A continuous approach of modeling tumorigenesis and axons regulation for the pancreatic cancer.

The pancreatic innervation undergoes dynamic remodeling during the development of pancreatic ductal adenocarcinoma (PDAC). Denervation experiments have shown that different types of axons can exert either pro- or anti-tumor effects, but conflicting results exist in the literature, leaving the overall influence of the nervous system on PDAC incompletely understood. To address this gap, we propose a continuous mathematical model of nerve-tumor interactions that allows in silico simulation of denervation at different phases of tumor development.

Tumorigenesis and axons regulation for the pancreatic cancer: A mathematical approach.

The nervous system is today recognized to play an important role in the development of cancer. Indeed, neurons extend long processes (axons) that grow and infiltrate tumors in order to regulate the progression of the disease in a positive or negative way, depending on the type of neuron considered. Mathematical modeling of this biological process allows to formalize the nerve-tumor interactions and to test hypotheses in silico to better understand this phenomenon.

Early stage prion assembly involves two subpopulations with different quaternary structures and a secondary templating pathway.

The dynamics of aggregation and structural diversification of misfolded, host-encoded proteins in neurodegenerative diseases are poorly understood. In many of these disorders, including Alzheimer's, Parkinson's and prion diseases, the misfolded proteins are self-organized into conformationally distinct assemblies or strains. The existence of intrastrain structural heterogeneity is increasingly recognized.

A bi-monomeric, nonlinear Becker-Döring-type system to capture oscillatory aggregation kinetics in prion dynamics.

In this article, in order to understand the appearance of oscillations observed in protein aggregation experiments, we propose, motivate and analyse mathematically the differential system describing the kinetics of the following reactions: [Formula: see text] with n finite or infinite. This system may be viewed as a variant of the seminal Becker-Döring system, and is capable of displaying sustained though damped oscillations.