Prokaryotic genomes of endosymbionts and parasites are examples of naturally evolved minimal cells, the study of which can shed light on life in its minimum form. Their diverse biology, their lack of a large set of orthologous genes and the existence of essential linage (and environmentally) specific genes all illustrate the diversity of genes building up naturally evolved minimal cells. This conclusion is reinforced by the fact that sometimes the same essential function is performed by genes (...) from different evolutionary origins. Nevertheless, all cells perform a set of life‐essential functions however different their cell machinery and environment in which they thrive. An upcoming challenge for biologists will be to discern, by studying differences and similarities in current biodiversity, how cells with reduced genomes have adapted while retaining all basic life‐supporting functions. (shrink)

Strong cell decomposition property has been proved in non-valuational weakly o-minimal expansions of ordered groups. In this note, we show that all o-minimal traces have strong cell decomposition property. Also after introducing the notion of irrational nonvaluational cut in arbitrary o-minimal structures, we show that every expansion of o-minimal structures by irrational nonvaluational cuts is an o-minimal trace.

Continuous extension cell decomposition in o-minimal structures was introduced by Simon Andrews to establish the open cell property in those structures. Here, we define strong $\mathrm{CE}$-cells in weakly o-minimal structures, and prove that every weakly o-minimal structure with strong cell decomposition has $\mathrm{SCE}$-cell decomposition if and only if its canonical o-minimal extension has $\mathrm{CE}$-cell decomposition. Then, we show that every weakly o-minimal structure with $\mathrm{SCE}$-cell decomposition satisfies $\mathrm{OCP}$. Our last result implies that every o- (...) class='Hi'>minimal structure in which every definable open set is a union of finitely many open $\mathrm{CE}$-cells, has $\mathrm{CE}$-cell decomposition. (shrink)

In [12], P. Scowcroft and L. van den Dries proved a cell decomposition theorem for p-adically closed fields. We work here with the notion of P-minimal fields defined by D. Haskell and D. Macpherson in [6]. We prove that a P-minimal field K admits cell decomposition if and only if K has definable selection. A preprint version in French of this result appeared as a prepublication [8].

C-minimality is a variant of o-minimality in which structures carry, instead of a linear ordering, a ternary relation interpretable in a natural way on set of maximal chains of a tree. This notion is discussed, a cell-decomposition theorem for C-minimal structures is proved, and a notion of dimension is introduced. It is shown that C-minimal fields are precisely valued algebraically closed fields. It is also shown that, if certain specific ‘bad’ functions are not definable, then algebraic closure has (...) the exchange property, and for definable sets dimension coincides with the rank obtained from algebraic closure. (shrink)

Oncogenic hyperplasia is the first and inevitable stage of formation of a (solid) tumor. This stage is also the core of many other proliferative diseases. The present work proposes the first minimal model that combines homeorhesis with oncogenic hyperplasia where the latter is regarded as a genotoxically activated homeorhetic dysfunction. This dysfunction is specified as the transitions of the fluid of cells from a fluid, homeorhetic state to a solid, hyperplastic-tumor state, and back. The key part of the (...) model is a nonlinear reaction-diffusion equation (RDE) where the biochemical-reaction rate is generalized to the one in the well-known Schlögl physical theory of the non-equilibrium phase transitions. A rigorous analysis of the stability and qualitative aspects of the model, where possible, are presented in detail. This is related to the spatially homogeneous case, i.e. when the above RDE is reduced to a nonlinear ordinary differential equation. The mentioned genotoxic activation is treated as a prevention of the quiescent G0-stage of the cell cycle implemented with the threshold mechanism that employs the critical concentration of the cellular fluid and the nonquiescent-cell-duplication time. The continuous tumor morphogeny is described by a time-space-dependent cellular-fluid concentration. There are no sharp boundaries (i.e. no concentration jumps exist) between the domains of the homeorhesis- and tumor-cell populations. No presumption on the shape of a tumor is used. To estimate a tumor in specific quantities, the model provides the time-dependent tumor locus, volume, and boundary that also points out the tumor shape and size. The above features are indispensable in the quantitative development of antiproliferative drugs or therapies and strategies to prevent oncogenic hyperplasia in cancer and other proliferative diseases. The work proposes an analytical-numerical method for solving the aforementioned RDE. A few topics for future research are suggested. (shrink)

We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a (...) locally o-minimal structure which admits local definable cell decomposition. (shrink)

Assembly of minimal genomes revealed many genes encoding unknown functions. Three overlooked functional categories account for some of them. Cells are prone to make errors and age. As a first key function, discrimination between proper and changed entities is indispensable. Discrimination requires management of information, an authentic, yet abstract, cur- rency of reality. For example proteins age, sometimes very fast. The cell must identify, then get rid of old proteins without destroying young ones. Implementing discrimination in cells (...) leads to the second set of functions, usually ignored. Being abstract, information must nevertheless be embodied into material entities, with unavoidable idiosyncratic properties. This brings about novel unmet needs. Hence, the buildup of cells elicits specific but awkward material implementations, ‘kludges’ that become essential under particular settings, while difficult to identify. Finally, a third functional category char- acterizes the need for growth, with metabolic implementations allowing the cell to put together the growth of its cytoplasm, membranes, and genome, spanning different spatial dimensions. Solving this metabolic quandary, critical for engineering novel synthetic biology chassis, uncovered an unexpected role for CTP synthetase as the coordinator of nonhomothetic growth. Because a significant number of SynBio constructs aim at creating cell factories we expect that they will be attacked by viruses (it is not by chance that the function of the CRISPR system was identified in industrial settings). Substantiating the role of CTP, natural selection has dealt with this hurdle via synthesis of the antimetabolite 30-deoxy-30,40-didehydro- CTP, recruited for antiviral immunity in all domains of life. (shrink)

Lipid vesicles are often used as compartment structures for preparing cell‐like systems and models of protocells, the hypothetical precursor structures of the first cells at the origin of life. Although the various artificially made vesicle systems are already remarkably complex, they are still very different from and much simpler than any known living cell. Nevertheless, the preparation and study of the structure and the dynamics of functionalized vesicle systems may contribute to a better understanding of biological cells, in (...) particular of the essential features of a living cell that are not found in the non‐living form of matter. The study of protocell models may possibly lead to a better understanding of the origin of the first cells. To avoid misunderstanding in this field of research, it would be useful if generally accepted definitions of terms like “artificial cells,” “synthetic cells,” “minimal cells,” “protocells,” and “primitive cells” exist. Editor's suggested further reading in BioEssaysSynthetic cells and organelles: compartmentalization strategies Abstract. (shrink)

We introduce a new notion of tame geometry for structures admitting an abstract notion of balls. The notion is named b-minimality and is based on definable families of points and balls. We develop a dimension theory and prove a cell decomposition theorem for b-minimal structures. We show that b-minimality applies to the theory of Henselian valued fields of characteristic zero, generalizing work by Denef–Pas [25, 26]. Structures which are o-minimal, v-minimal, or p-minimal and which satisfy some (...) slight extra conditions are also b-minimal, but b-minimality leaves more room for nontrivial expansions. The b-minimal setting is intended to be a natural framework for the construction of Euler characteristics and motivic or p-adic integrals. The b-minimal cell decomposition is a generalization of concepts of Cohen [11], Denef [15], and the link between cell decomposition and integration was first made by Denef [13]. (shrink)

The topology of definable sets in an o-minimal expansion of a group is not fully understood due to the lack of a triangulation theorem. Despite the general validity of the cell decomposition theorem, we do not know whether any definably compact set is a definable CW-complex. Moreover the closure of an o-minimal cell can have arbitrarily high Betti numbers. Nevertheless we prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group (...) are finitely generated and invariant under elementary extensions and expansions of the language. (shrink)

Genomic instability is a hallmark of cancer. Cancer cells that exhibit abnormal chromosomes are characteristic of most advanced tumours, despite the potential threat represented by accumulated genetic damage. Carcinogenesis involves a loss of key components of the genetic and signalling molecular networks; hence some authors have suggested that this is part of a trend of cancer cells to behave as simple, minimal replicators. In this study, we explore this conjecture and suggest that, in the case of cancer, (...) genomic instability has an upper limit that is associated with a minimal cancer cell network. Such a network would include (for a given microenvironment) the basic molecular components that allow cells to replicate and respond to selective pressures. However, it would also exhibit internal fragilities that could be exploited by appropriate therapies targeting the DNA repair machinery. The implications of this hypothesis are discussed. (shrink)

The aim of this paper is to assess the relevance of somatic evolution by natural selection to our understanding of cancer development. I do so in two steps. In the first part of the paper, I ask to what extent cancer cells meet the formal requirements for evolution by natural selection, relying on Godfrey-Smith’s (2009) framework of Darwinian populations. I argue that although they meet the minimal requirements for natural selection, cancer cells are not paradigmatic Darwinian populations. (...) In the second part of the paper, I examine the most important examples of adaptation in cancer cells. I argue that they are not significant accumulations of evolutionary changes, and that as a consequence natural selection plays a lesser role in their explanation. Their explanation, I argue, is best sought in the previously existing wiring of the healthy cells. (shrink)

O-minimal geometry generalizes both semialgebraic and subanalytic geometries, and has been very successful in solving special cases of some problems in arithmetic geometry, such as André–Oort conjecture. Among the many tools developed in an o-minimal setting are cohomology theories for abstract-definable continuous manifolds such as singular cohomology, sheaf cohomology and Čech cohomology, which have been used for instance to prove Pillay’s conjecture concerning definably compact groups. In the present thesis we elaborate an o-minimal de Rham cohomology theory (...) for abstract-definable $C^{\infty }$ manifolds in an o-minimal expansion of the real field which admits smooth cell decomposition and defines the exponential function. We can specify the o-minimal cohomology groups and attain some properties such as the existence of Mayer–Vietoris sequence and the invariance under abstract-definable $C^{\infty }$ diffeomorphisms. However, in order to obtain the invariance of our o-minimal cohomology under abstract-definable homotopy we must work in a tame context that defines sufficiently many primitives and assume the validity of a statement related to Bröcker’s question.Abstract prepared by Rodrigo Figueiredo.E-mail: [email protected]: https://doi.org/10.11606/T.45.2019.tde-28042019-181150. (shrink)

Microfluidic technology – the manipulation of fluids at micrometer scales – has revolutionized many areas of synthetic biology. The bottom‐up synthesis of “minimal” cell models has traditionally suffered from poor control of assembly conditions. Giant unilamellar vesicles (GUVs) are good models of living cells on account of their size and unilamellar membrane structure. In recent years, a number of microfluidic approaches for constructing GUVs has emerged. These provide control over traditionally elusive parameters of vesicular structure, such as size, (...) lamellarity, membrane composition, and internal contents. They also address sophisticated cellular functions such as division and protein synthesis. Microfluidic techniques for GUV synthesis can broadly be categorized as continuous‐flow based approaches and droplet‐based approaches. This review presents the state‐of‐the‐art of microfluidic technology, a robust platform for recapitulating complex cellular structure and function in synthetic models of biological cells. (shrink)

In this paper we develop a differential analogue of o-minimal cell decomposition for the theory CODF of closed ordered differential fields. Thanks to this differential cell decomposition we define a well-behaving dimension function on the class of definable sets in CODF. We conclude this paper by proving that this dimension is closely related to both the usual differential transcendence degree and the topological dimension associated, in this case, with a natural differential topology on ordered differential fields.

We introduce CE- cell decomposition , a modified version of the usual o-minimal cell decomposition. We show that if an o-minimal structure $\mathcal{R}$ admits CE-cell decomposition then any definable open set in $\mathcal{R}$ may be expressed as a finite union of definable open cells. The dense linear ordering and linear o-minimal expansions of ordered abelian groups are examples of such structures.

Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. We show that every definable nested family of closed and bounded subsets of a P-minimal field K has nonempty intersection. As an application we answer a question of Darnière and Halupczok showing that P-minimal fields satisfy the “extreme value property”: for every closed and bounded subset [math] and every interpretable continuous function [math] (where [math] denotes the value group), f(U) admits a maximal value. Two further corollaries are obtained (...) as a consequence of their work. The first one shows that every interpretable subset of [math] is already interpretable in the language of rings, answering a question of Cluckers and Halupczok. This implies in particular that every P-minimal field is polynomially bounded. The second one characterizes those P-minimal fields satisfying a classical cell preparation theorem as those having definable Skolem functions, generalizing a result of Mourgues. (shrink)

We study a reduct ${\mathcal{L}_*}$ of the ring language where multiplication is restricted to a neighbourhood of zero. The language is chosen such that for p-adically closed fields K, the ${\mathcal{L}_*}$ -definable subsets of K coincide with the semi-algebraic subsets of K. Hence structures (K, ${\mathcal{L}_*}$ ) can be seen as the p-adic counterpart of the o-minimal structure of semibounded sets. We show that in this language, p-adically closed fields admit cell decomposition, using cells similar to p-adic semi-algebraic (...) cells. From this we can derive quantifier-elimination, and give a characterization of definable functions. In particular, we conclude that multiplication can only be defined on bounded sets, and we consider the existence of definable Skolem functions. (shrink)

The recent development of RNA replicating protocells and capsules that enclose complex biosynthetic cascade reactions are encouraging signs that we are gradually getting better at mastering the complexity of biological systems. The road to truly cellular compartments is still very long, but concrete progress is being made. Compartmentalization is a crucial natural methodology to enable control over biological processes occurring within the living cell. In fact, compartmentalization has been considered by some theories to be instrumental in the creation of life. (...) With the advancement of chemical biology, artificial compartments that can mimic the cell as a whole, or that can be regarded as cell organelles, have recently received much attention. The membrane between the inner and outer environment of the compartment has to meet specific requirements, such as semi‐permeability, to allow communication and molecular transport over the border. The membrane can either be built from natural constituents or from synthetic polymers, introducing robustness to the capsule. (shrink)

Let be an o-minimal structure expanding a real closed field R. We show that any definable set in Rn can be stratified into cells, whose defining functions are smooth Lipschitz continuous functions with constant 2n3/2, which have additional regularity conditions on the derivatives of higher order.

Recently, Cluckers et al. developed a new axiomatic framework for tame non-Archimedean geometry, called Hensel minimality. It was extended to mixed characteristic together with the author. Hensel minimality aims to mimic o-minimality in both strong consequences and wide applicability. In this paper, we continue the study of Hensel minimality, in particular focusing on [Formula: see text]-h-minimality and [Formula: see text]-h-minimality, for [Formula: see text] a positive integer. Our main results include an analytic criterion for [Formula: see text]-h-minimality, preservation of [Formula: (...) see text]-h-minimality under coarsening of the valuation and [Formula: see text]-dimensional geometry. (shrink)

We prove that forp-optimal fields a cell decomposition theorem follows from methods going back to Denef’s paper [7]. We derive from it the existence of definable Skolem functions and strongp-minimality. Then we turn to stronglyp-minimal fields satisfying the Extreme Value Property—a property which in particular holds in fields which are elementarily equivalent to ap-adic one. For such fieldsK, we prove that every definable subset ofK×Kdwhose fibers overKare inverse images by the valuation of subsets of the value group is semialgebraic. (...) Combining the two we get a preparation theorem for definable functions onp-optimal fields satisfying the Extreme Value Property, from which it follows that infinite sets definable over such fields are in definable bijection iff they have the same dimension. (shrink)

Mesenchymal stem cells (MSCs) are present in fat tissues throughout the body, yet little is known regarding their biological role within epidural fat. We hypothesize that debridement of epidural fat and/or subsequent loss of MSCs within this tissue, disrupts homeostasis in the vertebral environment resulting in increased inflammation, fibrosis, and decreased neovascularization leading to poorer functional outcomes post‐injury/operatively. Clinically, epidural fat is commonly considered a space‐filling tissue with limited functionality and therefore typically discarded during surgery. However, the presence of (...) MSCs within epidural fat suggests that itis more biologically active than historically believed and may contribute to the regulation of homeostasis and regeneration in the dural environment. While the current literature supports our hypothesis, it will require additional experimentation to determine if epidural fat is an endogenous driver of repair and regeneration and if so, this tissue should be minimally perturbed from its original location in the spinal canal. Also see the video abstract here https://youtu.be/MIol_IWK1os. (shrink)

A weakly o-minimal structure image expanding an ordered group is called nonvaluational iff for every cut left angle bracketC,Dright-pointing angle bracket of definable in image, we have that inf{y−x:xset membership, variantC,yset membership, variantD}=0. The study of nonvaluational weakly o-minimal expansions of real closed fields carried out in [D. Macpherson, D. Marker, C. Steinhorn,Weakly o-minimal structures and real closed fields, Trans. Amer. Math. Soc. 352 5435–5483. MR1781273 (2001i:03079] suggests that this class is very close to the class of (...) o-minimal expansions of real closed fields. Here we further develop this analogy. We establish an o-minimal style cell decomposition for weakly o-minimal non-valuational expansions of ordered groups. For structures enjoying such a strong cell decomposition we construct a canonical o-minimal extension. Finally, we make attempts towards generalizing the o-minimal Euler characteristic to the class of sets definable in weakly o-minimal structures with the strong cell decomposition property. (shrink)

A eukaryotic “baby machine” has been developed that produces synchronized cultures that display up to four synchronous cell cycles. 1 That such cells can be produced implies that methods unable to produce successive synchronized cell cycles may not actually synchronize cells. But most important, the baby machine method now opens the way for the study of the cell cycle of minimally disturbed, artifact‐free, well‐synchronized, mammalian cells. BioEssays 24:499–501, 2002. © 2002 Wiley Periodicals, Inc.

Faire valoir un réalisme minimal c'est faire tenir ensemble deux exigences : celle d'un réalisme qui cherche à montrer que les relations exprimées par le langage n'existent pas seulement dans le langage, ni seulement dans l'esprit, mais qu'elles nous font connaître quelque chose du monde ; celle d'un nominalisme qui applique le rasoir d'Occam avec vigilance et refuse, non seulement de poser l'existence d'universels qui seraient des essences ou des propriétés, mais même de concevoir les relations elles-mêmes comme des (...) réalités existant dans un autre monde que celui des individus liés par elles. (shrink)

We prove a cell decomposition theorem for Presburger sets and introduce a dimension theory for Z-groups with the Presburger structure. Using the cell decomposition theorem we obtain a full classification of Presburger sets up to definable bijection. We also exhibit a tight connection between the definable sets in an arbitrary p-minimal field and Presburger sets in its value group. We give a negative result about expansions of Presburger structures and prove uniform elimination of imaginaries for Presburger structures within the (...) Presburger language. (shrink)

We develop a notion of cell decomposition suitable for studying weak p-adic structures definable). As an example, we consider a structure with restricted addition.

A new design principle is discussed for making a sufficiently complex cell for the creation of the first wet artificial life in the laboratory. The current approach is to attempt a minimal cell, which consists of a liposome that contains a minimal metabolic cycle for self-maintenance and self-replication. Given the lack of success with the minimal cell to date, the authors suggest it is possible to take an alternative approach to building the first wet artificial life form (...) that they have called the first cell. In this article, the concept of the first cell versus the minimal cell is discussed. The new design principle is supported by the following observations that are examined and developed from an Origins of Life perspective: That human development shows a U-shaped curve where the skills and developmental patterns of human infants are proficient at the first phase then decline and subsequently recover to a qualitatively better level. A review of spatial temporal dynamics using cellular automata studies shows that complexity generated at both the initial states and the time evolution dynamics can synthesize rich evolutionary processes. A chemical experiment exhibiting self-organizing dynamics results in the emergence of a self-propelling oil droplet that demonstrates the self-sustaining properties of a non-equilibrium state. Finally, the important design question Is life a contingent or deterministic phenomenon? is examined which asks whether a life form is a dynamic product of its surroundings or whether it is the inevitable outcome of prior events, and is discussed making reference to the characteristics of an art installation The Way Things Go. This contemporary masterpiece, which exhibits a long-lasting chain of unrelated causal events, serves as a theoretical model for discussion of evolutionary processes, suggesting that when it comes to designing wet artificial life forms in the laboratory, both contingent and deterministic processes should be taken into account. (shrink)

We introduce a very weak language L M on p-adic fields K, which is just rich enough to have exactly the same definable subsets of the line K that one has using the ring language. (In our context, definable always means definable with parameters.) We prove that the only definable functions in the language L M are trivial functions. We also give a definitional expansion $L\begin{array}{*{20}{c}} ' \\ M \\ \end{array} $ of L M in which K has quantifier elimination, (...) and we obtain a cell decomposition result for L M -definable sets. Our language L M can serve as a p-adic analogue of the very weak language (<) on the real numbers, to define a notion of minimality on the field of p-adic numbers and on related valued fields. These fields are not necessarily Henselian and may have positive characteristic. (shrink)

WHO II low grade glioma evolves inevitably to anaplastic transformation. Magnetic resonance imaging is a good non-invasive way to watch it, by hemodynamic and metabolic modifications, thanks to multinuclear spectroscopy 1H/31P. In this work we study a multi-scale minimal model of hemodynamics and metabolism applied to the study of gliomas. This mathematical analysis leads us to a fast-slow system. The control of the position of the stationary point brings to the concept of domain of viability. Starting from this system, (...) the equations bring to light the parameters that push glioma cells out of their domain of viability. Four fundamental factors are highlighted. The first two are cerebral blood flow and the rate of lactate transport through monocarboxylate transporters, which must be reduced in order to push glioma out of its domain of viability. Another factor is the intra arterial lactate, which must be increased. The last factor is pH, indeed a decrease of intra cellular pH could interfere with glioma growth. These reflections suggest that these four parameters could lead to new therapeutic strategies for the management of low grade gliomas. (shrink)

The possibility of obtaining stem cells from human embryos has given rise to an intensive legal and ethical debate. In this paper, attention is paid to the normative disparity and ambiguity in Europe. An argument for the need for a minimal legal harmonization is made; and a prudent and flexible way to reach this successfully is suggested. Establishing a common legal framework seems to be the only way to guarantee true competitiveness for the European scientific community.

The possibility of obtaining stem cells from human embryos has given rise to an intensive legal and ethical debate. In this paper, attention is paid to the normative disparity and ambiguity in Europe. An argument for the need for a minimal legal harmonization is made; and a prudent and flexible way to reach this successfully is suggested. Establishing a common legal framework seems to be the only way to guarantee true competitiveness for the European scientific community.

We prove, by explicit construction, that not all sets definable in polynomially bounded o-minimal structures have mild parameterization. Our methods do not depend on the bounds particular to the definition of mildness and therefore our construction is also valid for a generalized form of parameterization, which we call G-mild. Moreover, we present a cell decomposition result for certain o-minimal structures which may be of independent interest. This allows us to show how our construction can produce polynomially bounded, model (...) complete expansions of the real ordered field which, in addition to lacking G-mild parameterization, nonetheless still have analytic cell decomposition. (shrink)

We prove that in a semi-bounded o-minimal expansion of an ordered group every non-empty open definable set is a finite union of open cells.

Let M=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}=}$$\end{document} be a weakly o-minimal expansion of a dense linear order without endpoints. Some tame properties of sets and functions definable in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} which hold in o-minimal structures, are examined. One of them is the intermediate value property, say IVP. It is shown that strongly continuous definable functions in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} satisfy an extended version of IVP. After introducing a weak version of definable connectedness in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document}, we prove that strong cells in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} are weakly definably connected, so every set definable in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} is a finite union of its weakly definably connected components, provided that M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} has the strong cell decomposition property. Then, we consider a local continuity property for definable functions in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} and conclude some results on cell decomposition regarding that property. Finally, we extend the notion of having no dense graph which was examined for definable functions in and related to uniform finiteness, definable completeness, and others. We show that every weakly o-minimal structure M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} having cell decomposition, satisfies NDG, i.e. every definable function in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} has no dense graph. (shrink)

Neddylation, a ubiquitylation‐like post‐translational modification, is catalyzed by a cascade composed of three enzymes: E1 activating enzyme, E2 conjugating enzyme, and E3 ligase with cullins as physiological substrates. Specifically, neddylation E2 UBE2M couples with E3 RBX1 to neddylate cullins 1–4, whereas neddylation E2 UBE2F couples with E3 RBX2/SAG to neddylate cullin 5, leading to activation of CRL1‐4 (Cullin‐RING ligases 1–4) and CRL5, respectively. While over‐activation of the neddylation‐CRLs axis occurs frequently in many human cancers, how neddylation‐CRLs regulate the function of (...) immune cells, particularly Treg cells was previously unknown. To this end, we recently performed Treg selective knockout of two neddylation E2s and two E3s, individually, driven by Foxp3‐Cre, and found that while the Ube2f‐Sag E2/E3 pair plays a minimal role, if any, the Ube2m‐Rbx1 pair is essential for the maintenance of Treg functionality, since their deletion triggers robust inflammatory response with autoimmune phenotypes. Milder phenotype severity upon Treg KO of upstream Ube2m than that of downstream Rbx1 strongly suggested that Rbx1 regulates Treg function in a manner dependent and independent of neddylation. (shrink)

The development of synthetic biology calls for accurate understanding of the critical functions that allow construction and operation of a living cell. Besides coding for ubiquitous structures, minimal genomes encode a wealth of functions that dissipate energy in an unanticipated way. Analysis of these functions shows that they are meant to manage information under conditions when discrimination of substrates in a noisy background is preferred over a simple recognition process. We show here that many of these functions, including transporters (...) and the ribosome construction machinery, behave as would behave a material implementation of the informationmanaging agent theorized by Maxwell almost 150 years ago and commonly known as Maxwell’s demon (MxD). A core gene set encoding these functions belongs to the minimal genome required to allow the construction of an autonomous cell. These MxDs allow the cell to perform computations in an energy-efficient way that is vastly better than our contemporary computers. (shrink)

In [T. Brihaye, C. Michaux, C. Rivière, Cell decomposition and dimension function in the theory of closed ordered differential fields, Ann. Pure Appl. Logic .] the authors proved a cell decomposition theorem for the theory of closed ordered differential fields which generalizes the usual Cell Decomposition Theorem for o-minimal structures. As a consequence of this result, a well-behaving dimension function on definable sets in CODF was introduced. Here we continue the study of this cell decomposition in CODF by proving (...) three additional results. We first discuss the relation between the δ-cells introduced in the above-mentioned reference and the notion of Kolchin polynomial in differential algebra. We then prove two generalizations of classical decomposition theorems in o-minimal structures. More exactly we give a theorem of decomposition into definably d-connected components and a differential cell decomposition theorem for a particular class of definable functions in CODF. (shrink)

Julius Sachs (1832–1897), who has been quite rightly called “the father of plant physiology,” was a German physiologist of international standing, whose research interests contributed to virtually every branch of the plant sciences, and whose work presaged plant molecular biology and systems biology. Here, we focus on one of his last publications, from 1892, wherein he argued that the term “cell” (_Zelle_) is misleading and should be replaced by “energid” (_Energide_), which he defined as “a nucleus together with the corresponding (...) protoplasm that is governed by it,” based on his observations of coenocytic algae such as _Caulerpa_ whose nuclei “can only control” so much cytoplasm. Although most of his colleagues did not accept this novel terminology for the description of the “basic, minimal living unit” (_Elementarorganismus_) of animals, plants, and microbes, we argue that the energid concept prefigured the subsequent discovery of mRNA. We also argue that the resistance to the energid concept revolved around a deep-seated philosophical debate between those adhering to cell theory versus organismal theory. The first English translation of the seminal work by Sachs, “Physiologische Notizen. II. Beiträge zur Zellentheorie. a) Energiden und Zellen,” originally published in _Flora_ (75: 57–67, 1892), is provided as a separate article in this volume as part of the journal’s “Classics in Biological Theory” collection ( https://doi.org/10.1007/s13752-022-00399-w ); the original German version is available here as supplementary material in the online version of this article. (shrink)

Let be a weakly o‐minimal structure with the strong cell decomposition property. In this note, we show that the canonical o‐minimal extension of is the unique prime model of the full first order theory of over any set. We also show that if two weakly o‐minimal structures with the strong cell decomposition property are isomorphic then, their canonical o‐minimal extensions are isomorphic too. Finally, we show the uniqueness of the prime models in a complete weakly o‐ (...) class='Hi'>minimal theory with prime models. (shrink)

There is a lack of consensus on whether the derivation and use of human embryonic stem cells (hESCs) from embryos remaining after infertility treatment morally require the informed consent of third-party gamete donors who contributed to the creation of the embryos. The principal guidelines for oversight and funding of hESC research in the United States make minimal or no demands for consent from gamete donors. In this article, I consider the arguments supporting and opposing gamete donor consent for (...) hESC research and embryo research more broadly. I argue that it is not morally permissible to use leftover embryos in research without the informed consent of gamete donors, and that we should place restrictions on the use of existing hESC lines that may have been derived without informed consent. While the standard argument for this position relies on an appeal to gamete donors’ interest in controlling what happens with their genetic material, I identify shortcomings with the standard approach and seek instead to locate the deeper moral foundations for gamete donor consent in rights to bodily integrity. (shrink)

Let (M, ≤,...) denote a Boolean ordered o-minimal structure. We prove that a Boolean subalgebra of M determined by an algebraically closed subset contains no dense atoms. We show that Boolean algebras with finitely many atoms do not admit proper expansions with o-minimal theory. The proof involves decomposition of any definable set into finitely many pairwise disjoint cells, i.e., definable sets of an especially simple nature. This leads to the conclusion that Boolean ordered structures with o-minimal (...) theories are essentially bidefinable with Boolean algebras with finitely many atoms, expanded by naming constants. We also discuss the problem of existence of proper o-minimal expansions of Boolean algebras. (shrink)

We have compared two different laser-induced optical light traps for their utility in moving organelles within living animal cells and walled fungal cells. The first trap employed a continuous wave neodymium-yttrium aluminum garnet laser at a wavelength of 1.06 micron. A second trap was constructed using a titanium-sapphire laser tunable from 700 to 1000 nm. With the latter trap we were able to achieve much stronger traps with less laser power and without damage to either mitochondria or spindles. (...) Chromosomes and nuclei were easily displaced, nucleoli were separated and moved far away from interphase nuclei, and Woronin bodies were removed from septa. In comparison, these manipulations were not possible with the Nd-YAG laser-induced trap. The optical force trap induced by the tunable titanium-sapphire laser should find wide application in experimental cell biology because the wavelength can be selected for maximization of force production and minimization of energy absorption which leads to unwanted cell damage. (shrink)