Mathematical Modeling of Protein Misfolding Mechanisms in Neurological Diseases: A Historical Overview.

Felix Carbonell,Alan C Evans,Yasser Iturria-Medina

doi:10.3389/fneur.2018.00037

Felix Carbonell, Alan C Evans + Show 1 more

Open Access

https://doi.org/10.3389/fneur.2018.00037

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Abstract

Protein misfolding refers to a process where proteins become structurally abnormal and lose their specific 3-dimensional spatial configuration. The histopathological presence of misfolded protein (MP) aggregates has been associated as the primary evidence of multiple neurological diseases, including Prion diseases, Alzheimer’s disease, Parkinson’s disease, and Creutzfeldt-Jacob disease. However, the exact mechanisms of MP aggregation and propagation, as well as their impact in the long-term patient’s clinical condition are still not well understood. With this aim, a variety of mathematical models has been proposed for a better insight into the kinetic rate laws that govern the microscopic processes of protein aggregation. Complementary, another class of large-scale models rely on modern molecular imaging techniques for describing the phenomenological effects of MP propagation over the whole brain. Unfortunately, those neuroimaging-based studies do not take full advantage of the tremendous capabilities offered by the chemical kinetics modeling approach. Actually, it has been barely acknowledged that the vast majority of large-scale models have foundations on previous mathematical approaches that describe the chemical kinetics of protein replication and propagation. The purpose of the current manuscript is to present a historical review about the development of mathematical models for describing both microscopic processes that occur during the MP aggregation and large-scale events that characterize the progression of neurodegenerative MP-mediated diseases.

Highlights

Proteins, large molecules composed by amino acids, play a central role in biological processes and constitute the basis of all the living organisms
Proteins that fail to configure properly are called misfolded proteins (MP). These are thought to disrupt the function of cells, tissues, and organs [2, 3] and Mathematical Modeling of Protein Misfolding Mechanisms have been causally related to multiple conformational disorders, such as Prion diseases, Alzheimer’s disease (AD), Parkinson’s disease (PD), Creutzfeldt–Jakob disease, amyotrophic lateral sclerosis (ALS), and several other human degenerative disorders [1, 4,5,6,7]
We intended to provide an historical overview of the development of mathematical models for aggregation and propagation of MP in neurological diseases

Summary

INTRODUCTION

Large molecules composed by amino acids, play a central role in biological processes and constitute the basis of all the living organisms. Due to the acceptance of nucleated polymerization as a plausible mechanism for prion aggregation, incorporation of spatial spreading into the NPM seems to be a promising choice With this aim, Matthäus [43] used the diffusion approach within the discrete NPM in order to model prion spatial spreading over simple (i.e., one-dimensional) domains like the spine or the mouse visual system (see Eq A4 in Appendix in Supplementary Material). Matthäus [43] proved that the solutions of the NPM model with one-dimensional diffusion follow a traveling wave behavior Despite such characterization provided a clearer interpretation about the prion propagation speed along pre-defined spatial domains, the proposed model cannot be reduced to a simpler epidemiological-like system.

A Modern Approach

A Road to Brain Imaging Modeling

CONCLUSION