An improved stochastic modelling framework of biological networks: Case study modelling immunization in Alzheimer’s disease : A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy at Lincoln University

Abstract

Alzheimer disease (AD) attacks the brain and is the most common cause of dementia worldwide and it is classified to be the main cause of cognitive impairment in elderly people. Beta-amyloids (Aβ) and tau are aggregated to produce respectively plaques and tangles that are classified to be prime suspects for cell deaths in Alzheimer’s brain. Plaques target nerve cells to prevent their ability to contact each other in the correct way while tangles attack the transport system made of protein to be destroyed. However, the mechanisms that link Aβ and tau are still not fully understood. A recent proposed model (known immunization in AD model) not only examines pathways (DNA damage, p53 regulation, GSK3β activity, Aβ production and aggregation and tau dynamic and aggregation) involved in this relationship, but also how passive and active immunization against Aβ can indirectly reduce the level of tau pathologies. In this research, we stochastically model immunization in AD for better understanding of the relationship between Aβ and tau since noise in biology is a rule rather than expectation. This modelling is done using a proposed approach that combines Mapping Reduction Method (MRM) and Gillespie Stochastic Simulation Algorithm (GSSA). This combination increases the performance of GSSA by accelerating a single run of GSSA and explicitly includes concurrency feature. To validate MRM/GSSA, we compare it with GSSA itself and the modified Tau leap method classified to be one of the fastest version of GSSA. MRM/GSSA is not only faster than GSSA and comparable with the modified Tau-leap method, but also has more ability to represent stochastic feature and more reliable to be used for modelling any biochemical system than the modified tau leap method. Local sensitivity analysis (LSA) is stochastically and deterministically performed using MRM/GSSA and ordinary differential equations (ODEs) to investigate the behaviour of the immunization in AD model when parameters are perturbed, one at a time. A finite difference approximation method (FDM) is used to deterministically to perform LSA while FDM in conjunction with the common random number (CRN) is used to stochastically perform LSA. LSA is performed to (1) determine the maximum and minimum ranges of each parameter, (2) classify the most important species that contribute to the overall behaviour of the system and (3) identify pathways that dramatically changed in response to parameter perturbation. LSA using ODEs and MRM/GSSA indicates that p53 regulation, DNA damage pathway and GSK3β activity are not contributing to the overall behaviour of the system. Aβ production and aggregation, Tau dynamic and aggregation and immunisation pathways (passive and active) are the most important pathways that dramatically contribute to the overall behaviour of the system. LSA also demonstrates that parameters specific to p53, Mdm2 and Aβ are the most important parameters that contribute most to the variation in the system. Latin Hypercube Sampling and Partial Rank Correlation Coefficient (LHS/PRCC) are powerful tool employed with a minimum number of computer simulations in uncertainty analysis to monotonically relate the model outputs to the input parameters. We use LHS/PRCC to not only deterministically (ODEs), but also stochastically (MRM/GSSA) investigate the epistemic uncertainties of parameters of immunization in AD model. We explore at three different time points the effects of parameters on the key outputs of immunization in AD model (selected from the included pathways). This is to discover the most important parameters that uncertainties contribute to predication imprecision and rank these parameters by their importance in contributing to this imprecision. PRCC analysis using ODEs and MRM/GG demonstrates that binding relationship between p53 and Mdm2 and Mdm2 synthesis are the most important reactions that contribute to the behaviour of nearly all selected species in response to combination of LHS matrix. PRCC analysis using MRM/GSSA indicates some other parameters such as kgenROSGila and kbinE2UB also have strong correlation with the key outputs.