Rate Constant Change of Photo Reaction of Bacteriorhodopsin Observed in Trimeric Molecular System

To elucidate the time evolution of photo reaction of bacteriorhodopsin in glycerol mixed purple membrane at around 196 K under irradiation by red light, a kinetic model was constructed. The change of absorption with irradiation at times of 560 nm and 412 nm was analyzed for the purpose of determining reaction rates of photo reaction of bacteriorhodopsin and its product M intermediate. In this study it is shown that reaction rates of conversion from bacteriorhodopsin to the M intermediate can be explained by a set of linear differential equations. This model analysis concludes that bacteriorhodopsin in which constitutes a trimer unit with other two bacteriorhodopsin molecules changes into M intermediates in the 1.73 of reaction rate, in the initial step, and according to the number of M intermediate in a trimer unit, from three to one, the reaction rate of bacteriorhodopsin into M intermediates smaller as 1.73, 0.80, 0.19 which caused by influence of inter-molecular interaction between bacteriorhodopsin.

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Kinetic analysis of the partial synthesis of artemisinin: Photooxygenation to the intermediate hydroperoxide

Journal of Flow Chemistry ◽

10.1007/s41981-021-00181-2 ◽

2021 ◽

Author(s):

S. Triemer ◽

M. Schulze ◽

B. Wriedt ◽

R. Schenkendorf ◽

D. Ziegenbalg ◽

...

Keyword(s):

Mass Transfer ◽

Kinetic Model ◽

Flow Reactor ◽

Fluid Velocity ◽

Initial Step ◽

Reaction Rates ◽

Photon Flux ◽

Partial Synthesis ◽

Two Phase ◽

Drug Compound

AbstractThe price of the currently best available antimalarial treatment is driven in large part by the limited availability of its base drug compound artemisinin. One approach to reduce the artemisinin cost is to efficiently integrate the partial synthesis of artemisinin starting from its biological precursor dihydroartemisinic acid (DHAA) into the production process. The optimal design of such an integrated process is a complex task that is easier to solve through simulations studies and process modelling. In this article, we present a quantitative kinetic model for the photooxygenation of DHAA to an hydroperoxide, the essential initial step of the partial synthesis to artemisinin. The photooxygenation reactions were studied in a two-phase photo-flow reactor utilizing Taylor flow for enhanced mixing and fast gas-liquid mass transfer. A good agreement of the model and the experimental data was achieved for all combinations of photosensitizer concentration, photon flux, fluid velocity and both liquid and gas phase compositions. Deviations between simulated predictions and measurements for the amount of hydroperoxide formed are 7.1 % on average. Consequently, the identified and parameterized kinetic model is exploited to investigate different behaviors of the reactor under study. In a final step, the kinetic model is utilized to suggest attractive operating windows for future applications of the photooxygenation of DHAA exploiting reaction rates that are not affected by mass transfer limitations.

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Kinetic Modeling and Algorithm of Three-Component Reaction Network

10.22541/au.163253498.89665596/v1 ◽

2021 ◽

Author(s):

Yanping Zhang ◽

Li Xing ◽

Huan Liu ◽

Pingping Huang ◽

Chunjin Wei ◽

...

Keyword(s):

Kinetic Model ◽

Differential Equations ◽

Kinetic Modeling ◽

Basic Equation ◽

Reaction Rate ◽

Reaction Network ◽

Rate Coefficients ◽

Three Component Reaction ◽

Mathematical Techniques ◽

Concentration Curves

The definite solutions of the differential equations from a three-component triangle reaction network have been obtained by utilizing the concept of virtual component concentration and some mathematical techniques. The kinetic model forming from the above definite solutions reveals that the overall reaction rate will be affected by the distribution entropy of the rate coefficients. The improved eigenvector method including a basic equation, algorithm, and criterion has been proposed for calculating the rate coefficients from experimental concentration curves.

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COVID-19 pandemic dynamics in Ukraine after September 1, 2020

10.1101/2020.12.21.20248627 ◽

2020 ◽

Author(s):

Igor Nesteruk

Keyword(s):

Differential Equations ◽

Sir Model ◽

Model Parameters ◽

Unknown Parameters ◽

Epidemic Dynamics ◽

Direct Observations ◽

Long Duration ◽

Constant Change ◽

Reproduction Numbers ◽

Linear Differential

ABSTRACTBackgroundThe threats of the COVID-19 pandemic require the mobilization of scientists, including mathematicians. To understand how the number of cases increases versus time, various models based on direct observations of a random number of new cases and differential equations can be used. Complex mathematical models contain many unknown parameters, the values of which must be determined using a limited number of observations of the disease over time. Even long-term monitoring of the epidemic may not provide reliable estimates of its parameters due to the constant change of testing conditions, isolation of infected and quarantine. Therefore, simpler approaches should also be used, for example, some smoothing of the dependence of the number of cases on time and the known SIR (susceptible-infected-removed) model. These approaches allowed to detect the waves of pandemic in different countries and regions and to make adequate predictions of the duration, hidden periods, reproduction numbers, and final sizes of its waves. In particular, seven waves of the COVID-19 pandemic in Ukraine were investigated.ObjectiveWe will detect new epidemic waves in Ukraine that occurred after September 1, 2020 and estimate the epidemic characteristics with the use of generalized SIR model. Some predictions of the epidemic dynamics will be presented.MethodsIn this study we use the smoothing method for the dependence of the number of cases on time; the generalized SIR model for the dynamics of any epidemic wave, the exact solution of the linear differential equations and statistical approach developed before.ResultsSeventh and eights epidemic waves in Ukraine were detected and the reasons of their appearance were discussed. The optimal values of the SIR model parameters were calculated. The prediction for the COVID-19 epidemic dynamics in Ukraine is not very optimistic: new cases will not stop appearing until June 2021. Only mass vaccination and social distancing can change this trend.ConclusionsNew waves of COVID-19 pandemic can be detected, calculated and predicted with the use of rather simple mathematical simulations. The expected long duration of the pandemic forces us to be careful and in solidarity.The government and all Ukrainians must strictly adhere to quarantine measures in order to avoid fatal consequences.

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