Aβ aggregates .
A crucial step towards the formation of aggregation is the production of Aβ42 dimers, which is favoured by Aβ accumulation. Normally, Aβ monomers are cleared by proteolitic degradation or removal. Accumulation of Aβ peptides suggests an impairment of the physiological clearance mechanism. The importance of Aβ42 dimers in the aggregation process makes them natural targets for pharmacological intervention aiming at delaying onset and reducing symptoms of AD .
Proctor and coworkers [3, BIOMD0000000462] presented a minimalistic model of AD onset, based on the amyloid hypothesis, where Aβ plaque formation is triggered by an increased concentration of dimers. The model contains two main processes, one describing production and clearance of Aß42, and another describing (reversible) dimerization and plaque formation and growth. Given the low count of Aβ peptides in vivo, stochastic effects were taken into account.
Figure 2Diagram of the kinetic model of plaque formation. Figure taken from .
The results indicated that the probability of plaque formation was especially sensitive to rate of dimerisation, and dimers played a key role in seeding the aggregation process. However, by looking at the available SBML model [BIOMD0000000462], plaque formation and plaque growth are represented by two different reactions. Plaques are only allowed to form by reaction (aggregation) of two dimers, while subsequent plaque accumulation only "feeds" on monomers.The above mentioned results could therefore be a consequence of the initial modelling hypothesis, and this aspect would probably deserve further investigation.
More interestingly, the model indicated that increased plaque formation after the age of 60 years was consistent with an age-dependent decline in the clearance rate of Aß, rather than a clearance mechanism impaired since birth.A recent experimental study by Serrano-Pozo and coworkers  concluded that the size distribution of Aß plaques in AD patients does not change over time, which seems compatible with a scenario where the reduced Aß clearance rate would plateau rather than decrease indefinitely.
Figure 1Schematic representation of the amyloid hypothesis. Figure taken from .
The idea is that a lower clearance rate increases the probability of exceeding a critical threshold of Aβ42 concentration, over which the aggregation process overpowers the disaggregation, leading to plaque accumulation. The main goal of this study was to identify which kinetic mechanism was more sensitive to the value of its kinetic parameters, thereby identifying potential target areas for pharmacological treatment. Production and clearance of Aβ42 were parameterised using measured values for the production rate and steady-state concentrations of the peptides. The plaque formation process was simplified assuming that a "plaque" was formed after association of two dimers. Importantly, the system was not able to clear Aβ42 once in the dimerised or aggregated states .
Figure 3Results of the kinetic simulations over 100 years. Efficient Aß clearance (red) predicts low plaque formation, impaired clearance from birth (green) predicts high plaque formation since early age, while gradually decreasing clearance efficience (black) predicts the expected increase of plaque formation in later years. Figure taken from .
- Mattson MP. Pathways towards and away from Alzheimer's disease. Nature. 2004 Aug 5;430(7000):631-9.
- Bates et al. Clearance mechanisms of Alzheimer's amyloid-[beta] peptide: implications for therapeutic design and diagnostic tests. Mol Psychiatry. 2009 May;14(5):469-86.
- Proctor et al. Aggregation, impaired degradation and immunization targeting of amyloid-beta dimers in Alzheimer's disease: a stochastic modelling approach. Mol Neurodegener. 2012 Jul 2;7:32.
- Serrano-Pozo et al. Stable size distribution of amyloid plaques over the course of Alzheimer disease. J Neuropathol Exp Neurol. 2012 Aug;71(8):694-701.