Here we discuss the application and articulation of biological principles for mathematical modeling of morphogenesis in the case of mammary ductal morphogenesis, with an emphasis on the default state.
Abstract
Unlike inert objects, organisms and their cells have the ability to initiate activity by themselves, and thus change their properties or states even in the absence of an external cause. This crucial difference led us to search for principles suitable for the study organisms. We propose that cells follow the default state of proliferation with variation and motility, a principle of biological inertia. This means that in the presence of sufficient nutrients, cells will express their default state. We also propose a principle of variation that addresses two central features of organisms, variation and historicity. To address interdependence between parts, we use a third principle, the principle of organization: more specifically, the notion of the closure of constraints. Within this theoretical framework, constraints are specific theoretical entities defined by their relative stability with respect to the processes they constrain. Constraints are mutually dependent in an organized system and act on the default state. Here we discuss the application and articulation of these principles for mathematical modeling of morphogenesis in a specific case, that of mammary ductal morphogenesis, with an emphasis on the default state. Our model has both a biological component, the cells, and a physical component, the matrix that contains collagen fibers. Cells are agents that move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers are organized, they constrain the cells’ ability to move and to proliferate. This model exhibits a circularity that can be interpreted in terms of the closure of constraints. Implementing our mathematical model shows that constraints to the default state are sufficient to explain the formation of mammary epithelial structures. Finally, the success of this modeling effort suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism can be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace.
A new look at theoretical computer sciences by changing perspective with a biological approach.
Abstract
The analogy between living beings and computers was introduced with circumspection by Schrödinger and has been widely propagated since, rarely with a precise technical meaning. Critics of this perspective are numerous. We emphasize that this perspective is mobilized to justify what may be called a regressive reductionism by comparison with physics or the Cartesian method. Other views on the living are possible, and we focus on an epistemological and theoretical framework where historicity is central, and the regularities susceptible to mathematization are constraints whose existence is fundamentally precarious and historically contingent. We then propose to reinterpret the computer, no longer as a Turing machine but as constituted by constraints. This move allows us to understand that computation in the sense of Church-Turing is only a part of the theoretical determination of what actually happens in a computer when considering them in their larger theoretical context where historicity is also central.
We address the identity of biological organisms in scientific practices by combining relational and historical conceptions, and introduce a new symbol for that.
Abstract
We address the identity of biological organisms at play in experimental and modeling practices. We first examine the central tenets of two general conceptions, and we assess their respective strengths and weaknesses. The historical conception, on the one hand, characterizes organisms’ identity by looking at their past, and specifically at their genealogical connection with a common ancestor. The relational conception, on the other hand, interprets organisms’ identity by referring to a set of distinctive relations between their parts, and between the organism and its environment. While the historical and relational conceptions are understood as opposed and conflicting, we submit that they are also fundamentally complementary. Accordingly, we put forward a hybrid conception, in which historical and relational (and more specifically, organizational) aspects of organisms’ identity sustain and justify each other. Moreover, we argue that organisms’ identity is not only hybrid but also bounded, insofar as the compliance with specific identity criteria tends to vanish as time passes, especially across generations. We spell out the core conceptual framework of this conception, and we outline an original formal representation. We contend that the hybrid and bounded conception of organisms’ identity suits the epistemological needs of biological practices, particularly with regards to the generalization and reproducibility of experimental results, and the integration of mathematical models with experiments.
