Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Background: Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results: Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions: Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Nonenhanced arterial spin labeled carotid MR angiography using three-dimensional radial balanced steady-state free precession imaging.

PURPOSE: To optimize and preliminarily evaluate a three-dimensional (3D) radial balanced steady-state free precession (bSSFP) arterial spin labeled (ASL) sequence for nonenhanced MR angiography (MRA) of the extracranial carotid arteries. MATERIALS AND METHODS: The carotid arteries of 13 healthy subjects and 2 patients were imaged on a 1.5 Tesla MRI system using an undersampled 3D radial bSSFP sequence providing a scan time of ∼4 min and 1 mm(3) isotropic resolution. A hybridized scheme that combined pseudocontinuous and pulsed ASL was used to maximize arterial coverage. The impact of a post label delay period, the sequence repetition time, and radiofrequency (RF) energy configuration of pseudocontinuous labeling on the display of the carotid arteries was assessed with contrast-to-noise ratio (CNR) measurements. Faster, higher undersampled 2 and 1 min scans were tested. RESULTS: Using hybridized ASL MRA and a 3D radial bSSFP trajectory, arterial CNR was maximized with a post label delay of 0.2 s, repetition times ≥ 2.5 s (P < 0.05), and by eliminating RF energy during the pseudocontinuous control phase (P < 0.001). With higher levels of undersampling, the carotid arteries were displayed in ≤ 2 min. CONCLUSION: Nonenhanced MRA using hybridized ASL with a 3D radial bSSFP trajectory can display long lengths of the carotid arteries with 1 mm(3) isotropic resolution. J. Magn. Reson. Imaging 2015;41:1150-1156. © 2014 Wiley Periodicals, Inc.

Sulfuric acid - glucose separation using mixed-recycle steady state recycling chromatography

Batch chromatography is a widely used separation technique in a variety of fields meeting difficult separations. Several technologies for improving the performance of chromatography have been studied, including mixed-recycle steady state recycling (MR-SSR) chromatography. Design of MR-SSR has been commonly limited on 100 % purity constraint cases and empirical work. In this study a predictive design method was used to optimize feed pulse size and design a number of experimental MR-SSR separations for a solution of 20 % sulfuric acid and 100 g/L glucose. The design was under target product fraction purities of 98.7 % for H2SO4 and 95 % for glucose. The experiments indicate a maximum of 59 % increase in sulfuric acid productivity and 82 % increase for glucose when compared to corresponding batch separation. Eluent consumption was lowered by approximately 50 % using recycling chromatography. Within this study the target purities and yields set in design were not completely met, and further optimization of the process is deemed necessary.

Effect of the aerobic capacity on the validity of the anaerobic threshold for determination of the maximal lactate steady state in cycling

The maximal lactate steady state (MLSS) is the highest blood lactate concentration that can be identified as maintaining a steady state during a prolonged submaximal constant workload. The objective of the present study was to analyze the influence of the aerobic capacity on the validity of anaerobic threshold (AT) to estimate the exercise intensity at MLSS (MLSS intensity) during cycling. Ten untrained males (UC) and 9 male endurance cyclists (EC) matched for age, weight and height performed one incremental maximal load test to determine AT and two to four 30-min constant submaximal load tests on a mechanically braked cycle ergometer to determine MLSS and MLSS intensity. AT was determined as the intensity corresponding to 3.5 mM blood lactate. MLSS intensity was defined as the highest workload at which blood lactate concentration did not increase by more than 1 mM between minutes 10 and 30 of the constant workload. MLSS intensity (EC = 282.1 ± 23.8 W; UC = 180.2 ± 24.5 W) and AT (EC = 274.8 ± 24.9 W; UC = 187.2 ± 28.0 W) were significantly higher in trained group. However, there was no significant difference in MLSS between EC (5.0 ± 1.2 mM) and UC (4.9 ± 1.7 mM). The MLSS intensity and AT were not different and significantly correlated in both groups (EC: r = 0.77; UC: r = 0.81). We conclude that MLSS and the validity of AT to estimate MLSS intensity during cycling, analyzed in a cross-sectional design (trained x sedentary), do not depend on the aerobic capacity.

Exploring the neural entrainment to musical rhythms and meter : a steady-state evoked potential approach

Thèse de doctorat réalisé en cotutelle avec l'Université catholique de Louvain, Belgique (Faculté de médecine, Institut de Neuroscience)

The Steady-State and Transient Characteristic Analysis of Thermal Fixing a Photorefractive Hologram Grating in Lithium Niobate

The transient interaction between a refraction index grating and light beams during simultaneous writing and thermal fixing of a photorefractive hologram is investigated. With a diffusion- and photovoltaic-dominated carrier transport mechanism and carrier thermal activation (temperature dependent) considered in Fe:LiNbO3 crystal, from the standpoint of field-material coupling, the theoretical thermal fixing time and the space-charge field buildup, spatial distribution, and temperature dependence are given numerically by combining the band transport model with mobile ions with the coupled-wave equation

Comparing auditory steady state response and auditory brainstem response in normal hearing adults

This paper presents a study examining auditory steady state response (ASSR) assessments compared to auditory brainstem response (ABR) assessments. The study examines the relationship between behavioral thresholds, click- and toneburst-ABR thresholds, and ASSR thresholds for normal hearing subjects using the commercially available GSI Audera instrument.

Comparing auditory steady-state response and auditory brainstem response in normal hearing adults

This paper compares the auditory steady state response (ASSR) thresholds with the click-evoked and tone burst auditory brainstem response (ABR) thresholds in their ability to predict known behavioral thresholds in normal-hearing adults.

Gonadotrophins modulate hormone secretion and steady-state mRNA levels for activin receptors (type I, IIA, IIB) and inhibin co-receptor (betaglycan) in granulosa and theca cells from chicken prehierarchical and preovulatory follicles

Ovarian follicle development is regulated through endocrine and local mechanisms. Increasing evidence indicates roles for transforming growth factor beta superfamily members, including inhibins and activins. We recently identified divergent expression of mRNAs encoding activin receptors (ActR) and inhibin co-receptor betaglycan in chicken follicles at different stages of maturation. Here, we compare the actions of LH and FSH (0, 1, 10, 100 ng/ml) on levels of mRNA for ActRI, ActRIIA, ActRIIB and betaglycan in chicken granulosa and theca cells (GC and TC) from preovulatory (F1) and prehierarchical (6-8 mm) follicles. The expression of mRNAs for LH-R and FSH-R and production of inhibin A, oestradiol and progesterone were also quantified. FSH decreased ActRIIB and ActRI mRNA levels in 6-8 mm GC, whereas LH increased the mRNA levels. Both LH and FSH enhanced ActRIIA (5- and 8.5-fold) and betaglycan mRNA expression (2- and 3.5-fold) in 6-8 mm GC. In 6-8 mm TC, LH and FSH both increased the betaglycan mRNA level (7- and 3.5-fold respectively) but did not affect ActRI, ActRIIA and ActRIIB transcript levels. In F1 GC, both LH and FSH stimulated ActRI (2- and 2.4-fold), ActRIIB (3.2- and 2.7-fold) and betaglycan (7- and 4-fold) mRNA levels, while ActRIIA mRNA was unaffected. In F1 TC, LH and FSH reduced ActRIIA (35-50%) and increased (4.5- and 7.6-fold) betaglycan mRNA, but had no effect on ActRI and ActRIIB transcript levels. Results support the hypothesis that expression of ActR and betaglycan are differentially regulated by gonadotrophins during follicle maturation in the hen. This may represent an important mechanism for fine-tuning follicle responsiveness to local and systemic activins and inhibins.

Development and application of a novel algorithm for steady-state optimising control using dynamic information

A novel optimising controller is designed that leads a slow process from a sub-optimal operational condition to the steady-state optimum in a continuous way based on dynamic information. Using standard results from optimisation theory and discrete optimal control, the solution of a steady-state optimisation problem is achieved by solving a receding-horizon optimal control problem which uses derivative and state information from the plant via a shadow model and a state-space identifier. The paper analyzes the steady-state optimality of the procedure, develops algorithms with and without control rate constraints and applies the procedure to a high fidelity simulation study of a distillation column optimisation.

A stress relaxation model for the viscoelastic solids based on the steady-state creep equation

Creep and stress relaxation are inherent mechanical behaviors of viscoelastic materials. It is considered that both are different performances of one identical physical phenomenon. The relationship between the decay stress and time during stress relaxation has been derived from the power law equation of the steady-state creep. The model was used to analyse the stress relaxation curves of various different viscoelastic materials (such as pure polycrystalline ice, polymers, foods, bones, metal, animal tissues, etc.). The calculated results using the theoretical model agree with the experimental data very well. Here we show that the new mathematical formula is not only simple but its parameters have the clear physical meanings. It is suitable to materials with a very broad scope and has a strong predictive ability.

Steady state and dynamic modelling of nitrogen in the River Kennet: impacts of land use change since the 1930s

Steady state and dynamic models have been developed and applied to the River Kennet system. Annual nitrogen exports from the land surface to the river have been estimated based on land use from the 1930s and the 1990s. Long term modelled trends indicate that there has been a large increase in nitrogen transport into the river system driven by increased fertiliser application associated with increased cereal production, increased population and increased livestock levels. The dynamic model INCA Integrated Nitrogen in Catchments. has been applied to simulate the day-to-day transport of N from the terrestrial ecosystem to the riverine environment. This process-based model generates spatial and temporal data and reproduces the observed instream concentrations. Applying the model to current land use and 1930s land use indicates that there has been a major shift in the short term dynamics since the 1930s, with increased river and groundwater concentrations caused by both non-point source pollution from agriculture and point source discharges. �

Non-steady state heat conduction in composite walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.

A comparison of GOCE and drifter-based estimates of the North Atlantic steady-state surface circulation

Over the last decade, due to the Gravity Recovery And Climate Experiment (GRACE) mission and, more recently, the Gravity and steady state Ocean Circulation Explorer (GOCE) mission, our ability to measure the ocean’s mean dynamic topography (MDT) from space has improved dramatically. Here we use GOCE to measure surface current speeds in the North Atlantic and compare our results with a range of independent estimates that use drifter data to improve small scales. We find that, with filtering, GOCE can recover 70% of the Gulf Steam strength relative to the best drifter-based estimates. In the subpolar gyre the boundary currents obtained from GOCE are close to the drifter-based estimates. Crucial to this result is careful filtering which is required to remove small-scale errors, or noise, in the computed surface. We show that our heuristic noise metric, used to determine the degree of filtering, compares well with the quadratic sum of mean sea surface and formal geoid errors obtained from the error variance–covariance matrix associated with the GOCE gravity model. At a resolution of 100 km the North Atlantic mean GOCE MDT error before filtering is 5 cm with almost all of this coming from the GOCE gravity model.