Fitting Broadband Diffusion by Cable Modem in Portugal

The purpose of this article is to described the evolution of the number of residential subscribers of broadband fixed access by cable modem, in Portugal, on the period from 2000–2009. The pattern of evolution is estimated by fitting several models to the series, namely the following: exponential, Gompertz, Logistic, Bass and Michaelis-Menten. We fit the models to the data by nonlinear least squares, except in the exponential model where the linear version is fitted by ordinary least squares, using the internet freely available program R. This comparative study is in line with many others on the diffusion of technological innovations in the telecommunications sector, where the point is finding out if there is an early or a late take-off phenomenon. The Michaelis-Menten model is introduced for the first time in this approach. It allows to predict the later evolution in the series and reveals a qualitatively different behavior.Broadband, Technological Innovations, Diffusion Growth Models, Nonlinear Least Squares

Respiration rate model for mature green capsicum (Capsicum annum L.) under closed aerobic atmospheric conditions

The respiration rate of green capsicum cv. ‘Swarna’ fruits harvested at mature green stage were determined under closed system at 10, 15 and 20 ºC temperatures. A simple Michaelis-Menten kinetic model coupled with Arrhenius-type equation, which describes temperature as a function of respiration rate, was used to model the respiration rate of capsicum. The respiration rate model parameters at defined temperature were estimated by fitting the model to the experimental set of data by non-linear regression analysis method. The respiration rate of green mature capsicum was influenced by the temper¬ature. The Arrhenius equation well described the relationship between enzyme kinematics model parameters and temperature. The values of Michaelis-Menten constant for oxygen (Kmo2) and carbon dioxide (Kmco2) were found to vary from 2.14 to 3.92 and 1.33 to 3.24, respectively at different temperature. Experimental and predicted RRO2 values for mature green capsicum was found to be ranged from 9.54 to 14.54 and 11.81 to 17.52 mg/kg-h, respectively. Whereas, the experimental and predicted RRCO2 were 20.1 to 38.51 and 22.15 to 39.83 mg/ kg-h, respectively

Steady-state cerebral glucose concentrations and transport in the human brain

Understanding the mechanism of brain glucose transport across the blood- brain barrier is of importance to understanding brain energy metabolism. The specific kinetics of glucose transport nave been generally described using standard Michaelis-Menten kinetics. These models predict that the steady- state glucose concentration approaches an upper limit in the human brain when the plasma glucose level is well above the Michaelis-Menten constant for half-maximal transport, K(t). In experiments where steady-state plasma glucose content was varied from 4 to 30 mM, the brain glucose level was a linear function of plasma glucose concentration. At plasma concentrations nearing 30 mM, the brain glucose level approached 9 mM, which was significantly higher than predicted from the previously reported K(t) of ~4 mM (p < 0.05). The high brain glucose concentration measured in the human brain suggests that ablumenal brain glucose may compete with lumenal glucose for transport. We developed a model based on a reversible Michaelis-Menten kinetic formulation of unidirectional transport rates. Fitting this model to brain glucose level as a function of plasma glucose level gave a substantially lower K(t) of 0.6 ± 2.0 mM, which was consistent with the previously reported millimolar K(m) of GLUT-1 in erythrocyte model systems. Previously reported and reanalyzed quantification provided consistent kinetic parameters. We conclude that cerebral glucose transport is most consistently described when using reversible Michaelis-Menten kinetics

Kinetic modelling of in vitro data of PI3K, mTOR1, PTEN enzymes and on-target inhibitors Rapamycin, BEZ235, and LY294002

The phosphatidylinositide 3-kinases (PI3K) and mammalian target of rapamycin-1 (mTOR1) are two key targets for anti-cancer therapy. Predicting the response of the PI3K/AKT/mTOR1 signalling pathway to targeted therapy is made difficult because of network complexities. Systems biology models can help explore those complexities but the value of such models is dependent on accurate parameterisation. Motivated by a need to increase accuracy in kinetic parameter estimation, and therefore the predictive power of the model, we present a framework to integrate kinetic data from enzyme assays into a unified enzyme kinetic model. We present exemplar kinetic models of PI3K and mTOR1, calibrated on in vitro enzyme data and founded on Michaelis-Menten (MM) approximation. We describe the effects of an allosteric mTOR1 inhibitor (Rapamycin) and ATP-competitive inhibitors (BEZ2235 and LY294002) that show dual inhibition of mTOR1 and PI3K. We also model the kinetics of phosphatase and tensin homolog (PTEN), which modulates sensitivity of the PI3K/AKT/mTOR1 pathway to these drugs. Model validation with independent data sets allows investigation of enzyme function and drug dose dependencies in a wide range of experimental conditions. Modelling of the mTOR1 kinetics showed that Rapamycin has an IC50 independent of ATP concentration and that it is a selective inhibitor of mTOR1 substrates S6K1 and 4EBP1: it retains 40% of mTOR1 activity relative to 4EBP1 phosphorylation and inhibits completely S6K1 activity. For the dual ATP-competitive inhibitors of mTOR1 and PI3K, LY294002 and BEZ235, we derived the dependence of the IC50 on ATP concentration that allows prediction of the IC50 at different ATP concentrations in enzyme and cellular assays. Comparison of the drug effectiveness in enzyme and cellular assays showed that some features of these drugs arise from signalling modulation beyond the on-target action and MM approximation and require a systems-level consideration of the whole PI3K/PTEN/AKT/mTOR1 network in order to understand mechanisms of drug sensitivity and resistance in different cancer cell lines. We suggest that using these models in systems biology investigation of the PI3K/AKT/mTOR1 signalling in cancer cells can bridge the gap between direct drug target action and the therapeutic response to these drugs and their combinations

Species–area relationships in continuous vegetation : evidence from Palaearctic grasslands

Aim: Species-area relationships (SARs) are fundamental scaling laws in ecology although their shape is still disputed. At larger areas power laws best represent SARs. Yet, it remains unclear whether SARs follow other shapes at finer spatial grains in continuous vegetation. We asked which function describes SARs best at small grains and explored how sampling methodology or the environment influence SAR shape. Location: Palaearctic grasslands and other non-forested habitats. Taxa: Vascular plants, bryophytes and lichens. Methods: We used the GrassPlot database, containing standardised vegetation-plot data from vascular plants, bryophytes, and lichens spanning a wide range of grassland types throughout the Palaearctic and including 2057 nested-plot series with at least seven grain sizes ranging from 1 cm2 to 1024 m². Using non-linear regression, we assessed the appropriateness of different SAR functions (power, power quadratic, power breakpoint, logarithmic, Michaelis-Menten). Based on AICc, we tested whether the ranking of functions differed among taxa, methodological settings, biomes or vegetation types. Results: The power function was the most suitable function across the studied taxonomic groups. The superiority of this function increased from lichens to bryophytes to vascular plants to all three taxonomic groups together. The sampling method was highly influential as rooted-presence sampling decreased the performance of the power function. By contrast, biome and vegetation type had practically no influence on the superiority of the power law. Main conclusions: We conclude that SARs of sessile organisms at smaller spatial grains are best approximated by a power function. This coincides with several other comprehensive studies of SARs at different grain sizes and for different taxa, thus supporting the general appropriateness of the power function for modelling species diversity over a wide range of grain sizes. The poor performance of the Michaelis-Menten function demonstrates that richness within plant communities generally does not approach any saturation, thus calling into question the concept of minimal area

A century of enzyme kinetics. Should we believe in the Km and vmax estimates?

The application of the quasi-steady-state approximation (QSSA) in biochemical kinetics allows the reduction of a complex biochemical system with an initial fast transient into a simpler system. The simplified system yields insights into the behavior of the biochemical reaction, and analytical approximations can be obtained to determine its kinetic parameters. However, this process can lead to inaccuracies due to the inappropriate application of the QSSA. Here we present a number of approximate solutions and determine in which regions of the initial enzyme and substrate concentration parameter space they are valid. In particular, this illustrates that experimentalists must be careful to use the correct approximation appropriate to the initial conditions within the parameter space

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

Generic Schemes for Single Molecule Kinetics 2: Information Content of the Poisson Indicator

Recently, we described a pathway analysis technique (paper 1) for analyzing generic schemes for single-molecule kinetics based upon the first-passage time distribution. Here, we employ this method to derive expressions for the Poisson indicator, a measure of stochastic variation (essentially equivalent to the Fano factor and Mandel's Q parameter), for various renewal (memoryless) enzymatic reactions. We examine its dependence on substrate concentration, without assuming all steps follow Poissonian kinetics. Based upon fitting to the functional forms of the first two waiting time moments, we show that, to second order, the non-Poissonian kinetics are generally underdetermined but can be specified in certain scenarios. For an enzymatic reaction with an arbitrary intermediate topology, we identify a generic minimum of the Poisson indicator as a function of substrate concentration, which can be used to tune substrate concentration to the stochastic fluctuations and estimate the largest number of underlying consecutive links in a turnover cycle. We identify a local maximum of the Poisson indicator (with respect to substrate concentration) for a renewal process as a signature of competitive binding, either between a substrate and an inhibitor or between multiple substrates. Our analysis explores the rich connections between Poisson indicator measurements and microscopic kinetic mechanisms