A continuous-time mathematical model and discrete approximations for the aggregation of <i>β</i>-Amyloid
Azmy S. Ackleh, Saber Elaydi, G. Livadiotis, Amy Veprauskas
Abstract
-amyloid aggregation using concepts from chemical kinetics and population dynamics. We show the model conserves mass and establish conditions for the existence and stability of equilibria. We also develop two discrete-time approximations to the model that are dynamically consistent. We show numerically that the continuous-time model produces sigmoidal growth, while the discrete-time approximations may exhibit oscillatory dynamics. Finally, sensitivity analysis reveals that aggregate concentration is most sensitive to parameters involved in monomer production and nucleation, suggesting the need for good estimates of such parameters.
Topics & Concepts
Amyloid (mycology)Discrete time and continuous timeAggregate (composite)NeurodegenerationNucleationStability (learning theory)PopulationStatistical physicsBiological systemNeuroscienceMathematicsComputer scienceDiseaseChemistryBiologyPhysicsMaterials scienceNanotechnologyStatisticsMedicineThermodynamicsPathologyEnvironmental healthMachine learningInorganic chemistryAlzheimer's disease research and treatmentsPrion Diseases and Protein MisfoldingComputational Drug Discovery Methods