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We derive approximate expressions for pre- and post-steady state regimes of the velocity-substrate-inhibitor spaces of the Michaelis-Menten enzyme kinetic scheme with fully and partial competitive inhibition. Our refinement over the currently available standard quasi steady state approximation (sQSSA) seems to be valid over wide range of enzyme to substrate and enzyme to inhibitor concentration ratios. Further, we show that the enzyme-inhibitor-substrate system can exhibit temporally well-separated two different steady states with respect to both enzyme-substrate and enzyme-inhibitor complexes under certain conditions. We define the ratios fS = vmax/(KMS + e0) and fI = umax/(KMI + e0) as the acceleration factors with respect to the catalytic conversion of substrate and inhibitor into their respective products. Here KMS and KMI are the Michaelis-Menten parameters associated respectively with the binding of substrate and inhibitor with the enzyme, vmax and umax are the respective maximum reaction velocities and e0, s0, and i0 are total enzyme, substrate and inhibitor levels. When (fS/fI) < 1, then enzyme-substrate complex will show multiple steady states and it reaches the full-fledged steady state only after the depletion of enzyme-inhibitor complex. When (fS/fI) > 1, then the enzyme-inhibitor complex will show multiple steady states and it reaches the full-fledged steady state only after the depletion of enzyme-substrate complex. This multi steady-state behavior especially when (fS/fI) ≠ 1 is the root cause of large amount of error in the estimation of various kinetic parameters of fully and partial competitive inhibition schemes using sQSSA. Remarkably, we show that our refined expressions for the reaction velocities over enzyme-substrate-inhibitor space can control this error more significantly than the currently available sQSSA expressions. [ABSTRACT FROM AUTHOR]

The chemical etching of germanium in Br2 environment at elevated temperatures is described by the Michaelis–Menten equation. The validity limit of Michaelis–Menten kinetics is subjected to the detailed analysis. The steady-state etching rate requires synergy of two different process parameters. High purity gas should be directed to the substrate on which intermediate reaction product does not accumulate. Theoretical calculations indicate that maximum etching rate is maintained when 99.89% of the germanium surface is covered by the reaction product, and 99.9999967% of the incident Br2 molecules are reflected from the substrate surface. Under these conditions, single GeBr2 molecule is formed after 30 million collisions of Br2 molecules with the germanium surface. [ABSTRACT FROM AUTHOR]

Selenium plays an important, but vastly neglected role in human nutrition with a narrow gap between dietary deficiency and toxicity. For a potential biofortification of food with Se, as well as for toxicity-risk assessment in sites contaminated by Se, modelling of local and global Se cycling is essential. As bioavailability of Se for rice plants depends on the speciation of Se and the resulting interactions with mineral surfaces as well as the interaction with Se uptake mechanisms in plants, resulting plant Se content is complex to model. Unfortunately, simple experimental models to estimate Se uptake into plants from substrates have been lacking. Therefore, a mass balance of Se transfer between lithosphere (represented by kaolinite), hydrosphere (represented by a controlled nutrient solution), and biosphere (represented by rice plants) has been established. In a controlled, closed, lab-scale system, rice plants were grown hydroponically in nutrient solution supplemented with 0–10 000 μg L-1 Se of either selenate or selenite. Furthermore, in a series of batch experiments, adsorption and desorption were studied for selenate and selenite in competition with each of the major nutrient oxy-anions, nitrate, sulfate and phosphate. In a third step, the hydroponical plants experiments were coupled with sorption experiments to study synergy effects. These data were used to develop a mass balance fitting model of Se uptake and partitioning. Adsorption was well-described by Langmuir isotherms, despite competing anions, however, a certain percentage of Se always remained bio-unavailable to the plant. Uptake of selenate or selenite by transporters into the rice plant was fitted with the non-time differentiated Michaelis-Menten equation. Subsequent sequestration of Se to the shoot was better described using a substrate-inhibited variation of the Michaelis-Menten equation. These fitted parameters were then integrated into a mass balance model of Se transfer. [ABSTRACT FROM AUTHOR]

Purpose: To develop a general model that utilises a stochastic method to generate a vessel tree based on experimental data, and an associated irregular, macroscopic tumour. These will be used to evaluate two different methods for computing oxygen distribution. Methods: A vessel tree structure, and an associated tumour of 127 cm3, were generated, using a stochastic method and Bresenham’s line algorithm to develop trees on two different scales and fusing them together. The vessel dimensions were adjusted through convolution and thresholding and each vessel voxel was assigned an oxygen value. Diffusion and consumption were modelled using a Green’s function approach together with Michaelis-Menten kinetics. The computations were performed using a combined tree method (CTM) and an individual tree method (ITM). Five tumour sub-sections were compared, to evaluate the methods. Results: The oxygen distributions of the same tissue samples, using different methods of computation, were considerably less similar (root mean square deviation, RMSD≈0.02) than the distributions of different samples using CTM (0.001< RMSD<0.01). The deviations of ITM from CTM increase with lower oxygen values, resulting in ITM severely underestimating the level of hypoxia in the tumour. Kolmogorov Smirnov (KS) tests showed that millimetre-scale samples may not represent the whole. Conclusions: The stochastic model managed to capture the heterogeneous nature of hypoxic fractions and, even though the simplified computation did not considerably alter the oxygen distribution, it leads to an evident underestimation of tumour hypoxia, and thereby radioresistance. For a trustworthy computation of tumour oxygenation, the interaction between adjacent microvessel trees must not be neglected, why evaluation should be made using high resolution and the CTM, applied to the entire tumour. [ABSTRACT FROM AUTHOR]

Photosynthesis-irradiance (PI) curves are extensively used in field and laboratory research to evaluate the photon-use efficiency of plants. However, most existing models for PI curves focus on the relationship between the photosynthetic rate (Pn) and photosynthetically active radiation (PAR), and do not take account of the influence of environmental factors on the curve. In the present study, we used a new non-competitive inhibited Michaelis-Menten model (NIMM) to predict the co-variation of Pn, PAR, and the relative pollution index (I). We then evaluated the model with published data and our own experimental data. The results indicate that the Pn of plants decreased with increasing I in the environment and, as predicted, were all fitted well by the NIMM model. Therefore, our model provides a robust basis to evaluate and understand the influence of environmental pollution on plant photosynthesis. [ABSTRACT FROM AUTHOR]

Simulation models of leaf area index (LAI) and yield for cotton can provide a theoretical foundation for predicting future variations in yield. This paper analyses the increase in LAI and the relationships between LAI, dry matter, and yield for cotton under three soil conditioners near Korla, Xinjiang, China. Dynamic changes in cotton LAI were evaluated using modified logistic, Gaussian, modified Gaussian, log normal, and cubic polynomial models. Universal models for simulating the relative leaf area index (RLAI) were established in which the application rate of soil conditioner was used to estimate the maximum LAI (LAIm). In addition, the relationships between LAIm and dry matter mass, yield, and the harvest index were investigated, and a simulation model for yield is proposed. A feasibility analysis of the models indicated that the cubic polynomial and Gaussian models were less accurate than the other three models for simulating increases in RLAI. Despite significant differences in LAIs under the type and amount of soil conditioner applied, LAIm could be described by aboveground dry matter using Michaelis-Menten kinetics. Moreover, the simulation model for cotton yield based on LAIm and the harvest index presented in this work provided important theoretical insights for improving water use efficiency in cotton cultivation and for identifying optimal application rates of soil conditioners. [ABSTRACT FROM AUTHOR]

A number of proteins can aggregate into amyloid-like fibrils. It was noted that fibril elongation has similarities to an enzymatic reaction, where monomers or oligomers would play a role of substrate and nuclei/fibrils would play a role of enzyme. The question is how similar these processes really are. We obtained experimental data on insulin amyloid-like fibril elongation at the conditions where other processes which may impact kinetics of fibril formation are minor and fitted it using Michaelis-Menten equation. The correlation of the fit is very good and repeatable. It speaks in favour of enzyme-like model of fibril elongation. In addition, obtained and values at different conditions may help in better understanding influence of environmental factors on the process of fibril elongation. [ABSTRACT FROM AUTHOR]

We present the first computational kinetic model of polyamine metabolism in bloodstream-form Trypanosoma brucei, the causative agent of human African trypanosomiasis. We systematically extracted the polyamine pathway from the complete metabolic network while still maintaining the predictive capability of the pathway. The kinetic model is constructed on the basis of information gleaned from the experimental biology literature and defined as a set of ordinary differential equations. We applied Michaelis-Menten kinetics featuring regulatory factors to describe enzymatic activities that are well defined. Uncharacterised enzyme kinetics were approximated and justified with available physiological properties of the system. Optimisation-based dynamic simulations were performed to train the model with experimental data and inconsistent predictions prompted an iterative procedure of model refinement. Good agreement between simulation results and measured data reported in various experimental conditions shows that the model has good applicability in spite of there being gaps in the required data. With this kinetic model, the relative importance of the individual pathway enzymes was assessed. We observed that, at low-to-moderate levels of inhibition, enzymes catalysing reactions of de novo AdoMet (MAT) and ornithine production (OrnPt) have more efficient inhibitory effect on total trypanothione content in comparison to other enzymes in the pathway. In our model, prozyme and TSHSyn (the production catalyst of total trypanothione) were also found to exhibit potent control on total trypanothione content but only when they were strongly inhibited. Different chemotherapeutic strategies against T. brucei were investigated using this model and interruption of polyamine synthesis via joint inhibition of MAT or OrnPt together with other polyamine enzymes was identified as an optimal therapeutic strategy. [ABSTRACT FROM AUTHOR]

In this study, through phenomenological comparison of the velocity-force data of processive motor proteins, including conventional kinesin, cytoplasmic dynein and myosin V, I found that, the ratio between motor velocities of two different ATP concentrations is almost invariant for any substall, superstall or negative external loads. Therefore, the velocity of motors can be well approximated by a Michaelis-Menten like formula V=[ATP]k(F)L=([ATP]+KM), with L the step size, and k(F) the external load F dependent rate of one mechanochemical cycle of motor motion in saturated ATP solution. The difference of Michaelis-Menten constant KM for substall, superstall and negative external load indicates, the configurations at which ATP molecule can bind to motor heads for these three cases might be different, though the expression of k(F) as a function of F might be unchanged for any external load F. Verifications of this Michaelis-Menten like formula has also been done by fitting to the recent experimental data. [ABSTRACT FROM AUTHOR]