Comment on "Another look at the uniform rope sliding over the edge of a smooth table"

Comment on "Another look at the uniform rope sliding over the edge of a smooth table"

Energy-entropy-momentum time integration methods for coupled smooth dissipative problems

Esta tesis aborda la formulación, análisis e implementación de métodos numéricos de integración temporal para la solución de sistemas disipativos suaves de dimensión finita o infinita de manera que su estructura continua sea conservada. Se entiende por dichos sistemas aquellos que involucran acoplamiento termo-mecánico y/o efectos disipativos internos modelados por variables internas que siguen leyes continuas, de modo que su evolución es considerada suave. La dinámica de estos sistemas está gobernada por las leyes de la termodinámica y simetrías, las cuales constituyen la estructura que se pretende conservar de forma discreta. Para ello, los sistemas disipativos se describen geométricamente mediante estructuras metriplécticas que identifican claramente las partes reversible e irreversible de la evolución del sistema. Así, usando una de estas estructuras conocida por las siglas (en inglés) de GENERIC, la estructura disipativa de los sistemas es identificada del mismo modo que lo es la Hamiltoniana para sistemas conservativos. Con esto, métodos (EEM) con precisión de segundo orden que conservan la energía, producen entropía y conservan los impulsos lineal y angular son formulados mediante el uso del operador derivada discreta introducido para asegurar la conservación de la Hamiltoniana y las simetrías de sistemas conservativos. Siguiendo estas directrices, se formulan dos tipos de métodos EEM basados en el uso de la temperatura o de la entropía como variable de estado termodinámica, lo que presenta importantes implicaciones que se discuten a lo largo de esta tesis. Entre las cuales cabe destacar que las condiciones de contorno de Dirichlet son naturalmente impuestas con la formulación basada en la temperatura. Por último, se validan dichos métodos y se comprueban sus mejores prestaciones en términos de la estabilidad y robustez en comparación con métodos estándar. This dissertation is concerned with the formulation, analysis and implementation of structure-preserving time integration methods for the solution of the initial(-boundary) value problems describing the dynamics of smooth dissipative systems, either finite- or infinite-dimensional ones. Such systems are understood as those involving thermo-mechanical coupling and/or internal dissipative effects modeled by internal state variables considered to be smooth in the sense that their evolutions follow continuos laws. The dynamics of such systems are ruled by the laws of thermodynamics and symmetries which constitutes the structure meant to be preserved in the numerical setting. For that, dissipative systems are geometrically described by metriplectic structures which clearly identify the reversible and irreversible parts of their dynamical evolution. In particular, the framework known by the acronym GENERIC is used to reveal the systems' dissipative structure in the same way as the Hamiltonian is for conserving systems. Given that, energy-preserving, entropy-producing and momentum-preserving (EEM) second-order accurate methods are formulated using the discrete derivative operator that enabled the formulation of Energy-Momentum methods ensuring the preservation of the Hamiltonian and symmetries for conservative systems. Following these guidelines, two kind of EEM methods are formulated in terms of entropy and temperature as a thermodynamical state variable, involving important implications discussed throughout the dissertation. Remarkably, the formulation in temperature becomes central to accommodate Dirichlet boundary conditions. EEM methods are finally validated and proved to exhibit enhanced numerical stability and robustness properties compared to standard ones.

Targeting Gβγ signaling in arterial vascular smooth muscle proliferation: A novel strategy to limit restenosis

Restenosis continues to be a major problem limiting the effectiveness of revascularization procedures. To date, the roles of heterotrimeric G proteins in the triggering of pathological vascular smooth muscle (VSM) cell proliferation have not been elucidated. βγ subunits of heterotrimeric G proteins (Gβγ) are known to activate mitogen-activated protein (MAP) kinases after stimulation of certain G protein-coupled receptors; however, their relevance in VSM mitogenesis in vitro or in vivo is not known. Using adenoviral-mediated transfer of a transgene encoding a peptide inhibitor of Gβγ signaling (βARKct), we evaluated the role of Gβγ in MAP kinase activation and proliferation in response to several mitogens, including serum, in cultured rat VSM cells. Our results include the striking finding that serum-induced proliferation of VSM cells in vitro is mediated largely via Gβγ. Furthermore, we studied the effects of in vivo adenoviral-mediated βARKct gene transfer on VSM intimal hyperplasia in a rat carotid artery restenosis model. Our in vivo results demonstrated that the presence of the βARKct in injured rat carotid arteries significantly reduced VSM intimal hyperplasia by 70%. Thus, Gβγ plays a critical role in physiological VSM proliferation, and targeted Gβγ inhibition represents a novel approach for the treatment of pathological conditions such as restenosis.

20-Hydroxyeicosatetraenoic acid mediates calcium/calmodulin-dependent protein kinase II-induced mitogen-activated protein kinase activation in vascular smooth muscle cells

Norepinephrine (NE) and angiotensin II (Ang II), by promoting extracellular Ca2+ influx, increase Ca2+/calmodulin-dependent kinase II (CaMKII) activity, leading to activation of mitogen-activated protein kinase (MAPK) and cytosolic phospholipase A2 (cPLA2), resulting in release of arachidonic acid (AA) for prostacyclin synthesis in rabbit vascular smooth muscle cells. However, the mechanism by which CaMKII activates MAPK is unclear. The present study was conducted to determine the contribution of AA and its metabolites as possible mediators of CaMKII-induced MAPK activation by NE, Ang II, and epidermal growth factor (EGF) in vascular smooth muscle cells. NE-, Ang II-, and EGF-stimulated MAPK and cPLA2 were reduced by inhibitors of cytochrome P450 (CYP450) and lipoxygenase but not by cyclooxygenase. NE-, Ang II-, and EGF-induced increases in Ras activity, measured by its translocation to plasma membrane, were abolished by CYP450, lipoxygenase, and farnesyltransferase inhibitors. An AA metabolite of CYP450, 20-hydroxyeicosatetraenoic acid (20-HETE), increased the activities of MAPK and cPLA2 and caused translocation of Ras. These data suggest that activation of MAPK by NE, Ang II, and EGF is mediated by a signaling mechanism involving 20-HETE, which is generated by stimulation of cPLA2 by CaMKII. Activation of Ras/MAPK by 20-HETE amplifies cPLA2 activity and releases additional AA by a positive feedback mechanism. This mechanism of Ras/MAPK activation by 20-HETE may play a central role in the regulation of other cellular signaling molecules involved in cell proliferation and growth.

Characterization of the α1B-adrenergic receptor gene promoter region and hypoxia regulatory elements in vascular smooth muscle

We previously demonstrated that α1B-adrenergic receptor (AR) gene transcription, mRNA, and functionally coupled receptors increase during 3% O2 exposure in aorta, but not in vena cava smooth muscle cells (SMC). We report here that α1BAR mRNA also increases during hypoxia in liver and lung, but not heart and kidney. A single 2.7-kb α1BAR mRNA was detected in aorta and vena cava during normoxia and hypoxia. The α1BAR 5′ flanking region was sequenced to −2,460 (relative to ATG +1). Transient transfection experiments identify the minimal promoter region between −270 and −143 and sequence between −270 and −248 that are required for transcription of the α1BAR gene in aorta and vena cava SMC during normoxia and hypoxia. An ATTAAA motif within this sequence specifically binds aorta, vena cava, and DDT1MF-2 nuclear proteins, and transcription primarily initiates downstream of this motif at approximately −160 in aorta SMC. Sequence between −837 and −273 conferred strong hypoxic induction of transcription in aorta, but not in vena cava SMC, whereas the cis-element for the transcription factor, hypoxia-inducible factor 1, conferred hypoxia-induced transcription in both aorta and vena cava SMC. These data identify sequence required for transcription of the α1BAR gene in vascular SMC and suggest the atypical TATA-box, ATTAAA, may mediate this transcription. Hypoxia-sensitive regions of the α1BAR gene also were identified that may confer the differential hypoxic increase in α1BAR gene transcription in aorta, but not in vena cava SMC.

Smooth particle hydrodynamics study of surface defect machining for diamond turning of silicon

Acknowledgments The authors would like to thank EPSRC (EP/ K018345/1) and Royal Society-NSFC International Exchange Scheme for providing financial support to this research.

Both N-terminal myosin-binding and C-terminal actin-binding sites on smooth muscle caldesmon are required for caldesmon-mediated inhibition of actin filament velocity

It has been suggested that the tethering caused by binding of the N-terminal region of smooth muscle caldesmon (CaD) to myosin and its C-terminal region to actin contributes to the inhibition of actin-filament movement over myosin heads in an in vitro motility assay. However, direct evidence for this assumption has been lacking. In this study, analysis of baculovirus-generated N-terminal and C-terminal deletion mutants of chicken-gizzard CaD revealed that the major myosin-binding site on the CaD molecule resides in a 30-amino acid stretch between residues 24 and 53, based on the very low level of binding of CaDΔ24–53 lacking the residues 24–53 to myosin compared with the level of binding of CaDΔ54–85 missing the adjacent residues 54–85 or of the full-length CaD. As expected, deletion of the region between residues 24 and 53 or between residues 54 and 85 had no effect on either actin-binding or inhibition of actomyosin ATPase activity. Deletion of residues 24–53 nearly abolished the ability of CaD to inhibit actin filament velocity in the in vitro motility experiments, whereas CaDΔ54–85 strongly inhibited actin filament velocity in a manner similar to that of full-length CaD. Moreover, CaD1–597, which lacks the major actin-binding site(s), did not inhibit actin-filament velocity despite the presence of the major myosin-binding site. These data provide direct evidence for the inhibition of actin filament velocity in the in vitro motility assay caused by the tethering of myosin to actin through binding of both the CaD N-terminal region to myosin and the C-terminal region to actin.

Smooth muscle myosin mutants containing a single tryptophan reveal molecular interactions at the actin-binding interface

Elucidation of the molecular details of the cyclic actomyosin interaction requires the ability to examine structural changes at specific sites in the actin-binding interface of myosin. To study these changes dynamically, we have expressed two mutants of a truncated fragment of chicken gizzard smooth muscle myosin, which includes the motor domain and essential light chain (MDE). These mutants were engineered to contain a single tryptophan at (Trp-546) or near (Trp-625) the putative actin-binding interface. Both 546- and 625-MDE exhibited actin-activated ATPase and actin-binding activities similar to wild-type MDE. Fluorescence emission spectra and acrylamide quenching of 546- and 625-MDE suggest that Trp-546 is nearly fully exposed to solvent and Trp-625 is less than 50% exposed in the presence and absence of ATP, in good agreement with the available crystal structure data. The spectrum of 625-MDE bound to actin was quite similar to the unbound spectrum indicating that, although Trp-625 is located near the 50/20-kDa loop and the 50-kDa cleft of myosin, its conformation does not change upon actin binding. However, a 10-nm blue shift in the peak emission wavelength of 546-MDE observed in the presence of actin indicates that Trp-546, located in the A-site of the lower 50-kDa subdomain of myosin, exists in a more buried environment and may directly interact with actin in the rigor acto-S1 complex. This change in the spectrum of Trp-546 constitutes direct evidence for a specific molecular interaction between residues in the A-site of myosin and actin.

Slow cycling of unphosphorylated myosin is inhibited by calponin, thus keeping smooth muscle relaxed

A key unanswered question in smooth muscle biology is whether phosphorylation of the myosin regulatory light chain (RLC) is sufficient for regulation of contraction, or if thin-filament-based regulatory systems also contribute to this process. To address this issue, the endogenous RLC was extracted from single smooth muscle cells and replaced with either a thiophosphorylated RLC or a mutant RLC (T18A/S19A) that cannot be phosphorylated by myosin light chain kinase. The actin-binding protein calponin was also extracted. Following photolysis of caged ATP, cells without calponin that contained a nonphosphorylatable RLC shortened at 30% of the velocity and produced 65% of the isometric force of cells reconstituted with the thiophosphorylated RLC. The contraction of cells reconstituted with nonphosphorylatable RLC was, however, specifically suppressed in cells that contained calponin. These results indicate that calponin is required to maintain cells in a relaxed state, and that in the absence of this inhibition, dephosphorylated cross-bridges can slowly cycle and generate force. These findings thus provide a possible framework for understanding the development of latch contraction, a widely studied but poorly understood feature of smooth muscle.

Inactivation of calcium-activated chloride channels in smooth muscle by calcium/calmodulin-dependent protein kinase

To determine the mechanisms responsible for the termination of Ca2+-activated Cl− currents (ICl(Ca)), simultaneous measurements of whole cell currents and intracellular Ca2+ concentration ([Ca2+]i) were made in equine tracheal myocytes. In nondialyzed cells, or cells dialyzed with 1 mM ATP, ICl(Ca) decayed before the [Ca2+]i decline, whereas the calcium-activated potassium current decayed at the same rate as [Ca2+]i. Substitution of AMP-PNP or ADP for ATP markedly prolonged the decay of ICl(Ca), resulting in a rate of current decay similar to that of the fall in [Ca2+]i. In the presence of ATP, dialysis of the calmodulin antagonist W7, the Ca2+/calmodulin-dependent kinase II (CaMKII) inhibitor KN93, or a CaMKII-specific peptide inhibitor the rate of ICl(Ca) decay was slowed and matched the [Ca2+]i decline, whereas H7, a nonspecific kinase inhibitor with low affinity for CaMKII, was without effect. When a sustained increase in [Ca2+]i was produced in ATP dialyzed cells, the current decayed completely, whereas in cells loaded with 5′-adenylylimidodiphosphate (AMP-PNP), KN93, or the CaMKII inhibitory peptide, ICl(Ca) did not decay. Slowly decaying currents were repeatedly evoked in ADP- or AMP-PNP-loaded cells, but dialysis of adenosine 5′-O-(3-thiotriphosphate) or okadaic acid resulted in a smaller initial ICl(Ca), and little or no current (despite a normal [Ca2+]i transient) with a second stimulation. These data indicate that CaMKII phosphorylation results in the inactivation of calcium-activated chloride channels, and that transition from the inactivated state to the closed state requires protein dephosphorylation.

Epigallocathechin-3 Gallate Selectively Inhibits the PDGF-BB–induced Intracellular Signaling Transduction Pathway in Vascular Smooth Muscle Cells and Inhibits Transformation of sis-transfected NIH 3T3 Fibroblasts and Human Glioblastoma Cells (A172)

Enhanced activity of receptor tyrosine kinases such as the PDGF β-receptor and EGF receptor has been implicated as a contributing factor in the development of malignant and nonmalignant proliferative diseases such as cancer and atherosclerosis. Several epidemiological studies suggest that green tea may prevent the development of cancer and atherosclerosis. One of the major constituents of green tea is the polyphenol epigallocathechin-3 gallate (EGCG). In an attempt to offer a possible explanation for the anti-cancer and anti-atherosclerotic activity of EGCG, we examined the effect of EGCG on the PDGF-BB–, EGF-, angiotensin II-, and FCS-induced activation of the 44 kDa and 42 kDa mitogen-activated protein (MAP) kinase isoforms (p44mapk/p42mapk) in cultured vascular smooth muscle cells (VSMCs) from rat aorta. VSMCs were treated with EGCG (1–100 μM) for 24 h and stimulated with the above mentioned agonists for different time periods. Stimulation of the p44mapk/p42mapk was detected by the enhanced Western blotting method using phospho-specific MAP kinase antibodies that recognized the Tyr204-phosphorylated (active) isoforms. Treatment of VSMCs with 10 and 50 μM EGCG resulted in an 80% and a complete inhibition of the PDGF-BB–induced activation of MAP kinase isoforms, respectively. In striking contrast, EGCG (1–100 μM) did not influence MAP kinase activation by EGF, angiotensin II, and FCS. Similarly, the maximal effect of PDGF-BB on the c-fos and egr-1 mRNA expression as well as on intracellular free Ca2+ concentration was completely inhibited in EGCG-treated VSMCs, whereas the effect of EGF was not affected. Quantification of the immunoprecipitated tyrosine-phosphorylated PDGF-Rβ, phosphatidylinositol 3′-kinase, and phospholipase C-γ1 by the enhanced Western blotting method revealed that EGCG treatment effectively inhibits tyrosine phosphorylation of these kinases in VSMCs. Furthermore, we show that spheroid formation of human glioblastoma cells (A172) and colony formation of sis-transfected NIH 3T3 cells in semisolid agar are completely inhibited by 20–50 μM EGCG. Our findings demonstrate that EGCG is a selective inhibitor of the tyrosine phosphorylation of PDGF-Rβ and its downstream signaling pathway. The present findings may partly explain the anti-cancer and anti-atherosclerotic activity of green tea.

The Thrombospondin Receptor CD47 (IAP) Modulates and Associates with α2β1 Integrin in Vascular Smooth Muscle Cells

The carboxyl-terminal domain of thrombospondin-1 enhances the migration and proliferation of smooth muscle cells. Integrin-associated protein (IAP or CD47) is a receptor for the thrombospondin-1 carboxyl-terminal cell-binding domain and binds the agonist peptide 4N1K (kRFYVVMWKk) from this domain. 4N1K peptide stimulates chemotaxis of both human and rat aortic smooth muscle cells on gelatin-coated filters. The migration on gelatin is specifically blocked by monoclonal antibodies against IAP and a β1 integrin, rather than αvβ3 as found previously for 4N1K-stimulated chemotaxis of endothelial cells on gelatin. Both human and rat smooth muscle cells displayed a weak migratory response to soluble type I collagen; however, the presence of 4N1K peptide or intact thrombospondin-1 provoked a synergistic chemotactic response that was partially blocked by antibodies to α2 and β1 integrin subunits and to IAP. A combination of antiα2 and IAP monoclonal antibodies completely blocked chemotaxis. RGD peptide and antiαvβ3 mAb were without effect. 4N1K and thrombospondin-1 did not augment the chemotactic response of smooth muscle cells to fibronectin, vitronectin, or collagenase-digested type I collagen. Complex formation between α2β1 and IAP was detected by the coimmunoprecipitation of both α2 and β1 integrin subunits with IAP. These data suggest that IAP can associate with α2β1 integrin and modulate its function.

Localization of Autocrine Motility Factor Receptor to Caveolae and Clathrin-independent Internalization of Its Ligand to Smooth Endoplasmic Reticulum

Autocrine motility factor receptor (AMF-R) is a cell surface receptor that is also localized to a smooth subdomain of the endoplasmic reticulum, the AMF-R tubule. By postembedding immunoelectron microscopy, AMF-R concentrates within smooth plasmalemmal vesicles or caveolae in both NIH-3T3 fibroblasts and HeLa cells. By confocal microscopy, cell surface AMF-R labeled by the addition of anti-AMF-R antibody to viable cells at 4°C exhibits partial colocalization with caveolin, confirming the localization of cell surface AMF-R to caveolae. Labeling of cell surface AMF-R by either anti-AMF-R antibody or biotinylated AMF (bAMF) exhibits extensive colocalization and after a pulse of 1–2 h at 37°C, bAMF accumulates in densely labeled perinuclear structures as well as fainter tubular structures that colocalize with AMF-R tubules. After a subsequent 2- to 4-h chase, bAMF is localized predominantly to AMF-R tubules. Cytoplasmic acidification, blocking clathrin-mediated endocytosis, results in the essentially exclusive distribution of internalized bAMF to AMF-R tubules. By confocal microscopy, the tubular structures labeled by internalized bAMF show complete colocalization with AMF-R tubules. bAMF internalized in the presence of a 10-fold excess of unlabeled AMF labels perinuclear punctate structures, which are therefore the product of fluid phase endocytosis, but does not label AMF-R tubules, demonstrating that bAMF targeting to AMF-R tubules occurs via a receptor-mediated pathway. By electron microscopy, bAMF internalized for 10 min is located to cell surface caveolae and after 30 min is present within smooth and rough endoplasmic reticulum tubules. AMF-R is therefore internalized via a receptor-mediated clathrin-independent pathway to smooth ER. The steady state localization of AMF-R to caveolae implicates these cell surface invaginations in AMF-R endocytosis.

Binding of Insulin-like Growth Factor (IGF)–Binding Protein-5 to Smooth-Muscle Cell Extracellular Matrix Is a Major Determinant of the Cellular Response to IGF-I

Insulin-like growth factor–binding protein-5 (IGFBP-5) has been shown to bind to fibroblast extracellular matrix (ECM). Extracellular matrix binding of IGFBP-5 leads to a decrease in its affinity for insulin-like growth factor-I (IGF-I), which allows IGF-I to better equilibrate with IGF receptors. When the amount of IGFBP-5 that is bound to ECM is increased by exogenous addition, IGF-I’s effect on fibroblast growth is enhanced. In this study we identified the specific basic residues in IGFBP-5 that mediate its binding to porcine smooth-muscle cell (pSMC) ECM. An IGFBP-5 mutant containing alterations of basic residues at positions 211, 214, 217, and 218 had the greatest reduction in ECM binding, although three other mutants, R214A, R207A/K211N, and K202A/R206N/R207A, also had major decreases. In contrast, three other mutants, R201A/K202N/R206N/R208A, and K217N/R218A and K211N, had only minimal reductions in ECM binding. This suggested that residues R207 and R214 were the most important for binding, whereas alterations in K211 and R218, which align near them, had minimal effects. To determine the effect of a reduction in ECM binding on the cellular replication response to IGF-I, pSMCs were transfected with the mutant cDNAs that encoded the forms of IGFBPs with the greatest changes in ECM binding. The ECM content of IGFBP-5 from cultures expressing the K211N, R214A, R217A/R218A, and K202A/R206N/R207A mutants was reduced by 79.6 and 71.7%, respectively, compared with cells expressing the wild-type protein. In contrast, abundance of the R201A/K202N/R206N/R208A mutant was reduced by only 14%. Cells expressing the two mutants with reduced ECM binding had decreased DNA synthesis responses to IGF-I, but the cells expressing the R201A/K202N/R206N/R208A mutant responded well to IGF-I. The findings suggest that specific basic amino acids at positions 207 and 214 mediate the binding of IGFBP-5 to pSMC/ECM. Smooth-muscle cells that constitutively express the mutants that bind weakly to ECM are less responsive to IGF-I, suggesting that ECM binding of IGFBP-5 is an important variable that determines cellular responsiveness.

Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.