Braiding Braak and Braak: Staging patterns and model selection in network neurodegeneration

A Multiscale Closed-Loop Neurotoxicity Model of Alzheimer's Disease Progression Explains Functional Connectivity Alterations

The accumulation of amyloid-β (Aβ) and hyperphosphorylated-tau (hp-tau) are two classical histopathological biomarkers in Alzheimer's disease (AD). However, their detailed interactions with the electrophysiological changes at the meso- and macroscale are not yet fully understood. We developed a mechanistic multiscale model of AD progression, linking proteinopathy to its effects on neural activity and vice-versa. We integrated a heterodimer model of prion-like protein propagation and a brain network model of Jansen-Rit neural masses derived from human neuroimaging data whose parameters varied due to neurotoxicity. Results showed that changes in inhibition guided the electrophysiological alterations found in AD, and these changes were mainly attributed to Aβ effects. Additionally, we found a causal disconnection between cellular hyperactivity and interregional hypersynchrony contrary to previous beliefs. Finally, we demonstrated that early Aβ and hp-tau depositions' location determine the spatiotemporal profile of the proteinopathy. The presented model combines the molecular effects of both Aβ and hp-tau together with a mechanistic protein propagation model and network effects within a closed-loop model. This holds the potential to enlighten the interplay between AD mechanisms on various scales, aiming to develop and test novel hypotheses on the contribution of different AD-related variables to the disease evolution.

The Importance of Stem Cells Isolated from Human Dental Pulp and Exfoliated Deciduous Teeth as Therapeutic Approach in Nervous System Pathologies

Despite decades of research, no therapies are available to halt or slow down the course of neuro-degenerative disorders. Most of the drugs developed to fight neurodegeneration are aimed to alleviate symptoms, but none has proven adequate in altering the course of the pathologies. Cell therapy has emerged as an intriguing alternative to the classical pharmacological approach. Cell therapy consists of the transplantation of stem cells that can be obtained from various embryonal and adult tissues. Whereas the former holds notable ethical issue, adult somatic stem cells can be obtained without major concerns. However, most adult stem cells, such as those derived from the bone marrow, are committed toward the mesodermal lineage, and hence need to be reprogrammed to induce the differentiation into the neurons. The discovery of neural crest stem cells in the dental pulp, both in adults' molar and in baby teeth (dental pulp stem cells and stem cells from human exfoliated deciduous teeth, respectively) prompted researchers to investigate their utility as therapy in nervous system disorders. In this review, we recapitulate the advancements on the application of these stem cells in preclinical models of neurodegenerative diseases, highlighting differences and analogies in their maintenance, differentiation, and potential clinical application.

From random walks on networks to nonlinear diffusion

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great impact on the collective movement of the group. For this reason, many models in mathematical biology have incorporated crowding effects and managed to understand their implications. Here, we build on a previously developed framework for random walks on networks to show that in the continuum limit, the underlying stochastic process can be identified with a diffusion partial differential equation. The diffusion coefficient of the emerging equation is, in general, density dependent, and can be directly related to the transition probabilities of the random walk. Moreover, the relaxation time of the stochastic process is directly linked to the diffusion coefficient and also to the network structure, as it usually happens in the case of linear diffusion. As a specific example, we study the equivalent of a porous-medium-type equation on networks, which shows similar properties to its continuum equivalent. For this equation, self-similar solutions on a lattice and on homogeneous trees can be found, showing finite speed of propagation in contrast to commonly used linear diffusion equations. These findings also provide insights into reaction-diffusion systems with general diffusion operators, which have appeared recently in some applications.