(W-010) Modeling the evolution of activation marker distributions in flow cytometry data representing cell populations in patients dosed with immunomodulating agents

Hamid Bellout, PhD – Principal, Bellout LLC; Dina Stroopinsky, PhD – Research Principal Scientist, Takeda Development Centers America; Siddha Kasar, PhD – Scientific Director, Takeda Development Centers America; Gurpanna Saggu, PhD – Principal Scientist, Takeda Development Centers America; John Gibbs, PhD – Senior Director, Takeda Development Centers America; Allison Berger, PhD – Scientific Director, Takeda Development Centers America; Aleksander Chudnovsky, MD – Senior Medical DIrector, Takeda Development Centers America

Background: The growing emphasis on immunology in oncology and other therapeutic areas has increased the importance of modeling flow cytometry data. For example, subasumstat (TAK-981) has been shown to stimulate CD69 expression on NK cells both in vitro and in the peripheral blood of cancer patients in a Phase I clinical trial (NCT03648372) . Typically, we would use ordinary differential equations (ODEs) to model the median fluorescence intensity (MFI) of CD69 or the percent CD69 positive (%+) on NK cells. However, flow cytometry data shows the distribution of CD69 fluorescence intensities right-shifting and spreading under subasumstat administration, reflecting a stochastic process, from gene to mRNA to protein expression, that cannot be fully captured by ODE modeling.

Methods: Starting with a chemical master equation (CME), we derive a partial differential equation (PDE) governing the evolution of the distribution of CD69 expression on the NK cell population in a patient after a single dose of subasumstat. We then attempt to find necessary conditions for the model to be consistent with three key clinical observations: (a) homeostasis before treatment, (b) response to treatment, and (c) return of the distribution to the original homeostatic CD69 distribution.

Results: Theoretical as well as empirical comparison to the observed CD69 expression distributions at pre-dose, 24 hours after first dose, and 4 days after the second BIW dose (day 4) provided a relationship between the functional forms of the coefficients of the PDE required to fit the observed data.

Conclusions: The approach used is able to describe the evolution of the distribution of CD69 expression on NK cell populations in individual patients while constraining the parameter ranges that fit the data. This procedure can be generalized to establish conditions and parameter values allowing characterization of pre-treatment homeostasis and on-treatment dynamics of immune cell biomarker distributions as determined by flow cytometry. By capturing the richness of flow cytometry data (as opposed to modeling a scalar quantity such as MFI or %+), this approach can provide better quantification of key immunological processes in vitro, in vivo, and in patients.

Citations: [1] A Study of TAK-981 in People With Advanced Solid Tumors or Cancers of the Immune System, NCT03648372, clinicaltrials.gov.