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Principal Investigator  
Principal Investigator's Name: Arsalan Rahimabadi
Institution: Concordia University
Department: Department of Electrical and Computer Engineering
Proposed Analysis: Modeling tauopathy progression in the brain First discovered in 1975, tau is a multifunctional microtubule-associated protein (MAP) in the neuron, which many researchers have extensively studied its function to stabilize microtubules and encourage axonal prolongation (Baas, Qiang, 2019). Tau protein is natively unfolded, and in physiological conditions its tendency for aggregation is low. However, there are modifications, such as phosphorylation, truncation, glycosylation, glycation, deamidation, isomerization, nitration, methylation, ubiquitylation, and SUMOylation (Wang, Mandelkow, 2016), which may enable monomeric tau proteins to make aggregates. Tau aggregation characterizes neurodegenerative diseases known as tauopathies, including Alzheimer's disease (AD), Huntington disease (HD), Pick disease (PiD), progressive supranuclear palsy (PSP), argyrophilic grain disease (AGD), corticobasal degeneration (CBD), and frontotemporal dementia with parkinsonism-17 (FTDP-17). Though the potential of tau protein to induce such diseases has been confirmed by the identification of tau mutants in patients with FTDP-17 (Hutton et al., 1998), the mechanisms and pathways by which tau protein forms aggregates in tauopathies are not sufficiently comprehended. Moreover, due to the availability of in vitro measurement techniques, a major portion of previous findings are confined to in vitro (Congdon et al., 2008; Huseby et al., 2019), where high concentrations of free tau in the presence of an anionic aggregation inducer are used to support and accelerate aggregation, while the premier aim is to understand what happens in vivo, where tau monomers and filaments with various concentrations are inextricably interacted and simultaneously affected by other pathways, such as the protein turnover and clearance process. Therefore, to achieve our goal, which is developing a realistic computational model of tauopathy progression in the brain, we require to incorporate different processes, including modifications leading to aggregation, the aggregation itself, the degradation and synthesis of tau protein, and brain clearance pathways. Other characteristics of in vivo tau aggregation that significantly hamper the efforts to attain this goal are the anisotropy and inhomogeneity of the brain. This research project has been started by studying a linear aggregation scheme exploited to fit a model to in vitro data on the actin filament formation by Wegner and Engel, (1975). The first reason behind adopting this model was that there are in-vitro experiments showing the rate-limiting phase of tau nucleation step is dimerization (Congdon et al., 2008), and secondly, the model can at least be applied to predict the aggregation process of tau in vitro (Huseby et al., 2019). We have provided a complete analysis of the system of differential equations derived from the mentioned reaction scheme under arbitrary initial concentrations of tau species (Rahimabadi et al., 2020). Next, since tau deposition in the brain can be non-invasively investigated by positron emission tomography (PET) imaging using tau specific ligands, PET images were utilized to measure the capability of the model to predict longitudinal tau-PET. The meaningful discrepancies between the real follow-up PET images and the predicted outputs, particularly when the prediction time horizon increased, convinced us that more processes are needed to be account. Thus, since tau is a kinetically dynamic protein (Sato et al., 2018), we added a sub-model of tau turnover to our aggregation model. Additionally, owing to the fact that tau toxic species can be washed out from the brain either through extracellular pathways, like transport across the blood-brain barrier (BBB) (Tarasoff-Conway et al., 2015) or through intracellular ones, for instance the ubiquitin-proteasome system (Kiffin et al., 2006), a sub-model of clearance process was also inserted into our model. Although the augmented model could provide us with better predicted results, we were aware that without including a sub-model of the propagation of tau toxic species our model cannot predict the longitudinal tau-PET in the specified regions of interest (ROIs) of brain, especially for the longer prediction time horizon. This conclusion is based on the observation having been carried out when the injection of tau seeds into the mouse brain could induce the time-dependent spread of tau pathology from the inoculation sites to other synaptically connected brain regions (Clavaguera et al., 2009). To construct the propagation sub-model, we employed a Fickian diffusion model (Fick, 1855; Crank, 1979) whose diffusion coefficient matrix are determined using the effective diffusion tensor obtained from diffusion-weighted images (Van Hecke et al., 2015). Though the inclusion of the propagation sub-model has enhanced significantly the prediction of the longitudinal tau-PET (Rahimabadi et al., 2021), we plan to make the proposed model more sophisticated by taking more details of tauopathy progression into account, building their corresponding sub-models, and encapsulating them in our model with respect to a quote attributed to Einstein: “Everything should be made as simple as possible, but no simpler.” Finally, thanks to the fact that this research project is a bridge between neuroscience and engineering, we have been applying several theories concerning dynamical systems and computational mathematics during the modeling and simulation procedure. Baas, P. W. and Qiang, L. (2019). Tau: it’s not what you think. Trends in cell biology 29, 452–461 Clavaguera, F., Bolmont, T., Crowther, R. A., Abramowski, D., Frank, S., Probst, A., et al. (2009). Transmission and spreading of tauopathy in transgenic mouse brain. Nature cell biology 11, 909–913 Congdon, E. E., Kim, S., Bonchak, J., Songrug, T., Matzavinos, A., and Kuret, J. (2008). Nucleation dependent tau filament formation the importance of dimerization and an estimation of elementary rate constants. Journal of Biological Chemistry 283, 13806–13816 Crank, J. (1979). The mathematics of diffusion (Oxford university press) Fick, A. (1855). Ueber diffusion. Annalen der Physik 170, 59–86 Huseby, C. J., Bundschuh, R., and Kuret, J. (2019). The role of annealing and fragmentation in human tau aggregation dynamics. Journal of Biological Chemistry 294, 4728–4737 Hutton, M., Lendon, C. L., Rizzu, P., Baker, M., Froelich, S., Houlden, H., et al. (1998). Association of missense and 5-splice-site mutations in tau with the inherited dementia ftdp-17. Nature 393, 702–705 Kiffin, R., Bandyopadhyay, U., and Cuervo, A. M. (2006). Oxidative stress and autophagy. Antioxidants & redox signaling 8, 152–162 Rahimabadi, A., Soucy JP., and Benali H. (2021). A comprehensive computational model of tauopathy progression using PET imaging. OHBM Conference Rahimabadi, A., Soucy JP., and Benali H. (2020). Effect of initial concentrations on a computational model of tau aggregation in tauopathies. OHBM Conference Sato, C., Barthe´lemy, N. R., Mawuenyega, K. G., Patterson, B. W., Gordon, B. A., Jockel-Balsarotti, J., et al. (2018). Tau kinetics in neurons and the human central nervous system. Neuron 97, 1284–1298 Tarasoff-Conway, J. M., Carare, R. O., Osorio, R. S., Glodzik, L., Butler, T., Fieremans, E., et al. (2015). Clearance systems in the brain-implications for Alzheimer disease. Nature reviews neurology 11, 457 Van Hecke, W., Emsell, L., and Sunaert, S. (2015). Diffusion tensor imaging: a practical handbook (Springer) Wang, Y. and Mandelkow, E. (2016). Tau in physiology and pathology. Nature Reviews Neuroscience 17, 22–35
Additional Investigators  
Investigator's Name: Habib Benali
Proposed Analysis: Dr. Benali is the supervisor of my project.