Computational Verification of Large Logical Models—Application to the Prediction of T Cell Response to Checkpoint Inhibitors

Abstract

At the crossroad between biology and mathematical modeling, computational systems biology can contribute to a mechanistic understanding of high-level biological phenomenon. But as knowledge accumulates, the size and complexity of mathematical models increase, calling for the development of efficient dynamical analysis methods. Here, we propose the use of two approaches for the development and analysis of complex cellular network models. A first approach, called "model verification" and inspired by unitary testing in software development, enables the formalization and automated verification of validation criteria for whole models or selected sub-parts. When combined with efficient analysis methods, this approach is suitable for continuous testing, thereby greatly facilitating model development. A second approach, called "value propagation," enables efficient analytical computation of the impact of specific environmental or genetic conditions on the dynamical behavior of some models. We apply these two approaches to the delineation and the analysis of a comprehensive model for T cell activation, taking into account CTLA4 and PD-1 checkpoint inhibitory pathways. While model verification greatly eases the delineation of logical rules complying with a set of dynamical specifications, propagation provides interesting insights into the different potential of CTLA4 and PD-1 immunotherapies. Both methods are implemented and made available in the all-inclusive CoLoMoTo Docker image, while the different steps of the model analysis are fully reported in two companion interactive jupyter notebooks, thereby ensuring the reproduction of our results.

Calcium Signaling Is Impaired in PTEN-Deficient T Cell Acute Lymphoblastic Leukemia

“…Here we constructed a mathematical model to uncover the functional links between TCR, PTEN and calcium flux. Several logical models have depicted TCR signaling (44)(45)(46)(47). Yet, in contrast to all these previous models designed for peripheral T cells, our model is adapted to thymocytes, as it takes into account the strength of TCR signaling, which is a crucial feature for thymic selection.…”

Modelling of Immune Checkpoint Network Explains Synergistic Effects of Combined Immune Checkpoint Inhibitor Therapy and the Impact of Cytokines in Patient Response

“…Combining this model with more complex complementary models might be more insightful to answer other types of questions. Two recent models have been published on immune checkpoint therapies [8,9]. If these models show a good overlap with our model, they focus on different aspects: Hernandez et al provide a very detailed model (up to 200 nodes) of the downstream effect of CTLA4 and PD1 and focus on the methodology to explore such complex models, whereas Bolouri et al developed a model exploring the steps involved in CD8+ T cell exhaustion and the impact on the efficacy of the treatments.…”

“…Mathematical modelling has already proved to be useful in cancer analyses using nonlinear continuous approaches [6,7], and more and more models are being developed to understand the immune response and effect of therapies [8,9]. Logical formalism has been used in particular for its simplicity and its versatility, considering the limited available data that are used to build these models [10].…”

Logical and experimental modeling of cytokine and eicosanoid signaling in psoriatic keratinocytes

“…A comparison of the impact of Th17- and Th1-derived cytokines was investigated by a value propagation study, as described in ( Hernandez et al, 2020 ). The same analysis was also performed for each cytokine individually.…”