The Duke University
Mathematical Biology Colloquium
Upcoming Seminars:
- Friday, March 22, 2024, 12:00pm, Physics 119, Mathematical Biology Seminar
A model of oocyte population dynamics for fish oogenesis
Louis Fostier (INRAE)
- We introduce and analyze a size-structured oocyte population model, with non local nonlinearities on recruitment, growth and mortality rates to take into account interactions between cells. We pay special attention to the form of the recruitment term, and its influence on the asymptotic behavior of the cell population.
This model is well-suited for representing oocyte population dynamics within the fish ovary. The nonlocal nonlinearities enable us to capture the diverse feedback mechanisms acting on the growth of oocytes of varying sizes and on the recruitment of new oocytes.
We firstly investigate the existence and uniqueness of global bounded solutions by transforming the partial differential equation into an equivalent system of integral equations, which can be solved using the Contraction Mapping Principle.
In a second step, we investigate the asymptotic behavior of the model. Under an additional assumption regarding the form of the growth rate, we can, with the use of a classical time-scaling transformation, reduce the study to that of a equation with linear growth speed and nonlinear inflow boundary condition. Using arguments from the theory of abstract semilinear Cauchy problems, we investigate the local stability of stationary solutions of this equation by reducing it to a characteristic equation involving the eigenvalues of the linearized problem around equilibrium states.
When the mortality rate is zero, the study of existence and stability of stationary solutions is simplified. Explicit calculations can be carried out in certain interesting cases.
- Friday, March 29, 2024, 12:00pm, Physics 119, Mathematical Biology Seminar
Modelling G protein-coupled receptors (GPCRs) compartmentalized signaling
Leo Darrigade (INRAE)
- G protein-coupled receptors (GPCRs) are membrane receptors that play a pivotal role in the regulation of reproduction and behavior in humans. Upon binding to specific ligands, they trigger a local cAMP production. Activated receptor are then internalized to different endosomal compartments where they can continue signaling before being recycled or destroyed. Recent studies showed that the different pools of cAMP have different effect on the cell.
In the first part of the talk, I will present a piecewise deterministic Markov process (PDMP) of intracellular signaling. The stochastic part of the model accounts for formation, coagulation, fragmentation and recycling of intracellular vesicles which contain the receptor, whereas the deterministic part of the model represents evolution of chemical reactions due to signaling activity of the receptor. We are interested in the existence of and convergence to a stationary measure. I will present different cases for which we were able to obtain results in this direction.
In the second part of the talk, I will present the numerical workflow (SBML, PEtab and PyPESTO) we use to fit ODEs model of GPCR signaling to longitudinal measure of chemical concentrations (BRET data).
- Friday, April 5, 2024, 12:00pm, Physics 119, Mathematical Biology Seminar
A mathematical model for receptive field refinement during development
Jennifer Crodelle (Middlebury College, Mathematics)
- TBA
- Friday, April 26, 2024, 12:00pm, Physics 119, Mathematical Biology Seminar
TBA
Samuel Isaacson (Boston University, Mathematics and Statistics)
- TBA
- Friday, September 20, 2024, 12:00pm, Physics 119, Mathematical Biology Seminar
TBA
Jeseth Delgado Vela (Duke University, Civil and Environmental Engineering)
- TBA
- Friday, September 27, 2024, 12:00pm, Physics 119, Mathematical Biology Seminar
TBA
Mansoor Haider (North Carolina State University, Mathematics)
- TBA
Lunch after the talk with the speaker for interested participants.
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