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Review
. 2018 Feb 2:9:37.
doi: 10.3389/fneur.2018.00037. eCollection 2018.

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

Felix Carbonell  1 , Yasser Iturria-Medina  2   3 , Alan C Evans  2   3
Affiliations
Review

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

Felix Carbonell et al. Front Neurol. .

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.

Keywords: mathematical modeling; misfolded protein; neurodegeneration; prion-like hypothesis; therapeutic interventions.

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Figures

Figure 1
Figure 1
Different neurodegenerative disorders present disease-specific MPs and characteristic anatomical progression patterns. (A) Aβ plaques in the cortex of an Alzheimer’s disease (AD) patient. (B) Tau neurofibrillary tangle in a neuron of an AD patient. (C) α-synuclein inclusion in a neuron from a Parkinson’s disease (PD) patient. (D) TDP-43 inclusion in a motoneuron of the spinal cord from a patient with ALS. Scale bars are 50 mm in (A) and 20 mm in (B–D). (E) In Alzheimer’s disease (AD), Aβ deposits are first observed in the neocortex (NC) and are then detected in all cortical, diencephalic and basal ganglia structures (in a caudal direction) and in the brainstem, and occasionally in the cerebellum (8, 9). (F) Tau aggregates develop in the locus coeruleus, then in the transentorhinal and ENT regions and subsequently in the hippocampal formation and in broad areas of the NC (10, 11). (G) In PD, the progression of α-synuclein pathology follows an ascending pattern from the brainstem to the telencephalon (9, 11). The earliest lesions can be detected in the olfactory bulb, and in the dorsal motor nucleus of the vagus nerve (DMX) in the medulla oblongata. At later stages, the α-synuclein aggregates are found more rostrally through the brainstem via the pons and midbrain, in the basal forebrain and, ultimately, in the NC. (H) In ALS, initial TDP43 inclusions are seen in the agranular motor cortex (AGN), in the brainstem motor nuclei of cranial nerves XII–X, VII and V, and in α-motor neurons in the spinal cord. Later stages of disease are characterized by the presence of TDP43 pathology in the prefrontal neocortex (PFN), brainstem reticular formation, precerebellar nuclei, pontine gray, and the red nucleus. Subsequently, prefrontal and postcentral neocortices, as well as striatal neurons, are affected by pathological TDP43, before the pathology is found in anteromedial portions of the temporal lobe, including the hippocampus (9, 12). AC, allocortex; BFB, basal forebrain; BN, brainstem nuclei; BSM, brainstem somatomotor nuclei; ENT, entorhinal cortex; MTC, mesiotemporal cortex; SC9, spinal cord gray-matter lamina IX; SN, substantia nigra; TH, thalamus. Figures (A–D) and (E–H) were adapted with permission from Ref. (13, 14), respectively.
Figure 2
Figure 2
Schematic representation of prion aggregation mechanisms. Native (sphere) prion molecules undergo conformational changes that lead to an abnormal (cube) configuration (Step 1). This event is unfavorable because the abnormal configuration is either unstable (Step 2) or sensitive to clearance. According to the template-assisted model (24), prions in their abnormal configuration interact with native prions (Step 3) and convert them into the abnormal configuration (Step 4). The NPM proposes that abnormal prions can interact with molecules in a similar state (Step 5), the oligomeric species formed are unstable and grow by the incorporation of abnormal prion molecules (Step 6) and dissociate (Step 7) until a stable nucleus is formed. Such a stable prion aggregate can then grow indefinitely from one or both ends and can also break into smaller fragments (Step 8) that act as new nuclei. Figure reproduced from Brundin et al. (25) with the permission of the journal.
Figure 3
Figure 3
Multifactorial causal model. (A) Brain multimodal images and cognitive evaluations. (B) State space vectors (S), characterizing the brain’s multifactorial alteration levels with regard to a baseline. (C) Causal multifactorial propagation network capturing the direct interactions among regions (for each biological factor/imaging modality) or among factors (for each brain region). Diagonal blocks in the matrix correspond to a unique biological factor, with diagonal elements accounting for intra-regional effects and off-diagonal elements accounting for inter-regional alterations spreading across physical connections. Off-diagonal blocks correspond to the direct interactions between two different factors (e.g., glucose metabolism impact on tissue properties, or vice versa). (D) System has an output vector (β), representing the influence of the brain’s multifactorial state space on the cognitive state. Figure adapted from Iturria-Medina et al. (100) with permission of the journal.
Figure 4
Figure 4
Tentative inhibition of amyloid aggregation/propagation by three different strategies (103). Drug 1 should lower the effective monomer concentration. Lowering the monomer concentration would inhibit de novo formation and slow down polymer elongation. Drug 2 should block growing polymer ends. In the context of macroscopically linear polymers, this would be equivalent to either blocking or capping the ends of the polymers. Drug 3 should increase the polymer breakage rate. Based on numerical simulations, Masel and Jansen (103) found that therapeutics following drug strategy (2) were the most promising ones, while the remaining strategies may be ineffective or even accelerate the amyloid formation process at low drug doses. Figure reproduced from Masel and Jansen (103) with permission of the journal.
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References

    1. Dobson CM. Protein folding and misfolding. Nature (2003) 426:884–90.10.1038/nature02261 - DOI - PubMed
    1. Walker LC, Levine H. The cerebral proteopathies. Neurobiol Aging (2000) 21:559–61.10.1016/S0197-4580(00)00160-3 - DOI - PubMed
    1. Walker LC, Levine H. The cerebral proteopathies. Mol Neurobiol (2000) 21:83–95.10.1385/MN:21:1-2:083 - DOI - PubMed
    1. Dobson CM. Protein misfolding diseases: getting out of shape. Nature (2002) 418:729–30.10.1038/418729a - DOI - PubMed
    1. Braak H, Braak E. Neuropathological stageing of Alzheimer-related changes. Acta Neuropathol (1991) 82:239–59.10.1007/BF00308809 - DOI - PubMed

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