Evolution of phenotypic plasticity leads to tumor heterogeneity with implications for therapy.

Cancer is a significant global health issue, with treatment challenges arising from intratumor heterogeneity. This heterogeneity stems mainly from somatic evolution, causing genetic diversity within the tumor, and phenotypic plasticity of tumor cells leading to reversible phenotypic changes. However, the interplay of both factors has not been rigorously investigated. Here, we examine the complex relationship between somatic evolution and phenotypic plasticity, explicitly focusing on the interplay between cell migration and proliferation. This type of phenotypic plasticity is essential in glioblastoma, the most aggressive form of brain tumor. We propose that somatic evolution alters the regulation of phenotypic plasticity in tumor cells, specifically the reaction to changes in the microenvironment. We study this hypothesis using a novel, spatially explicit model that tracks individual cells' phenotypic and genetic states. We assume cells change between migratory and proliferative states controlled by inherited and mutation-driven genotypes and the cells' microenvironment. We observe that cells at the tumor edge evolve to favor migration over proliferation and vice versa in the tumor bulk. Notably, different genetic configurations can result in this pattern of phenotypic heterogeneity. We analytically predict the outcome of the evolutionary process, showing that it depends on the tumor microenvironment. Synthetic tumors display varying levels of genetic and phenotypic heterogeneity, which we show are predictors of tumor recurrence time after treatment. Interestingly, higher phenotypic heterogeneity predicts poor treatment outcomes, unlike genetic heterogeneity. Our research offers a novel explanation for heterogeneous patterns of tumor recurrence in glioblastoma patients.

The impact of tumor associated macrophages on tumor biology under the lens of mathematical modelling: A review.

In this article, we review the role of mathematical modelling to elucidate the impact of tumor-associated macrophages (TAMs) in tumor progression and therapy design. We first outline the biology of TAMs, and its current application in tumor therapies, and their experimental methods that provide insights into tumor cell-macrophage interactions. We then focus on the mechanistic mathematical models describing the role of macrophages as drug carriers, the impact of macrophage polarized activation on tumor growth, and the role of tumor microenvironment (TME) parameters on the tumor-macrophage interactions. This review aims to identify the synergies between biological and mathematical approaches that allow us to translate knowledge on fundamental TAMs biology in addressing current clinical challenges.

Understanding fibrosis pathogenesis via modeling macrophage-fibroblast interplay in immune-metabolic context.

Fibrosis is a progressive biological condition, leading to organ dysfunction in various clinical settings. Although fibroblasts and macrophages are known as key cellular players for fibrosis development, a comprehensive functional model that considers their interaction in the metabolic/immunologic context of fibrotic tissue has not been set up. Here we show, by transcriptome-based mathematical modeling in an in vitro system that represents macrophage-fibroblast interplay and reflects the functional effects of inflammation, hypoxia and the adaptive immune context, that irreversible fibrosis development is associated with specific combinations of metabolic and inflammatory cues. The in vitro signatures are in good alignment with transcriptomic profiles generated on laser captured glomeruli and cortical tubule-interstitial area, isolated from human transplanted kidneys with advanced stages of glomerulosclerosis and interstitial fibrosis/tubular atrophy, two clinically relevant conditions associated with organ failure in renal allografts. The model we describe here is validated on tissue based quantitative immune-phenotyping of biopsies from transplanted kidneys, demonstrating its feasibility. We conclude that the combination of in vitro and in silico modeling represents a powerful systems medicine approach to dissect fibrosis pathogenesis, applicable to specific pathological conditions, and develop coordinated targeted approaches.

Roadmap on plasticity and epigenetics in cancer.

The role of plasticity and epigenetics in shaping cancer evolution and response to therapy has taken center stage with recent technological advances including single cell sequencing. This roadmap article is focused on state-of-the-art mathematical and experimental approaches to interrogate plasticity in cancer, and addresses the following themes and questions: is there a formal overarching framework that encompasses both non-genetic plasticity and mutation-driven somatic evolution? How do we measure and model the role of the microenvironment in influencing/controlling non-genetic plasticity? How can we experimentally study non-genetic plasticity? Which mathematical techniques are required or best suited? What are the clinical and practical applications and implications of these concepts?

BIO-LGCA: A cellular automaton modelling class for analysing collective cell migration.

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics-understood as population behaviour arising from the interplay of the constituting discrete cells-can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments.

Improving personalized tumor growth predictions using a Bayesian combination of mechanistic modeling and machine learning.

Background: In clinical practice, a plethora of medical examinations are conducted to assess the state of a patient's pathology producing a variety of clinical data. However, investigation of these data faces two major challenges. Firstly, we lack the knowledge of the mechanisms involved in regulating these data variables, and secondly, data collection is sparse in time since it relies on patient's clinical presentation. The former limits the predictive accuracy of clinical outcomes for any mechanistic model. The latter restrains any machine learning algorithm to accurately infer the corresponding disease dynamics. Methods: Here, we propose a novel method, based on the Bayesian coupling of mathematical modeling and machine learning, aiming at improving individualized predictions by addressing the aforementioned challenges. Results: We evaluate the proposed method on a synthetic dataset for brain tumor growth and analyze its performance in predicting two relevant clinical outputs. The method results in improved predictions in almost all simulated patients, especially for those with a late clinical presentation (>95% patients show improvements compared to standard mathematical modeling). In addition, we test the methodology in two additional settings dealing with real patient cohorts. In both cases, namely cancer growth in chronic lymphocytic leukemia and ovarian cancer, predictions show excellent agreement with reported clinical outcomes (around 60% reduction of mean squared error). Conclusions: We show that the combination of machine learning and mathematical modeling approaches can lead to accurate predictions of clinical outputs in the context of data sparsity and limited knowledge of disease mechanisms.

Mechanical Control of Cell Proliferation Increases Resistance to Chemotherapeutic Agents.

While many cellular mechanisms leading to chemotherapeutic resistance have been identified, there is an increasing realization that tumor-stroma interactions also play an important role. In particular, mechanical alterations are inherent to solid cancer progression and profoundly impact cell physiology. Here, we explore the influence of compressive stress on the efficacy of chemotherapeutics in pancreatic cancer spheroids. We find that increased compressive stress leads to decreased drug efficacy. Theoretical modeling and experiments suggest that mechanical stress decreases cell proliferation which in turn reduces the efficacy of chemotherapeutics that target proliferating cells. Our work highlights a mechanical form of drug resistance and suggests new strategies for therapy.

Modelling collective cell motion: are on- and off-lattice models equivalent?

Biological processes, such as embryonic development, wound repair and cancer invasion, or bacterial swarming and fruiting body formation, involve collective motion of cells as a coordinated group. Collective cell motion of eukaryotic cells often includes interactions that result in polar alignment of cell velocities, while bacterial patterns typically show features of apolar velocity alignment. For analysing the population-scale effects of these different alignment mechanisms, various on- and off-lattice agent-based models have been introduced. However, discriminating model-specific artefacts from general features of collective cell motion is challenging. In this work, we focus on equivalence criteria at the population level to compare on- and off-lattice models. In particular, we define prototypic off- and on-lattice models of polar and apolar alignment, and show how to obtain an on-lattice from an off-lattice model of velocity alignment. By characterizing the behaviour and dynamical description of collective migration models at the macroscopic level, we suggest the type of phase transitions and possible patterns in the approximative macroscopic partial differential equation descriptions as informative equivalence criteria between on- and off-lattice models. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Investigating the Physical Effects in Bacterial Therapies for Avascular Tumors.

Tumor-targeting bacteria elicit anticancer effects by infiltrating hypoxic regions, releasing toxic agents and inducing immune responses. Although current research has largely focused on the influence of chemical and immunological aspects on the mechanisms of bacterial therapy, the impact of physical effects is still elusive. Here, we propose a mathematical model for the anti-tumor activity of bacteria in avascular tumors that takes into account the relevant chemo-mechanical effects. We consider a time-dependent administration of bacteria and analyze the impact of bacterial chemotaxis and killing rate. We show that active bacterial migration toward tumor hypoxic regions provides optimal infiltration and that high killing rates combined with high chemotactic values provide the smallest tumor volumes at the end of the treatment. We highlight the emergence of steady states in which a small population of bacteria is able to constrain tumor growth. Finally, we show that bacteria treatment works best in the case of tumors with high cellular proliferation and low oxygen consumption.

On the Immunological Consequences of Conventionally Fractionated Radiotherapy.

Emerging evidence demonstrates that radiotherapy induces immunogenic death on tumor cells that emit immunostimulating signals resulting in tumor-specific immune responses. However, the impact of tumor features and microenvironmental factors on the efficacy of radiation-induced immunity remains to be elucidated. Herein, we use a calibrated model of tumor-effector cell interactions to investigate the potential benefits and immunological consequences of radiotherapy. Simulations analysis suggests that radiotherapy success depends on the functional tumor vascularity extent and reveals that the pre-treatment tumor size is not a consistent determinant of treatment outcomes. The one-size-fits-all approach of conventionally fractionated radiotherapy is predicted to result in some overtreated patients. In addition, model simulations also suggest that an arbitrary increase in treatment duration does not necessarily result in better tumor control. This study highlights the potential benefits of tumor-immune ecosystem profiling during treatment planning to better harness the immunogenic potential of radiotherapy.

A minimal modeling framework of radiation and immune system synergy to assist radiotherapy planning.

Recent evidence indicates the ability of radiotherapy to induce local and systemic tumor-specific immune responses as a result of immunogenic cell death. However, fractionation regimes routinely used in clinical practice typically ignore the synergy between radiation and the immune system, and instead attempt to completely eradicate tumors by the direct lethal effect of radiation on cancer cells. This paradigm is expected to change in the near future due to the potential benefits of considering radiation-induced antitumor immunity during treatment planning. Towards this goal, we propose a minimal modeling framework based on key aspects of the tumor-immune system interplay to simulate the effects of radiation on tumors and the immunological consequences of radiotherapy. The impacts of tumor-associated vasculature and intratumoral oxygen-mediated heterogeneity on treatment outcomes are ininvestigated. The model provides estimates of the minimum radiation doses required for tumor eradication given a certain number of treatment fractions. Moreover, estimates of treatment duration for disease control given predetermined fractional radiation doses can be also obtained. Although theoretical in nature, this study motivates the development and establishment of immune-based decision-support tools in radiotherapy planning.

On the Impact of Chemo-Mechanically Induced Phenotypic Transitions in Gliomas.

Tumor microenvironment is a critical player in glioma progression, and novel therapies for its targeting have been recently proposed. In particular, stress-alleviation strategies act on the tumor by reducing its stiffness, decreasing solid stresses and improving blood perfusion. However, these microenvironmental changes trigger chemo-mechanically induced cellular phenotypic transitions whose impact on therapy outcomes is not completely understood. In this work we analyze the effects of mechanical compression on migration and proliferation of glioma cells. We derive a mathematical model of glioma progression focusing on cellular phenotypic plasticity. Our results reveal a trade-off between tumor infiltration and cellular content as a consequence of stress-alleviation approaches. We discuss how these novel findings increase the current understanding of glioma/microenvironment interactions and can contribute to new strategies for improved therapeutic outcomes.

Multidimensional Analysis Integrating Human T-Cell Signatures in Lymphatic Tissues with Sex of Humanized Mice for Prediction of Responses after Dendritic Cell Immunization.

Mice transplanted with human cord blood-derived hematopoietic stem cells (HSCs) became a powerful experimental tool for studying the heterogeneity of human immune reconstitution and immune responses in vivo. Yet, analyses of human T cell maturation in humanized models have been hampered by an overall low immune reactivity and lack of methods to define predictive markers of responsiveness. Long-lived human lentiviral induced dendritic cells expressing the cytomegalovirus pp65 protein (iDCpp65) promoted the development of pp65-specific human CD8+ T cell responses in NOD.Cg-Rag1 tm1Mom -Il2rγ tm1Wj humanized mice through the presentation of immune-dominant antigenic epitopes (signal 1), expression of co-stimulatory molecules (signal 2), and inflammatory cytokines (signal 3). We exploited this validated system to evaluate the effects of mouse sex in the dynamics of T cell homing and maturation status in thymus, blood, bone marrow, spleen, and lymph nodes. Statistical analyses of cell relative frequencies and absolute numbers demonstrated higher CD8+ memory T cell reactivity in spleen and lymph nodes of immunized female mice. In order to understand to which extent the multidimensional relation between organ-specific markers predicted the immunization status, the immunophenotypic profiles of individual mice were used to train an artificial neural network designed to discriminate immunized and non-immunized mice. The highest accuracy of immune reactivity prediction could be obtained from lymph node markers of female mice (77.3%). Principal component analyses further identified clusters of markers best suited to describe the heterogeneity of immunization responses in vivo. A correlation analysis of these markers reflected a tissue-specific impact of immunization. This allowed for an organ-resolved characterization of the immunization status of individual mice based on the identified set of markers. This new modality of multidimensional analyses can be used as a framework for defining minimal but predictive signatures of human immune responses in mice and suggests critical markers to characterize responses to immunization after HSC transplantation.

Image analysis of immune cell patterns in the human mammary gland during the menstrual cycle refines lymphocytic lobulitis.

PURPOSE: To improve microscopic evaluation of immune cells relevant in breast cancer oncoimmunology, we aim at distinguishing normal infiltration patterns from lymphocytic lobulitis by advanced image analysis. We consider potential immune cell variations due to the menstrual cycle and oral contraceptives in non-neoplastic mammary gland tissue. METHODS: Lymphocyte and macrophage distributions were analyzed in the anatomical context of the resting mammary gland in immunohistochemically stained digital whole slide images obtained from 53 reduction mammoplasty specimens. Our image analysis workflow included automated regions of interest detection, immune cell recognition, and co-registration of regions of interest. RESULTS: In normal lobular epithelium, seven CD8[Formula: see text] lymphocytes per 100 epithelial cells were present on average and about 70% of this T-lymphocyte population was lined up along the basal cell layer in close proximity to the epithelium. The density of CD8[Formula: see text] T-cell was 1.6 fold higher in the luteal than in the follicular phase in spontaneous menstrual cycles and 1.4 fold increased under the influence of oral contraceptives, and not co-localized with epithelial proliferation. CD4[Formula: see text] T-cells were infrequent. Abundant CD163[Formula: see text] macrophages were widely spread, including the interstitial compartment, with minor variation during the menstrual cycle. CONCLUSIONS: Spatial patterns of different immune cell subtypes determine the range of normal, as opposed to inflammatory conditions of the breast tissue microenvironment. Advanced image analysis enables quantification of hormonal effects, refines lymphocytic lobulitis, and shows potential for comprehensive biopsy evaluation in oncoimmunology.

Therapeutic Potential of Bacteria against Solid Tumors.

Intentional bacterial infections can produce efficacious antitumor responses in mice, rats, dogs, and humans. However, low overall success rates and intense side effects prevent such approaches from being employed clinically. In this work, we titered bacteria and/or the proinflammatory cytokine TNFα in a set of established murine models of cancer. To interpret the experiments conducted, we considered and calibrated a tumor-effector cell recruitment model under the influence of functional tumor-associated vasculature. In this model, bacterial infections and TNFα enhanced immune activity and altered vascularization in the tumor bed. Information to predict bacterial therapy outcomes was provided by pretreatment tumor size and the underlying immune recruitment dynamics. Notably, increasing bacterial loads did not necessarily produce better long-term tumor control, suggesting that tumor sizes affected optimal bacterial loads. Short-term treatment responses were favored by high concentrations of effector cells postinjection, such as induced by higher bacterial loads, but in the longer term did not correlate with an effective restoration of immune surveillance. Overall, our findings suggested that a combination of intermediate bacterial loads with low levels TNFα administration could enable more favorable outcomes elicited by bacterial infections in tumor-bearing subjects. Cancer Res; 77(7); 1553-63. ©2017 AACR.

In silico analysis of cell cycle synchronisation effects in radiotherapy of tumour spheroids.

Tumour cells show a varying susceptibility to radiation damage as a function of the current cell cycle phase. While this sensitivity is averaged out in an unperturbed tumour due to unsynchronised cell cycle progression, external stimuli such as radiation or drug doses can induce a resynchronisation of the cell cycle and consequently induce a collective development of radiosensitivity in tumours. Although this effect has been regularly described in experiments it is currently not exploited in clinical practice and thus a large potential for optimisation is missed. We present an agent-based model for three-dimensional tumour spheroid growth which has been combined with an irradiation damage and kinetics model. We predict the dynamic response of the overall tumour radiosensitivity to delivered radiation doses and describe corresponding time windows of increased or decreased radiation sensitivity. The degree of cell cycle resynchronisation in response to radiation delivery was identified as a main determinant of the transient periods of low and high radiosensitivity enhancement. A range of selected clinical fractionation schemes is examined and new triggered schedules are tested which aim to maximise the effect of the radiation-induced sensitivity enhancement. We find that the cell cycle resynchronisation can yield a strong increase in therapy effectiveness, if employed correctly. While the individual timing of sensitive periods will depend on the exact cell and radiation types, enhancement is a universal effect which is present in every tumour and accordingly should be the target of experimental investigation. Experimental observables which can be assessed non-invasively and with high spatio-temporal resolution have to be connected to the radiosensitivity enhancement in order to allow for a possible tumour-specific design of highly efficient treatment schedules based on induced cell cycle synchronisation.

Integrative physical oncology.

Cancer is arguably the ultimate complex biological system. Solid tumors are microstructured soft matter that evolves as a consequence of spatio-temporal events at the intracellular (e.g., signaling pathways, macromolecular trafficking), intercellular (e.g., cell-cell adhesion/communication), and tissue (e.g., cell-extracellular matrix interactions, mechanical forces) scales. To gain insight, tumor and developmental biologists have gathered a wealth of molecular, cellular, and genetic data, including immunohistochemical measurements of cell type-specific division and death rates, lineage tracing, and gain-of-function/loss-of-function mutational analyses. These data are empirically extrapolated to a diagnosis/prognosis of tissue-scale behavior, e.g., for clinical decision. Integrative physical oncology (IPO) is the science that develops physically consistent mathematical approaches to address the significant challenge of bridging the nano (nm)-micro (µm) to macro (mm, cm) scales with respect to tumor development and progression. In the current literature, such approaches are referred to as multiscale modeling. In the present article, we attempt to assess recent modeling approaches on each separate scale and critically evaluate the current 'hybrid-multiscale' models used to investigate tumor growth in the context of brain and breast cancers. Finally, we provide our perspective on the further development and the impact of IPO.

Mathematical Oncology: How Are the Mathematical and Physical Sciences Contributing to the War on Breast Cancer?

Mathematical modeling has recently been added as a tool in the fight against cancer. The field of mathematical oncology has received great attention and increased enormously, but over-optimistic estimations about its ability have created unrealistic expectations. We present a critical appraisal of the current state of mathematical models of cancer. Although the field is still expanding and useful clinical applications may occur in the future, managing over-expectation requires the proposal of alternative directions for mathematical modeling. Here, we propose two main avenues for this modeling: 1) the identification of the elementary biophysical laws of cancer development, and 2) the development of a multiscale mathematical theory as the framework for models predictive of tumor growth. Finally, we suggest how these new directions could contribute to addressing the current challenges of understanding breast cancer growth and metastasis.