The modern definition of enzymology is synonymous with the Michaelis–Menten equation instituted by Leonor Michaelis and Maud Menten. Most textbooks, or chapters within, discussing enzymology start ...with the derivation of the equation under the assumption of rapid equilibrium (as done by Michaelis–Menten) or steady state (as modified by Briggs and Haldane) conditions to highlight the importance of this equation as the bedrock on which interpretation of enzyme kinetic results is dependent. However, few textbooks or monographs take the effort of placing the equation within its right historical context and discuss the assumptions that have gone into its institution. This guide will dwell on these in substantial detail. Further, this guide will attempt to instil a sense of appreciation for the mathematical curve rectangular hyperbola, its unique attributes and how ubiquitous the curve is in biological systems. To conclude, this guide will discuss the limitations of the equation, and the method it embodies, and trace the journey of how investigators are attempting to move beyond the steady‐state approach and the Michaelis–Menten equation into full progress curve, pre–steady state and single‐turnover kinetic analysis to obtain greater insights into enzyme kinetics and catalysis.
The article talks about the primacy of the Michaelis–Menten equation as a framework for the quantitative understanding of enzyme kinetics. It dwells upon the mathematical elegance of and the assumptions that went into framing the equation. Further, it traces the history of the equation and the growth of the field beyond it. The image shows an artistic rendering of the crowded interiors of a cell and the equation dictating how macromolecular interactions of catalytic nature happen.
The oxygen isotope signature of water is a powerful tracer of water movement from plants to the global scale. However, little is known about the short‐term variability of oxygen isotopes leaving the ...ecosystem via transpiration, as high‐frequency measurements are lacking. A laser spectrometer was coupled to a gas‐exchange chamber directly estimating branch‐level fluxes in order to evaluate the short‐term variability of the isotopic composition of transpiration (δE) and to investigate the role of isotopic non‐steady‐state transpiration under natural conditions in cork‐oak trees (Quercus suber) during distinct Mediterranean seasons. The measured δ¹⁸O of transpiration (δE) deviated from isotopic steady state throughout most of the day even when leaf water at the evaporating sites was near isotopic steady state. High agreement was found between estimated and modeled δE values assuming non‐steady‐state enrichment of leaf water. Isoforcing, that is, the influence of the transpirational δ¹⁸O flux on atmospheric values, deviated from steady‐state calculations but daily means were similar between steady state and non‐steady state. However, strong daytime isoforcing on the atmosphere implies that short‐term variations in δE are likely to have consequences for large‐scale applications, for example, partitioning of ecosystem fluxes or satellite‐based applications.
To reduce the current ripples of finite control set model predictive control, this paper proposes a continuous voltage vector model-free predictive current control method for the surface mounted ...permanent magnet synchronous motor (SMPMSM). In the proposed method, the continuous phase and the amplitude of the voltage vector are optimized in a sequence based on their uncoupling feature, and then the steady-state current fluctuation can be reduced. Only six active voltage vectors are enumerated, and the optimal phase is obtained by establishing the Lagrange interpolation polynomial between the cost function and the phase of voltage vectors. Then, the amplitude of the voltage vector with the optimal phase is optimized based on the principle of minimizing the cost function, and the optimal voltage vector is synthesized by a three-vector method. In addition, the ultra-local model of the SMPMSM drive system from the previous study is used to improve the robustness of the proposed method. The current dynamic and steady-state responses are demonstrated through the simulation and experimental results.
This paper presents a new algorithm, called steady-state and generational evolutionary algorithm, which combines the fast and steadily tracking ability of steady-state algorithms and good diversity ...preservation of generational algorithms, for handling dynamic multiobjective optimization. Unlike most existing approaches for dynamic multiobjective optimization, the proposed algorithm detects environmental changes and responds to them in a steady-state manner. If a change is detected, it reuses a portion of outdated solutions with good distribution and relocates a number of solutions close to the new Pareto front based on the information collected from previous environments and the new environment. This way, the algorithm can quickly adapt to changing environments and thus is expected to provide a good tracking ability. The proposed algorithm is tested on a number of bi- and three-objective benchmark problems with different dynamic characteristics and difficulties. Experimental results show that the proposed algorithm is very competitive for dynamic multiobjective optimization in comparison with state-of-the-art methods.
In order to provide more sensitive monitoring results, the time dynamics and steady-state operating conditions should be separately monitored by distinguishing time information from the steady-state ...counterpart. However, it is a more challenging task for batch processes because they vary from phase to phase presenting multiple steady states and complex dynamic characteristics. To address the above issue, a concurrent monitoring strategy of multiphase steady states and process dynamics is developed for batch processes in this paper. On one hand, multiple local models are constructed to identify a steady derivation from the normal operating condition for different phases. On the other hand, based on the recognition that the process dynamics can be considered to be irrelevant with the steady states, a global model is built to detect the dynamics anomalies by monitoring the time variations. Corresponding to alarms issued by different statistics, different operating statuses are indicated with meaningful physical interpretation and deep process understanding. To illustrate the feasibility and efficacy, the proposed algorithm is applied to the injection molding process, which is a typical multiphase batch process.
Purpose
To develop a steady‐state saturation with radial readout chemical exchange saturation transfer (starCEST) for acquiring CEST images at 3 Tesla (T). The polynomial Lorentzian line‐shape ...fitting approach was further developed for extracting amideCEST intensities at this field.
Method
StarCEST MRI using periodically rotated overlapping parallel lines with enhanced reconstruction‐based spatial sampling was implemented to acquire Z‐spectra that are robust to brain motion. Multi‐linear singular value decomposition postprocessing was applied to enhance the CEST SNR. The egg white phantom studies were performed at 3T to reveal the contributions to the 3.5 ppm CEST signal. Based on the phantom validation, the amideCEST peak was quantified using the polynomial Lorentzian line‐shape fitting, which exploits the inverse relationship between Z‐spectral intensity and the longitudinal relaxation rate in the rotating frame. The 3D turbo spin echo CEST was also performed to compare with the starCEST method.
Results
The amideCEST peak showed a negligible peak B1 dependence between 1.2 µT and 2.4 µT. The amideCEST images acquired with starCEST showed much improved image quality, SNR, and motion robustness compared to the conventional 3D turbo spin echo CEST method with the same scan time. The amideCEST contrast extracted by the polynomial Lorentzian line‐shape fitting method trended toward a stronger gray matter signal (1.32% ± 0.30%) than white matter (0.92% ± 0.08%; P = .02, n = 5). When calculating the magnetization transfer contrast and T1‐corrected rotating frame relaxation rate maps, amideCEST again was not significantly different for white matter and gray matter.
Conclusion
Rapid multi‐slice amideCEST mapping can be achieved by the starCEST method (< 5 min) at 3T by combing with the polynomial Lorentzian line‐shape fitting method.
This paper presents two new rotor configurations for the line start permanent-magnet synchronous motors (PMSMs). The first configuration proposed here uses inset consequent magnet pole arrangement ...with double cage, and results into improved starting performance when compared to the other rotor configurations previously used. The second configuration proposed uses a combination of circumferentially and radially magnetized magnets (hybrid rotor), with induced magnet poles, which results into improved synchronous performance. Two-dimensional finite-element analysis has been employed in the analysis of transient and steady-state performances. The experimental prototypes for the second configuration are built and tested extensively. To demonstrate the effectiveness of the hybrid rotor configuration, an additional prototype is made that employs the circumferentially magnetized magnets (spoke magnet type rotor), and performance of the proposed rotor is benchmarked with this. Analysis, simulation, and experimental results indicate that the proposed rotor configuration leads to improved steady-state performance, by utilizing 10% less magnet volume than the benchmarked spoke rotor. The proposed configurations are also suitable for inverter-fed brushless dc, and PMSMs.
This paper addressed a well-documented open problem regarding multiple unmanned aerial vehicles (multi-UAVs) formation keeping. A cooperative guidance control method based on the back-stepping ...approach is proposed to rapidly form the desired formation and reach the multi-UAV steady state. The UAV formation system consists of four UAVs, forming a regular triangle formation. One of the UAVs is a virtual leader and is located at the center of the triangle; the other three UAVs are located at the vertices of the triangle. The forward speed of leader is used as the forward direction of the formation, and the followers follow the leader in a formation flight. The error dynamics model of each follower is established by using the leader guidance mechanism, and the communication mode between any two UAVs is established based on graph theory. In addition, the guidance control law is obtained via the back-stepping approach. We reasonably construct the Lyapunov function to prove the stability of the proposed cooperative guidance control law in formation aggregation and keeping. Moreover, the proposed method is compared with the model prediction method (MPC) and the Lyapunov method to further verify the effectiveness of the proposed method. The simulation results show that each UAV can converge to the desired motion trajectory and fly in the desired formation with fast convergence speed and small steady-state error.
In this paper, we consider the problem of system identification when side-information is available on the steady-state gain (SSG) of the system. We formulate a general nonparametric identification ...method as an infinite-dimensional constrained convex program over the reproducing kernel Hilbert space (RKHS) of stable impulse responses. The objective function of this optimization problem is the empirical loss regularized with the norm of RKHS, and the constraint is considered for enforcing the integration of the SSG side-information. The proposed formulation addresses both the discrete-time and continuous-time cases. We show that this program has a unique solution obtained by solving an equivalent finite-dimensional convex optimization. This solution has a closed-form when the empirical loss and regularization functions are quadratic and exact side-information is considered. We perform extensive numerical comparisons to verify the efficiency of the proposed identification methodology.
The steady-state performance of modular multilevel converter (MMC) can be optimized by the following methods: circulating current injection, third-harmonic signal injection, and average capacitor ...voltage control. However, most of the papers, due to the deficiencies of their MMC models, are limited to the study of adopting just one method and only optimizing a single-aspect of the performance. Thus, this article proposes a general MMC model for the comprehensive study of the steady-state performance optimization. The general model is built based on an equilibrium equation between the internal quantities and the external quantities of the MMC. This general model is capable of analyzing the optimization where the optimizing methods are combined and used to improve the multiaspect performance of the MMC. In addition, more influence factors are taken into account; hence, the calculation error can be smaller than 1% and even the minor effect of each optimizing method can be reflected. The proposed model is compared with traditional models; and it is found that both dc and fundamental components in modulation signals will be affected by the injected circulating current, rather than the constant values in the traditional models. Finally, the proposed MMC model is verified by both simulation and experiment.
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