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Membrane progestin receptors (mPRs) are responsible for mediating the rapid, nongenomic activity of progestins and belong to the G protein-coupled receptor (GPCR) family. mPRs are also considered as attractive proteins to draw a new medicinal approach. In this study, we optimized a procedure for the expression and purification of recombinant human mPRα protein (hmPRα) by a methylotropic yeast, Pichia pastoris, expression system. The protein expressed in crude membrane fractions exhibited a binding affinity of Kd = 3.8 nM and Bmax = 288.8 fmol/mg for progesterone. These results indicated that the hmPRα expressed in yeast was active. Solubilized hmPRα was purified through three column chromatography steps. A nickel-nitrilotriacetic acid (Ni-NTA) column was first used, and the mPRα proteins were then bound to cellulose resin with free amino groups (Cellufine Amino) and finally passed through an SP-Sepharose column. The optimization of expression and purification conditions resulted in a high yield of purified hmPRα (1.3–1.5 mg from 1 L culture). The purified hmPRα protein demonstrated progesterone binding (Kd = 5.2 nM and Bmax = 111.6 fmol/mg). The results indicated that we succeeded in solubilizing and purifying hmPRα in an active form. Sufficient amount of active hmPRα protein will support the establishment of applications for the screening of ligands for mPRα.

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In this paper, we apply the improved Kudryashov method for finding exact solution and then solitary wave solutions of the Chafee-Infante equation and (2+1)-dimensional breaking soliton equation, where mathematical software Maple-13 is used as an important mathematical tool for removing calculation complexity, justification of the solutions and its graphical representations.

Abstract:In this paper, Butcher's fifth order Runge-Kutta (RK5) and fourth order Runge-Kutta (RK4) methods have been employed to solve the Initial Value Problems (IVP) involving third order Ordinary Differential Equations (ODE). These two proposed methods are quite proficient and practically well suited for solving engineering problems based on such problems. To obtain the accuracy of the numerical outcome for this study, we have compared the approximate results with the exact results and found a good agreement between the exact and approximate solutions. In addition, to achieve more accuracy in the solution, the step size needs to be very small. Moreover, the error terms have been analyzed for these two methods and also compared by an appropriate example.