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No full textPoznańDicer is an enzyme responsible for processing double-stranded RNAs and plays a key role in an RNAi mechanism. Structural insight into the Dicer is provided by the crystal structure of eukaryotic Dicer from Giardia intestinalis. It has been proposed that the structure has three structurally rigid regions that are connected by the flexible hinges. Flexibility of the Dicer is believed to be a critical feature for its function. Spatial arrangement of the RNA-recognition and the catalytic regions is crucial for producing small RNAs of defined length. It has been suggested that in the Giardia Dicer a Platform domain may help in specific arrangement of these regions. To learn more about the role of the Platform domain in Giardia Dicer, we have performed molecular dynamics (MD) simulations of the whole Dicer (WT Dicer) and the Dicer with a deleted platform domain (ΔPlf Dicer). The MD simulations were carried out in an implicit solvent model with two implementations of analytic Generalized Born (GB) solvation model in CHARMM: GBMV (Generalized Born using Molecular Volume) and GBSW (Generalized Born with simple Switching). To detect the key global motions of the Dicer, a principal component analysis (PCA) of the obtained MD trajectories has been used. To further explore the motion of the Dicer, we performed a domain motion analysis with the DYNDOM program. The simulations show that both WT Dicer and ΔPlf Dicer display flexibility which can be described as a movement of two or three domains. The removal of the Platform substantially changed the flexibility and arrangement of these domains. During the MD simulations of ΔPlf Dicer an large movement of the RNA-recognition domain was observed
No full textPoznańA new variant of Newton's method based on contra harmonic mean has been developed and its convergence properties have been discussed. The order of convergence of the proposed method is six. Starting with a suitably chosen x0, the method generate sa sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. In terms of computational cost, it requires evaluations of only two functions and two first order derivatives per iteration. This implies that efficiency index of our method is 1.5651. The proposed method is comparable with the methods of Parhi, and Gupta [15] and that of Kou and Li [8]. It does not require the evaluation of the second order derivative of the given function as required in the family of Chebyshev-Halley type methods. The efficiency of the method is tested on a number of numerical examples. It is observed that our method takes lesser number of iterations than Newton’s method and the other third order variants of Newton´s method. In comparison with the sixth order methods, it behaves either similarly or better for the examples considered
No full textPoznańThe reductive perturbation method has been employed to derive the Korteweg–deVries (KdV) equation for small but finite amplitude electrostatic ion-acoustic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters to reveal different solutions, i.e. bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points called “blowup” solutions in addition to the propagation of explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as ionosphere
No full textPoznańWe present and apply two complementary calculation methods used in phononic crystal studies: the finite difference time domain (FDTD) method and the plain wave method (PWM). The FDTD technique allows to simulate the time dependence of a wave packet of vibrational modes propagating through a composite and to determine the transmission coefficient. The PWM method is used for the determination of the phononic dispersion relation in systems with discrete translational symmetry. We use both methods for investigating the effect of periodic interface perturbations on the spectrum of longitudinal vibrational modes in 1D phononic crystals composed of semiconducting materials. The material parameters in the composites under consideration are modulated in the nanoscale
