ONCO Subgroup Contributed Talks

Pujan Shrestha

Texas A&M University

"An ODE-SDE Model for Ct-DNA dynamics"

Effective cancer therapies, while continuously improving, are often constrained by lower detection limits of disease. Tumor-immune dynamics in this limit present one of the most pressing knowledge gaps as cancer ultimate escape or elimination are often determined following an intervening period of population equilibrium sustained at low population size. Population dynamics in this small-population limit are affected by intrinsic noise in the tumor-immune interaction, as are estimates of population disease burden by extrinsic noise in acquiring such estimates through associated biomarkers. We present a modeling framework that investigates the interactions between tumor cells and the immune system in the small population regime, focusing on how these interactions influence biomarker levels. The framework combines deterministic elements, which describe tumor growth and immune responses, with stochastic components that capture the inherent variability in biomarker release. We use a system of ordinary differential equations (ODEs) to represent the tumor-immune dynamics between an adaptive immune compartment, immunogenic tumor cells, and evasive tumor cells. The immune system’s role in controlling tumor growth is reflected in the tumor-immune interaction terms. Apoptotic death via tumor-immune interactions and necrotic death via the tumor competition under a shared carrying capacity both contribute to the release of a tumor biomarker. We focus on applying our model to ct-DNA, wherein we frame ct-DNA dynamics using a stochastic differential equation (SDE). This SDE framework accounts for the variability in ct-DNA release due to the dynamic tumor-immune interactions, as well as inherent biological noise, such as DNA degradation and clearance. By coupling the ODE system of equations for tumor-immune dynamics with the SDE for ct-DNA release, we can use the model to study the fluctuations in ct-DNA levels driven by tumor-immune dynamics and exogenous sampling noise.

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Keith Chambers

University of Oxford

"Adipocyte-derived lipids promote phenotypic bistability in a structured population model for melanoma growth"

Melanoma cells exhibit a continuum of proliferative to invasive phenotypes. While single-cell and spatial transcriptomics have enabled biologists to quantify the distribution of phenotype amongst melanoma cells, a complete mechanistic understanding is currently lacking. A key issue is the impact of adipocyte-derived lipids, whose uptake by melanoma cells drives an invasive response that may lead to metastasis. To address this, we have developed a phenotype-structured model for melanoma cell populations that couples the phenotype dynamics to the essential aspects of intracellular lipid metabolism and the extracellular microenvironment. In this talk, I will first introduce a single-cell ODE model that illustrates how lipid uptake gives rise to phenotypic bistability in melanoma cells. I will then show how a phenotype-structured population model, whose advection term is informed by the single-cell model, exhibits a range of qualitative behaviours, including cyclic solutions and bimodal phenotypic distributions. Together, these results increase understanding of the role played by adipocyte-derived lipids and other microenvironment factors in shaping the distribution of phenotype in melanoma cell populations. We speculate that our modelling framework may also be applicable to other lipid-rich tumours (e.g. breast and ovarian cancers) that are commonly associated with increased metastasis.

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Fabian Spill

University of Birmingham

"Regulation of Intra- and Intercellular Metabolite Transport in Cancer Metabolism"

Metabolite transport is essential for cellular homeostasis, energy production, and metabolic adaptation. In cancer, dysregulated transport sustains tumor growth and alters redox balance. The mitochondrial solute carrier SLC25A10 facilitates succinate, malate, and phosphate exchange, influencing central carbon metabolism. However, its transport kinetics and physiological directionality remain poorly understood. We present a mathematical model of SLC25A10 based on a ping-pong kinetic mechanism, capturing competitive dynamics between malate and succinate. Our simulations reveal that under normal conditions, malate flux dominates due to its higher binding affinity. However, in succinate dehydrogenase (SDH) dysfunction, excess succinate induces a transient efflux shift and phosphate flux reversal. If experimentally validated, this metabolic shift could serve as a biomarker for tumors with SDH mutations. Integrating our kinetic model with genome-scale metabolic networks, we highlight the role of mitochondrial transport in cancer metabolism. Specifically, in multiple myeloma, metabolic crosstalk between plasma cells and bone marrow stromal cells is key to tumor progression. Our findings demonstrate the power of mathematical modeling in uncovering transport-mediated metabolic vulnerabilities, offering potential therapeutic targets for cancer and metabolic diseases.

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Chenxu Zhu

Institute for Computational Biomedicine - Disease Modeling

"Machine learning-assisted mechanistic modeling to predict disease progression in acute myeloid leukemia patients"

Blood cell formation is a complex process which is driven by hematopoietic stem cells (HSCs). HSCs give rise to progenitors and precursors which eventually produce mature blood cells, such as white blood cells, red blood cells, and platelets. Acute myeloid leukemia (AML) is an aggressive blood cancer which originates from leukemic stem cells (LSCs) and is characterized by the accumulation of aberrant immature cells, referred to as leukemic blasts. Due to the impairment of healthy blood cell formation, many AML patients suffer from life-threatening complications, such as bleeding or infection. Although treated with high-dose chemotherapy, many patients relapse and need salvage therapy. To reveal the mechanisms of disease progression and relapse, we proposed a mathematical model that accounts for competition of HSCs and LSCs in the stem cell niche and physiological feedback regulations before, during, and after chemotherapy. We fit the model to data of 7 individual patients and simulate variations of the treatment protocol. Our simulation results can recapitulate the non-monotonic recovery of HSCs observed in relapsing patients. The model suggests using the decline of HSC counts during remission as an indication for salvage therapy in patients lacking minimal residual disease markers. To bring our model closer to clinical applications, we propose a machine learning assisted mechanistic model that ensuring adherence to biological principles while learning from a larger clinical AML dataset. By embedding mechanistic constraints into machine learning, we aim to identify patient-specific predictors of relapse while preserving biological interpretability.

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Veronika Hofmann

Technical University of Munich

"Spectral Spatial Analysis of Cancer Biopsies: Validation through in-silico data and extension to logistic growth models"

MD Anderson's Enderling lab recently invented a spectral spatial analysis method for estimating tumor cell diffusivity and proliferation rate from single-point-in-time biopsies of breast cancer. In combination with clinical data from the patients these parameters could help identify a new biomarker for radiotherapy. In their first study, they investigate the relationship between the power spectral density (PSD) of the three-dimensional reaction-diffusion (RD) equation with exponential growth (as model of spreading cancer cells) and the two-point correlation function of the cell distribution in the biopsy (a spatial statistic). Their results make the approach seem promising, and this work aims to validate and extend their findings. Firstly, we develop a model to generate in-silico data to validate the parameter estimation method. This is done by solving the RD equation for different growth terms (exponential and logistic), adding Gaussian noise and 'translating' its continuous results into spatial point patterns which are interpreted as cell nuclei in the 'biopsy', and then applying the method to see if the original parameters can be retrieved. This model contains several features: dimensionality can be switched between 2D and 3D, cell size can be adjusted, cuts can be added to the point pattern, and in the 3D case, biopsy thickness is variable and the plane where the slice through the 'tumor' is made can be freely chosen. And secondly, the spectral analysis method is altered by proposing a numerical solution to the PSD of the RD equation with logistic growth (valid for arbitrary dimensions). Logistic growth is assumed to be the more realistic model, however, it is harder to handle as no analytical solution is available for the equation, and hence neither for the PSD. The validation results from the in-silico data are assessed and their meaning for the application to real patient data is discussed under consideration of the different types of cell growth.

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