Data driven model discovery and interpretation for CAR T-cell killing using sparse identification and latent variables

Abstract

In the development of cell-based cancer therapies, quantitative mathematical models of cellular interactions are instrumental in understanding treatment efficacy. Efforts to validate and interpret mathematical models of cancer cell growth and death hinge first on proposing a precise mathematical model, then analyzing experimental data in the context of the chosen model. In this work, we present the first application of the sparse identification of non-linear dynamics (SINDy) algorithm to a real biological system in order discover cell-cell interaction dynamics in in vitro experimental data, using chimeric antigen receptor (CAR) T-cells and patient-derived glioblastoma cells. By combining the techniques of latent variable analysis and SINDy, we infer key aspects of the interaction dynamics of CAR T-cell populations and cancer. Importantly, we show how the model terms can be interpreted biologically in relation to different CAR T-cell functional responses, single or double CAR T-cell-cancer cell binding models, and density-dependent growth dynamics in either of the CAR T-cell or cancer cell populations. We show how this data-driven model-discovery based approach provides unique insight into CAR T-cell dynamics when compared to an established model-first approach. These results demonstrate the potential for SINDy to improve the implementation and efficacy of CAR T-cell therapy in the clinic through an improved understanding of CAR T-cell dynamics.

From biological data to oscillator models using SINDy

“…However, such large amounts of high-quality data are often not available in experimental setups, which has lead e.g. Brummer et al(53) to reject the use of SINDy-PI in their work.…”

“…However, the SINDy method has been scarcely applied to real data. Examples include data from generic systems (48,49), settlement data (50), gene expression data (51) and mainly experimental data from predator-prey dynamics (52)(53)(54), where SINDy was able to identify relevant aspects of the respective biological systems.…”

“…However, such large amounts of high-quality data are often not available in experimental setups, which has lead e.g. Brummer et al (53) to reject the use of SINDy-PI in their work. Nevertheless, the SINDy-PI extension provides the unique possibility to identify rational terms in a model within a sparsity promoting regression framework and we want investigate if SINDy-PI is able to discover either the underlying model or at least provide information on the rational nonlinearities in the Goodwin model.…”

Model discovery approach enables non-invasive measurement of intra-tumoral fluid transport in dynamic MRI

“…This is largely because neither the higher-order and spatial cross-derivatives, nor products of these terms are readily interpretable with respect to the physics at hand, and storage of each of these 4D arrays may be memory-expensive. Additionally, we utilize L2 regression for simplicity and efficiency, as opposed to sparse objective functions such as LASSO or SR3, which are typically used in model discovery frameworks ( 30, 40 ). For this reason, we refer to our method as function regression, instead of model discovery, as it utilizes a set library constructed from prior knowledge of the physics problem at hand.…”

“…In the original implementation of SINDy, L1 or SR3 regression is used to enforce sparsity ( 28 ). This implementation often involves a parameter sweep and selection of an appropriate sparsity-enforcing parameter through Pareto Front analysis ( 40 ). However, due to the large number of regressions which need to be performed for spatially localized parameterization, the authors opt for L2 regression, avoiding the problem of spatially localized hyperparameter tuning.…”