public 59:29

Louis Fostier : A model of oocyte population dynamics for fish oogenesis

  -   Mathematical Biology ( 85 Views )

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.

public 53:20

Dean Bottino : Evaluating Strategies for Overcoming Rituximab (R) Resistance Using a Quantitative Systems Pharmacology (QSP) model of Antibody-Dependent Cell-mediated Cytotoxicity & Phagocytosis (ADCC & ADCP): An Academic/Industrial Collaboration

  -   Mathematical Biology ( 76 Views )

Despite the impressive performance of rituximab (R) containing regimens like R-CHOP in CD20+ Non-Hodgkin’s Lymphoma (NHL), 30-60% of R-naïve NHL patients are estimated to be resistant, and approximately 60% of those patients will not respond to subsequent single agent R treatment. Given that antibody dependent cell mediated cytotoxicity (ADCC) and phagocytosis (ADCP) are thought to be the major mechanisms of action of Rituximab, increasing the activation levels of natural killer (NK) and macrophage (MP) cells may be one strategy for overcoming R resistance.

During (and after) the Fields Institute Industrial Problem Solving Workshop in August 2019, academic participants and industry mentors developed and calibrated to literature data a quantitative systems pharmacology (QSP) model of ADCC/ADCP to interrogate which mechanisms of R resistance could be overcome by increased NK or MP activation, and how much effector cell activation would be required to overcome a given degree and mechanism of R resistance.

This work was motivated by a real-world pharmaceutical drug development question, and the academic-industry interactions during and after the workshop resulted in sharknado plots as well as a published QSP model (presented at American Association of Cancer Research Annual Meeting, 2021) that was able to address some of the key questions around overcoming R resistance. The published model was then incorporated into an in-house QSP model supporting the development of a Takeda investigational drug which is being developed to restore R sensitivity in an R-resistant patient population.