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Linear Algebra in Biomolecular Modeling
Published in Leslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias, Handbook of Linear Algebra, 2006
The RMSD is basically the smallest average coordinate errors of the structures for all possible rotations Q of structure Y to fit structure X. It is called the Procrustes problem for its analogy to the Greek story about cutting a person’s legs to fit a fixed-sized iron bed. Note that X and Y may be the coordinate matrices for the same (A = B) or different (A ≠ B) proteins and therefore, each pair of corresponding atoms do not have to be of the same type (when A ≠ B). However, the number of atoms selected to compare must be the same from A and B (# rows of X = #rows of Y).
A Study of Crime in India Through Statistical Analysis
Published in Durgesh Kumar Mishra, Nilanjan Dey, Bharat Singh Deora, Amit Joshi, ICT for Competitive Strategies, 2020
B. Mittal, A. K. Verma, S. Bagai
The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) (or sometimes root-mean-squared error) is used to measure the differences between the values predicted by the model and the values observed. RMSE is always greater or equal to zero, and a value of 0 indicates a perfect fit to the data. The lower the RMSE, the better the model.
Concurrent validation of the Noraxon MyoMotion wearable inertial sensors in change-of-direction and jump-landing tasks
Published in Sports Biomechanics, 2022
Pieter Heuvelmans, Anne Benjaminse, Ruben Bolt, Jochen Baumeister, Egbert Otten, Alli Gokeler
Concurrent validity was assessed using cross-correlation (XCORR), root mean square deviation (RMSD), and amplitude difference (ΔAMP) between lower extremity joint kinematics recorded by the WIS and OMB systems. XCORR is a measure of agreement between two time series (Islam et al., 2020). Level of agreement was interpreted as ‘poor’ if XCORR <0.40, ‘fair’ if XCORR 0.40–0.75, and ‘excellent’ if XCORR >0.75 (Kadaba et al., 1989), as used in a recent study with a similar design albeit for different correlation measures (Di Paolo et al., 2021). RMSD is a measure of error and was calculated by taking the square root of the average of squared deviations (Robinson et al., 2014). ΔAMP is also a measure of error and was calculated by taking the maximum difference in amplitude between waveforms. When compared to taking the absolute difference in range of motion, ΔAMP is better suited to describe error between waveforms because it quantifies noise rather than implying that it is part of the physiological range of motion of a joint. ΔAMP was defined as WIS minus OMB data. Level of error was interpreted as ‘low’ if the measure of error ≤5° (Di Paolo et al., 2021). Due to the tasks being focused on the dominant leg, only the joint kinematics of the dominant leg are reported.
Synthesis, crystal structure, hirshfeld surface analysis, molecular docking and molecular dynamics studies of novel olanzapinium 2,5-dihydroxybenzoate as potential and active antipsychotic compound
Published in Journal of Experimental Nanoscience, 2022
V. Natchimuthu, Mohnad Abdalla, Manasi Yadav, Ishita Chopra, Anushka Bhrdwaj, Khushboo Sharma, S. Ravi, Krishnan Ravikumar, Khalid J. Alzahrani, Tajamul Hussain, Anuraj Nayarisseri
The MD simulation provided details of conformational changes in protein and ligand over the trajectory of 100 ns. The simulation diagram is for structural analysis by RMSD and RMSF, ligand properties, and protein–ligand interaction. Based on the structural assessment, the functionality of ligand molecules could be anticipated. The RMSD (root mean square deviation) graph suggests structural activity of protein–ligand interaction; lower the RMSD confers greater stability of the interface. Whilst RMSF (root mean square fluctuation) graph refers to the mobility of proteins Cα residue; a greater number of peaks stipulates more flexibility in proteins backbone.
Molecular Docking , ADMET and Pharmacokinetic properties predictions of some di-aryl Pyridinamine derivatives as Estrogen Receptor (Er+) Kinase Inhibitors
Published in Egyptian Journal of Basic and Applied Sciences, 2022
Sagiru Hamza Abdullahi, Adamu Uzairu, Gideon Adamu Shallangwa, Sani Uba, Abdullahi Bello Umar
The docked complex of compound 31 was utilized as the initial structure for the molecular dynamic simulation study using Desmond 2019–4 software package in the present research work because it exhibits best docking scores as well as hydrogen bond energy. MD simulation generates a model for the ligand-receptor state very close to the natural environment, which offers a noble opportunity to examine the strength and continuity of the H-bonds profile. Protein and ligand flexibility was taken into consideration in MD simulation, this paves the way for advanced examination of the consistency of the docking outcomes and residues in the binding site of a receptor and their nature of interactions with inhibitors can also be explored during the simulation process [21]. The complex was tested for root mean square deviation (RMSD), root mean square fluctuation (RMSF), radius of gyration (Rg) and number of H-bonds formed between the inhibitors and the receptor after the simulation process was completed. The system is well equilibrated and remained stable throughout the simulation as revealed by the analysis of trajectory. RMSD values of the backbone of the protein alone and that of the ligand-protein complex were computed to explore the stability of the complex. Final RMSD values of the complex and protein lie below 2.00 Å for the 1 ns simulation, which illustrates the rigidity of the protein structure in the presence of the ligand during MD simulation. The ligand and the protein systems reached equilibrium at 0.28 ns and 0.4 ns, respectively. The RMSD value of the ligand is lower than that of the protein, which illustrates the stability of the ligand in the active site of the protein. Figure 23 shows the RMSD values of the protein and the ligand.