Mathematical Modeling of Protein Dynamics

Wednesday, June 16 at 04:15am (PDT)
Wednesday, June 16 at 12:15pm (BST)
Wednesday, June 16 08:15pm (KST)

SMB2021 SMB2021 Follow Tuesday (Wednesday) during the "MS12" time block.
Note: this minisymposia has multiple sessions. The second session is MS11-DDMB (click here).

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Suzanne S. SINDI (University of California, Merced, USA)


Proteins are fundamental building blocks of life. Their dynamics - both with respect to folding and their spatio-temporal dynamics - are critical to the normal function of biological systems. When proteins misfold, they are often associated with disease. For example, Alzheimer’s and Parkinson’s disease, results from the accumulation and aggregation of incorrectly folded proteins. These diseases can be genetic or spontaneous and in the special case of prion disease infectious. This minisymposium brings together researchers (biologists, biophysicists and mathematicians) with the goal of exploring the latest approaches (both experimental and mathematical) for studying protein dynamics, with a particular emphasis on protein misfolding diseases.


(INRAE, Jouy-en-Josas, FRANCE)
"to be announced"
to be announced

Maria Carla TESI

(Universitá di Bologna, ITALY)
"The synergistic interplay between two proteins: a mathematical model for Alzheimer's disease"
There is currently a great deal of interest in the scientific community in investigating the effects of the synergistic interplay of Amyloid beta and tau on the dynamics of Alzheimer’s disease. I will present a mathematical model for the onset and progression of Alzheimer’s disease based on transport and diffusion equations for the two proteins. In the model neurons are treated as a continuous medium and structured by their degree of mal- functioning. Three different mechanisms are assumed to be relevant for the temporal evolution of the disease: i) diffusion and agglomeration of soluble Amyloid beta, ii) effects of misfolded tau protein and iii) neuron-to-neuron prion-like transmission of the disease. These processes are modelled by a system of Smoluchowski equations for the Amyloid beta concentration, an evolution equation for the dynamics of tau protein and a kinetic-type transport equation for the distribution function of the degree of malfunctioning of neurons. The latter equation contains an integral term describing the random onset of the disease as a jump process localized in particularly sensitive areas of the brain. I will explain the structure of the model and give a hint of the main results obtained. Eventually I will also show the output of some numerical simulations, of some significance even if performed in an over-simplified 2D geometry.

Léon Matar TINE

(Université de Lyon, FRANCE)
"Analysis and numerical simulations of a reaction-diffusion model with fixed active bodies: Application to Alzheimer's disease."
This talk focuses on a spatial interaction model of two substances (or molecules), one of which, concentration f, is produced by bodies located in- side the considered domain and is acting as an activator (positive effect) or a growth factor for the second substance which concentration is denoted by g. The substance or molecules of concentration g on the contrary acts as an inhibitor or a shrinkage for the substance f because of its cytotoxic effect on the bodies activity. The main goal is to analyze the dynamics and propose an adapted numerical approach for the simulation of such kind of model described above where existing bodies (sources for one of the substance) have polygonal shape and their activity can be altered by the presence of the second substance or molecule. For convenience and in accordance with [1] the bodies are taken as fix in the domain. In [1] authors introduced a model based on a discrete growth-fragmentation system with spatial diffusion in order to analyze the early stages of Alzheimer disease. Their model, containing at least five equations and fourteen parameters, aims at representing the process of repli- cation and spatial diffusion of Aβ-oligomers molecules in the neighborhood of neurons. They describe the whole process from Aβ-monomers molecules assembling first into proto-oligomers (unstable polymers) and then into Aβ- oligomers (stable polymers). In [1] the authors carried out a modeling work for the description and simulation of the model where oligomers neurotoxic effect is taken into account. Numerical difficulties are linked to this modeling. A first difficulty is to take into account the geometrical form of active bodies which can be arbitrary. Another difficulty is to manage the sent cytotoxic signals from the substance (or molecule) of concentration g to bodies. In fact, the efficacity of the signal depends on the distance from where it is sent. [1] M. Andrade-Restrepo, P. Lemarre, L. Pujo-Menjouet, L. M. Tine, and S. I. Ciuperca. Modeling the spatial propagation of Aβ oligomers in alzheimer’s disease. In CEMRACS 2018 - Numerical and mathematical modeling for biological and medical applications: deterministic, proba- bilistic and statistical descriptions, pages 1–10, Marseille, France, Jul. 2018


(Université de Lyon, FRANCE)
"Alzheimer and Prion: a dangerous liaison"
Alzheimer’s disease (AD) is a fatal incurable disease leading to progressive neuron destruction. AD is caused in part by the accumulation in the brain of Aβ monomers aggregating into oligomers and fibrils. Oligomers are amongst the most toxic structures as they can interact with neurons via membrane receptors, including PrPc proteins. This interaction leads to the misconformation of PrPc into pathogenic oligomeric prions, PrPol. We develop here a model describing in vitro Aβ polymerization process. We include interactions between oligomers and PrPc, causing the misconformation of PrPc into PrPol.

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Virtual conference of the Society for Mathematical Biology, 2021.