A quantitative theoretical model for the development of malignancy in ductal carcinoma in situ

Tumor growth and calcification in evolving microenvironmental geometries

In this paper, we apply the diffuse domain framework developed in Chen and Lowengrub (Tumor growth in complex, evolving microenvironmental geometries: A diffuse domain approach, J. Theor. Biol. 361 (2014) 14-30) to study the effects of a deformable basement membrane (BM) on the growth of a tumor in a confined, ductal geometry, such as ductal carcinoma in situ (DCIS). We use a continuum model of tumor microcalcification and investigate the tumor extent beyond the microcalcification. In order to solve the governing equations efficiently, we develop a stable nonlinear multigrid finite difference method. Two dimensional simulations are performed where the adhesion between tumor cells and the basement membrane is varied. Additional simulations considering the variation of duct radius and membrane stiffness are also conducted. The results demonstrate that enhanced membrane deformability promotes tumor growth and tumor calcification. When the duct radius is small, the cell-BM adhesion is weak or when the membrane is slightly deformed, the mammographic and pathologic tumor extents are linearly correlated, as predicted by Macklin et al. (J. Theor. Biol. 301 (2012) 122-140) using an agent-based model that does not account for the deformability of the basement membrane and the active forces that the membrane imparts on the tumor cells. Interestingly, we predict that when the duct radius is large, there is strong cell-BM adhesion or the membrane is highly deformed, the extents of the mammographic and pathologic tumors are instead quadratically correlated. The simulations can help surgeons to measure DCIS surgical margins while removing less non-cancerous tissue, and can improve targeting of intra- and post-operative radiotherapy.

Integrating Models to Quantify Environment-Mediated Drug Resistance

Drug resistance is the single most important driver of cancer treatment failure for modern targeted therapies, and the dialog between tumor and stroma has been shown to modulate the response to molecularly targeted therapies through proliferative and survival signaling. In this work, we investigate interactions between a growing tumor and its surrounding stroma and their role in facilitating the emergence of drug resistance. We used mathematical modeling as a theoretical framework to bridge between experimental models and scales, with the aim of separating intrinsic and extrinsic components of resistance in BRAF-mutated melanoma; the model describes tumor-stroma dynamics both with and without treatment. Integration of experimental data into our model revealed significant variation in either the intensity of stromal promotion or intrinsic tissue carrying capacity across animal replicates. Cancer Res; 77(19); 5409-18. ©2017 AACR.

Evolutionary game theory: cells as players

In two papers we review game theory applications in biology below the level of cognitive living beings. It can be seen that evolution and natural selection replace the rationality of the actors appropriately. Even in these micro worlds, competing situations and cooperative relationships can be found and modeled by evolutionary game theory. Also those units of the lowest levels of life show different strategies for different environmental situations or different partners. We give a wide overview of evolutionary game theory applications to microscopic units. In this first review situations on the cellular level are tackled. In particular metabolic problems are discussed, such as ATP-producing pathways, secretion of public goods and cross-feeding. Further topics are cyclic competition among more than two partners, intra- and inter-cellular signalling, the struggle between pathogens and the immune system, and the interactions of cancer cells. Moreover, we introduce the theoretical basics to encourage scientists to investigate problems in cell biology and molecular biology by evolutionary game theory.

Microenvironmental acidosis in carcinogenesis and metastases: new strategies in prevention and therapy

Much effort is currently devoted to developing patient-specific cancer therapy based on molecular characterization of tumors. In particular, this approach seeks to identify driver mutations that can be blocked through small molecular inhibitors. However, this approach is limited by extensive intratumoral genetic heterogeneity, and, not surprisingly, even dramatic initial responses are typically of limited duration as resistant tumor clones rapidly emerge and proliferate. We propose an alternative approach based on observations that while tumor evolution produces genetic divergence, it is also associated with striking phenotypic convergence that loosely correspond to the well-known cancer “hallmarks”. These convergent properties can be described as driver phenotypes and may be more consistently and robustly expressed than genetic targets. To this purpose, it is necessary to identify strategies that are critical for cancer progression and metastases, and it is likely that these driver phenotypes will be closely related to cancer “hallmarks”. It appears that an antiacidic approach, by targetting a driver phenotype in tumors, may be thought as a future strategy against tumors in either preventing the occurrence of cancer or treating tumor patients with multiple aims, including the improvement of efficacy of existing therapies, possibly reducing their systemic side effects, and controlling tumor growth, progression, and metastasis. This may be achieved with existing molecules such as proton pump inhibitors (PPIs) and buffers such as sodium bicarbonate, citrate, or TRIS.

Extracellular vesicles as a platform for 'liquid biopsy' in glioblastoma patients

Extracellular vesicles (EVs) are cell-secreted vesicles that range from 30-2000 nm in size. These vesicles are secreted by both normal and neoplastic cells. Physiologically, EVs serve multiple critical biologic functions, including cellular remodeling, intracellular communication, modulation of the tumor microenvironment and regulation of immune function. Because EVs contain genetic and proteomic contents that reflect the cell of origin, it is possible to detect tumor-specific material in EVs secreted by cancer cells. Importantly, EVs secreted by cancer cells transgress anatomic compartments and can be detected in the blood, cerebrospinal fluid, and other biofluids of cancer patients. In this context, there is a growing interest in analyzing EVs from the biofluid of cancer patients as a means of disease diagnosis and therapeutic monitoring. In this article, we review the development of EVs as a diagnostic platform for the most common form of brain cancer, glioblastoma, discuss potential clinical translational opportunities and identify the central challenges associated with future clinical applications.

Heterogeneity and proliferation of invasive cancer subclones in game theory models of the Warburg effect

OBJECTIVES

The Warburg effect, a switch from aerobic energy production to anaerobic glycolysis, promotes tumour proliferation and motility by inducing acidification of the tumour microenvironment. Therapies that reduce acidity could impair tumour growth and invasiveness. I analysed the dynamics of cell proliferation and of resistance to therapies that target acidity, in a population of cells, under the Warburg effect.

MATERIALS AND METHODS

The dynamics of mutant cells with increased glycolysis and motility has been assessed in a multi-player game with collective interactions in the framework of evolutionary game theory. Perturbations of the level of acidity in the microenvironment have been used to simulate the effect of therapies that target glycolysis.

RESULTS

The non-linear effects of glycolysis induce frequency-dependent clonal selection leading to coexistence of glycolytic and non-glycolytic cells within a tumour. Mutants with increased motility can invade such a polymorphic population and spread within the tumour. While reducing acidity may produce a sudden reduction in tumour cell proliferation, frequency-dependent selection enables it to adapt to the new conditions and can enable the tumour to restore its original levels of growth and invasiveness.

CONCLUSIONS

The acidity produced by glycolysis acts as a non-linear public good that leads to coexistence of cells with high and low glycolysis within the tumour. Such a heterogeneous population can easily adapt to changes in acidity. Therapies that target acidity can only be effective in the long term if the cost of glycolysis is high, that is, under non-limiting oxygen concentrations. Their efficacy, therefore, is reduced when combined with therapies that impair angiogenesis.

Enrichment map profiling of the cancer invasion front suggests regulation of colorectal cancer progression by the bone morphogenetic protein antagonist, gremlin-1

The cancer invasion front (CIF), a spatially-recognized area due to the frequent presence of peritumoral desmoplastic reaction, represents a cancer site where many hallmarks of cancer metastasis occur. It is now strongly suggested that the desmoplastic microenvironment holds crucial information for determining tumor development and progression. Despite extensive research on tumor-host cell interactions at CIFs, the exact paracrine molecular network that is hardwired into the proteome of the stromal and cancer subpopulations remains partially understood. Here, we interrogated the signaling pathways and the molecular functional signatures across the proteome of a desmoplastic coculture model system of colorectal cancer progression. We discovered a group of bone morphogenetic protein (BMP) antagonists that coordinates major biological programs in CIFs, including cell proliferation, invasion, migration and differentiation processes. Using a mathematical model of cancer cell progression, coupled to in vitro cell migration assays, we demonstrated that the prominent BMP antagonist gremlin-1 (GREM1) may trigger motility of cancer cell cohorts. Our data collectively demonstrate that the desmoplastic CIFs deploy a microenvironmental signature, based on BMP antagonism, in order to regulate the motogenic fates of cancer cell cohorts invading the adjacent stroma.

Automated reconstruction algorithm for identification of 3D architectures of cribriform ductal carcinoma in situ

Ductal carcinoma in situ (DCIS) is a pre-invasive carcinoma of the breast that exhibits several distinct morphologies but the link between morphology and patient outcome is not clear. We hypothesize that different mechanisms of growth may still result in similar 2D morphologies, which may look different in 3D. To elucidate the connection between growth and 3D morphology, we reconstruct the 3D architecture of cribriform DCIS from resected patient material. We produce a fully automated algorithm that aligns, segments, and reconstructs 3D architectures from microscopy images of 2D serial sections from human specimens. The alignment algorithm is based on normalized cross correlation, the segmentation algorithm uses histogram equilization, Otsu's thresholding, and morphology techniques to segment the duct and cribra. The reconstruction method combines these images in 3D. We show that two distinct 3D architectures are indeed found in samples whose 2D histological sections are similarly identified as cribriform DCIS. These differences in architecture support the hypothesis that luminal spaces may form due to different mechanisms, either isolated cell death or merging fronds, leading to the different architectures. We find that out of 15 samples, 6 were found to have 'bubble-like' cribra, 6 were found to have 'tube-like' criba and 3 were 'unknown.' We propose that the 3D architectures found, 'bubbles' and 'tubes', account for some of the heterogeneity of the disease and may be prognostic indicators of different patient outcomes.

Systemic buffers inhibit carcinogenesis in TRAMP mice

PURPOSE

Hypoxia and acidosis develop in in situ tumors as cellular expansion increases the diffusion distance of substrates and metabolites from blood vessels deep to the basement membrane. Prior studies of breast and cervical cancer revealed that cellular adaptation to microenvironmental hypoxia and acidosis is associated with the transition from in situ to invasive cancer. We hypothesized that decreased acidosis in intraductal tumors would alter environmental selection pressures for acid adapted phenotypes and delay or prevent evolution to invasive cancer.

MATERIALS AND METHODS

A total of 37 C57BL/6 TRAMP mice were randomized to a control group or to 1 of 4 treatment groups. In the latter groups 200 mM sodium bicarbonate were added to drinking water starting between ages 4 and 10 weeks.

RESULTS

In all 18 controls prostate cancer developed that was visible on 3-dimensional ultrasound at a mean age of 13 weeks. They died within 52 weeks (median 37). When sodium bicarbonate therapy commenced before age 6 weeks in 10 mice, all reached senescence (age 76 weeks) without radiographic evidence of prostate cancer. Histological sections of the prostates in this cohort showed hyperplasia but no cancer in 70% of mice and minimal well differentiated cancer in the remainder. When therapy commenced after age 6 weeks in 9 mice, prostate cancer development was no different from that in controls.

CONCLUSIONS

Immunohistochemical staining for carbonic anhydrase 9 in regions of ductal hyperplasia showed increased expression in controls vs the early treatment group. Regional pH perturbation in in situ tumors may be a simple, inexpensive and effective cancer prevention strategy.

Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): from microscopic measurements to macroscopic predictions of clinical progression

Ductal carcinoma in situ (DCIS)--a significant precursor to invasive breast cancer--is typically diagnosed as microcalcifications in mammograms. However, the effective use of mammograms and other patient data to plan treatment has been restricted by our limited understanding of DCIS growth and calcification. We develop a mechanistic, agent-based cell model and apply it to DCIS. Cell motion is determined by a balance of biomechanical forces. We use potential functions to model interactions with the basement membrane and amongst cells of unequal size and phenotype. Each cell's phenotype is determined by genomic/proteomic- and microenvironment-dependent stochastic processes. Detailed "sub-models" describe cell volume changes during proliferation and necrosis; we are the first to account for cell calcification. We introduce the first patient-specific calibration method to fully constrain the model based upon clinically-accessible histopathology data. After simulating 45 days of solid-type DCIS with comedonecrosis, the model predicts: necrotic cell lysis acts as a biomechanical stress relief and is responsible for the linear DCIS growth observed in mammography; the rate of DCIS advance varies with the duct radius; the tumour grows 7-10mm per year--consistent with mammographic data; and the mammographic and (post-operative) pathologic sizes are linearly correlated--in quantitative agreement with the clinical literature. Patient histopathology matches the predicted DCIS microstructure: an outer proliferative rim surrounds a stratified necrotic core with nuclear debris on its outer edge and calcification in the centre. This work illustrates that computational modelling can provide new insight on the biophysical underpinnings of cancer. It may 1-day be possible to augment a patient's mammography and other imaging with rigorously-calibrated models that help select optimal surgical margins based upon the patient's histopathologic data.

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.

The interrelating dynamics of hypoxic tumor microenvironments and cancer cell phenotypes in cancer metastasis

The interrelating dynamics of the primary tumor cells and their surrounding microenvironment might determine phenotypic characteristics of disseminated tumor cells and contribute to cancer metastasis. Cytoprotective mechanisms (e.g., energy metabolism control, DNA damage response, global translation control and unfolded protein response) exert selective pressure in the tumor microenvironment. In particular, adaptation to hypoxia is vital for survival of malignant cells in the tumor and at distant sites such as the bone marrow. In addition to the stress response, the ability of tumor cells to undergo certain cellular re-differentiation programmes like the epithelial-mesenchymal transition (EMT), which is linked to cancer stemness, appears to be important for successful cancer cell spread. Here we will discuss the selection pressures that eventually lead to the formation of overt metastases. We will focus the properties of the microenvironment including (i) metabolic and cytoprotective programs that ensure survival of disseminated tumor cells, (ii) blood vessel structure, and (iii) the hypoxia-normoxia switch as well as intrinsic factors affecting the evolvement of novel tumor cell populations.

A multiscale model of the bone marrow and hematopoiesis

The bone marrow is necessary for renewal of all hematopoietic cells and critical for maintenance of a wide range of physiologic functions. Multiple human diseases result from bone marrow dysfunction. It is also the site in which liquid tumors, including leukemia and multiple myeloma, develop as well as a frequent site of metastases. Understanding the complex cellular and microenvironmental interactions that govern normal bone marrow function as well as diseases and cancers of the bone marrow would be a valuable medical advance. Our goal is the development of a spatially-explicit in silico model of the bone marrow to understand both its normal function and the evolutionary dynamics that govern the emergence of bone marrow malignancy. Here we introduce a multiscale computational model of the bone marrow that incorporates three distinct spatial scales, cell, hematopoietic subunit, whole marrow. Our results, using parameter estimates from literature, recapitulates normal bone marrow function and suggest an explanation for the fractal-like structure of trabeculae and sinuses in the marrow, which would be an optimization of the hematopoietic function in order to maximize the number of mature blood cells produced daily within the volumetric restrictions of the marrow.

Hybrid models of tumor growth

Cancer is a complex, multiscale process in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. The multiscale nature of cancer requires mathematical modeling approaches that can handle multiple intracellular and extracellular factors acting on different time and space scales. Hybrid models provide a way to integrate both discrete and continuous variables that are used to represent individual cells and concentration or density fields, respectively. Each discrete cell can also be equipped with submodels that drive cell behavior in response to microenvironmental cues. Moreover, the individual cells can interact with one another to form and act as an integrated tissue. Hybrid models form part of a larger class of individual-based models that can naturally connect with tumor cell biology and allow for the integration of multiple interacting variables both intrinsically and extrinsically and are therefore perfectly suited to a systems biology approach to tumor growth.