Evaluation of rate law approximations in bottom-up kinetic models of metabolism.

BackgroundThe mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question.ResultsIn this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations.ConclusionsOverall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches

Detailed Enzyme Kinetics in Terms of Biochemical Species: Study of Citrate Synthase

The compulsory-ordered ternary catalytic mechanism for two-substrate two-product enzymes is analyzed to account for binding of inhibitors to each of the four enzyme states and to maintain the relationship between the kinetic constants and the reaction equilibrium constant. The developed quasi-steady flux expression is applied to the analysis of data from citrate synthase to determine and parameterize a kinetic scheme in terms of biochemical species, in which the effects of pH, ionic strength, and cation binding to biochemical species are explicitly accounted for in the analysis of the data. This analysis provides a mechanistic model that is consistent with the data that have been used support competing hypotheses regarding the catalytic mechanism of this enzyme

Transcranial direct current stimulation of right dorsolateral prefrontal cortex does not affect model-based or model-free reinforcement learning in humans

There is broad consensus that the prefrontal cortex supports goal-directed, model-based decision-making. Consistent with this, we have recently shown that model-based control can be impaired through transcranial magnetic stimulation of right dorsolateral prefrontal cortex in humans. We hypothesized that an enhancement of model-based control might be achieved by anodal transcranial direct current stimulation of the same region. We tested 22 healthy adult human participants in a within-subject, double-blind design in which participants were given Active or Sham stimulation over two sessions. We show Active stimulation had no effect on model-based control or on model-free ('habitual') control compared to Sham stimulation. These null effects are substantiated by a power analysis, which suggests that our study had at least 60% power to detect a true effect, and by a Bayesian model comparison, which favors a model of the data that assumes stimulation had no effect over models that assume stimulation had an effect on behavioral control. Although we cannot entirely exclude more trivial explanations for our null effect, for example related to (faults in) our experimental setup, these data suggest that anodal transcranial direct current stimulation over right dorsolateral prefrontal cortex does not improve model-based control, despite existing evidence that transcranial magnetic stimulation can disrupt such control in the same brain region

Unpredictability of metabolism—the key role of metabolomics science in combination with next-generation genome sequencing

Next-generation sequencing provides technologies which sequence whole prokaryotic and eukaryotic genomes in days, perform genome-wide association studies, chromatin immunoprecipitation followed by sequencing and RNA sequencing for transcriptome studies. An exponentially growing volume of sequence data can be anticipated, yet functional interpretation does not keep pace with the amount of data produced. In principle, these data contain all the secrets of living systems, the genotype–phenotype relationship. Firstly, it is possible to derive the structure and connectivity of the metabolic network from the genotype of an organism in the form of the stoichiometric matrix N. This is, however, static information. Strategies for genome-scale measurement, modelling and predicting of dynamic metabolic networks need to be applied. Consequently, metabolomics science—the quantitative measurement of metabolism in conjunction with metabolic modelling—is a key discipline for the functional interpretation of whole genomes and especially for testing the numerical predictions of metabolism based on genome-scale metabolic network models. In this context, a systematic equation is derived based on metabolomics covariance data and the genome-scale stoichiometric matrix which describes the genotype–phenotype relationship

Mathematical modelling of the ischaemic heart

Recent advances in high performance computing combined with increasing knowledge of them kinetics of biochemical reactions and transport processes have allowed us to develop mathematical models that describe various aspects of cardiac physiology. These models include both single cell and three-dimensional tissue models that simulate important features of cardiac electrophysiology, mechanics, and metabolism. We have begun to couple these models with the goal of creating a fully integrated cardiac model that can describe the pathophysiology of the ischaemic heart. Here we present an outline of this work

Simultaneous determination of low free Mg2+ and pH in human sickle cells using 31P NMR spectroscopy.

The concentrations of free magnesium, [Mg(2+)](free), [H(+)], and [ATP] are important in the dehydration of red blood cells from patients with sickle cell anemia, but they are not easily measured. Consequently, we have developed a rapid, noninvasive NMR spectroscopic method using the phosphorus chemical shifts of ATP and 2,3-diphosphoglycerate (DPG) to determine [Mg(2+)](free) and pH(i) simultaneously in fully oxygenated whole blood. The method employs theoretical equations expressing the observed chemical shift as a function of pH, K(+), and [Mg(2+)](free), over a pH range of 5.75-8.5 and [Mg(2+)](free) range 0-5 mm. The equations were adjusted to allow for the binding of hemoglobin to ATP and DPG, which required knowledge of the intracellular concentrations of ATP, DPG, K(+), and hemoglobin. Normal oxygenated whole blood (n = 33) had a pH(i) of 7.20 +/- 0.02, a [Mg(2+)](free) of 0.41 +/- 0.03 mm, and [DPG] of 7.69 +/- 0.47 mm. Under the same conditions, whole sickle blood (n = 9) had normal [ATP] but significantly lower pH(i) (7.10 +/- 0.03) and [Mg(2+)](free) (0.32 +/- 0.05 mm) than normal red cells, whereas [DPG] (10.8 +/- 1.2 mm) was significantly higher. Because total magnesium was normal in sickle cells, the lower [Mg(2+)](free) could be attributed to increased [DPG] and therefore greater magnesium binding capacity of sickle cells

Management of urinary tract infection by early-career general practitioners in Australia

Rationale, aims, and objectives: Urinary tract infection (UTI) is a common presentation to general practitioners (GPs). There is increasing antimicrobial resistance in urinary pathogens in many healthcare systems. Adherence to principles of antimicrobial stewardship is important to combat this problem. Our aim was to describe the prevalence of presentations of clinically diagnosed new UTI to early-career GPs, to describe management choices made, and to identify associations of prescribing antibiotics at the index consultation for UTI. Method: This is a cross-sectional analysis of the Registrar Clinical Encounters in Training cohort study. Early-career GPs from five Australian states (urban to very remote practices) collected data on 60 consecutive patient encounters during each of three 6-month training terms. Proportions of problems being new UTIs, antibiotics prescribed, urine microscopy and culture ordered were calculated. Univariate and multivariable logistic regressions established associations of patient, registrar, and practice factors with prescribing antibiotics for a new UTI. Results: One thousand three hundred thirty-three early-career GPs diagnosed 2850 new UTIs from 189 736 consultations (1.5%; 95% CI, 1.4-1.6). Antibiotics were prescribed at 86% (95% CI, 84.7-87.2) of these index consultations. Antibiotic choice followed Australian therapeutic guideline recommendations. Urine microscopy and culture were requested at the index consultation less than recommended by guidelines in men, 69.2% (95% CI, 62.6-75.1), and children, 80.8% (95% CI, 76.4-84.6). Adults were significantly more likely to be treated with antibiotics at the index consultation than children under 16. Conclusions: A new UTI is a common presentation to Australian early-career GPs. There is general adherence to guidelines for antibiotic choice in UTIs. Further research is needed, however, to understand some decisions made when managing UTI in children and men. This may reflect diagnostic uncertainty with consequent attention to antibiotic stewardship by deferring antibiotic prescription

Mathematical tasks: exploration of different types of mathematical tasks to the teaching of mathematics in 1st and 2nd cycle of basic education

Relatório de estágio de mestrado em Ensino do 1.º e 2.º Ciclo do Ensino BásicoO presente relatório de estágio foi desenvolvido ao longo do 2.º ano do Mestrado em Ensino do 1.º e 2.º Ciclo do Ensino Básico e tem como um dos objetivos compreender se é possível articular diferentes tipos de tarefas matemáticas, com um grau de desafio mais elevado, com os objetivos presentes no programa curricular em vigor. Além disso, pretendeu-se detetar as principais dificuldades dos alunos perante os tipos de tarefas apresentadas, bem como se contribuíram para o desenvolvimento do pensamento matemático dos alunos. O contexto educativo no qual se realizou esta investigação foi uma turma do 3.º ano e do 5.º ano de escolaridade, sendo que a metodologia adotada foi a investigação qualitativa, com contornos de investigação-ação. Para tal, os principais instrumentos de recolha de dados foram a observação direta, as notas de campo, as gravações de vídeo e as fichas de trabalho realizadas pelos alunos ao longo das sessões de intervenção pedagógica. A importância de proporcionar aos alunos um ensino de matemática estimulante e desafiador é um tema que tem ganho relevo ao longo dos anos uma vez que se tenta adotar uma visão construtivista do ensino e aprendizagem, em que o aluno adota um papel de relevo na construção de conhecimentos. As tarefas matemáticas devem ser diversificadas e com um grau de desafio adequado aos diferentes alunos de cada contexto, promovendo a discussão e partilha de ideias, modificando a visão de muitos alunos de que a matemática é um conjunto de processos rotineiros. Em ambos os contextos educativos, os alunos demonstraram-se empenhados na resolução das tarefas, apresentando algumas dificuldades no início da sua resolução uma vez que não se encontravam familiarizados com o tipo de tarefa que lhes era apresentado. A motivação foi um dos aspetos mais difíceis de manter devido à visão negativa de alguns alunos perante esta área curricular. Os resultados obtidos demonstraram que é possível articular diferentes tipos de tarefas matemáticas, com um grau de desafio mais elevado com o programa curricular, uma vez que os alunos conseguiram resolver as tarefas apresentadas, participando em discussões promotoras de aprendizagens significativas.The present report was developed over 2nd year of the Master in teaching 1st and 2nd cycle of basic education and it has as one of the aims understanding if it is possible to articulate different types of mathematical tasks, with a higher challenge degree, with the objectives present in the curriculum. Besides that, it was investigated the main difficulties of students in the resolution of the tasks presented, as well if it contributed to the development of the students mathematical thinking. The educational context in which this investigation was develop was a class of 3rd year and 5th year of schooling, and the adopted methodology was qualitative research with research-action outlines. To this end, the main collection data tools were the direct observation, field notes, video recordings and worksheets made by students throughout the educational intervention sessions. The importance of providing students a stimulating and challenging mathematical education is a theme that has gained emphasis over the years since it tries to adopt a constructivist view of teaching and learning, in which the student takes a major role in building knowledge. The mathematical tasks should be diversified and with an appropriate challenge degree to different students in each context, promoting discussion and sharing ideas, changing the view of many students that mathematics is a series of routine processes. In both educational contexts, students proved to be engaged in solving the tasks, presenting some difficulties at the beginning of the resolution because they weren’t familiar with the type of task that was present to them. The motivation was one of the most difficult aspects to maintain due to the negative view of some students towards this curriculum area. The results showed that it is possible to articulate different types of mathematical tasks with a higher challenge degree with the curriculum, since the students were able to solve the given tasks, participating in discussions that promote meaningful learning