Graphic rules in steady and non-steady state enzyme kinetics

Graphic methods, when applied to enzyme kinetics, can provide a visually intuitive relation between calculations and reaction graphs. This will not only greatly raise the efficiency of calculations but also significantly help the analysis of enzyme kinetic mechanisms. In this paper, four graphic rules are presented. Rules 1-3 are established for steady state enzyme-catalyzed reaction systems and Rule 4 is for non-steady state ones. In comparison with conventional graphic methods which can only be applied to steady state systems, the present rules have the following merits. 1) Complicated and tedious calculations can be greatly simplified; for example, in calculating the concentrations of enzyme species for the bi-bi random mechanism, the calculation work can be reduced 8-fold compared with the King-Altman's method. 2) A great deal of wasted labor can be avoided; for example, in calculating the rate of product formation for the same mechanism, the operation of finding and removing the 96 reciprocally canceled terms is no longer needed because they automatically disappear during the derivation. 3) Final results can be easily and safely checked by a formula provided in each of the graphic rules. 4) Non-steady state systems can also be treated by the present graphic method; for example, applying Rule 4, one can directly write out the solution for a non-steady state enzyme-catalyzed system, without the need to follow more difficult and complicated operations to solve differential equations. The mathematical proofs of Rules 1-4 are given in Appendices A-D (in the Miniprint), respectively.     

Studies of fungal growth and intermediary carbon metabolism under steady and non-steady state conditions

The physiology of Aspergillus nidulans strain 224 has been studied under conditions of batch- and glucose-limited chemostat-culture and the effect of different steady state growth rates and dissolved oxygen tensions (DOT) examined. Measurements of the specific activities of selected glucose enzymes, the extent of oxygen uptake inhibition by glycolytic inhibitors, and radiorespirometric analyses were made in order to follow the variations in glucose catabolism, which occurred under these conditions. Greatly increased activity of the hexosemonophosphate (HMP) pathway was found during: (i) exponential growth of batch cultures; (ii) at near maximum specific growth rates (μ = 0.072 hr^?1) (DOT = 156 mm Hg); and (iii) at low DOT levels (<30 mm Hg) (μ = 0.050 hr^?1) in chemostat cultures. These changes in glucose eatabolism have been discussed in terms of the biosynthetic demands of the fungus under the influence of changing growth pressures. Preliminary studies also have been made of transition state behavior following stepwise alteration of the DOT. A new steady state was established after 4–5 culture doublings during which period an “overshoot” in HMP pathway activity occurred; these kinetics are indicative of a derepression of certain glucose enzymes. Low molecular weight phenols are synthesized during the exponential phase in batch cultures and these are further metabliized to a major secondary metabolite, melanin, at the onset of stationary phase conditions. The kinetics of tyrosinase production in steady state chemostats differs from those that might be predicted for an enzyme associated solely with secondary metabolism. A primary physiological role for this oxidase in Aspergillus nidulans has been postulated.     

Graphical rules for non-steady state enzyme kinetic

The exiting graphical methods in enzyme kinetics can be used only within the scope of steady state reactions. In this paper, two graphical rules are presented to deal with the non-steady state enzyme catalysed reaction systems. According to Rule 1 we can immediately write out the phase concentration of enzyme species. The calculation work such as setting up differential equations, making Laplace transformation, expanding determinants, which are both tedious and liable to error, are completely saved. By means of Rule 2 the secular equations for the consecutive first-order reactions can be written out directly without need of setting up differential equations, expanding determinants, etc., that would otherwise be laborious and prone to errors. In addition, two check formulae are also presented for these two graphical methods, respectively. They are useful in order for avoiding the omission of terms during calculations, especially, for complicated mechanisms.     

An adaptive state estimator for detecting contaminants in bioreactors

An algorithm is presented for detecting the appearance of contaminants during batch or fed-batch fermentations, using only presently available on-line measurements. Its adaptive nature enables it to rely on almost no prior knowledge of the real process. The necessary on-line measurements are total biomass and its production rate; it is also shown how a physical variable such as oxygen uptake can be used alone instead. The algorithm's properties are studied theoretically and through simulations. These were confirmed by on-line experimental results, obtained with a Yeast culture, both pure and contaminated by a Bacteria. The algorithm does not detect contaminants when none are there, and it also provides a convergent estimate of a pure culture's specific growth rate. Contaminated cultures are recognized by the algorithm, and this detection can be made more or less conservative. After detection, the various estimates may diverge, due to general observability difficulties, though this divergence can itself be monitored. Moreover, the algorithm is easy to tune and its qualitative behavior is quite insensitive to its adjustable parameters. A practical criterion and scheme for implementation are proposed. The generality of the approach, which far exceeds the experimental system used, is finally discussed.     

Eu-Detect: An algorithm for detecting eukaryotic sequences in metagenomic data sets

Physical partitioning techniques are routinely employed (during sample preparation stage) for segregating the prokaryotic and eukaryotic fractions of metagenomic samples. In spite of these efforts, several metagenomic studies focusing on bacterial and archaeal populations have reported the presence of contaminating eukaryotic sequences in metagenomic data sets. Contaminating sequences originate not only from genomes of micro-eukaryotic species but also from genomes of (higher) eukaryotic host cells. The latter scenario usually occurs in the case of host-associated metagenomes. Identification and removal of contaminating sequences is important, since these sequences not only impact estimates of microbial diversity but also affect the accuracy of several downstream analyses. Currently, the computational techniques used for identifying contaminating eukaryotic sequences, being alignment based, are slow, inefficient, and require huge computing resources. In this article, we present Eu-Detect, an alignment-free algorithm that can rapidly identify eukaryotic sequences contaminating metagenomic data sets. Validation results indicate that on a desktop with modest hardware specifications, the Eu-Detect algorithm is able to rapidly segregate DNA sequence fragments of prokaryotic and eukaryotic origin, with high sensitivity. A Web server for the Eu-Detect algorithm is available at http://metagenomics.atc.tcs.com/Eu-Detect/.     

Rapid media transition: An experimental approach for steady state analysis of metabolic pathways

Commonly steady state analysis of microbial metabolism is performed under well defined physiological conditions in continuous cultures with fixed external rates. However, most industrial bioprocesses are operated in fed‐batch mode under non‐stationary conditions, which cannot be realized in chemostat cultures. A novel experimental setup—rapid media transition—enables steady state perturbation of metabolism on a time scale of several minutes in parallel to operating bioprocesses. For this purpose, cells are separated from the production process and transferred into a lab‐scale stirred‐tank reactor with modified environmental conditions. This new approach was evaluated experimentally in four rapid media transition experiments with Escherichia coli from a fed‐batch process. We tested the reaction to different carbon sources entering at various points of central metabolism. In all cases, the applied substrates (glucose, succinate, acetate, and pyruvate) were immediately utilized by the cells. Extracellular rates and metabolome data indicate a metabolic steady state during the short‐term cultivation. Stoichiometric analysis revealed distribution of intracellular fluxes, which differs drastically subject to the applied carbon source. For some reactions, the variation of flux could be correlated to changes of metabolite concentrations. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

An exact steady state solution of Fisher's geometric model and other models

Because nearly neutral substitutions are thought to contribute substantially to molecular evolution, and much of our insight about the workings of nearly neutral evolution relies on theory, solvable models of this process are of particular interest. Here, I present an analytical method for solving models of nearly neutral evolution at steady state. The steady state solution applies to any constant fitness landscape under a dynamic of successive fixations, each of which occurs on the background of the population's most recent common ancestor. Because this dynamic neglects the effects of polymorphism in the population beyond the mutant allele under consideration, the steady state solution provides a decent approximation of evolutionary dynamics when the population mutation rate is low (Nu<1). To demonstrate the method, I apply it to two examples: Fisher's geometric model (FGM), and a simple model of molecular evolution. Since recent papers have studied the steady state behavior of FGM under this dynamic, I analyze its behavior in detail and compare the results with previous work.     

新一代测序的拷贝数变异检测算法研究与设计

基于不同的测序技术,基因拷贝数变异的检测方法有多种,但时间复杂度较高,而新一代测序技术的发展为基因拷贝数变异检测的研究开辟了新领域。通过仿真实验、置换检验设计出一种新的基于新一代测序的拷贝数变异检测算法。不同于其它算法,本算法无需参考样本,通过直接研究比对后的序列以及reads与拷贝数的关系,来研究检测拷贝数变异,实验结果表明在时间复杂度上能提高50%以上的运算速度,这对今后拷贝数与疾病的研究具有重要意义。     

Analysis of steady state photosynthesis in alfalfa leaves

A method for carrying out kinetic tracer studies of steady state photosynthesis in whole leaves has been developed. An apparatus that exposes whole leaves to ¹⁴CO₂ under steady state conditions, while allowing individual leaf samples to be removed as a function of time, has been constructed. Labeling data on the incorporation of ¹⁴C into Medicago sativa L. metabolite pools are reported. A carbon dioxide uptake rate of 79 micromoles ¹⁴CO₂ per milligram chlorophyll per hour was observed at a CO₂ level slightly below that of air. Several actively turning over pools of early and intermediate metabolites, including 3-phosphoglyceric acid, glycerate, citrate, and uridine diphosphoglucose, showed label saturation after approximately 10 to 20 minutes of photosynthesis with ¹⁴CO₂ under steady state conditions. Alanine labeling increased more rapidly at first, and then at a lower rate as saturation was approached. Sucrose was a major product of photosynthesis and label saturation of the sucrose pool was not observed. Labeled carbon appeared rapidly in secondary metabolites. The steady state apparatus used has numerous advantages, including leaf temperature control, protection against leaf dehydration, high illumination, known ¹⁴CO₂ specific radioactivity, and provision for control and adjustment of ¹⁴CO₂ concentration. The apparatus allows for experiments of long duration and for sufficient sample points to define clearly the metabolic steady state.