The C-terminus of Protein Tyrosine Phosphatase 1B (PTP1B) includes an α-helix α7), which forms an allosteric binding site 20 å away from the active site. This helix is specific to PTP1B and its truncation decreases the catalytic activity significantly. Here, molecular dynamics (MD) simulations in the presence and absence of α7 were performed to investigate the role played by α7. The highly mobile α7 was found to maintain its contacts with loop 11 (L11)α3 helix throughout the simulations. The interactions of Tyr152 on L11, Tyr176, Thr177 on the catalytically important WPD loop and Ser190 on α3 are important for the conformational stability and the concerted motions of the regions surrounding the WPD loop. In the absence of α7, L11 and WPD loop move away from their crystal structure conformations, resulting in the loss of the interactions in this region, and a decrease in the residue displacement correlations in the vicinity of WPD loop. Therefore, we suggest that one of the functionally important roles of α7 may be to limit the L11 and α3 motions, and, facilitate the WPD loop motions. Truncation of α7 in PTP1B is found to affect distant regions as well, such as the substrate recognition site and the phosphate binding-loop (P-loop), changing the conformations of these regions significantly. Our results show that the PTP1B specific α7 is important for the conformation and dynamics of the WPD loop, and also may play a role in ligand binding.

Time series analysis is applied on the collective coordinates obtained from principal component analysis of independent molecular dynamics simulations of alpha-amylase inhibitor tendamistat and immunity protein of colicin E7 based on the Calpha coordinates history. Even though the principal component directions obtained for each run are considerably different, the dynamics information obtained from these runs are surprisingly similar in terms of time series models and parameters. There are two main differences in the dynamics of the two proteins: the higher density of low frequencies and the larger step sizes for the interminima motions of colicin E7 than those of alpha-amylase inhibitor, which may be attributed to the higher number of residues of colicin E7 and/or the structural differences of the two proteins. The cumulative density function of the low frequencies in each run conforms to the expectations from the normal mode analysis. When different runs of alpha-amylase inhibitor are projected on the same set of eigenvectors, it is found that principal components obtained from a certain conformational region of a protein has a moderate explanation power in other conformational regions and the local minima are similar to a certain extent, while the height of the energy barriers in between the minima significantly change. As a final remark, time series analysis tools are further exploited in this study with the motive of explaining the equilibrium fluctuations of proteins.

The dynamics of alpha-amylase inhibitor tendamistat around its native state is investigated using time series analysis of the principal components of the C(alpha) atomic displacements obtained from molecular dynamics trajectories. Collective motion along a principal component is modeled as a homogeneous nonstationary process, which is the result of the damped oscillations in local minima superimposed on a random walk. The motion in local minima is described by a stationary autoregressive moving average model, consisting of the frequency, damping factor, moving average parameters and random shock terms. Frequencies for the first 50 principal components are found to be in the 3-25 cm(-1) range, which are well correlated with the principal component indices and also with atomistic normal mode analysis results. Damping factors, though their correlation is less pronounced, decrease as principal component indices increase, indicating that low frequency motions are less affected by friction. The existence of a positive moving average parameter indicates that the stochastic force term is likely to disturb the mode in opposite directions for two successive sampling times, showing the modes tendency to stay close to minimum. All these four parameters affect the mean square fluctuations of a principal mode within a single minimum. The inter-minima transitions are described by a random walk model, which is driven by a random shock term considerably smaller than that for the intra-minimum motion. The principal modes are classified into three subspaces based on their dynamics: essential, semiconstrained, and constrained, at least in partial consistency with previous studies. The Gaussian-type distributions of the intermediate modes, called "semiconstrained" modes, are explained by asserting that this random walk behavior is not completely free but between energy barriers.

Effects of ligand binding on protein dynamics are studied via molecular dynamics (MD) simulations on two different enzymes, dihydrofolate reductase (DHFR) and triosephosphate isomerase (TIM), in their unliganded (free) and liganded states. Domain motions in MD trajectories are analyzed by collectivities and rotation angles along the principal components (PCs). DHFR in the free state has well-defined domain rotations, whereas rotations are slightly damped in the binary complex with nicotinamide adenine dinucleotide phosphate (NADPH), and remarkably distorted in the presence of NADP(+) , showing that NADP(+) is solely responsible for the loss of correlation of the domains in DHFR. Although mean square fluctuations of MD simulations in the same PC subspaces are similar for different ligation states, linear stochastic time series models show that backbone flexibility along the first five PCs is decreased upon NADPH and NADP(+) binding in subpicosecond scale. This shows that mobility of the protein along the PCs is closely related with intraminimum dynamics, and alterations in ligation states may change the intraminimum dynamics significantly. Low vibrational frequencies of the alpha-carbon atoms of DHFR are determined from the time series models of a larger number of low indexed PCs, and it is found that number of modes in the lowest frequencies is reduced upon ligand binding. A similar result is obtained for TIM in the unliganded and dihydroxyacetone phosphate bound states. We suggest that stochastic time series modeling is a promising method to be used in determining subtle perturbations in protein dynamics.

Statistical analysis employing regression trees is utilized, for the first time, for a PLA-based biocomposite system aiming to extract knowledge in order to guide researchers toward intelligent selection of experimental conditions for desired tensile strength values. For the construction of the database, experimental data on PLA-based composites from past publications was collected using online sources such as ScienceDirect, Elsevier, ACS, and Google. The final data set that was built using 26 papers (out of ∼150 initially screened) published between 1999 and 2018 contained 135 experimental data points. The response variable was selected as tensile strength, and 23 features regarding composite synthesis were included involving manufacturing method and temperature for compounding and testing, molecular weight of the PLA used, chemical composition of the composite, and type of filler employed in synthesis. Unbiased cross validation error of the regression tree was found to be 12–17 MPa, with coefficient of determination for prediction (R p 2) value equal to 0.5–0.7 showing moderate-to-high prediction accuracy. Results indicated the following: (i) The feature in top node of the tree is the method used for manufacturing/testing rather than the type of filler employed and the composition of the composite (i.e., PLA content). PLA-based composites manufactured by solvent casting and direct mixing displayed significantly lower tensile strength values whereas biocomposites manufactured through other techniques involving compression, injection, melt blending, hot pressing, and aqueous suspension result in relatively higher tensile strength values. (ii) The molecular weight of the PLA had a significant influence in predicting the final tensile strength of the composite. The composites manufacatured employing PLA with molecular weight in the range of 275–400 kDa displayed high tensile strength values. (iii) The temperature employed during test specimen preparation for tensile strength measurements (following compounding step) seemed to play a critical role in the determination of tensile strength, and an optimum test temperature to yield the highest tensile strength possibly exists for each manufacturing method.

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Phase I outliers, unless screened during process parameter estimation, are known to deteriorate Phase II performance of process control charts. Reweighting estimators, ie, trimming outlier subgroups and individual observations, were suggested in the literature to improve both the robustness and efficiency of the resulting parameter estimates. In the current study, effects of various reweighted estimators at different trimming levels on the Phase II performance of S‐charts are elucidated using computer simulations including isolated and mixtures of contamination models. Outlier magnitudes in the simulations are held at a moderately low level to mimic industrial practice. Subtleties, such as varying Type I error rate among different trimming levels with respect to quantiles of dispersion estimates, prevent a single method to be revealed as the best performing one under all circumstances, and choice of estimators and trimming levels should depend on the number of subgroups in Phase I and the specifics of the process. Nevertheless, S‐chart using scale M‐estimator with logistic ρ and location M‐estimator at 2% trimming generally stands out in terms of Phase II performance, and high trimming levels are particularly recommended for high number of Phase I subgroups.