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. This model takes into account the pro- or anti-tumor properties of different types of axons (sympathetic or sensory) and their distinct remodeling dynamics during PDAC development. We observe a "shift effect" where an initial pro-tumor effect of sympathetic axon denervation is later outweighed by the anti-tumor effect of sensory axon denervation, leading to a transition from an overall protective to a deleterious role of the nervous system on PDAC tumorigenesis. Our model also highlights the importance of the impact of sympathetic axon remodeling dynamics on tumor progression. These findings may guide strategies targeting the nervous system to improve PDAC treatment.

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. In this work, we introduce a system of differential equations modeling the progression of pancreatic ductal adenocarcinoma (PDAC) coupled with associated changes in axonal innervation. The study of the asymptotic behavior of the model confirms the experimental observations that PDAC development is correlated with the type and densities of axons in the tissue. We study then the identifiability and the sensitivity of the model parameters. The identifiability analysis informs on the adequacy between the parameters of the model and the experimental data and the sensitivity analysis on the most contributing factors on the development of cancer. It leads to significant insights on the main neural checkpoints and mechanisms controlling the progression of pancreatic cancer. Finally, we give an example of a simulation of the effects of partial or complete denervation that sheds lights on complex correlation between the healthy, pre-cancerous and cancerous cell densities and axons with opposite functions.

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.

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. However, the underlying processes of emergence and coevolution of structurally distinct assemblies are not mechanistically understood. Here, we show that early prion replication generates two subsets of structurally different assemblies by two sequential processes of formation, regardless of the strain considered. The first process corresponds to a quaternary structural convergence, by reducing the parental strain polydispersity to generate small oligomers. The second process transforms these oligomers into larger ones, by a secondary autocatalytic templating pathway requiring the prion protein. This pathway provides mechanistic insights into prion structural diversification, a key determinant for prion adaptation and toxicity.