Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

Stable-Isotope and Trace Element Time Series from Fedchenko Glacier (Pamirs) Snow/Firn Cores

In summer 2005, two pilot snow/firn cores were obtained at 5365 and 5206 m a.s.l. on Fedchenko glacier, Pamirs, Tajikistan, the world's longest and deepest alpine glacier. The well-defined seasonal layering appearing in stable-isotope and trace element distribution identified the physical links controlling the climate and aerosol concentration signals. Air temperature and humidity/precipitation were the primary determinants of stable-isotope ratios. Most precipitation over the Pamirs originated in the Atlantic. In summer, water vapor was re-evaporated from semi-arid regions in central Eurasia. The semi-arid regions contribute to non-soluble aerosol loading in snow accumulated on Fedchenko glacier. In the Pamir core, concentrations of rare earth elements, major and other elements were less than those in the Tien Shan but greater than those in Antarctica, Greenland, the Alps and the Altai. The content of heavy metals in the Fedchenko cores is 2-14 times lower than in the Altai glaciers. Loess from Afghan-Tajik deposits is the predominant lithogenic material transported to the Pamirs. Trace elements generally showed that aerosol concentration tended to increase on the windward slopes during dust storms but tended to decrease with altitude under clear conditions. The trace element profile documented one of the most severe droughts in the 20th century.

Three-Dimensional Mechanics of Yakutat Convergence in the Southern Alaskan Plate Corner

Three-dimensional numerical models are used to investigate the mechanical evolution of the southern Alaskan plate corner where the Yakutat and the Pacific plates converge on the North American plate. The evolving model plate boundary consists of Convergent, Lateral, and Subduction subboundaries with flow separation of incoming material into upward or downward trajectories forming dual, nonlinear advective thermal/mechanical anomalies that fix the position of major subaerial mountain belts. The model convergent subboundary evolves into two teleconnected orogens: Inlet and Outlet orogens form at locations that correspond with the St. Elias and the Central Alaska Range, respectively, linked to the East by the Lateral boundary. Basins form parallel to the orogens in response to the downward component of velocity associated with subduction. Strain along the Lateral subboundary varies as a function of orogen rheology and magnitude and distribution of erosion. Strain-dependent shear resistance of the plate boundary associated with the shallow subduction zone controls the position of the Inlet orogen. The linkages among these plate boundaries display maximum shear strain rates in the horizontal and vertical planes where the Lateral subboundary joins the Inlet and Outlet orogens. The location of the strain maxima shifts with time as the separation of the Inlet and Outlet orogens increases. The spatiotemporal predictions of the model are consistent with observed exhumation histories deduced from thermochronology, as well as stratigraphic studies of synorogenic deposits. In addition, the complex structural evolution of the St Elias region is broadly consistent with the predicted strain field evolution. Citation: Koons, P. O., B. P. Hooks, T. Pavlis, P. Upton, and A. D. Barker (2010), Three-dimensional mechanics of Yakutat convergence in the southern Alaskan plate corner, Tectonics, 29, TC4008, doi: 10.1029/2009TC002463.

Relating Crevassing to Non-Linear Strain in the Floating Part of Jakobshavn Isbrae, West Greenland

Jakobshavn Isbrae is a major ice stream that drains the west-central Greenland ice sheet and becomes afloat in Jakobshavn Isfiord (69degreesN, 49degreesW), where it has maintained the world's fastest-known sustained velocity and calving rate (7 km a(-1)) for at least four decades. The floating portion is approximately 12 km long and 6 km wide. Surface elevations and motion vectors were determined photogrammetrically for about 500 crevasses on the floating ice, and adjacent grounded ice, using aerial photographs obtained 2 weeks apart in July 1985. Surface strain rates were computed from a mesh of 399 quadrilateral elements having velocity measurements at each corner. It is shown that heavy crevassing of floating ice invalidates the assumptions of linear strain theory that (i) surface strain in the floating ice is homogeneous in both space and time, (ii) the squares and products of strain components are nil, and (iii) first- and second-order rotation components are small compared to strain components. Therefore, strain rates and rotation rates were also computed using non-linear strain theory. The percentage difference between computed linear and non-linear second invariants of strain rate per element were greatest (mostly in the range 40-70%) where crevassing is greatest. Isopleths of strain rate parallel and transverse to flow and elevation isopleths relate crevassing to known and inferred pinning points.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

Loop formulation of the supersymmetric nonlinear O(N) sigma model

We derive the fermion loop formulation for the supersymmetric nonlinear O(N) sigma model by performing a hopping expansion using Wilson fermions. In this formulation the fermionic contribution to the partition function becomes a sum over all possible closed non-oriented fermion loop configurations. The interaction between the bosonic and fermionic degrees of freedom is encoded in the constraints arising from the supersymmetry and induces flavour changing fermion loops. For N ≥ 3 this leads to fermion loops which are no longer self-avoiding and hence to a potential sign problem. Since we use Wilson fermions the bare mass needs to be tuned to the chiral point. For N = 2 we determine the critical point and present boson and fermion masses in the critical regime.

Comparison of theoretical fixation stability of three devices employed in medial opening wedge high tibial osteotomy: a finite element analysis.

BACKGROUND Medial open wedge high tibial osteotomy is a well-established procedure for the treatment of unicompartmental osteoarthritis and symptomatic varus malalignment. We hypothesized that different fixation devices generate different fixation stability profiles for the various wedge sizes in a finite element (FE) analysis. METHODS Four types of fixation were compared: 1) first and 2) second generation Puddu plates, and 3) TomoFix plate with and 4) without bone graft. Cortical and cancellous bone was modelled and five different opening wedge sizes were studied for each model. Outcome measures included: 1) stresses in bone, 2) relative displacement of the proximal and distal tibial fragments, 3) stresses in the plates, 4) stresses on the upper and lower screw surfaces in the screw channels. RESULTS The highest load for all fixation types occurred in the plate axis. For the vast majority of the wedge sizes and fixation types the shear stress (von Mises stress) was dominating in the bone independent of fixation type. The relative displacements of the tibial fragments were low (in μm range). With an increasing wedge size this displacement tended to increase for both Puddu plates and the TomoFix plate with bone graft. For the TomoFix plate without bone graft a rather opposite trend was observed.For all fixation types the occurring stresses at the screw-bone contact areas pulled at the screws and exceeded the allowable threshold of 1.2 MPa for at least one screw surface. Of the six screw surfaces that were studied, the TomoFix plate with bone graft showed a stress excess of one out of twelve and without bone graft, five out of twelve. With the Puddu plates, an excess stress occurred in the majority of screw surfaces. CONCLUSIONS The different fixation devices generate different fixation stability profiles for different opening wedge sizes. Based on the computational simulations, none of the studied osteosynthesis fixation types warranted an intransigent full weight bearing per se. The highest fixation stability was observed for the TomoFix plates and the lowest for the first generation Puddu plate. These findings were revealed in theoretical models and need to be validated in controlled clinical settings.

A class of exact Navier-Stokes solutions for homogeneous flat-plate boundary layers and their linear stability

We introduce a new boundary layer formalism on the basis of which a class of exact solutions to the Navier–Stokes equations is derived. These solutions describe laminar boundary layer flows past a flat plate under the assumption of one homogeneous direction, such as the classical swept Hiemenz boundary layer (SHBL), the asymptotic suction boundary layer (ASBL) and the oblique impingement boundary layer. The linear stability of these new solutions is investigated, uncovering new results for the SHBL and the ASBL. Previously, each of these flows had been described with its own formalism and coordinate system, such that the solutions could not be transformed into each other. Using a new compound formalism, we are able to show that the ASBL is the physical limit of the SHBL with wall suction when the chordwise velocity component vanishes while the homogeneous sweep velocity is maintained. A corresponding non-dimensionalization is proposed, which allows conversion of the new Reynolds number definition to the classical ones. Linear stability analysis for the new class of solutions reveals a compound neutral surface which contains the classical neutral curves of the SHBL and the ASBL. It is shown that the linearly most unstable Görtler–Hämmerlin modes of the SHBL smoothly transform into Tollmien–Schlichting modes as the chordwise velocity vanishes. These results are useful for transition prediction of the attachment-line instability, especially concerning the use of suction to stabilize boundary layers of swept-wing aircraft.

Plate fixation of extra-articular fractures of the proximal phalanx: do new implants cause less problems?

BACKGROUND Limited range of finger motion is a frequent complication after plate fixation of phalangeal fractures. The purpose of this study was to evaluate the results of plate fixation of extra-articular fractures of the proximal phalanx using current low-profile mini-fragment-systems. METHODS From 2006 to 2012, 32 patients with 36 extra-articular fractures of the proximal phalanx of the triphalangeal fingers were treated with open reduction and plate fixation (ORPF) using 1.2 and 1.5 mm mini-fragment systems. Patients presenting with open fractures grade 2 and 3 or relevant laceration of adjacent structures were excluded from the study. We retrospectively evaluated the rate of mal-union or non-union after ORPF, the need for revision surgery, for plate removal, and for tenolysis. Data were analyzed for further complications with regard to infections or complex regional pain syndrome (CRPS). RESULTS No infections were noted. Five patients developed transient symptoms of CRPS. Six weeks postoperatively, total active finger motion (TAM) averaged 183°, and all 32 patients underwent formal hand therapy. At the latest follow-up or at the time of plate removal, respectively, the mean TAM improved to 213°. Extension lag of proximal interphalangeal joints was found in 67 % of all fractured fingers. Secondary surgery was necessary in 14 of 32 patients (2 corrective osteotomies, 12 plate removals including 7 procedures explicitly because of reduced mobility). CONCLUSIONS Despite of new implant designs significant problems persist. Adhesions of extensor tendons leading to limited range of finger motion are still the most frequent complications after ORPF of proximal phalangeal fractures, even in absence of significant soft-tissue damage. LEVEL OF EVIDENCE Therapeutic, Retrospective, Level IV.

Fluid-related inclusions in Alpine high-pressure peridotite reveal trace element recycling during subduction-zone dehydration of serpentinized mantle (Cima di Gagnone, Swiss Alps).

Serpentinites release at sub-arc depths volatiles and several fluid-mobile trace elements found in arc magmas. Constraining element uptake in these rocks and defining the trace element composition of fluids released upon serpentinite dehydration can improve our understanding of mass transfer across subduction zones and to volcanic arcs. The eclogite-facies garnet metaperidotite and chlorite harzburgite bodies embedded in paragneiss of the subduction melange from Cima di Gagnone derive from serpentinized peridotite protoliths and are unique examples of ultramafic rocks that experienced subduction metasomatism and devolatilization. In these rocks, metamorphic olivine and garnet trap polyphase inclusions representing the fluid released during high-pressure breakdown of antigorite and chlorite. Combining major element mapping and laser-ablation ICP-MS bulk inclusion analysis, we characterize the mineral content of polyphase inclusions and quantify the fluid composition. Silicates, Cl-bearing phases, sulphides, carbonates, and oxides document post-entrapment mineral growth in the inclusions starting immediately after fluid entrapment. Compositional data reveal the presence of two different fluid types. The first (type A) records a fluid prominently enriched in fluid-mobile elements, with Cl, Cs, Pb, As, Sb concentrations up to 10(3) PM (primitive mantle), similar to 10(2) PM Tit Ba, while Rb, B, Sr, Li, U concentrations are of the order of 10(1) PM, and alkalis are similar to 2 PM. The second fluid (type B) has considerably lower fluid-mobile element enrichments, but its enrichment patterns are comparable to type A fluid. Our data reveal multistage fluid uptake in these peridotite bodies, including selective element enrichment during seafloor alteration, followed by fluid-rock interaction along with subduction metamorphism in the plate interface melange. Here, infiltration of sediment-equilibrated fluid produced significant enrichment of the serpentinites in As, Sb, B, Pb, an enriched trace element pattern that was then transferred to the fluid released at greater depth upon serpentine dehydration (type A fluid). The type B fluid hosted by garnet may record the composition of the chlorite breakdown fluid released at even greater depth. The Gagnone study-case demonstrates that serpentinized peridotites acquire water and fluid-mobile elements during ocean floor hydration and through exchange with sediment-equilibrated fluids in the early subduction stages. Subsequent antigorite devolatilization at subarc depths delivers aqueous fluids to the mantle wedge that can be prominently enriched in sediment-derived components, potentially triggering arc magmatism without the need of concomitant dehydration/melting of metasediments or altered oceanic crust.

Probing the moduli dependence of refined topological amplitudes

With the aim of providing a worldsheet description of the refined topological string, we continue the study of a particular class of higher derivative couplings Fg,n in the type II string effective action compactified on a Calabi–Yau threefold. We analyse first order differential equations in the anti-holomorphic moduli of the theory, which relate the Fg,n to other component couplings. From the point of view of the topological theory, these equations describe the contribution of non-physical states to twisted correlation functions and encode an obstruction for interpreting the Fg,n as the free energy of the refined topological string theory. We investigate possibilities of lifting this obstruction by formulating conditions on the moduli dependence under which the differential equations simplify and take the form of generalised holomorphic anomaly equations. We further test this approach against explicit calculations in the dual heterotic theory.

A transposable element insertion in APOB causes cholesterol deficiency in Holstein cattle

Cholesterol deficiency, a new autosomal recessive inherited genetic defect in Holstein cattle, has been recently reported to have an influence on the rearing success of calves. The affected animals show unresponsive diarrhea accompanied by hypocholesterolemia and usually die within the first weeks or months of life. Here, we show that whole genome sequencing combined with the knowledge about the pedigree and inbreeding status of a livestock population facilitates the identification of the causative mutation. We resequenced the entire genomes of an affected calf and a healthy partially inbred male carrying one copy of the critical 2.24-Mb chromosome 11 segment in its ancestral state and one copy of the same segment with the cholesterol deficiency mutation. We detected a single structural variant, homozygous in the affected case and heterozygous in the non-affected carrier male. The genetic makeup of this key animal provides extremely strong support for the causality of this mutation. The mutation represents a 1.3kb insertion of a transposable LTR element (ERV2-1) in the coding sequence of the APOB gene, which leads to truncated transcripts and aberrant splicing. This finding was further supported by RNA sequencing of the liver transcriptome of an affected calf. The encoded apolipoprotein B is an essential apolipoprotein on chylomicrons and low-density lipoproteins, and therefore, the mutation represents a loss of function mutation similar to autosomal recessive inherited familial hypobetalipoproteinemia-1 (FHBL1) in humans. Our findings provide a direct gene test to improve selection against this deleterious mutation in Holstein cattle.

Nitinol Stent Oversizing in Patients Undergoing Popliteal Artery Revascularization: A Finite Element Study

Nitinol stent oversizing is frequently performed in peripheral arteries to ensure a desirable lumen gain. However, the clinical effect of mis-sizing remains controversial. The goal of this study was to provide a better understanding of the structural and hemodynamic effects of Nitinol stent oversizing. Five patient-specific numerical models of non-calcified popliteal arteries were developed to simulate the deployment of Nitinol stents with oversizing ratios ranging from 1.1 to 1.8. In addition to arterial biomechanics, computational fluid dynamics methods were adopted to simulate the physiological blood flow inside the stented arteries. Results showed that stent oversizing led to a limited increase in the acute lumen gain, albeit at the cost of a significant increase in arterial wall stresses. Furthermore, localized areas affected by low Wall Shear Stress increased with higher oversizing ratios. Stents were also negatively impacted by the procedure as their fatigue safety factors gradually decreased with oversizing. These adverse effects to both the artery walls and stents may create circumstances for restenosis. Although the ideal oversizing ratio is stent-specific, this study showed that Nitinol stent oversizing has a very small impact on the immediate lumen gain, which contradicts the clinical motivations of the procedure.

Nonlinear dimension reduction in pathway-based genome-wide association analysis

Pathway based genome wide association study evolves from pathway analysis for microarray gene expression and is under rapid development as a complementary for single-SNP based genome wide association study. However, it faces new challenges, such as the summarization of SNP statistics to pathway statistics. The current study applies the ridge regularized Kernel Sliced Inverse Regression (KSIR) to achieve dimension reduction and compared this method to the other two widely used methods, the minimal-p-value (minP) approach of assigning the best test statistics of all SNPs in each pathway as the statistics of the pathway and the principal component analysis (PCA) method of utilizing PCA to calculate the principal components of each pathway. Comparison of the three methods using simulated datasets consisting of 500 cases, 500 controls and100 SNPs demonstrated that KSIR method outperformed the other two methods in terms of causal pathway ranking and the statistical power. PCA method showed similar performance as the minP method. KSIR method also showed a better performance over the other two methods in analyzing a real dataset, the WTCCC Ulcerative Colitis dataset consisting of 1762 cases, 3773 controls as the discovery cohort and 591 cases, 1639 controls as the replication cohort. Several immune and non-immune pathways relevant to ulcerative colitis were identified by these methods. Results from the current study provided a reference for further methodology development and identified novel pathways that may be of importance to the development of ulcerative colitis.^