Mathematical models of the transitions between endocrine therapy responsive and resistant states in breast cancer

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Towards early diagnosis of Alzheimer's disease: advances in immune-related blood biomarkers and computational approaches

Alzheimer's disease has an increasing prevalence in the population world-wide, yet current diagnostic methods based on recommended biomarkers are only available in specialized clinics. Due to these circumstances, Alzheimer's disease is usually diagnosed late, which contrasts with the currently available treatment options that are only effective for patients at an early stage. Blood-based biomarkers could fill in the gap of easily accessible and low-cost methods for early diagnosis of the disease. In particular, immune-based blood-biomarkers might be a promising option, given the recently discovered cross-talk of immune cells of the central nervous system with those in the peripheral immune system. Here, we give a background on recent advances in research on brain-immune system cross-talk in Alzheimer's disease and review machine learning approaches, which can combine multiple biomarkers with further information (e.g. age, sex, APOE genotype) into predictive models supporting an earlier diagnosis. In addition, mechanistic modeling approaches, such as agent-based modeling open the possibility to model and analyze cell dynamics over time. This review aims to provide an overview of the current state of immune-system related blood-based biomarkers and their potential for the early diagnosis of Alzheimer's disease.

Modeling of Mouse Experiments Suggests that Optimal Anti-Hormonal Treatment for Breast Cancer is Diet-Dependent

Estrogen receptor positive breast cancer is frequently treated with anti-hormonal treatment such as aromatase inhibitors (AI). Interestingly, a high body mass index has been shown to have a negative impact on AI efficacy, most likely due to disturbances in steroid metabolism and adipokine production. Here, we propose a mathematical model based on a system of ordinary differential equations to investigate the effect of high-fat diet on tumor growth. We inform the model with data from mouse experiments, where the animals are fed with high-fat or control (normal) diet. By incorporating AI treatment with drug resistance into the model and by solving optimal control problems we found differential responses for control and high-fat diet. To the best of our knowledge, this is the first attempt to model optimal anti-hormonal treatment for breast cancer in the presence of drug resistance. Our results underline the importance of considering high-fat diet and obesity as factors influencing clinical outcomes during anti-hormonal therapies in breast cancer patients.

Can Systems Biology Advance Clinical Precision Oncology?

Precision oncology is perceived as a way forward to treat individual cancer patients. However, knowing particular cancer mutations is not enough for optimal therapeutic treatment, because cancer genotype-phenotype relationships are nonlinear and dynamic. Systems biology studies the biological processes at the systems' level, using an array of techniques, ranging from statistical methods to network reconstruction and analysis, to mathematical modeling. Its goal is to reconstruct the complex and often counterintuitive dynamic behavior of biological systems and quantitatively predict their responses to environmental perturbations. In this paper, we review the impact of systems biology on precision oncology. We show examples of how the analysis of signal transduction networks allows to dissect resistance to targeted therapies and inform the choice of combinations of targeted drugs based on tumor molecular alterations. Patient-specific biomarkers based on dynamical models of signaling networks can have a greater prognostic value than conventional biomarkers. These examples support systems biology models as valuable tools to advance clinical and translational oncological research.

Optimal solution of the fractional order breast cancer competition model

In this article, a fractional order breast cancer competition model (F-BCCM) under the Caputo fractional derivative is analyzed. A new set of basis functions, namely the generalized shifted Legendre polynomials, is proposed to deal with the solutions of F-BCCM. The F-BCCM describes the dynamics involving a variety of cancer factors, such as the stem, tumor and healthy cells, as well as the effects of excess estrogen and the body's natural immune response on the cell populations. After combining the operational matrices with the Lagrange multipliers technique we obtain an optimization method for solving the F-BCCM whose convergence is investigated. Several examples show that a few number of basis functions lead to the satisfactory results. In fact, numerical experiments not only confirm the accuracy but also the practicability and computational efficiency of the devised technique.

Personalized Medicine for Neuroblastoma: Moving from Static Genotypes to Dynamic Simulations of Drug Response

High-risk neuroblastoma is an aggressive childhood cancer that is characterized by high rates of chemoresistance and frequent metastatic relapse. A number of studies have characterized the genetic and epigenetic landscape of neuroblastoma, but due to a generally low mutational burden and paucity of actionable mutations, there are few options for applying a comprehensive personalized medicine approach through the use of targeted therapies. Therefore, the use of multi-agent chemotherapy remains the current standard of care for neuroblastoma, which also conceptually limits the opportunities for developing an effective and widely applicable personalized medicine approach for this disease. However, in this review we outline potential approaches for tailoring the use of chemotherapy agents to the specific molecular characteristics of individual tumours by performing patient-specific simulations of drug-induced apoptotic signalling. By incorporating multiple layers of information about tumour-specific aberrations, including expression as well as mutation data, these models have the potential to rationalize the selection of chemotherapeutics contained within multi-agent treatment regimens and ensure the optimum response is achieved for each individual patient.

Quantifying the Landscape and Transition Paths for Proliferation-Quiescence Fate Decisions

The cell cycle, essential for biological functions, experiences delicate spatiotemporal regulation. The transition between G1 and S phase, which is called the proliferation–quiescence decision, is critical to the cell cycle. However, the stability and underlying stochastic dynamical mechanisms of the proliferation–quiescence decision have not been fully understood. To quantify the process of the proliferation–quiescence decision, we constructed its underlying landscape based on the relevant gene regulatory network. We identified three attractors on the landscape corresponding to the G0, G1, and S phases, individually, which are supported by single-cell data. By calculating the transition path, which quantifies the potential barrier, we built expression profiles in temporal order for key regulators in different transitions. We propose that the two saddle points on the landscape characterize restriction point (RP) and G1/S checkpoint, respectively, which provides quantitative and physical explanations for the mechanisms of Rb governing the RP while p21 controlling the G1/S checkpoint. We found that Emi1 inhibits the transition from G0 to G1, while Emi1 in a suitable range facilitates the transition from G1 to S. These results are partially consistent with previous studies, which also suggested new roles of Emi1 in the cell cycle. By global sensitivity analysis, we identified some critical regulatory factors influencing the proliferation–quiescence decision. Our work provides a global view of the stochasticity and dynamics in the proliferation–quiescence decision of the cell cycle.

Applications of personalised signalling network models in precision oncology

As our ability to provide in-depth, patient-specific characterisation of the molecular alterations within tumours rapidly improves, it is becoming apparent that new approaches will be required to leverage the power of this data and derive the full benefit for each individual patient. Systems biology approaches are beginning to emerge within this field as a potential method of incorporating large volumes of network level data and distilling a coherent, clinically-relevant prediction of drug response. However, the initial promise of this developing field is yet to be realised. Here we argue that in order to develop these precise models of individual drug response and tailor treatment accordingly, we will need to develop mathematical models capable of capturing both the dynamic nature of drug-response signalling networks and key patient-specific information such as mutation status or expression profiles. We also review the modelling approaches commonly utilised within this field, and outline recent examples of their use in furthering the application of systems biology for a precision medicine approach to cancer treatment.

Disentangling a complex response in cell reprogramming and probing the Waddington landscape by automatic construction of Petri nets

We analyzed the developmental switch to sporulation of a multinucleate Physarum polycephalum plasmodial cell, a complex response to phytochrome photoreceptor activation. Automatic construction of Petri nets representing finite state machines assembled from trajectories of differential gene expression in single cells revealed alternative, genotype-dependent interconnected developmental routes and identified reversible steps, metastable states, commitment points, and subsequent irreversible steps together with molecular signatures associated with cell fate decision and differentiation. Formation of cyclic transits identified by transition invariants in mutants that are locked in a proliferative state is remarkable considering the view that oncogenic alterations may cause the formation of cancer attractors. We conclude that the Petri net approach is useful to probe the Waddington landscape of cellular reprogramming, to disentangle developmental routes for the reconstruction of the gene regulatory network, and to understand how genetic alterations or physiological conditions reshape the landscape eventually creating new basins of attraction. Unraveling the complexity of pathogenesis, disease progression, drug response or the analysis of attractor landscapes in other complex systems of uncertain structure might be additional fields of application.

Exposing the Underlying Relationship of Cancer Metastasis to Metabolism and Epithelial-Mesenchymal Transitions

Cancer is a disease governed by the underlying gene regulatory networks. The hallmarks of cancer have been proposed to characterize the cancerization, e.g., abnormal metabolism, epithelial to mesenchymal transition (EMT), and cancer metastasis. We constructed a metabolism-EMT-metastasis regulatory network and quantified its underlying landscape. We identified four attractors, characterizing epithelial, abnormal metabolic, mesenchymal, and metastatic cell states, respectively. Importantly, we identified an abnormal metabolic state. Based on the transition path theory, we quantified the kinetic transition paths among these different cell states. Our results for landscape and paths indicate that metastasis is a sequential process: cells tend to first change their metabolism, then activate the EMT and eventually reach the metastatic state. This demonstrates the importance of the temporal order for different gene circuits switching on or off during metastatic progression of cancer cells and underlines the cascading regulation of metastasis through an abnormal metabolic intermediate state.

Hybrid modeling frameworks of tumor development and treatment

Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathways, or variable receptor expression; and extrinsic, such as differences in nutrient supply, crosstalk with stromal or immune cells, or variable composition of the surrounding extracellular matrix. Tumors are also characterized by high cellular heterogeneity and dynamically changing tumor microenvironments. The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. Modeling such complex systems and predicting how tumors will respond to therapies require mathematical models that can handle various types of information and combine diverse theoretical methods on multiple temporal and spatial scales, that is, hybrid models. In this update, we discuss the progress that has been achieved during the last 10 years in the area of the hybrid modeling of tumors. The classical definition of hybrid models refers to the coupling of discrete descriptions of cells with continuous descriptions of microenvironmental factors. To reflect on the direction that the modeling field has taken, we propose extending the definition of hybrid models to include of coupling two or more different mathematical frameworks. Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization, fluid dynamics, game theory, and machine learning. All these methods will be illustrated with applications to tumor development and various anticancer treatments.

This article is characterized under:

Analytical and Computational Methods > Computational Methods

Translational, Genomic, and Systems Medicine > Therapeutic Methods

Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

Systems biology: perspectives on multiscale modeling in research on endocrine-related cancers

Drawing on concepts from experimental biology, computer science, informatics, mathematics and statistics, systems biologists integrate data across diverse platforms and scales of time and space to create computational and mathematical models of the integrative, holistic functions of living systems. Endocrine-related cancers are well suited to study from a systems perspective because of the signaling complexities arising from the roles of growth factors, hormones and their receptors as critical regulators of cancer cell biology and from the interactions among cancer cells, normal cells and signaling molecules in the tumor microenvironment. Moreover, growth factors, hormones and their receptors are often effective targets for therapeutic intervention, such as estrogen biosynthesis, estrogen receptors or HER2 in breast cancer and androgen receptors in prostate cancer. Given the complexity underlying the molecular control networks in these cancers, a simple, intuitive understanding of how endocrine-related cancers respond to therapeutic protocols has proved incomplete and unsatisfactory. Systems biology offers an alternative paradigm for understanding these cancers and their treatment. To correctly interpret the results of systems-based studies requires some knowledge of how in silico models are built, and how they are used to describe a system and to predict the effects of perturbations on system function. In this review, we provide a general perspective on the field of cancer systems biology, and we explore some of the advantages, limitations and pitfalls associated with using predictive multiscale modeling to study endocrine-related cancers.

A landscape view on the interplay between EMT and cancer metastasis

The epithelial-mesenchymal transition (EMT) is a basic developmental process that converts epithelial cells to mesenchymal cells. Although EMT might promote cancer metastasis, the molecular mechanisms for it remain to be fully clarified. To address this issue, we constructed an EMT-metastasis gene regulatory network model and quantified the potential landscape of cancer metastasis-promoting system computationally. We identified four steady-state attractors on the landscape, which separately characterize anti-metastatic (A), metastatic (M), and two other intermediate (I1 and I2) cell states. The tetrastable landscape and the existence of intermediate states are consistent with recent single-cell measurements. We identified one of the two intermediate states I1 as the EMT state. From a MAP approach, we found that for metastatic progression cells need to first undergo EMT (enter the I1 state), and then become metastatic (switch from the I1 state to the M state). Specifically, for metastatic progression, EMT genes (such as ZEB) should be activated before metastasis genes (such as BACH1). This suggests that temporal order is important for the activation of cellular programs in biological systems, and provides a possible mechanism of EMT-promoting cancer metastasis. To identify possible therapeutic targets from this landscape view, we performed sensitivity analysis for individual molecular factors, and identified optimal interventions for landscape control. We found that minimizing transition actions more effectively identifies optimal combinations of targets that induce transitions between attractors than single-factor sensitivity analysis. Overall, the landscape view not only suggests that intermediate states increase plasticity during cell fate decisions, providing a possible source for tumor heterogeneity that is critically important in metastatic progress, but also provides a way to identify therapeutic targets for preventing cancer progression.

Identifying the optimal anticancer targets from the landscape of a cancer-immunity interaction network

Cancer immunotherapy, an approach of targeting immune cells to attack tumor cells, has been suggested to be a promising way for cancer treatment recently. However, the successful application of this approach warrants a deeper understanding of the intricate interplay between cancer cells and the immune system. Especially, the mechanisms of immunotherapy remain elusive. In this work, we constructed a cancer-immunity interplay network by incorporating interactions among cancer cells and some representative immune cells, and uncovered the potential landscape of the cancer-immunity network. Three attractors emerge on the landscape, representing the cancer state, the immune state, and the hybrid state, which can correspond to escape, elimination, and equilibrium phases in the immunoediting theory, respectively. We quantified the transition processes between the cancer state and the immune state by calculating transition actions and identifying the corresponding minimum action paths (MAPs) between these two attractors. The transition actions, directly calculated from the high dimensional system, are correlated with the barrier heights from the landscape, but provide a more precise description of the dynamics of a system. By optimizing the transition actions from the cancer state to the immune state, we identified some optimal combinations of anticancer targets. Our combined approach of the landscape and optimization of transition actions offers a framework to study the stochastic dynamics and identify the optimal combination of targets for the cancer-immunity interplay, and can be applied to other cell communication networks or gene regulatory networks.

Phenotypic Plasticity and Cell Fate Decisions in Cancer: Insights from Dynamical Systems Theory

Waddington's epigenetic landscape, a famous metaphor in developmental biology, depicts how a stem cell progresses from an undifferentiated phenotype to a differentiated one. The concept of "landscape" in the context of dynamical systems theory represents a high-dimensional space, in which each cell phenotype is considered as an "attractor" that is determined by interactions between multiple molecular players, and is buffered against environmental fluctuations. In addition, biological noise is thought to play an important role during these cell-fate decisions and in fact controls transitions between different phenotypes. Here, we discuss the phenotypic transitions in cancer from a dynamical systems perspective and invoke the concept of "cancer attractors"-hidden stable states of the underlying regulatory network that are not occupied by normal cells. Phenotypic transitions in cancer occur at varying levels depending on the context. Using epithelial-to-mesenchymal transition (EMT), cancer stem-like properties, metabolic reprogramming and the emergence of therapy resistance as examples, we illustrate how phenotypic plasticity in cancer cells enables them to acquire hybrid phenotypes (such as hybrid epithelial/mesenchymal and hybrid metabolic phenotypes) that tend to be more aggressive and notoriously resilient to therapies such as chemotherapy and androgen-deprivation therapy. Furthermore, we highlight multiple factors that may give rise to phenotypic plasticity in cancer cells, such as (a) multi-stability or oscillatory behaviors governed by underlying regulatory networks involved in cell-fate decisions in cancer cells, and (b) network rewiring due to conformational dynamics of intrinsically disordered proteins (IDPs) that are highly enriched in cancer cells. We conclude by discussing why a therapeutic approach that promotes "recanalization", i.e., the exit from "cancer attractors" and re-entry into "normal attractors", is more likely to succeed rather than a conventional approach that targets individual molecules/pathways.

Integrating network reconstruction with mechanistic modeling to predict cancer therapies

Signal transduction networks are often rewired in cancer cells. Identifying these alterations will enable more effective cancer treatment. We developed a computational framework that can identify, reconstruct, and mechanistically model these rewired networks from noisy and incomplete perturbation response data and then predict potential targets for intervention. As a proof of principle, we analyzed a perturbation data set targeting epidermal growth factor receptor (EGFR) and insulin-like growth factor 1 receptor (IGF1R) pathways in a panel of colorectal cancer cells. Our computational approach predicted cell line-specific network rewiring. In particular, feedback inhibition of insulin receptor substrate 1 (IRS1) by the kinase p70S6K was predicted to confer resistance to EGFR inhibition, suggesting that disrupting this feedback may restore sensitivity to EGFR inhibitors in colorectal cancer cells. We experimentally validated this prediction with colorectal cancer cell lines in culture and in a zebrafish (Danio rerio) xenograft model.

Quantifying the landscape and kinetic paths for epithelial-mesenchymal transition from a core circuit

Epithelial-mesenchymal transition (EMT), as a crucial process in embryonic development and cancer metastasis, has been investigated extensively. However, how to quantify the global stability and transition dynamics for EMT under fluctuations remains to be elucidated. Starting from a core EMT genetic circuit composed of three key proteins or microRNAs (microRNA-200, ZEB and SNAIL), we uncovered the potential landscape for the EMT process. Three attractors emerge from the landscape, which correspond to epithelial, mesenchymal and partial EMT states respectively. Based on the landscape, we analyzed two important quantities of the EMT system: the barrier heights between different basins of attraction that describe the degree of difficulty for EMT or backward transition, and the mean first passage time (MFPT) that characterizes the kinetic transition rate. These quantities can be harnessed as measurements for the stability of cell types and the degree of difficulty of transitions between different cell types. We also calculated the minimum action paths (MAPs) by path integral approaches. The MAP delineates the transition processes between different cell types quantitatively. We propose two different EMT processes: a direct EMT from E to P, and a step-wise EMT going through an intermediate state, depending on different extracellular environments. The landscape and kinetic paths we acquired offer a new physical and quantitative way for understanding the mechanisms of EMT processes, and indicate the possible roles for the intermediate states.

Endocrine resistance in breast cancer--An overview and update

Tumors that express detectable levels of the product of the ESR1 gene (estrogen receptor-α; ERα) represent the single largest molecular subtype of breast cancer. More women eventually die from ERα+ breast cancer than from either HER2+ disease (almost half of which also express ERα) and/or from triple negative breast cancer (ERα-negative, progesterone receptor-negative, and HER2-negative). Antiestrogens and aromatase inhibitors are largely indistinguishable from each other in their abilities to improve overall survival and almost 50% of ERα+ breast cancers will eventually fail one or more of these endocrine interventions. The precise reasons why these therapies fail in ERα+ breast cancer remain largely unknown. Pharmacogenetic explanations for Tamoxifen resistance are controversial. The role of ERα mutations in endocrine resistance remains unclear. Targeting the growth factors and oncogenes most strongly correlated with endocrine resistance has proven mostly disappointing in their abilities to improve overall survival substantially, particularly in the metastatic setting. Nonetheless, there are new concepts in endocrine resistance that integrate molecular signaling, cellular metabolism, and stress responses including endoplasmic reticulum stress and the unfolded protein response (UPR) that provide novel insights and suggest innovative therapeutic targets. Encouraging evidence that drug combinations with CDK4/CDK6 inhibitors can extend recurrence free survival may yet translate to improvements in overall survival. Whether the improvements seen with immunotherapy in other cancers can be achieved in breast cancer remains to be determined, particularly for ERα+ breast cancers. This review explores the basic mechanisms of resistance to endocrine therapies, concluding with some new insights from systems biology approaches further implicating autophagy and the UPR in detail, and a brief discussion of exciting new avenues and future prospects.

The overshoot and phenotypic equilibrium in characterizing cancer dynamics of reversible phenotypic plasticity

The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which extends the cellular hierarchy proposed by the classical cancer stem cell (CSC) theory. Since it is still questionable if the phenotypic plasticity is a crucial improvement to the hierarchical model or just a minor extension to it, it is worthwhile to explore the dynamic behavior characterizing the reversible phenotypic plasticity. In this study we compare the hierarchical model and the reversible model in predicting the cell-state dynamics observed in biological experiments. Our results show that the hierarchical model shows significant disadvantages over the reversible model in describing both long-term stability (phenotypic equilibrium) and short-term transient dynamics (overshoot) in cancer cell populations. In a very specific case in which the total growth of population due to each cell type is identical, the hierarchical model predicts neither phenotypic equilibrium nor overshoot, whereas the reversible model succeeds in predicting both of them. Even though the performance of the hierarchical model can be improved by relaxing the specific assumption, its prediction to the phenotypic equilibrium strongly depends on a precondition that may be unrealistic in biological experiments. Moreover, it still does not show as rich dynamics as the reversible model in capturing the overshoots of both CSCs and non-CSCs. By comparison, it is more likely for the reversible model to correctly predict the stability of the phenotypic mixture and various types of overshoot behavior.

Unfolding the Role of Stress Response Signaling in Endocrine Resistant Breast Cancers

The unfolded protein response (UPR) is an ancient stress response that enables a cell to manage the energetic stress that accompanies protein folding. There has been a significant recent increase in our understanding of the UPR, how it integrates physiological processes within cells, and how this integration can affect cancer cells and cell fate decisions. Recent publications have highlighted the role of UPR signaling components on mediating various cell survival pathways, cellular metabolism and bioenergenics, and autophagy. We address the role of UPR on mediating endocrine therapy resistance and estrogen receptor-positive breast cancer cell survival.