Progressive erosion of genetic and epigenetic variation in callus-derived cocoa (Theobroma cacao) plants

Relatively little is known about the timing of genetic and epigenetic forms of somaclonal variation arising from callus growth. We surveyed for both types of change in cocoa (Theobroma cacao) plants regenerated from calli of various ages, and also between tissues from the source trees. For genetic change, we used 15 single sequence repeat (SSR) markers from four source trees and from 233 regenerated plants. For epigenetic change, we used 386 methylation-sensitive amplified polymorphism (MSAP) markers on leaf and explant (staminode) DNA from two source trees and on leaf DNA from 114 regenerants. Genetic variation within source trees was limited to one slippage mutation in one leaf. Regenerants were far more variable, with 35% exhibiting at least one mutation. Genetic variation initially accumulated with culture age but subsequently declined. MSAP (epigenetic) profiles diverged between leaf and staminode samples from source trees. Multivariate analysis revealed that leaves from regenerants occupied intermediate eigenspace between leaves and staminodes of source plants but became progressively more similar to source tree leaves with culture age. Statistical analysis confirmed this rather counterintuitive finding that leaves of ‘late regenerants’ exhibited significantly less genetic and epigenetic divergence from source leaves than those exposed to short periods of callus growth.

A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Assessing hepatic metabolic changes during progressive colonization of germ-free mouse by 1H NMR spectroscopy

It is well known that gut bacteria contribute significantly to the host homeostasis, providing a range of benefits such as immune protection and vitamin synthesis. They also supply the host with a considerable amount of nutrients, making this ecosystem an essential metabolic organ. In the context of increasing evidence of the link between the gut flora and the metabolic syndrome, understanding the metabolic interaction between the host and its gut microbiota is becoming an important challenge of modern biology.1-4 Colonization (also referred to as normalization process) designates the establishment of micro-organisms in a former germ-free animal. While it is a natural process occurring at birth, it is also used in adult germ-free animals to control the gut floral ecosystem and further determine its impact on the host metabolism. A common procedure to control the colonization process is to use the gavage method with a single or a mixture of micro-organisms. This method results in a very quick colonization and presents the disadvantage of being extremely stressful5. It is therefore useful to minimize the stress and to obtain a slower colonization process to observe gradually the impact of bacterial establishment on the host metabolism. In this manuscript, we describe a procedure to assess the modification of hepatic metabolism during a gradual colonization process using a non-destructive metabolic profiling technique. We propose to monitor gut microbial colonization by assessing the gut microbial metabolic activity reflected by the urinary excretion of microbial co-metabolites by 1H NMR-based metabolic profiling. This allows an appreciation of the stability of gut microbial activity beyond the stable establishment of the gut microbial ecosystem usually assessed by monitoring fecal bacteria by DGGE (denaturing gradient gel electrophoresis).6 The colonization takes place in a conventional open environment and is initiated by a dirty litter soiled by conventional animals, which will serve as controls. Rodents being coprophagous animals, this ensures a homogenous colonization as previously described.7 Hepatic metabolic profiling is measured directly from an intact liver biopsy using 1H High Resolution Magic Angle Spinning NMR spectroscopy. This semi-quantitative technique offers a quick way to assess, without damaging the cell structure, the major metabolites such as triglycerides, glucose and glycogen in order to further estimate the complex interaction between the colonization process and the hepatic metabolism7-10. This method can also be applied to any tissue biopsy11,12.

On the distortion of turbulence by a progressive surface wave

A rapid-distortion model is developed to investigate the interaction of weak turbulence with a monochromatic irrotational surface water wave. The model is applicable when the orbital velocity of the wave is larger than the turbulence intensity, and when the slope of the wave is sufficiently high that the straining of the turbulence by the wave dominates over the straining of the turbulence by itself. The turbulence suffers two distortions. Firstly, vorticity in the turbulence is modulated by the wave orbital motions, which leads to the streamwise Reynolds stress attaining maxima at the wave crests and minima at the wave troughs; the Reynolds stress normal to the free surface develops minima at the wave crests and maxima at the troughs. Secondly, over several wave cycles the Stokes drift associated with the wave tilts vertical vorticity into the horizontal direction, subsequently stretching it into elongated streamwise vortices, which come to dominate the flow. These results are shown to be strikingly different from turbulence distorted by a mean shear flow, when `streaky structures' of high and low streamwise velocity fluctuations develop. It is shown that, in the case of distortion by a mean shear flow, the tendency for the mean shear to produce streamwise vortices by distortion of the turbulent vorticity is largely cancelled by a distortion of the mean vorticity by the turbulent fluctuations. This latter process is absent in distortion by Stokes drift, since there is then no mean vorticity. The components of the Reynolds stress and the integral length scales computed from turbulence distorted by Stokes drift show the same behaviour as in the simulations of Langmuir turbulence reported by McWilliams, Sullivan & Moeng (1997). Hence we suggest that turbulent vorticity in the upper ocean, such as produced by breaking waves, may help to provide the initial seeds for Langmuir circulations, thereby complementing the shear-flow instability mechanism developed by Craik & Leibovich (1976). The tilting of the vertical vorticity into the horizontal by the Stokes drift tends also to produce a shear stress that does work against the mean straining associated with the wave orbital motions. The turbulent kinetic energy then increases at the expense of energy in the wave. Hence the wave decays. An expression for the wave attenuation rate is obtained by scaling the equation for the wave energy, and is found to be broadly consistent with available laboratory data.

Progressive palaeoenvironmental change during the Late Barremian-Early Aptian as prelude to Oceanic Anoxic Event 1a: Evidence from the Gorgo a Cerbara section (Umbria-Marche basin, central Italy)

During Oceanic Anoxic Event 1a (OAE 1a, 120 Ma; Li et al., 2008), organic carbon-rich layers were deposited in marine environments under anoxic conditions on a global scale. In this study, palaeoenvironmental conditions leading to this event are characterised by studying the Upper Barremian to the Lower Aptian succession of the Gorgo a Cerbara section (central Italy). For this, an integrated multi-proxy approach (δ13Ccarb; δ13Corg; δ18O; phosphorus; Total Organic Carbon, TOC; bulk-rock mineralogy, as well as redox-sensitive trace elements — RSTEs) has been applied. During the LateBarremian, thin organic-rich layers occur episodically, and associated Corg:Ptot ratios indicate the presence of intermittent dysoxic to anoxic conditions. Coarse correlations are observed between TOC, P and biogenic silica contents, indicating links between P availability, productivity, and TOC preservation. However, the corresponding δ13Ccarb and δ18O records remain quite stable, indicating that these brief periods of enhanced TOC preservation did not have sufficient impact on the marine carbon reservoir to deviate δ13C records. Around the Barremian–Aptian boundary, TOC-enriched layers become more frequent. These layers correlate with negative excursions in the δ13Ccarb and δ13Corg records, possibly due to a warming period as indicated by the δ18O record. During the earliest Aptian, this warming trend is reverted into a cooling trend, which is then followed by an important warming step near the onset of Oceanic Anoxic Event 1a (OAE 1a). During this time period, organic-rich intervals occur, which are characterised by the progressive increase in RSTE. The warming step prior the onset of OAE 1a is associated with the well-known negative spike in δ13Ccarb and δ13Corg records, an important peak in P accumulation, RSTE enrichments and Corg:Ptot ratios indicating the prevalence of anoxic conditions. The Selli Level itself may document a cooling phase. RSTE enrichments and Corg:Ptot ratios confirm the importance of anoxic conditions during OAE 1a at this site. The Gorgo a Cerbara section is interpreted to reflect the progressive impact of palaeoenvironmental change related to the formation of the Ontong-Java plate-basalt plateau, which started already around the Barremian–Aptian boundary and culminated into OAE 1a.

Prediction of a typhoon using a fine-mesh NWP model

The ECMWF operational grid point model (with a resolution of 1.875° of latitude and longitude) and its limited area version (with a resolution of !0.47° of latitude and longitude) with boundary values from the global model have been used to study the simulation of the typhoon Tip. The fine-mesh model was capable of simulating the main structural features of the typhoon and predicting a fall in central pressure of 60 mb in 3 days. The structure of the forecast typhoon, with a warm core (maximum potential temperature anomaly 17 K). intense swirling wind (maximum 55 m s-1 at 850 mb) and spiralling precipitation patterns is characteristic of a tropical cyclone. Comparison with the lower resolution forecast shows that the horizontal resolution is a determining factor in predicting not only the structure and intensity but even the movement of these vortices. However, an accurate and refined initial analysis is considered to be a prerequisite for a correct forecast of this phenomenon.

Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications

A moving mesh approach for modelling avascular tumour growth

A key step in many numerical schemes for time-dependent partial differential equations with moving boundaries is to rescale the problem to a fixed numerical mesh. An alternative approach is to use a moving mesh that can be adapted to focus on specific features of the model. In this paper we present and discuss two different velocity-based moving mesh methods applied to a two-phase model of avascular tumour growth formulated by Breward et al. (2002) J. Math. Biol. 45(2), 125-152. Each method has one moving node which tracks the moving boundary. The first moving mesh method uses a mesh velocity proportional to the boundary velocity. The second moving mesh method uses local conservation of volume fraction of cells (masses). Our results demonstrate that these moving mesh methods produce accurate results, offering higher resolution where desired whilst preserving the balance of fluxes and sources in the governing equations.