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

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.

Challenges and Opportunities Modeling the Dynamic Tumor Matrisome

We need novel strategies to target the complexity of cancer and, particularly, of metastatic disease. As an example of this complexity, certain tissues are particularly hospitable environments for metastases, whereas others do not contain fertile microenvironments to support cancer cell growth. Continuing evidence that the extracellular matrix (ECM) of tissues is one of a host of factors necessary to support cancer cell growth at both primary and secondary tissue sites is emerging. Research on cancer metastasis has largely been focused on the molecular adaptations of tumor cells in various cytokine and growth factor environments on 2-dimensional tissue culture polystyrene plates. Intravital imaging, conversely, has transformed our ability to watch, in real time, tumor cell invasion, intravasation, extravasation, and growth. Because the interstitial ECM that supports all cells in the tumor microenvironment changes over time scales outside the possible window of typical intravital imaging, bioengineers are continuously developing both simple and sophisticated in vitro controlled environments to study tumor (and other) cell interactions with this matrix. In this perspective, we focus on the cellular unit responsible for upholding the pathologic homeostasis of tumor-bearing organs, cancer-associated fibroblasts (CAFs), and their self-generated ECM. The latter, together with tumoral and other cell secreted factors, constitute the "tumor matrisome". We share the challenges and opportunities for modeling this dynamic CAF/ECM unit, the tools and techniques available, and how the tumor matrisome is remodeled (e.g., via ECM proteases). We posit that increasing information on tumor matrisome dynamics may lead the field to alternative strategies for personalized medicine outside genomics.

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.

Biological constraints as norms in evolution

Biology seems to present local and transitory regularities rather than immutable laws. To account for these historically constituted regularities and to distinguish them from mathematical invariants, Montévil and Mossio (Journal of Theoretical Biology 372:179-191, 2015) have proposed to speak of constraints. In this article we analyse the causal power of these constraints in the evolution of biodiversity, i.e., their positivity, but also the modality of their action on the directions taken by evolution. We argue that to fully account for the causal power of these constraints on evolution, they must be thought of in terms of normativity. In this way, we want to highlight two characteristics of the evolutionary constraints. The first, already emphasised as reported by Gould (The structure of evolutionary theory, Harvard University Press, 2002), is that these constraints are both produced by and producing biological evolution and that this circular causation creates true novelties. The second is that this specific causality, which generates unpredictability in evolution, stems not only from the historicity of biological constraints, but also from their internalisation through the practices of living beings.

Genetic Causation in Complex Regulatory Systems: An Integrative Dynamic Perspective

The logic of genetic discovery has changed little over time, but the focus of biology is shifting from simple genotype-phenotype relationships to complex metabolic, physiological, developmental, and behavioral traits. In light of this, the traditional reductionist view of individual genes as privileged difference-making causes of phenotypes is re-examined. The scope and nature of genetic effects in complex regulatory systems, in which dynamics are driven by regulatory feedback and hierarchical interactions across levels of organization are considered. This review argues that it is appropriate to treat genes as specific actual difference-makers for the molecular regulation of gene expression. However, they are often neither stable, proportional, nor specific as causes of the overall dynamic behavior of regulatory networks. Dynamical models, properly formulated and validated, provide the tools to probe cause-and-effect relationships in complex biological systems, allowing to go beyond the limitations of genetic reductionism to gain an integrative understanding of the causal processes underlying complex phenotypes.

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.

Understanding Drivers of Variation and Predicting Variability Across Levels of Biological Organization

Differences within a biological system are ubiquitous, creating variation in nature. Variation underlies all evolutionary processes and allows persistence and resilience in changing environments; thus, uncovering the drivers of variation is critical. The growing recognition that variation is central to biology presents a timely opportunity for determining unifying principles that drive variation across biological levels of organization. Currently, most studies that consider variation are focused at a single biological level and not integrated into a broader perspective. Here we explain what variation is and how it can be measured. We then discuss the importance of variation in natural systems, and briefly describe the biological research that has focused on variation. We outline some of the barriers and solutions to studying variation and its drivers in biological systems. Finally, we detail the challenges and opportunities that may arise when studying the drivers of variation due to the multi-level nature of biological systems. Examining the drivers of variation will lead to a reintegration of biology. It will further forge interdisciplinary collaborations and open opportunities for training diverse quantitative biologists. We anticipate that these insights will inspire new questions and new analytic tools to study the fundamental questions of what drives variation in biological systems and how variation has shaped life.

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".

On biological individuation

In this paper, we understand the emergence of life as a pure individuation process. Individuation already occurs in open thermodynamics systems near equilibrium. We understand such open systems, as already recursively characterized (R₁) by the relation between their internal properties, and their boundary conditions. Second, global properties emerge in such physical systems. We interpret this change as the fact that their structure is the recursive result of their operations (R₂). We propose a simulation of the emergence of life in Earth by a mapping (R) through which (R₁R₂) operators are applied to themselves, so that R_N = (R₁R₂)_N. We suggest that under specific thermodynamic (open systems out of equilibrium) and chemical conditions (autocatalysis, kinetic dynamic stability), this mapping can go up to a limit characterized by a fixed-point equation: [Formula: see text]. In this equation, ([Formula: see text]) symbolizes a regime of permanent resonance characterizing the biosphere, as open from inside, by the recursive differential relation between the biosphere and all its holobionts. As such the biosphere is closed on itself as a pure differential entity. ([Formula: see text]) symbolizes the regime of permanent change characterizing the emergence of evolution in the biosphere. As such the biosphere is closed on itself, by the principle of descent with modifications, and by the fact that every holobiont evolves in a niche, while evolving with it.

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.

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.

The Life of Behavior

Neuroscience needs behavior. However, it is daunting to render the behavior of organisms intelligible without suppressing most, if not all, references to life. When animals are treated as passive stimulus-response, disembodied and identical machines, the life of behavior perishes. Here, we distill three biological principles (materiality, agency, and historicity), spell out their consequences for the study of animal behavior, and illustrate them with various examples from the literature. We propose to put behavior back into context, with the brain in a species-typical body and with the animal's body situated in the world; stamp Newtonian time with nested ontogenetic and phylogenetic processes that give rise to individuals with their own histories; and supplement linear cause-and-effect chains and information processing with circular loops of purpose and meaning. We believe that conceiving behavior in these ways is imperative for neuroscience.

An applied mathematician's perspective on Rosennean Complexity

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Analysis of Rosen's theories with a focus on their mathematical content.

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Provides links of Rosen's work with most recent research into mathematical modelling.

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Possible implementations of ’closure to efficient causation’ in models are discussed.

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Critical analysis of Rosen's use of category theory.

The theoretical biologist Robert Rosen developed a highly original approach for investigating the question “What is life?”, the most fundamental problem of biology. Considering that Rosen made extensive use of mathematics it might seem surprising that his ideas have only rarely been implemented in mathematical models. On the one hand, Rosen propagates relational models that neglect underlying structural details of the components and focus on relationships between the elements of a biological system, according to the motto “throw away the physics, keep the organisation”. Rosen's strong rejection of mechanistic models that he implicitly associates with a strong form of reductionism might have deterred mathematical modellers from adopting his ideas for their own work. On the other hand Rosen's presentation of his modelling framework, (M, R) systems, is highly abstract which makes it hard to appreciate how this approach could be applied to concrete biological problems. In this article, both the mathematics as well as those aspects of Rosen's work are analysed that relate to his philosophical ideas. It is shown that Rosen's relational models are a particular type of mechanistic model with specific underlying assumptions rather than a fundamentally different approach that excludes mechanistic models. The strengths and weaknesses of relational models are investigated by comparison with current network biology literature. Finally, it is argued that Rosen's definition of life, “organisms are closed to efficient causation”, should be considered as a hypothesis to be tested and ideas how this postulate could be implemented in mathematical models are presented.

Sleeping Beauty and the Microenvironment Enchantment: Microenvironmental Regulation of the Proliferation-Quiescence Decision in Normal Tissues and in Cancer Development

Cells from prokaryota to the more complex metazoans cease proliferating at some point in their lives and enter a reversible, proliferative-dormant state termed quiescence. The appearance of quiescence in the course of evolution was essential to the acquisition of multicellular specialization and compartmentalization and is also a central aspect of tissue function and homeostasis. But what makes a cell cease proliferating even in the presence of nutrients, growth factors, and mitogens? And what makes some cells "wake up" when they should not, as is the case in cancer? Here, we summarize and discuss evidence showing how microenvironmental cues such as those originating from metabolism, extracellular matrix (ECM) composition and arrangement, neighboring cells and tissue architecture control the cellular proliferation-quiescence decision, and how this complex regulation is corrupted in cancer.

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.

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.

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

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace.

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.

Why do we need theories?

Theories organize knowledge and construct objectivity by framing observations and experiments. The elaboration of theoretical principles is examined in the light of the rich interactions between physics and mathematics. These two disciplines share common principles of construction of concepts and of the proper objects of inquiry. Theory construction in physics relies on mathematical symmetries that preserve the key invariants observed and proposed by such theory; these invariants buttress the idea that the objects of physics are generic and thus interchangeable and they move along specific trajectories which are uniquely determined, in classical and relativistic physics. In contrast to physics, biology is a historical science that centers on the changes that organisms experience while undergoing ontogenesis and phylogenesis. Biological objects, namely organisms, are not generic but specific; they are individuals. The incessant changes they undergo represent the breaking of symmetries, and thus the opposite of symmetry conservation, a central component of physical theories. This instability corresponds to the changes of the environment and the phenotypes. Inspired by Galileo's principle of inertia, the "default state" of inert matter, we propose a "default state" for biological dynamics following Darwin's first principle, "descent with modification" that we transform into "proliferation with variation and motility" as a property that spans life, including cells in an organism. These dissimilarities between theories of the inert and of biology also apply to causality: biological causality is to be understood in relation to the distinctive role that constraints assume in this discipline. Consequently, the notion of cause will be reframed in a context where constraints to activity are seen as the core component of biological analyses. Finally, we assert that the radical materiality of life rules out distinctions such as "software vs. hardware."