Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Myostatin is a key mediator between energy metabolism and endurance capacity of skeletal muscle

Myostatin (Mstn) participates in the regulation of skeletal muscle size and has emerged as a regulator of muscle metabolism. Here, we hypothesized that lack of myostatin profoundly depresses oxidative phosphorylation-dependent muscle function. Toward this end, we explored Mstn/ mice as a model for the constitutive absence of myostatin and AAV-mediated overexpression of myostatin propeptide as a model of myostatin blockade in adult wild-type mice. We show that muscles from Mstn/ mice, although larger and stronger, fatigue extremely rapidly. Myostatin deficiency shifts muscle from aerobic toward anaerobic energy metabolism, as evidenced by decreased mitochondrial respiration, reduced expression of PPAR transcriptional regulators, increased enolase activity, and exercise-induced lactic acidosis. As a consequence, constitutively reduced myostatin signaling diminishes exercise capacity, while the hypermuscular state of Mstn/ mice increases oxygen consumption and the energy cost of running. We wondered whether these results are the mere consequence of the congenital fiber-type switch toward a glycolytic phenotype of constitutive Mstn/ mice. Hence, we overexpressed myostatin propeptide in adult mice, which did not affect fiber-type distribution, while nonetheless causing increased muscle fatigability, diminished exercise capacity, and decreased Pparb/d and Pgc1a expression. In conclusion, our results suggest that myostatin endows skeletal muscle with high oxidative capacity and low fatigability, thus regulating the delicate balance between muscle mass, muscle force, energy metabolism, and endurance capacity.

Blockade of ActRIIB signaling triggers muscle fatigability and metabolic myopathy

Myostatin regulates skeletal muscle size via the activin receptor IIB (ActRIIB). However, its effect on muscle energy metabolism and energy dependent muscle function remains largely unexplored. This question needs to be solved urgently since various therapies for neuromuscular diseases based on blockade of ActRIIB signaling are being developed. Here we show in mice that four months of pharmacological abrogation of ActRIIB signaling by treatment with soluble ActRIIB-Fc triggers extreme muscle fatigability. This is associated with elevated serum lactate levels and a severe metabolic myopathy in the mdx mouse, an animal model of Duchenne muscular dystrophy. Blockade of ActRIIB signaling down-regulates Porin, a crucial ADP/ATP shuttle between cytosol and mitochondrial matrix leading to a consecutive deficiency of oxidative phosphorylation as measured by in vivo Phophorus Magnetic Resonance Spectroscopy (31P-MRS). Further, ActRIIB blockade reduces muscle capillarization, which further compounds the metabolic stress. We show that ActRIIB regulates key determinants of muscle metabolism, such as Pparβ, Pgc1α, and Pdk4 thereby optimizing different components of muscle energy metabolism. In conclusion, ActRIIB signaling endows skeletal muscle with high oxidative capacity and low fatigability. The severe metabolic side effects following ActRIIB blockade caution against deploying this strategy, at least in isolation, for treatment of neuromuscular disorders.

Dystrophin-related protein, utrophin, in normal and dystrophic human fetal skeletal muscle.

Dystrophin is the product of the Duchenne muscular dystrophy (DMD) gene. Dystrophin-related protein (utrophin), an autosomal homologue of dystrophin, was studied in skeletal muscle from normal fetuses aged 9-26 weeks and one stillbirth of 41 weeks' gestation, and compared with low- and high-risk DMD fetuses aged 9-20 weeks. Utrophin was present at the sarcolemma from before 9 weeks' gestation, although there was variability in intensity both within and between myotubes. Sarcolemmal immunolabelling became more uniform, and levels of utrophin increased to a maximum at approximately 17-18 weeks. Levels then declined, until by 26 weeks sarcolemmal labelling was negligible and levels were similar to adult control muscle. By 41 weeks there was virtually no sarcolemmal labelling, although immunolabelling of capillaries was bright. Similar results were obtained with normal and DMD fetal muscle. Utrophin is therefore expressed in the presence and absence of dystrophin and down-regulated before birth in normal fetal muscle fibres. Samples were not available to determine whether or when, utrophin levels decline in DMD fetal muscle. On Western blots, utrophin was shown to have a smaller relative molecular mass than adult dystrophin, but similar to the fetal isoform. Blood vessels were brightly immunolabelled at all ages, although utrophin immunolabelling of peripheral nerves increased with gestational age.

Characterisation of dystrophin during development of human skeletal muscle.

Dystrophin, the 427 x 10(3) Mr product of the Duchenne muscular dystrophy (DMD) gene, was studied in human foetal skeletal muscle from 9 to 26 weeks of gestation. Dystrophin could be detected from at least 9 weeks of gestation at the sarcolemmal membrane of most myotubes, though there was differential staining with antibodies raised to various regions of the protein. Dystrophin immunostaining increased and became more uniform with age and by 26 weeks of gestation there was intense sarcolemmal staining of all myotubes. On a Western blot, a doublet of smaller relative molecular mass than that seen in adult tissue was detected in all foetuses studied. There was a gradual increase in abundance of the upper band from 9 to 26 weeks, and the lower band, although present in low amounts in young foetuses, increased significantly between 20 and 26 weeks of gestation. These data indicate that there are several specific isoforms of dystrophin present in developing skeletal muscle, though the role of these is unknown.

Muscular weakness in the mdx mouse.

mdx mice are believed to be virtually free from neuromuscular symptoms, despite the presence of a degenerative/regenerative process that involves all skeletal muscles. We analyzed both the spontaneous motility and treadmill motor activity of mdx mice aged 15 days to 6 months. Our results indicate that there is an early period, between the end of the second and up to the fifth week of life, when mdx mice experience extreme weakness. After this critical period, both spontaneous motility and endurance of mdx mice, although lower than those of controls, do not show statistically significant differences up to 6 months of age. We also carried out a detailed histological analysis of proximal and distal muscle groups in mdx mice during this early critical motility period. The occurrence of extensive necrosis followed by regeneration and involving proximal muscles before distal ones was documented in mice as young as 16-17 days of age and reached a peak at day 18. We conclude that dystrophin deficiency induces muscle degeneration and significant weakness in mdx mice, but only in an early period. Later on, during development, mdx mice adapt to the lack of this protein and do not show detectable in vivo functional muscle impairment up to 6 months of age.

Childhood trauma: methods for the identification of physeal fractures in non-adult skeletal remains

Objectives Today, fractures at the growth plate (or physis) are common injuries in children, but provide challenges of identification in skeletonized remains. Clinical studies provide detailed information on the mechanisms, locations, age of occurrence, and complications associated with physeal fractures, enabling the development of new criteria for identifying this injury in non-adults. To test these criteria, skeletal remains from five rural and urban medieval cemeteries were examined. Methods The sample consisted of 961 skeletons (0-17 years) with open epiphyses. Macroscopic observation looked for any irregularities of the metaphysis or epiphysis which was consistent with the clinical appearance of physeal fractures or resulting complications. Radiographic examination was applied to identify fracture lines or early growth arrest. Results This study revealed 12 cases of physeal trauma (1.2%). Physeal fractures occurred predominantly at the distal end (75%), and while they were identified in all age categories, they were most frequent in those aged 12-17 years (0.2% TPR). The humerus was the most commonly affected location (3/12 or 25%). Conclusions This study highlights the potential for recognizing physeal fractures in children of all ages, enhancing our understanding of non-adult trauma, and enabling us to assign a more precise age of the injury to build up a picture of their activities in the past.