Biology subjects

Stankova, K.

Publications and source records attributed to Stankova, K..

15 recordsLinked to original sources

bioRxiv2026

Persister cells and their effects on cancer stabilization therapy

Some cancers have the ability to persist under treatment. Persister cancer cells can be a small subpopulation of cancer cells that enter a dormant or quiescent state, thereby evading the effects of chemotherapy, targeted therapy, or immunotherapy. Motivated by these observations, we develop and investigate an evolutionary game theory model that captures the interactions between three types of cancer cells: treatment-sensitive, drug-tolerant persister, and treatment-resistant cells. In our model, persister cells transition into resistant cells at a rate that can depend on the treatment intensity. We analyze the model's equilibria and derive conditions for their existence and stability. In particular, we show that an equilibrium in which sensitive and resistant cells coexist is stable when intra-type competition is stronger than inter-type competition. We also show that equilibria in which only one cell type persists require the transition rate to exceed an explicit threshold determined by the treatment dose and competition parameters. Our findings reveal that persister cells can both stabilize and destabilize tumor dynamics, depending on treatment and cell type-transition rates, highlighting the importance of accounting for persister behavior in designing effective evolutionary therapies.

cancer biology↗

bioRxiv2026

Robust and Quality-of-Life-Aware Treatment Protocols in NSCLC using Deep Reinforcement Learning

Under current systemic treatment of metastatic cancer, a drug is frequently prescribed at maximum tolerable dose (MTD) until either unacceptable toxicity or progression. Unfortunately, in many patients this treatment strategy leads to the development of treatment resistance. Evolutionary therapy approaches aim to forestall or delay treatment resistance in cancer by exploiting eco-evolutionary interactions. A well-known implementation is the adaptive therapy protocol of Zhang et al., in which tumour burden thresholds are used to guide strategic treatment holidays. Deep reinforcement learning (DRL) has recently been used to optimise these approaches. However, research combining DRL with evolutionary therapy approaches has so far focused on time to progression (TTP) as a performance metric, and has not quantified safety in terms of robustness to delayed treatment restart or included patient preferences regarding quality of life (QoL) in treatment design. In our study, we use a DRL agent informed by a mathematical two-population tumour growth model to design treatment schedules for patients with non-small cell lung cancer (NSCLC). The agent is trained on a virtual patient cohort using parameters previously fitted to data from patients with NSCLC treated with erlotinib. Beyond TTP, we focus on improving robustness to delayed treatment restart and on how individual preferences and values impact QoL experienced during treatment. We compare TTP, robustness and QoL under the DRL policy, the adaptive therapy protocol of Zhang et al., and MTD. We introduce a robustness metric ``margin-to-failure'' (MTF), and compare quality-adjusted-survival (QAS) across different patient preference profiles. Finally, we explore reward shaping to assess how QoL preferences can be incorporated into DRL-based treatment design. To evaluate our results, we consider different decision intervals, defined as the time between dosing adjustments. The DRL policy achieved greater median TTP, MTF, and QAS across all treatment decision intervals compared to the other two protocols. As decision intervals increased, TTP under DRL declined gradually towards that achieved under MTD. In contrast, the Zhang et al. protocol performed inconsistently and could result in premature progression. Additionally, a population-level policy trained on a cohort of virtual patients produced an interpretable treatment rule that extended TTP for most previously unseen patients and indicated that treatment should resume at a lower tumour burden when monitoring is less frequent. These findings show that DRL can balance the benefit of preserving drug-sensitive cells to suppress resistance against the risk of unsafe tumour regrowth. Reward shaping further showed how treatment strategies could be adjusted to reflect different patient preferences. Together, these results provide a biologically informed approach for designing robust and patient-centred evolutionary therapies in fast-growing cancers such as NSCLC.

systems biology↗

bioRxiv2026

Initial tumor composition shapes resistance evolution and treatment outcomes in non-small cell lung cancer

Drug resistance is a leading cause of treatment failure in non-small cell lung cancer (NSCLC), yet how resistance evolves during treatment and whether its fitness consequences depend on tumor composition remains poorly understood. Using a game-theoretic mathematical model fitted to longitudinal in-vitro data from alectinib-sensitive and alectinib-resistant H3122 NSCLC cells grown under different treatment and microenvironmental conditions, we found that the fitness effect of evolving resistance depended critically on the initial proportion of resistant cells in the tumor. When resistant cells were initially rare, resistance evolved faster and increasing resistance was associated with a growth advantage. When resistant cells were initially frequent, increasing resistance was associated with a fitness cost. In both cases, increasing resistance eroded treatment efficacy. In the gain-of-resistance regime, stabilization therapy could maintain a stable tumor equilibrium only if resistant cells were excluded. Maximum tolerated dosing was not always optimal for maximizing time to progression; intermediate doses performed better when they kept the initial tumor growth rate close to zero. These results suggest that evolutionary therapy for NSCLC should account not only for the abundance of resistant cells, but also for how resistance is evolving and what fitness consequences it currently carries in individual patients.

cancer biology↗

bioRxiv2026

Assessing the Operational Feasibility of Evolutionary Therapy in Metastatic Non-Small Cell Lung Cancer

Evolutionary cancer therapy (ECT) applies principles of evolutionary game theory to prolong the effectiveness of cancer treatment by curbing the development of treatment resistance. It was shown to increase time to progression while decreasing the cumulative drug dose. ECT individually tailors treatment schedules for patients based on their cancer dynamics and, thus, requires regular follow-up and precise measurements of the cancer burden. The current literature on ECT often overlooks clinical realities, such as rather long intervals between tests, possible appointment delays and measurement errors, in the development of the treatment protocols. In this study, we assess the clinical feasibility of ECT for metastatic non-small cell lung cancer (NSCLC). We create virtual patients with cancer dynamics described by the polymorphic Gompertzian model, based on data from the START-TKI clinical trial. We assess the effects of longer test intervals, measurement error and appointment delays on the expected time to progression under the evolutionary therapy protocols. We show that a higher containment level, although it increases time to progression in the models predictions, may lead to premature treatment failure in the presence of measurement error and appointment delay. Further, we show that the ECT protocol with a single containment bound is more robust to the clinical realities than the protocol with two bounds. Finally, we show that a dynamically adjusted treatment protocol can be beneficial for individual patients, but requires a thorough follow-up. This study contributes to the design of a clinical trial and the future clinical implementation of evolutionary therapy for NSCLC.

cancer biology↗

bioRxiv2025

Which evolutionary game-theoretic model best captures non-small cell lung cancer dynamics?

Understanding and predicting the eco-evolutionary dynamics of cancer requires identifying mathematical models that best capture tumor growth and treatment response. In this study, we fit a family of two-population models to in-vitro data from non-small cell lung cancer (NSCLC), tracking drug-sensitive and drug-resistant cells under varying environmental conditions. The dataset, originally presented by Kaznatcheev et al., includes conditions with and without the drug Alectinib and cancer-associated fibroblasts (CAFs). We compare combinations of growth models (logistic, Gompertz, von Bertalanffy) and drug efficacy terms (Norton-Simon, linear, ratio-dependent) to identify which best explains the observed dynamics. Our models incorporate density dependence, frequency-dependent competition, and drug response, enabling mechanistic interpretation of tumor cell interactions. The logistic model with ratio-dependent drug efficacy best fits monoculture data. Using growth parameters from monocultures, we infer inter-type competition coefficients in co-cultures. We find that growth rate and carrying capacity are stable across CAF conditions, while competition and drug efficacy parameters shift, altering interaction dynamics. Notably, CAFs promote coexistence between resistant and sensitive cells, whereas Alectinib induces competitive exclusion. Our results underscore the need to evaluate both model fit and biological plausibility to guide therapeutic modeling of cancer. Author summaryHow cancer cells grow, compete, and respond to treatment depends not only on the drug, but also on their ecological context, including interactions with other cells and components of the tumor microenvironment. In this study, we explore how different mathematical models capture the behavior of non-small cell lung cancer (NSCLC) cells under various conditions. We focus on two cell populations: one sensitive to treatment, and one resistant. Using in-vitro data, we compare growth models and drug response types to identify which model best explains the observed population dynamics. We also investigate how different factors, such as the drug Alectinib and cancer-associated fibroblasts (CAFs), change the way cancer cells interact. Our game-theoretic approach allows us to quantify how these external conditions affect competition between cell types, revealing when resistant and sensitive cells can coexist. These findings contribute to a deeper understanding of tumor ecology and may support the development of adaptive cancer therapies that anticipate evolutionary responses to treatment.

systems biology↗

bioRxiv2024

Migrastatic Therapy as a Potential Game-Changer inAdaptive Cancer Treatment

Adaptive therapy, which anticipates and counters the evolution of resistance in cancer cells, has gained significant traction, especially following the success of the Zhang et al.s protocol in treating metastatic castrate-resistant prostate cancer. While several adaptive therapies have now advanced to clinical trials, none currently incorporates migrastatics, i.e. treatments designed to inhibit cancer cell metastasis. In this study, we propose integrating migrastatics into adaptive therapy protocols and evaluate the potential benefits of using a game-theoretic spatial model. Our results demonstrate that combining adaptive therapy with migrastatics effectively delays the onset of metastasis and reduces both the number and size of metastases across most cancer scenarios analyzed. This approach not only extends the time to the first metastasis but also enhances the overall efficacy of adaptive therapies. Our findings suggest a promising new direction for cancer treatment, where adaptive therapy, in combination with migrastatic agents, can target both the evolution of resistance and the metastatic spread of cancer cells.

cancer biology↗

bioRxiv2023

Polymorphic Gompertzian model of cancer validated with in vitro and in vivo data

Mathematical modeling plays an important role in our understanding and targeting therapy resistance mechanisms in cancer. The polymorphic Gompertzian model, analyzed theoretically by Viossat and Noble, describes a heterogeneous cancer population consisting of therapy sensitive and resistant cells. This theoretically promising model has not previously been validated with real-world data. In this study, we provide this validation. We demonstrate that the polymorphic Gompertzian model successfully captures trends in both in vitro and in vivo data on non-small cell lung cancer (NSCLC) dynamics under treatment. Additionally, for the in vivo data of tumor dynamics in patients undergoing treatment, we compare the polymorphic Gompertzian model to the classical oncologic models, which were previously identified as the models that fit this data best. We show that the polymorphic Gompertzian model can successfully capture the U-shape trend in tumor size during cancer relapse, which can not be fitted with the classical oncologic models. In general, the polymorphic Gompertzian model corresponds well to both in vitro and in vivo real-world data, suggesting it as a candidate for improving the efficacy of cancer therapy, for example through evolutionary/adaptive therapies.

cancer biology↗

bioRxiv2022

How to use transcriptomic data for game-theoretic modeling of treatment-induced resistance in cancer cells?A case study in patient-derived glioblastoma organoids

Game theory is a powerful tool to model strategic decision making, but also interactions within Darwinian biological systems, such as cancer. As such, in the past decades, game-theoretical models have helped to understand cancer, its response to various treatments, and to design better therapies. However, to fully utilize the potential of game-theoretical modelling in designing better anti-cancer therapies, we need more information on cancer population (ecological) and strategy (evolutionary) dynamics in response to treatment for each patient and their tumors. Here we explore how transcriptomics data can be utilized as an input of game-theoretical models for predicting evolutionary response to irradiation in patient-derived glioblastoma organoids. For that purpose, we utilize both supervised and unsupervised machine learning methods to identify relevant cancer cell types and how their proportions change over time in the organoids. We then fit these proportions to the replicator dynamics, the most common evolutionary game dynamics, to predict both transient evolutionary dynamics and evolutionary stable strategy (ESS) cell proportions. Our predictions in glioblastoma organoids suggest that hypoxia is the most important factor in identifying short-term response to irradiation, while this seems much less relevant for the long-term response corresponding to the ESSs. Further, we conclude that supervised methods are the best way to estimate cancer evolutionary dynamics when therapy resistance is a qualitative evolutionary trait. We believe that our methodology can help in designing better therapies through testing evolutionary responses in patient-derived organoids, while in parallel the ecological response can be tracked through serum biomarkers and imaging in the corresponding patients.

cancer biology↗

bioRxiv2021

Improving mathematical models of cancer by including resistance to therapy: a study in non-small cell lung cancer

We examined a dataset of 590 Non-Small Cell Lung Cancer patients treated with either chemotherapy or immunotherapy using a game-theoretic model that includes both the evolution of therapy resistance and a cost of resistance. We tested whether the game-theoretic model provides a better fit than classical mathematical models of population growth (exponential, logistic, classic Bertalanffy, general Bertalanffy, Gompertz, general Gompertz). To our knowledge, this is the first time a large clinical patient cohort (as opposed to only in-vitro data) has been used to apply a game-theoretic cancer model. The game-theoretic model provided a better fit to the tumor dynamics of the 590 Non-Small Cell Lung Cancer patients than any of the non-evolutionary population growth models. This was not simply due to having more parameters in the game-theoretic model. The game-theoretic model was seemingly able to fit more accurately patients whose tumor burden exhibit a U-shaped trajectory over time. We explained how this game-theoretic model provides predictions of future tumor growth based on just a few initial measurements. Using the estimates for treatment-specific parameters, we then explored alternative treatment protocols and their expected impact on tumor growth and patient outcome. As such, the model could possibly be used to suggest patient-specific optimal treatment regimens with the goal of minimizing final tumor burden. Therapeutic protocols based on game-theoretic modeling can help to predict tumor growth, and could potentially improve patient outcome in the future. The model invites evolutionary therapies that anticipate and steer the evolution of therapy resistance.

cancer biology↗

bioRxiv2021

On stability of the Darwinian dynamics

Here we analyze Darwinian dynamics of cancer introduced in [1], extended by including a competition matrix, and evaluate (i) when the eco-evolutionary equilibrium is positive and (ii) when the eco-evolutionary equilibrium is asymptotically stable.

cancer biology↗

bioRxiv2021

Female choice can explain the fertilization pattern in oaks

We extend a two-step lottery model of Craft et al. to test the hypothesis that oak trees pursue a form of within-flower female choice to increase the diversity of fathers. Oak trees produce six ovules per flower while maturing just one acorn. When assuming a random ovule selection - which is a natural assumption in the absence of other hypotheses - observed fertilization patterns in oaks cannot be explained: long-distance fertilization is unusually common, even as nearby oak trees may be absent as pollen donors. Our model demonstrates how producing multiple ovules per flower permits selection for rare, distant fathers. The number of ovules per flower that maximizes paternal diversity increases with the number of trees. We introduce a cost function for ovule production for which six ovules per flower balance these costs with the benefits of diversifying fathers. Using data from two published field studies, 7 of 8 investigated maternal oaks had actual paternal diversity indices (average diversity index of 15.42) that fit the female choice hypothesis (estimated diversity of 14.66) significantly better than assuming a random selection from the six available ovules (estimated diversity of 7.649). A third field study permitted us to compare paternity by distance classes for two maternal trees. Both fit the female choice model better than random ovule selection.

ecology↗

bioRxiv2021

Classical Mathematical Models for Prediction of Response to Chemotherapy and Immunotherapy

Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest textbook models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume measurements of patients undergoing chemotherapy or cancer immunotherapy for solid tumors. We used a large dataset of 1472 patients with three or more measurements per target lesion, of which 652 patients had six or more data points. We show that the early treatment response shows only moderate correlation with the final treatment response, demonstrating the need for nuanced models. We then perform a head-to-head comparison of six classical models which are widely used in the field: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. Several models provide a good fit to tumor volume measurements, with the Gompertz model providing the best balance between goodness of fit and number of parameters. Similarly, when fitting to early treatment data, the general Bertalanffy and Gompertz models yield the lowest mean absolute error to forecasted data, indicating that these models could potentially be effective at predicting treatment outcome. In summary, we provide a quantitative benchmark for classical textbook models and state-of-the art models of human tumor growth. We publicly release an anonymized version of our original data, providing the first benchmark set of human tumor growth data for evaluation of mathematical models. Author SummaryMathematical oncology uses quantitative models for prediction of tumor growth and treatment response. The theoretical foundation of mathematical oncology is provided by six classical mathematical models: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. These models have been introduced decades ago, have been used in thousands of scientific articles and are part of textbooks and curricula in mathematical oncology. However, these models have not been systematically tested in clinical data from actual patients. In this study, we have collected quantitative tumor volume measurements from thousands of patients in five large clinical trials of cancer immunotherapy. We use this dataset to systematically investigate how accurately mathematical models can describe tumor growth, showing that there are pronounced differences between models. In addition, we show that two of these models can predict tumor response to immunotherapy and chemotherapy at later time points when trained on early tumor growth dynamics. Thus, our article closes a conceptual gap in the literature and at the same time provides a simple tool to predict response to chemotherapy and immunotherapy on the level of individual patients.

cancer biology↗

bioRxiv2021

Is the Success of Adaptive Therapy in Metastatic Castrate Resistant Prostate Cancer Influenced by Cell-Type-Dependent Production of Prostate Specific Antigen?

Prostate-specific antigen (PSA) is the most common serum marker for prostate cancer. It is used to detect prostate cancer, to assess responses to treatment and recently even to determine when to switch treatment on and off in adaptive therapy protocols. However, the correlation between PSA and tumor volume is poorly understood. There is empirical evidence that some cancer cell types produce more PSA than others. Still, recent mathematical cancer models assume either that all cell types contribute equally to PSA levels, or that only specific subpopulations produce PSA at a fixed rate. Here, we compare time to competitive release of the PSA-based adaptive therapy protocol by Zhang et al. with that of the standard of care based on continuous maximum tolerable dose under different assumptions on PSA production. In particular, we assume that androgen dependent, androgen producing, and androgen independent cells may contribute to the PSA production to different extents. Our results show that, regardless the assumption on how much each type contributes to PSA production, the time to competitive release is always longer under adaptive therapy than under the standard of care. However, in some cases, e.g., if the androgen-independent cells are the only PSA producers, adaptive therapy protocol by Zhang et al. cannot be applied, because the PSA value never reaches half of its initial size and therefore therapy is never discontinued. Furthermore, we observe that in the adaptive therapy protocol, the number of treatment cycles and their length strongly depend on the assumptions about the PSA contribution of the three types. Our results support the belief that a better understanding of patient-specific PSA dynamics will lead to more successful adaptive therapies.

cancer biology↗

bioRxiv2021

Coordination games in cancer

We propose a model of cancer initiation and progression where tumor growth is modulated by an evolutionary coordination game. Evolutionary games of cancer are widely used to model frequency-dependent cell interactions with the most studied games being the Prisoners Dilemma and public goods games. Coordination games, by their more obscure and less evocative nature, are left understudied, despite the fact that, as we argue, they offer great potential in understanding and treating cancer. In this paper we present the conditions under which coordination games between cancer cells evolve, we propose aspects of cancer that can be modeled as results of coordination games, and explore the ways through which coordination games of cancer can be exploited for therapy.

cancer biology↗

bioRxiv2019

Non-Equilibrial Evolutionary Dynamics in Undersaturated Communities

A.The concept of the evolutionary stable strategy (ESS) has been fundamental to the development of evolutionary game theory. It represents an equilibrial evolutionary state in which no rare invader can grow in population size. With additional work, the ESS concept has been formalized and united with other stability concepts such as convergent stability, neighborhood invasion stability, and mutual invisibility. Other work on evolutionary models, however, shows the possibility of unstable and/or non-equilibrial dynamics such as limit cycles and evolutionary suicide. Such "pathologies" remain outside of a well-defined context, especially the currently defined stability concepts of evolutionary games. Ripa et al. (2009) offer a possible reconciliation between work on non-equilibrial dynamics and the ESS concept. They noticed that the systems they analyzed show non-equilibrial dynamics when under-saturated and "far" from the ESS and that getting "closer" to the ESS through the addition of more species stabilized their systems. To that end, we analyzed three models of evolution, two predator-prey models and one competition model of evolutionary suicide, to see how the degree of saturation affects the stability of the system. In the predator-prey models, stability is linked to the degree of saturation. Specifically, a fully saturated community will only show stable dynamics, and unstable dynamics occur only when the community is under-saturated. With the competition model, we demonstrate it to be permanently under-saturated, likely showing such extreme dynamics for this reason. Though not a general proof, our analysis of the models provide evidence of the link between community saturation and evolutionary dynamics. Our results offer a possible placement of these evolutionary "pathologies" into a wider framework. In addition, the results concur with previous results showing greater evolutionary response to less biodiversity and clarifies the effect of extrinsic vs. intrinsic non-equilibrial evolutionary dynamics on a community.

evolutionary biology↗