A Difference Version of Nori's Theorem

We consider (Frobenius) difference equations over (F_q(s,t), phi) where phi fixes t and acts on F_q(s) as the Frobenius endomorphism. We prove that every semisimple, simply-connected linear algebraic group G defined over F_q can be realized as a difference Galois group over F_{q^i}(s,t) for some i in N. The proof uses upper and lower bounds on the Galois group scheme of a Frobenius difference equation that are developed in this paper. The result can be seen as a difference analogue of Nori's Theorem which states that G(F_q) occurs as (finite) Galois group over F_q(s).Comment: 29 page

Contractility Dominates Adhesive Ligand Density in Regulating Cellular De-adhesion and Retraction Kinetics

Cells that are enzymatically detached from a solid substrate rapidly round up as the tensile prestress in the cytoskeleton is suddenly unopposed by cell–ECM adhesions. We recently showed that this retraction follows sigmoidal kinetics with time constants that correlate closely with cortical stiffness values. This raises the promising prospect that these de-adhesion measurements may be used for high-throughput screening of cell mechanical properties; however, an important limitation to doing so is the possibility that the retraction kinetics may also be influenced and potentially rate-limited by the time needed to sever matrix adhesions. In this study, we address this open question by separating contributions of contractility and adhesion to cellular de-adhesion and retraction kinetics. We first develop serum-free conditions under which U373 MG glioma cells can be cultured on substrates of fixed fibronectin density without direct matrix contributions from the medium. We show that while spreading area increases with ECM protein density, cortical stiffness and the time constants of retraction do not. Conversely, addition of lysophosphatidic acid (LPA) to stimulate cell contractility strongly speeds retraction, independent of the initial matrix protein density and LPA’s contributions to spreading area. All of these trends hold in serum-rich medium commonly used in tissue culture, with the time constants of retraction much more closely tracking cortical stiffness than adhesive ligand density or cell spreading. These results support the use of cellular de-adhesion measurements to track cellular mechanical properties

Experimental Evaluation of Seed Limitation in Alpine Snowbed Plants

Background: The distribution and abundance of plants is controlled by the availability of seeds and of sites suitable for establishment. The relative importance of these two constraints is still contentious and possibly varies among species and ecosystems. In alpine landscapes, the role of seed limitation has traditionally been neglected, and the role of abiotic gradients emphasized. Methodology/Principal Findings: We evaluated the importance of seed limitation for the incidence of four alpine snowbed species (Achillea atrata L., Achillea clusiana Tausch, Arabis caerulea L., Gnaphalium hoppeanum W. D. J. Koch) in local plant communities by comparing seedling emergence, seedling, juvenile and adult survival, juvenile and adult growth, flowering frequency as well as population growth rates lambda of experimental plants transplanted into snowbed patches which were either occupied or unoccupied by the focal species. In addition, we accounted for possible effects of competition or facilitation on these rates by including a measure of neighbourhood biomass into the analysis. We found that only A. caerulea had significantly lower seedling and adult survival as well as a lower population growth rate in unoccupied sites whereas the vital rates of the other three species did not differ among occupied and unoccupied sites. By contrast, all species were sensitive to competitive effects of the surrounding vegetation in terms of at least one of the studied rates. Conclusions/Significance: We conclude that seed and site limitation jointly determine the species composition of these snowbed plant communities and that constraining site factors include both abiotic conditions and biotic interactions. The traditional focus on abiotic gradients for explaining alpine plant distribution hence appears lopsided. The influence of seed limitation on the current distribution of these plants casts doubt on their ability to readily track shifting habitats under climate change unless seed production is considerably enhanced under a warmer climate

Inherent Interfacial Mechanical Gradients in 3D Hydrogels Influence Tumor Cell Behaviors

Cells sense and respond to the rigidity of their microenvironment by altering their morphology and migration behavior. To examine this response, hydrogels with a range of moduli or mechanical gradients have been developed. Here, we show that edge effects inherent in hydrogels supported on rigid substrates also influence cell behavior. A Matrigel hydrogel was supported on a rigid glass substrate, an interface which computational techniques revealed to yield relative stiffening close to the rigid substrate support. To explore the influence of these gradients in 3D, hydrogels of varying Matrigel content were synthesized and the morphology, spreading, actin organization, and migration of glioblastoma multiforme (GBM) tumor cells were examined at the lowest (<50 µm) and highest (>500 µm) gel positions. GBMs adopted bipolar morphologies, displayed actin stress fiber formation, and evidenced fast, mesenchymal migration close to the substrate, whereas away from the interface, they adopted more rounded or ellipsoid morphologies, displayed poor actin architecture, and evidenced slow migration with some amoeboid characteristics. Mechanical gradients produced via edge effects could be observed with other hydrogels and substrates and permit observation of responses to multiple mechanical environments in a single hydrogel. Thus, hydrogel-support edge effects could be used to explore mechanosensitivity in a single 3D hydrogel system and should be considered in 3D hydrogel cell culture systems

Biophysical mechanisms of single-cell interactions with microtopographical cues

Biophysical cues encoded in the extracellular matrix (ECM) are increasingly being explored to control cell behavior in tissue engineering applications. Recently, we showed that cell adhesion to microtopographical structures (“micropegs”) can suppress proliferation in a manner that may be blunted by inhibiting cellular contractility, suggesting that this effect is related to altered cell-scaffold mechanotransduction. We now directly investigate this possibility at the microscale through a combination of live-cell imaging, single-cell mechanics methods, and analysis of gene expression. Using time-lapse imaging, we show that when cells break adhesive contacts with micropegs, they form F-actin-filled tethers that extend and then rupture at a maximum, critical length that is greater than trailing-edge tethers observed on topographically flat substrates. This critical tether length depends on myosin activation, with inhibition of Rho-associated kinase abolishing topography-dependent differences in tether length. Using cellular de-adhesion and atomic force microscopy indentation measurements, we show that the micropegs enhance cell-scaffold adhesive interactions without changing whole-cell elasticity. Moreover, micropeg adhesion increases expression of specific mechanotransductive genes, including RhoA GTPase and myosin heavy chain II, and, in myoblasts, the functional marker connexin 43. Together, our data support a model in which microtopographical cues alter the local mechanical microenvironment of cells by modulating adhesion and adhesion-dependent mechanotransductive signaling

Neuroinflammation, Mast Cells, and Glia: Dangerous Liaisons

The perspective of neuroinflammation as an epiphenomenon following neuron damage is being replaced by the awareness of glia and their importance in neural functions and disorders. Systemic inflammation generates signals that communicate with the brain and leads to changes in metabolism and behavior, with microglia assuming a pro-inflammatory phenotype. Identification of potential peripheral-to-central cellular links is thus a critical step in designing effective therapeutics. Mast cells may fulfill such a role. These resident immune cells are found close to and within peripheral nerves and in brain parenchyma/meninges, where they exercise a key role in orchestrating the inflammatory process from initiation through chronic activation. Mast cells and glia engage in crosstalk that contributes to accelerate disease progression; such interactions become exaggerated with aging and increased cell sensitivity to stress. Emerging evidence for oligodendrocytes, independent of myelin and support of axonal integrity, points to their having strong immune functions, innate immune receptor expression, and production/response to chemokines and cytokines that modulate immune responses in the central nervous system while engaging in crosstalk with microglia and astrocytes. In this review, we summarize the findings related to our understanding of the biology and cellular signaling mechanisms of neuroinflammation, with emphasis on mast cell-glia interactions

Spontaneous hyaline cartilage regeneration can be induced in an osteochondral defect created in the femoral condyle using a novel double-network hydrogel

<p>Abstract</p> <p>Background</p> <p>Functional repair of articular osteochondral defects remains a major challenge not only in the field of knee surgery but also in tissue regeneration medicine. The purpose is to clarify whether the spontaneous hyaline cartilage regeneration can be induced in a large osteochondral defect created in the femoral condyle by means of implanting a novel double-network (DN) gel at the bottom of the defect.</p> <p>Methods</p> <p>Twenty-five mature rabbits were used in this study. In the bilateral knees of each animal, we created an osteochondral defect having a diameter of 2.4-mm in the medial condyle. Then, in 21 rabbits, we implanted a DN gel plug into a right knee defect so that a vacant space of 1.5-mm depth (in Group I), 2.5-mm depth (in Group II), or 3.5-mm depth (in Group III) was left. In the left knee, we did not apply any treatment to the defect to obtain the control data. All the rabbits were sacrificed at 4 weeks, and the gross and histological evaluations were performed. The remaining 4 rabbits underwent the same treatment as used in Group II, and real-time PCR analysis was performed at 4 weeks.</p> <p>Results</p> <p>The defect in Group II was filled with a sufficient volume of the hyaline cartilage tissue rich in proteoglycan and type-2 collagen. The Wayne's gross appearance and histology scores showed that Group II was significantly greater than Group I, III, and Control (p < 0.012). The relative expression level of type-2 collagen, aggrecan, and SOX9 mRNAs was significantly greater in Group II than in the control group (p < 0.023).</p> <p>Conclusions</p> <p>This study demonstrated that spontaneous hyaline cartilage regeneration can be induced <it>in vivo </it>in an osteochondral defect created in the femoral condyle by means of implanting the DN gel plug at the bottom of the defect so that an approximately 2-mm deep vacant space was intentionally left in the defect. This fact has prompted us to propose an innovative strategy without cell culture to repair osteochondral lesions in the femoral condyle.</p

From Molecular Signal Activation to Locomotion: An Integrated, Multiscale Analysis of Cell Motility on Defined Matrices

The adhesion, mechanics, and motility of eukaryotic cells are highly sensitive to the ligand density and stiffness of the extracellular matrix (ECM). This relationship bears profound implications for stem cell engineering, tumor invasion and metastasis. Yet, our quantitative understanding of how ECM biophysical properties, mechanotransductive signals, and assembly of contractile and adhesive structures collude to control these cell behaviors remains extremely limited. Here we present a novel multiscale model of cell migration on ECMs of defined biophysical properties that integrates local activation of biochemical signals with adhesion and force generation at the cell-ECM interface. We capture the mechanosensitivity of individual cellular components by dynamically coupling ECM properties to the activation of Rho and Rac GTPases in specific portions of the cell with actomyosin contractility, cell-ECM adhesion bond formation and rupture, and process extension and retraction. We show that our framework is capable of recreating key experimentally-observed features of the relationship between cell migration and ECM biophysical properties. In particular, our model predicts for the first time recently reported transitions from filopodial to “stick-slip” to gliding motility on ECMs of increasing stiffness, previously observed dependences of migration speed on ECM stiffness and ligand density, and high-resolution measurements of mechanosensitive protrusion dynamics during cell motility we newly obtained for this study. It also relates the biphasic dependence of cell migration speed on ECM stiffness to the tendency of the cell to polarize. By enabling the investigation of experimentally-inaccessible microscale relationships between mechanotransductive signaling, adhesion, and motility, our model offers new insight into how these factors interact with one another to produce complex migration patterns across a variety of ECM conditions

Matrix Rigidity Induces Osteolytic Gene Expression of Metastatic Breast Cancer Cells

Nearly 70% of breast cancer patients with advanced disease will develop bone metastases. Once established in bone, tumor cells produce factors that cause changes in normal bone remodeling, such as parathyroid hormone-related protein (PTHrP). While enhanced expression of PTHrP is known to stimulate osteoclasts to resorb bone, the environmental factors driving tumor cells to express PTHrP in the early stages of development of metastatic bone disease are unknown. In this study, we have shown that tumor cells known to metastasize to bone respond to 2D substrates with rigidities comparable to that of the bone microenvironment by increasing expression and production of PTHrP. The cellular response is regulated by Rho-dependent actomyosin contractility mediated by TGF-ß signaling. Inhibition of Rho-associated kinase (ROCK) using both pharmacological and genetic approaches decreased PTHrP expression. Furthermore, cells expressing a dominant negative form of the TGF-ß receptor did not respond to substrate rigidity, and inhibition of ROCK decreased PTHrP expression induced by exogenous TGF-ß. These observations suggest a role for the differential rigidity of the mineralized bone microenvironment in early stages of tumor-induced osteolysis, which is especially important in metastatic cancer since many cancers (such as those of the breast and lung) preferentially metastasize to bone