On end extensions of models of subsystems of peano arithmetic

AbstractWe survey results and problems concerning subsystems of Peano Arithmetic. In particular, we deal with end extensions of models of such theories. First, we discuss the results of Paris and Kirby (Logic Colloquium ’77, North-Holland, Amsterdam, 1978, pp. 199–209) and of Clote (Fund. Math. 127 (1986) 163; Fund. Math. 158 (1998) 301), which generalize the MacDowell and Specker theorem (Proc. Symp. on Foundation of Mathematics, Warsaw, 1959, Pergamon Press, Oxford, 1961, p. 257–263) we also discuss a related problem of Kaufmann (On existence of Σn end extensions, Lecture Notes in Mathematics, Vol. 859, Springer, Berlin, 1980, pp. 92). Then we sketch an alternative proof of Clote's theorem, using the arithmetized completeness theorem in the spirit of McAloon (Trans. Amer. Math. Soc. 239 (1978) 253) and Paris (Some conservation results for fragments of arithmetic, Lecture Notes in Mathematics, Vol. 890, Springer, Berlin, 1981, p. 251)

Epibionts from the Cerro Gordo Member of the Lime Creek Formation (Upper Devonian), Rockford, Iowa

Epibionts and borings are common on brachiopods from the Cerro Gordo Member of the Lime Creek Formation (Upper Devonian) at Rockford, Iowa. Occurrences and distributions of epibionts are best explained by attachment and subsequent growth on either living or dead brachiopods. Distribution of Spirorbis, a calcareous worm tube, is best explained by random attachment of worm larvae on living or dead brachiopods. Cornulites, a conical shell of uncertain affinity, commonly occurs with its aperture oriented toward the anterior commissure of brachiopods, suggesting attachment to living shells and subsequent growth in response to the feeding currents of the brachiopod. Some tabulate corals (auloporids) and some bryozoa (Hederella sp.) display growth patterns toward, or parallel to, the plane of commissure of brachiopods. Such patterns are understandable if these colonial epibionts grew on living brachiopods, taking advantage of the brachiopods\u27 feeding currents. Circular borings and dendritic grooves are common on the brachiopod shells and may have caused the death of some brachiopods. Because the Cerro Gordo Member of the Lime Creek Formation was deposited on a muddy seafloor, attachment sites for small suspension feeders were limited. In this environment, brachiopod shells and horn corals provided relatively mud-free sites where epibionts could attach, grow, and survive

Emergence of homeostatic epithelial packing and stress dissipation through divisions oriented along the long cell axis.

Cell division plays an important role in animal tissue morphogenesis, which depends, critically, on the orientation of divisions. In isolated adherent cells, the orientation of mitotic spindles is sensitive to interphase cell shape and the direction of extrinsic mechanical forces. In epithelia, the relative importance of these two factors is challenging to assess. To do this, we used suspended monolayers devoid of ECM, where divisions become oriented following a stretch, allowing the regulation and function of epithelial division orientation in stress relaxation to be characterized. Using this system, we found that divisions align better with the long, interphase cell axis than with the monolayer stress axis. Nevertheless, because the application of stretch induces a global realignment of interphase long axes along the direction of extension, this is sufficient to bias the orientation of divisions in the direction of stretch. Each division redistributes the mother cell mass along the axis of division. Thus, the global bias in division orientation enables cells to act collectively to redistribute mass along the axis of stretch, helping to return the monolayer to its resting state. Further, this behavior could be quantitatively reproduced using a model designed to assess the impact of autonomous changes in mitotic cell mechanics within a stretched monolayer. In summary, the propensity of cells to divide along their long axis preserves epithelial homeostasis by facilitating both stress relaxation and isotropic growth without the need for cells to read or transduce mechanical signals.We thank D. Farquharson and S. Townsend at the University College London workshop and Joel Jennings and Richard Adams for help with model development. B.B. and J.B. thank Cancer Research UK, the Biotechnology and Biological Sciences Research Council (BBSRC) (Grant BB/K009001), the French Institut National du Cancer, and Matthieu Piel for support. T.P.J.W. and A.D. were supported by the Engineering and Physical Sciences Research Council. A.R.H. was supported by the BBSRC (Grant BB/K013521 to G.C. and A.K.), and M.L. was supported by the Agency for Science Technology and Research (Singapore) and the Wellcome Trust.This is the accepted manuscript of a paper published in the Proceedings of the National Academy of Sciences (Wyatt et al., PNAS 2015, 112, 18, 5726-5731, doi:10.1073/pnas.1420585112). The final version is available at http://dx.doi.org/10.1073/pnas.142058511

Cortical cell stiffness is independent of substrate mechanics

Cortical stiffness is an important cellular property that changes during migration, adhesion and growth. Previous atomic force microscopy (AFM) indentation measurements of cells cultured on deformable substrates have suggested that cells adapt their stiffness to that of their surroundings. Here we show that the force applied by AFM to a cell results in a significant deformation of the underlying substrate if this substrate is softer than the cell. This ‘soft substrate effect’ leads to an underestimation of a cell’s elastic modulus when analysing data using a standard Hertz model, as confirmed by finite element modelling and AFM measurements of calibrated polyacrylamide beads, microglial cells and fibroblasts. To account for this substrate deformation, we developed a ‘composite cell–substrate model’. Correcting for the substrate indentation revealed that cortical cell stiffness is largely independent of substrate mechanics, which has major implications for our interpretation of many physiological and pathological processes

Mitotic Rounding Alters Cell Geometry to Ensure Efficient Bipolar Spindle Formation

Accurate animal cell division requires precise coordination of changes in the structure of the microtubule-based spindle and the actin-based cell cortex. Here, we use a series of perturbation experiments to dissect the relative roles of actin, cortical mechanics, and cell shape in spindle formation. We find that, whereas the actin cortex is largely dispensable for rounding and timely mitotic progression in isolated cells, it is needed to drive rounding to enable unperturbed spindle morphogenesis under conditions of confinement. Using different methods to limit mitotic cell height, we show that a failure to round up causes defects in spindle assembly, pole splitting, and a delay in mitotic progression. These defects can be rescued by increasing microtubule lengths and therefore appear to be a direct consequence of the limited reach of mitotic centrosome-nucleated microtubules. These findings help to explain why most animal cells round up as they enter mitosis

Cortical cell stiffness is independent of substrate mechanics.

Cortical stiffness is an important cellular property that changes during migration, adhesion and growth. Previous atomic force microscopy (AFM) indentation measurements of cells cultured on deformable substrates have suggested that cells adapt their stiffness to that of their surroundings. Here we show that the force applied by AFM to a cell results in a significant deformation of the underlying substrate if this substrate is softer than the cell. This 'soft substrate effect' leads to an underestimation of a cell's elastic modulus when analysing data using a standard Hertz model, as confirmed by finite element modelling and AFM measurements of calibrated polyacrylamide beads, microglial cells and fibroblasts. To account for this substrate deformation, we developed a 'composite cell-substrate model'. Correcting for the substrate indentation revealed that cortical cell stiffness is largely independent of substrate mechanics, which has major implications for our interpretation of many physiological and pathological processes

F-actin dynamics regulates mammalian organ growth and cell fate maintenance.

BACKGROUND & AIMS: In vitro, several data indicate that cell function can be regulated by the mechanical properties of cells and of the microenvironment. Cells measure these features by developing forces via their actomyosin cytoskeleton, and respond accordingly by transducing forces into biochemical signals that instruct cell behavior. Among these, the transcriptional coactivators YAP/TAZ recently emerged as key factors mediating multiple responses to actomyosin contractility. However, whether mechanical cues regulate adult liver tissue homeostasis, and whether this occurs through YAP/TAZ, remains largely unaddressed. METHODS & RESULTS: Here we show that the F-actin capping protein CAPZ is a critical negative regulator of actomyosin contractility and mechanotransduction. Capzb inactivation alters stress fiber and focal adhesion dynamics leading to enhanced myosin activity, increased cellular traction forces, and increased liver stiffness. In vitro, this rescues YAP from inhibition by a small geometry; in vivo, inactivation of Capzb in the adult mouse liver induces YAP activation in parallel to the Hippo pathway, causing extensive hepatocyte proliferation and leading to striking organ overgrowth. Moreover, Capzb is required for the maintenance of the differentiated hepatocyte state, for metabolic zonation, and for gluconeogenesis. In keeping with changes in tissue mechanics, inhibition of the contractility regulator ROCK, or deletion of the Yap1 mechanotransducer, reverse the phenotypes emerging in Capzb-null livers. CONCLUSIONS: These results indicate a previously unrecognized role for CAPZ in tuning the mechanical properties of cells and tissues, which is required in hepatocytes for the maintenance of the differentiated hepatocyte state and to regulate organ size. More in general, it indicates for the first time a physiological role of mechanotransduction in maintaining tissue homeostasis in mammals. LAY SUMMARY: The mechanical properties of cells and tissues (i.e. whether they are soft or stiff) are thought to be important regulators of cell behavior. A recent advancement in our understanding of these phenomena has been the identification of YAP and TAZ as key factors mediating the biological responses of cells to mechanical signals in vitro. However, whether the mechanical properties of cells and/or the mechanical regulation of YAP/TAZ are relevant for mammalian tissue physiology remains unknown. Here we challenge this issue by genetic inactivation of CAPZ, a protein that regulates the cytoskeleton, i.e. the cells' scaffold by which they sense mechanical cues. We found that inactivation of CAPZ alters cells' and liver tissue's mechanical properties, leading to YAP hyperactivation. In turn, this profoundly alters liver physiology, causing organ overgrowth, defects in liver cell differentiation and metabolism. These results reveal a previously uncharacterized role for mechanical signals for the maintenance of adult liver homeostasis.This work was supported by AIRC (Associazione Italiana per la Ricerca sul Cancro) Investigator Grant 15307, WCR (Worldwide Cancer Research) Grant 15-1192, CARIPARO Eccellenza Program 2017 and University of Padua BIRD Grant to SD, AIRC ‘Hard ROCK Café’ Fellowship to GS, Marie Sklodowska-Curie Individual Fellowship (796547) to AG, AIRC Special Program Molecular Clinical Oncology ‘5 per mille’ 10016 to SB, UK Medical Research Council and Sackler Foundation Doctoral Training Grant RG70550 to ACL, UK Medical Research Council Career Development Award G1100312/1 and an Isaac Newton Trust Research Grant 17.24(p) to KF

F-actin dynamics regulates mammalian organ growth and cell fate maintenance.

BACKGROUND & AIMS: In vitro, several data indicate that cell function can be regulated by the mechanical properties of cells and of the microenvironment. Cells measure these features by developing forces via their actomyosin cytoskeleton, and respond accordingly by transducing forces into biochemical signals that instruct cell behavior. Among these, the transcriptional coactivators YAP/TAZ recently emerged as key factors mediating multiple responses to actomyosin contractility. However, whether mechanical cues regulate adult liver tissue homeostasis, and whether this occurs through YAP/TAZ, remains largely unaddressed. METHODS & RESULTS: Here we show that the F-actin capping protein CAPZ is a critical negative regulator of actomyosin contractility and mechanotransduction. Capzb inactivation alters stress fiber and focal adhesion dynamics leading to enhanced myosin activity, increased cellular traction forces, and increased liver stiffness. In vitro, this rescues YAP from inhibition by a small geometry; in vivo, inactivation of Capzb in the adult mouse liver induces YAP activation in parallel to the Hippo pathway, causing extensive hepatocyte proliferation and leading to striking organ overgrowth. Moreover, Capzb is required for the maintenance of the differentiated hepatocyte state, for metabolic zonation, and for gluconeogenesis. In keeping with changes in tissue mechanics, inhibition of the contractility regulator ROCK, or deletion of the Yap1 mechanotransducer, reverse the phenotypes emerging in Capzb-null livers. CONCLUSIONS: These results indicate a previously unrecognized role for CAPZ in tuning the mechanical properties of cells and tissues, which is required in hepatocytes for the maintenance of the differentiated hepatocyte state and to regulate organ size. More in general, it indicates for the first time a physiological role of mechanotransduction in maintaining tissue homeostasis in mammals. LAY SUMMARY: The mechanical properties of cells and tissues (i.e. whether they are soft or stiff) are thought to be important regulators of cell behavior. A recent advancement in our understanding of these phenomena has been the identification of YAP and TAZ as key factors mediating the biological responses of cells to mechanical signals in vitro. However, whether the mechanical properties of cells and/or the mechanical regulation of YAP/TAZ are relevant for mammalian tissue physiology remains unknown. Here we challenge this issue by genetic inactivation of CAPZ, a protein that regulates the cytoskeleton, i.e. the cells' scaffold by which they sense mechanical cues. We found that inactivation of CAPZ alters cells' and liver tissue's mechanical properties, leading to YAP hyperactivation. In turn, this profoundly alters liver physiology, causing organ overgrowth, defects in liver cell differentiation and metabolism. These results reveal a previously uncharacterized role for mechanical signals for the maintenance of adult liver homeostasis.This work was supported by AIRC (Associazione Italiana per la Ricerca sul Cancro) Investigator Grant 15307, WCR (Worldwide Cancer Research) Grant 15-1192, CARIPARO Eccellenza Program 2017 and University of Padua BIRD Grant to SD, AIRC ‘Hard ROCK Café’ Fellowship to GS, Marie Sklodowska-Curie Individual Fellowship (796547) to AG, AIRC Special Program Molecular Clinical Oncology ‘5 per mille’ 10016 to SB, UK Medical Research Council and Sackler Foundation Doctoral Training Grant RG70550 to ACL, UK Medical Research Council Career Development Award G1100312/1 and an Isaac Newton Trust Research Grant 17.24(p) to KF

Retinal regions shape human and murine Müller cell proteome profile and functionality

The human macula is a highly specialized retinal region with pit‐like morphology and rich in cones. How Müller cells, the principal glial cell type in the retina, are adapted to this environment is still poorly understood. We compared proteomic data from cone‐ and rod‐rich retinae from human and mice and identified different expression profiles of cone‐ and rod‐associated Müller cells that converged on pathways representing extracellular matrix and cell adhesion. In particular, epiplakin (EPPK1), which is thought to play a role in intermediate filament organization, was highly expressed in macular Müller cells. Furthermore, EPPK1 knockout in a human Müller cell‐derived cell line led to a decrease in traction forces as well as to changes in cell size, shape, and filopodia characteristics. We here identified EPPK1 as a central molecular player in the region‐specific architecture of the human retina, which likely enables specific functions under the immense mechanical loads in vivo