Modeling mammary organogenesis from biological first principles: Cells and their physical constraints

Mathematical Modeling in the Study of Organisms and Their Parts

Mathematical modeling is a very powerful tool to understand natural phenomena. Such a tool carries its own assumptions and should always be used critically. In this chapter we highlight the key ingredients and steps of modeling and focus on their biological interpretation. Particularly, we discuss the role of theoretical principles in writing models. We also highlight the meaning and interpretation of equations. The main aim of this chapter is to facilitate the interaction between biologists and mathematical modelers. We focus on the case of cell proliferation and motility in the context of multicellular organisms.

Modeling Mammary Organogenesis from Biological First Principles: A Systems Biology Approach

Stromal-epithelial interactions mediate mammary gland development and the formation and progression of breast cancer. To study these interactions in vitro, 3D models are essential. We have successfully developed novel 3D in vitro models that allow the formation of mammary gland structures closely resembling those found in vivo and that respond to the hormonal cues that regulate mammary gland morphogenesis and function. Due to their simplicity when compared to in vivo studies, and to their accessibility to visualization in real time, these models are well suited to conceptual and mathematical modeling.

Reimagining Cancer: Moving from the Cellular to the Tissue Level

The current universally accepted explanation of cancer origin and behavior, the somatic mutation theory, is cell-centered and rooted in perturbation of gene function independent of the external environmental context. However, tumors consist of various epithelial and stromal cell populations temporally and spatially organized into an integrated neoplastic community, and they can have properties similar to normal tissues. Accordingly, we review specific normal cellular and tissue traits and behaviors with adaptive temporal and spatial self-organization that result in ordered patterns and structures. A few recent theories have described these tissue-level cancer behaviors, invoking a conceptual shift from the cellular level and highlighting the need for methodologic approaches based on the analysis of complex systems. We propose extending the analytical approach of regulatory networks to the tissue level and introduce the concept of "cancer attractors." These concepts require reevaluation of cancer imaging and investigational approaches and challenge the traditional reductionist approach of cancer molecular biology.

A computational model of organism development and carcinogenesis resulting from cells' bioelectric properties and communication

A sound theory of biological organization is clearly missing for a better interpretation of observational results and faster progress in understanding life complexity. The availability of such a theory represents a fundamental progress in explaining both normal and pathological organism development. The present work introduces a computational implementation of some principles of a theory of organism development, namely that the default state of cells is proliferation and motility, and includes the principle of variation and organization by closure of constraints. In the present model, the bioelectric context of cells and tissue is the field responsible for organization, as it regulates cell proliferation and the level of communication driving the system's evolution. Starting from a depolarized (proliferative) cell, the organism grows to a certain size, limited by the increasingly polarized state after successive proliferation events. The system reaches homeostasis, with a depolarized core (proliferative cells) surrounded by a rim of polarized cells (non-proliferative in this condition). This state is resilient to cell death (random or due to injure) and to limited depolarization (potentially carcinogenic) events. Carcinogenesis is introduced through a localized event (a spot of depolarized cells) or by random depolarization of cells in the tissue, which returns cells to their initial proliferative state. The normalization of the bioelectric condition can reverse this out-of-equilibrium state to a new homeostatic one. This simplified model of embryogenesis, tissue organization and carcinogenesis, based on non-excitable cells' bioelectric properties, can be made more realistic with the introduction of other components, like biochemical fields and mechanical interactions, which are fundamental for a more faithful representation of reality. However, even a simple model can give insight for new approaches in complex systems and suggest new experimental tests, focused in its predictions and interpreted under a new paradigm.

Soft Statistical Mechanics for Biology

The multilevel organization of nature is self-evident: proteins do interact among them to give rise to an organized metabolism and the same hierarchical organization is in action for gene expression, tissue and organ architectures, and ecological systems.The still more common approach to such state of affairs is to think that causally relevant events originate from the lower level in the form of perturbations, that climb up the hierarchy reaching the ultimate layer of macroscopic behavior (e.g., causing a specific disease). Such rigid bottom-up causative model is unable to offer realistic models of many biological phenomena.Complex network approach allows to uncover the nature of multilevel organization, but in order to operationally define the organization principles of biological systems, we need to go further and complement network approach with sensible measures of order and organization. These measures, while keeping their original physical meaning, must not impose theoretical premises not verifiable in biological frameworks. We will show here how relatively simple and largely hypothesis-free multidimensional statistics tools can satisfactorily meet these criteria.

Mechanical Pressure Driving Proteoglycan Expression in Mammographic Density: a Self-perpetuating Cycle?

Regions of high mammographic density (MD) in the breast are characterised by a proteoglycan (PG)-rich fibrous stroma, where PGs mediate aligned collagen fibrils to control tissue stiffness and hence the response to mechanical forces. Literature is accumulating to support the notion that mechanical stiffness may drive PG synthesis in the breast contributing to MD. We review emerging patterns in MD and other biological settings, of a positive feedback cycle of force promoting PG synthesis, such as in articular cartilage, due to increased pressure on weight bearing joints. Furthermore, we present evidence to suggest a pro-tumorigenic effect of increased mechanical force on epithelial cells in contexts where PG-mediated, aligned collagen fibrous tissue abounds, with implications for breast cancer development attributable to high MD. Finally, we summarise means through which this positive feedback mechanism of PG synthesis may be intercepted to reduce mechanical force within tissues and thus reduce disease burden.

Matrix Composition Modulates Vitamin D3's Effects on 3D Collagen Fiber Organization by MCF10A Cells

Vitamin D3 (vitD3) has been implicated in various cellular functions affecting multiple tissue types. Epidemiological and laboratory studies suggest that vitD3 may be effective as a preventive or therapeutic option for breast cancer. However, randomized clinical trials have yet to confirm these suggestions. Breast neoplasias can arise from developmental alterations; based on this evidence, we seek to understand vitD3's role in normal breast development, particularly its role in epithelial morphogenetic processes such as ductal elongation, branching, and alveolar formation. These processes require extensive changes in the extracellular microenvironment, such as collagen fiber organization, and are largely influenced by hormones. Here, we build upon our past work to shed light on calcitriol's effects on collagen fiber organization by breast epithelial cells, and how such effects are modulated by extracellular matrix composition. We embedded MCF10A normal human breast epithelial cells in two different matrices-collagen type I and collagen type I + 10% Matrigel; treatment with calcitriol resulted in flatter epithelial structures. Next, using two-photon microscopy, we examined changes in collagen fiber organization and corresponding changes in epithelial structures. Applying a novel three-dimensional (3D) image analysis method, we show that increasing doses of calcitriol result in denser collagen fiber bundles in the localized area surrounding the epithelial structures, and that these bundles are aligned in a more parallel direction to epithelial structures when exposed to the highest vitD3 dose. Changed patterns in fiber organization may explain the flattening of epithelial structures; in turn, changes in biophysical forces in the matrix abutting these structures may be responsible for changes in the referred patterns. Addition of 10% Matrigel dampened the effects of calcitriol on both epithelial morphogenesis and fiber organization. Overall, we report novel functions of calcitriol in the breast epithelium and add to the growing body of evidence documenting how hormones affect biophysical processes.

TMT based deep proteome analysis of buffalo mammary epithelial cells and identification of novel protein signatures during lactogenic differentiation

The lactating mammary gland harbours numerous matured alveoli with their lumen surrounded by differentiated mammary epithelial cells (MECs), which are exclusively involved in milk synthesis and secretion. Buffalo (Bubalus bubalis) is the second major milk-producing animal, and its physiology is different from cattle. The complete protein machinery involved in MECs differentiation is still not defined in ruminants, in particular, buffalo. Therefore, we have studied the differential expression of regulated proteins in the in vitro grown buffalo MECs (BuMECs) at different time points (on 3, 6, 12, and 15 days) of their differentiation in the presence of lactogenic hormones. TMT-based MS analysis identified 4,934 proteins; of them, 681 were differentially expressed proteins (DEPs). The principal component analysis suggested a highly heterogeneous expression of DEPs at the four-time points of hormone treatment, with most of them (307) attained the highest expression on 12 days. Bioinformatics analysis revealed the association of DEPs with 24 KEGG pathways. We observed few new proteins, namely ABCA13, IVL, VPS37, CZIB, RFX7, Rab5, TTLL12, SMEK1, GDI2, and TMEM131 in BuMECs. The function of one of the highly upregulated proteins, namely involucrin in the differentiation of BuMECs was confirmed based on biochemical inhibition assay. The results further conclude that the proteins with higher abundance can be considered as the potential biomarkers for differentiation, and they may have a significant association with the lactation process in buffalo too. The proteome dataset obtained can be used to understand the species-specific variations among other lactating animals.

The cancer puzzle: Welcome to organicism

During the fifty years since President Nixon declared the "War on Cancer", those inside and outside the cancer community have witnessed the systematic moving of the goalposts attitude to accommodate evidence into an inadequate theory, that is, the Somatic Mutation Theory (SMT). This sorry state promoted a renewable yearly promise that at the end of the next 10-year period the promises uttered in 1971 would become reality. Each failure triggered calls to do more of the same research under the same theory, routinely using more and more sophisticated technology. Meanwhile, in the last few years, an unambiguous general consensus has emerged acknowledging that this overall long, intensive effort has failed, and that it is likely that the solution to the cancer problem resides elsewhere, namely, in alternative theoretical principles of biology. In this essay we concentrate, first, on the big picture, from the philosophical stance (reductionism versus organicism) to the need to adopt rigorous theories. From this novel perspective we conceptualize cancer as a disease of tissue organization akin to development gone awry. Finally, having identified both a promising stance and a useful theory, i.e., the tissue organization field theory (TOFT), we call for abandoning the SMT and for adopting the more promising TOFT.

Forecasting sensitive targets of the kynurenine pathway in pancreatic adenocarcinoma using mathematical modeling

In this study, a new mathematical model was established and validated to forecast and define sensitive targets in the kynurenine pathway (Kynp) in pancreatic adenocarcinoma (PDAC). Using the Panc-1 cell line, genetic profiles of Kynp molecules were tested. qPCR data were implemented in the algorithm programming (fmincon and lsqnonlin function) to estimate 35 parameters of Kynp variables by Matlab 2017b. All tested parameters were defined as non-negative and bounded. Then, based on experimental data, the function of the fmincon equation was employed to estimate the approximate range of each parameter. These calculations were confirmed by qPCR and Western blot. The correlation coefficient (R) between model simulation and experimental data (72 hours, in intervals of 6 hours) of every variable was >0.988. The analysis of reliability and predictive accuracy depending on qPCR and Western blot data showed high predictive accuracy of the model; R was >0.988. Using the model calculations, kynurenine (x3, a6), GPR35 (x4, a8), NF-kβp105 (x7, a16), and NF-kβp65 (x8, a18) were recognized as sensitive targets in the Kynp. These predicted targets were confirmed by testing gene and protein expression responses. Therefore, this study provides new interdisciplinary evidence for Kynp-sensitive targets in the treatment of PDAC.

From Wingspread to CLARITY: a personal trajectory

In the three decades since endocrine disruption was conceptualized at the Wingspread Conference, we have witnessed the growth of this multidisciplinary field and the accumulation of evidence showing the deleterious health effects of endocrine-disrupting chemicals. It is only within the past decade that, albeit slowly, some changes regarding regulatory measures have taken place. In this Perspective, we address some historical points regarding the advent of the endocrine disruption field and the conceptual changes that endocrine disruption brought about. We also provide our personal recollection of the events triggered by our serendipitous discovery of oestrogenic activity in plastic, a founder event in the field of endocrine disruption. This recollection ends with the CLARITY study as an example of a discordance between 'science for its own sake' and 'regulatory science' and leads us to offer a perspective that could be summarized by the motto attributed to Ludwig Boltzmann: "Nothing is more practical than a good theory".

The Quest for System-Theoretical Medicine in the COVID-19 Era

Precision medicine and molecular systems medicine (MSM) are highly utilized and successful approaches to improve understanding, diagnosis, and treatment of many diseases from bench-to-bedside. Especially in the COVID-19 pandemic, molecular techniques and biotechnological innovation have proven to be of utmost importance for rapid developments in disease diagnostics and treatment, including DNA and RNA sequencing technology, treatment with drugs and natural products and vaccine development. The COVID-19 crisis, however, has also demonstrated the need for systemic thinking and transdisciplinarity and the limits of MSM: the neglect of the bio-psycho-social systemic nature of humans and their context as the object of individual therapeutic and population-oriented interventions. COVID-19 illustrates how a medical problem requires a transdisciplinary approach in epidemiology, pathology, internal medicine, public health, environmental medicine, and socio-economic modeling. Regarding the need for conceptual integration of these different kinds of knowledge we suggest the application of general system theory (GST). This approach endorses an organism-centered view on health and disease, which according to Ludwig von Bertalanffy who was the founder of GST, we call Organismal Systems Medicine (OSM). We argue that systems science offers wider applications in the field of pathology and can contribute to an integrative systems medicine by (i) integration of evidence across functional and structural differentially scaled subsystems, (ii) conceptualization of complex multilevel systems, and (iii) suggesting mechanisms and non-linear relationships underlying the observed phenomena. We underline these points with a proposal on multi-level systems pathology including neurophysiology, endocrinology, immune system, genetics, and general metabolism. An integration of these areas is necessary to understand excess mortality rates and polypharmacological treatments. In the pandemic era this multi-level systems pathology is most important to assess potential vaccines, their effectiveness, short-, and long-time adverse effects. We further argue that these conceptual frameworks are not only valid in the COVID-19 era but also important to be integrated in a medicinal curriculum.

Information, programme, signal: dead metaphors that negate the agency of organisms

The metaphorical adoption of the concepts of information, program and signal introduced into biology the logic and implicit causal structure of the mathematical theories of information; this is inimical to biology. In turn, those metaphors have hindered the development of a theory of organisms by transferring the agency of organisms to natural selection and to DNA. Moreover, those metaphors introduced into biology the dualism software-hardware and a Laplacian causal structure. Instead, we propose to uphold the agency of the living by adopting three foundational principles for a theory of organisms: namely, 1) the principle of biological inertia (i.e., the default state of cells is proliferation and motility), 2) the principle of variation, and 3) the principle of organization.

Complexity in Biological Organization: Deconstruction (and Subsequent Restating) of Key Concepts

The “magic” word complexity evokes a multitude of meanings that obscure its real sense. Here we try and generate a bottom-up reconstruction of the deep sense of complexity by looking at the convergence of different features shared by complex systems. We specifically focus on complexity in biology but stressing the similarities with analogous features encountered in inanimate and artefactual systems in order to track an integrative path toward a new “mainstream” of science overcoming the actual fragmentation of scientific culture.

Cancer associated fibroblast: Mediators of tumorigenesis

It is well accepted that the tumor microenvironment plays a pivotal role in cancer onset, development, and progression. The majority of clinical interventions are designed to target either cancer or stroma cells. These emphases have been directed by one of two prevailing theories in the field, the Somatic Mutation Theory and the Tissue Organization Field Theory, which represent two seemingly opposing concepts. This review proposes that the two theories are mutually inclusive and should be concurrently considered for cancer treatments. Specifically, this review discusses the dynamic and reciprocal processes between stromal cells and extracellular matrices, using pancreatic cancer as an example, to demonstrate the inclusivity of the theories. Furthermore, this review highlights the functions of cancer associated fibroblasts, which represent the major stromal cell type, as important mediators of the known cancer hallmarks that the two theories attempt to explain.

Over a century of cancer research: Inconvenient truths and promising leads

Despite over a century of intensive efforts, the great gains promised by the War on Cancer nearly 50 years ago have not materialized. Since 1999, we have analyzed the lack of progress in explaining and "curing" cancer by examining the merits of the premises that determine how cancer is understood and treated. Our ongoing critical analyses have aimed at clarifying the sources of misunderstandings at the root of the cancer puzzle while providing a plausible and comprehensive biomedical perspective as well as a new theory of carcinogenesis that is compatible with evolutionary theory. In this essay, we explain how this new theory, the tissue organization field theory (TOFT), can help chart a path to progress for cancer researchers by explaining features of cancer that remain unexplainable from the perspective of the still hegemonic somatic mutation theory (SMT) and its variants. Of equal significance, the premises underlying the TOFT offer new perspectives on basic biological phenomena.

Glycemia Regulation: From Feedback Loops to Organizational Closure

Endocrinologists apply the idea of feedback loops to explain how hormones regulate certain bodily functions such as glucose metabolism. In particular, feedback loops focus on the maintenance of the plasma concentrations of glucose within a narrow range. Here, we put forward a different, organicist perspective on the endocrine regulation of glycaemia, by relying on the pivotal concept of closure of constraints. From this perspective, biological systems are understood as organized ones, which means that they are constituted of a set of mutually dependent functional structures acting as constraints, whose maintenance depends on their reciprocal interactions. Closure refers specifically to the mutual dependence among functional constraints in an organism. We show that, when compared to feedback loops, organizational closure can generate much richer descriptions of the processes and constraints at play in the metabolism and regulation of glycaemia, by making explicit the different hierarchical orders involved. We expect that the proposed theoretical framework will open the way to the construction of original mathematical models, which would provide a better understanding of endocrine regulation from an organicist perspective.

Phenotypic transitions enacted by simulated microgravity do not alter coherence in gene transcription profile

Cells in simulated microgravity undergo a reversible morphology switch, causing the appearance of two distinct phenotypes. Despite the dramatic splitting into an adherent-fusiform and a floating-spherical population, when looking at the gene-expression phase space, cell transition ends up in a largely invariant gene transcription profile characterized by only mild modifications in the respective Pearson's correlation coefficients. Functional changes among the different phenotypes emerging in simulated microgravity using random positioning machine are adaptive modifications-as cells promptly recover their native phenotype when placed again into normal gravity-and do not alter the internal gene coherence. However, biophysical constraints are required to drive phenotypic commitment in an appropriate way, compatible with physiological requirements, given that absence of gravity foster cells to oscillate between different attractor states, thus preventing them to acquire a exclusive phenotype. This is a proof-of-concept of the adaptive properties of gene-expression networks supporting very different phenotypes by coordinated 'profile preserving' modifications.

Understanding Multicellularity: The Functional Organization of the Intercellular Space

The aim of this paper is to provide a theoretical framework to understand how multicellular systems realize functionally integrated physiological entities by organizing their intercellular space. From a perspective centered on physiology and integration, biological systems are often characterized as organized in such a way that they realize metabolic self-production and self-maintenance. The existence and activity of their components rely on the network they realize and on the continuous management of the exchange of matter and energy with their environment. One of the virtues of the organismic approach focused on organization is that it can provide an understanding of how biological systems are functionally integrated into coherent wholes. Organismic frameworks have been primarily developed by focusing on unicellular life. Multicellularity, however, presents additional challenges to our understanding of biological systems, related to how cells are capable to live together in higher-order entities, in such a way that some of their features and behaviors are constrained and controlled by the system they realize. Whereas most accounts of multicellularity focus on cell differentiation and increase in size as the main elements to understand biological systems at this level of organization, we argue that these factors are insufficient to provide an understanding of how cells are physically and functionally integrated in a coherent system. In this paper, we provide a new theoretical framework to understand multicellularity, capable to overcome these issues. Our thesis is that one of the fundamental theoretical principles to understand multicellularity, which is missing or underdeveloped in current accounts, is the functional organization of the intercellular space. In our view, the capability to be organized in space plays a central role in this context, as it enables (and allows to exploit all the implications of) cell differentiation and increase in size, and even specialized functions such as immunity. We argue that the extracellular matrix plays a crucial active role in this respect, as an evolutionary ancient and specific (non-cellular) control subsystem that contributes as a key actor to the functional specification of the multicellular space and to modulate cell fate and behavior. We also analyze how multicellular systems exert control upon internal movement and communication. Finally, we show how the organization of space is involved in some of the failures of multicellular organization, such as aging and cancer.

Vitamin D3 constrains estrogen's effects and influences mammary epithelial organization in 3D cultures

Vitamin D3 (vitD3) and its active metabolite, calcitriol (1,25-(OH)₂D₃), affect multiple tissue types by interacting with the vitamin D receptor (VDR). Although vitD3 deficiency has been correlated with increased incidence of breast cancer and less favorable outcomes, randomized clinical trials have yet to provide conclusive evidence on the efficacy of vitD3 in preventing or treating breast cancer. Additionally, experimental studies are needed to assess the biological plausibility of these outcomes. The mammary gland of VDR KO mice shows a florid phenotype revealing alterations of developmental processes that are largely regulated by mammotropic hormones. However, most research conducted on vitD3's effects used 2D cell cultures and supra-physiological doses of vitD3, conditions that spare the microenvironment in which morphogenesis takes place. We investigated the role of vitD3 in mammary epithelial morphogenesis using two 3D culture models. VitD3 interfered with estrogen's actions on T47D human breast cancer cells in 3D differently at different doses, and recapitulated what is observed in vivo. Also, vitD3 can act autonomously and affected the organization of estrogen-insensitive MCF10A cells in 3D collagen matrix by influencing collagen fiber organization. Thus, vitD3 modulates mammary tissue organization independent of its effects on cell proliferation.

From single cells to tissue self-organization

Self-organization is a process by which interacting cells organize and arrange themselves in higher order structures and patterns. To achieve this, cells must have molecular mechanisms to sense their complex local environment and interpret it to respond accordingly. A combination of cell-intrinsic and cell-extrinsic cues are decoded by the single cells dictating their behaviour, their differentiation and symmetry-breaking potential driving development, tissue remodeling and regenerative processes. A unifying property of these self-organized pattern-forming systems is the importance of fluctuations, cell-to-cell variability, or noise. Cell-to-cell variability is an inherent and emergent property of populations of cells that maximize the population performance instead of the individual cell, providing tissues the flexibility to develop and maintain homeostasis in diverse environments. In this review, we will explore the role of self-organization and cell-to-cell variability as fundamental properties of multicellularity-and the requisite of single-cell resolution for its understanding. Moreover, we will analyze how single cells generate emergent multicellular dynamics observed at the tissue level 'travelling' across different scales: spatial, temporal and functional.

3D organizational mapping of collagen fibers elucidates matrix remodeling in a hormone-sensitive 3D breast tissue model

Hormones play an important role in normal and diseased breast tissue development. However, they can also disrupt cell-matrix interactions and their role in extracellular matrix reorganization during epithelial morphogenesis remains poorly understood, partly due to a lack of sensitive approaches for matrix characterization. Here, we assess the hormonal regulation of matrix reorganization in a three-dimensional (3D) breast tissue culture model using a novel metric, i.e., 3D directional variance, to characterize the 3D organization of collagen fibers visualized via high-resolution, second harmonic generation imaging. This metric enables resolving and quantifying patterns of spatial organization throughout the matrix surrounding epithelial structures treated with 17β-estradiol (E2) alone, and E2 in combination with either promegestone, a progestogen, or prolactin. Addition of promegestone results in the most disorganized fibers, while the E2 alone treatment leads to the most organized ones. Location-dependent organization mapping indicates that only the prolactin treatment leads to significant heterogeneities in the regional organization of collagen fibers, with higher levels of alignment observed at the end of the elongated epithelial structures. The observed collagen organization patterns for all groups persist for tens of micrometers. In addition, a comparison between 3D directional variance and typical 2D analysis approaches reveals an improved sensitivity of the 3D metric to identify organizational heterogeneities and differences among treatment groups. These results demonstrate that 3D directional variance is sensitive to subtle changes in the extracellular micro-environment and has the potential to elucidate reciprocal cell-matrix interactions in the context of numerous applications involving the study of normal and diseased tissue morphogenesis.

Characterization of MCF-12A cell phenotype, response to estrogens, and growth in 3D

Background

Three-dimensional cultures of mammary epithelial cells allow for biologically-relevant studies of the development of the mammary gland in rodents and humans under normal and pathological conditions, like carcinogenesis. Under these conditions, mammotropic hormones play significant roles in tissue morphogenesis. Therefore, a system that recreates the normal, hormonally responsive epithelium would be a valuable tool to study the normal state and its transition to carcinogenesis. MCF-12A cells have been claimed to be non-tumorigenic mammary epithelial cells with reported sensitivity to estrogens. In this study, we aimed at characterizing MCF-12A cells for use in a hormone-responsive 3D culture system to determine their usefulness as a tool to identify normal and abnormal microenvironmental cues.

Methods

MCF-12A cells were single-cell cloned in order to investigate their heterogeneous makeup. The parental cells were then treated with estradiol to investigate proliferative and transcriptional responses through the estrogen receptor alpha. Finally, parental cells and epithelial-like cell-derived clones were seeded in rat-tail collagen I to profile the morphogenesis of multicellular 3D structures. The resultant structures were then analyzed using unsupervised morphometric analysis.

Results

MCF-12A cells consist of epithelial-like colonies which shed elongated, freely growing cells on the colony's edges. The cells express E-cadherin as well as mesenchymal vimentin but do not express markers associated with myoepithelial cells or fibroblasts. Treatment with estradiol does not affect either the proliferation rate or the induction of gene expression in MCF-12A cells. Parental MCF-12A cells form acini, solid spheres and elongated branching ducts when grown in rat-tail collagen type I matrix, the geometries and distribution of which are altered following the removal of fibroblast-like cells.

Conclusions

MCF-12A cells are a heterogeneous pseudo-epithelial cell line capable of forming a variety of multicellular structures in 3D culture. We found no indication that the cells display estrogen-responsive characteristics, thus refuting previous studies which reported estrogen responsiveness. We report that MCF-12A cells are not suited for use in studies in which differential behaviors of "normal" and "cancerous" estrogen-responsive cells are to be compared.

A Primer on Mathematical Modeling in the Study of Organisms and Their Parts

Mathematical modeling is a very powerful tool for understanding natural phenomena. Such a tool carries its own assumptions and should always be used critically. In this chapter, we highlight the key ingredients and steps of modeling and focus on their biological interpretation. In particular, we discuss the role of theoretical principles in writing models. We also highlight the meaning and interpretation of equations. The main aim of this chapter is to facilitate the interaction between biologists and mathematical modelers. We focus on the case of cell proliferation and motility in the context of multicellular organisms.

An Integrative Approach Toward Biology, Organisms, and Cancer

Over the last two decades, we have challenged the hegemony of the somatic mutation theory of carcinogenesis (SMT) based on the lack of theoretical coherence of the premises adopted by its followers. We offered instead a theoretical alternative, the tissue organization field theory (TOFT), that is based on the premises that cancer is a tissue-based disease and that proliferation and motility is the default state of all cells. We went on to use a theory-neutral experimental protocol that simultaneously tested the TOFT and the SMT. The results of this test favored adopting the TOFT and rejecting the SMT. Recently, an analysis of the differences between the Physics of the inanimate and that of the living matter has led us to propose principles for the construction of a much needed theory of organisms. The three biological principles are (a) a default state, (b) a principle of variation, and (c) one of organization. The TOFT, defined as "development gone awry," fits well within the principles that we propose for a theory of organisms. This radical conceptual change opened up the possibility of anchoring mathematical modeling on genuine biological principles. By identifying constraints to the default state, multilevel biomechanical explanations become as legitimate as the molecular ones on which other modelers that adopt the SMT rely. Expanding research based on the premises of our theory of organisms will enrich a comprehensive understanding of normal development and of the one that goes awry.

Marriages of mathematics and physics: A challenge for biology

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of "geometric judgments" from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) "space" should be revisited for the purposes of life sciences.

The biological default state of cell proliferation with variation and motility, a fundamental principle for a theory of organisms

The principle of inertia is central to the modern scientific revolution. By postulating this principle Galileo at once identified a pertinent physical observable (momentum) and a conservation law (momentum conservation). He then could scientifically analyze what modifies inertial movement: gravitation and friction. Inertia, the default state in mechanics, represented a major theoretical commitment: there is no need to explain uniform rectilinear motion, rather, there is a need to explain departures from it. By analogy, we propose a biological default state of proliferation with variation and motility. From this theoretical commitment, what requires explanation is proliferative quiescence, lack of variation, lack of movement. That proliferation is the default state is axiomatic for biologists studying unicellular organisms. Moreover, it is implied in Darwin's "descent with modification". Although a "default state" is a theoretical construct and a limit case that does not need to be instantiated, conditions that closely resemble unrestrained cell proliferation are readily obtained experimentally. We will illustrate theoretical and experimental consequences of applying and of ignoring this principle.

Toward a theory of organisms: Three founding principles in search of a useful integration

Organisms, be they uni- or multi-cellular, are agents capable of creating their own norms; they are continuously harmonizing their ability to create novelty and stability, that is, they combine plasticity with robustness. Here we articulate the three principles for a theory of organisms, namely: the default state of proliferation with variation and motility, the principle of variation and the principle of organization. These principles profoundly change both biological observables and their determination with respect to the theoretical framework of physical theories. This radical change opens up the possibility of anchoring mathematical modeling in biologically proper principles.

Theoretical principles for biology: Variation

Darwin introduced the concept that random variation generates new living forms. In this paper, we elaborate on Darwin's notion of random variation to propose that biological variation should be given the status of a fundamental theoretical principle in biology. We state that biological objects such as organisms are specific objects. Specific objects are special in that they are qualitatively different from each other. They can undergo unpredictable qualitative changes, some of which are not defined before they happen. We express the principle of variation in terms of symmetry changes, where symmetries underlie the theoretical determination of the object. We contrast the biological situation with the physical situation, where objects are generic (that is, different objects can be assumed to be identical) and evolve in well-defined state spaces. We derive several implications of the principle of variation, in particular, biological objects show randomness, historicity and contextuality. We elaborate on the articulation between this principle and the two other principles proposed in this special issue: the principle of default state and the principle of organization.

Theoretical principles for biology: Organization

In the search of a theory of biological organisms, we propose to adopt organization as a theoretical principle. Organization constitutes an overarching hypothesis that frames the intelligibility of biological objects, by characterizing their relevant aspects. After a succinct historical survey on the understanding of organization in the organicist tradition, we offer a specific characterization in terms of closure of constraints. We then discuss some implications of the adoption of organization as a principle and, in particular, we focus on how it fosters an original approach to biological stability, as well as and its interplay with variation.

Carcinogenesis explained within the context of a theory of organisms

For a century, the somatic mutation theory (SMT) has been the prevalent theory to explain carcinogenesis. According to the SMT, cancer is a cellular problem, and thus, the level of organization where it should be studied is the cellular level. Additionally, the SMT proposes that cancer is a problem of the control of cell proliferation and assumes that proliferative quiescence is the default state of cells in metazoa. In 1999, a competing theory, the tissue organization field theory (TOFT), was proposed. In contraposition to the SMT, the TOFT posits that cancer is a tissue-based disease whereby carcinogens (directly) and mutations in the germ-line (indirectly) alter the normal interactions between the diverse components of an organ, such as the stroma and its adjacent epithelium. The TOFT explicitly acknowledges that the default state of all cells is proliferation with variation and motility. When taking into consideration the principle of organization, we posit that carcinogenesis can be explained as a relational problem whereby release of the constraints created by cell interactions and the physical forces generated by cellular agency lead cells within a tissue to regain their default state of proliferation with variation and motility. Within this perspective, what matters both in morphogenesis and carcinogenesis is not only molecules, but also biophysical forces generated by cells and tissues. Herein, we describe how the principles for a theory of organisms apply to the TOFT and thus to the study of carcinogenesis.