It has become commonplace to employ principal component analysis to reveal the most important motions in proteins. This method is more commonly known by its acronym, PCA. While most popular molecular ...dynamics packages inevitably provide PCA tools to analyze protein trajectories, researchers often make inferences of their results without having insight into how to make interpretations, and they are often unaware of limitations and generalizations of such analysis. Here we review best practices for applying standard PCA, describe useful variants, discuss why one may wish to make comparison studies, and describe a set of metrics that make comparisons possible. In practice, one will be forced to make inferences about the essential dynamics of a protein without having the desired amount of samples. Therefore, considerable time is spent on describing how to judge the significance of results, highlighting pitfalls. The topic of PCA is reviewed from the perspective of many practical considerations, and useful recipes are provided.
How can an income tax system be designed to exploit human nature and a free market to create a poverty free society, while balancing budgets without disproportional tax burdens? Such a tax system, ...with universal character, is deduced from the following guiding principles: (1) a single tax rate applies to all income types and levels; (2) the tax rate adjusts to satisfy budget projections; (3) government transfer only supplements the income of households with self-generated income below the poverty line; (4) deductions for basic living expenses, itemized investments and capital losses are allowed; (5) deductions cannot be applied to government transfer. A general framework emerges with three parameters that determine a minimum allowed tax deduction, a maximum allowed itemized deduction, and a maximum deduction defined by income percentage. An income distribution that mimics the United States, and a series of log-normal distributions are considered to quantitatively compare detailed characteristics of this tax system to progressive and flat tax systems. To minimize government dependency while maximizing after-tax income, the effective tax rate (ETR) as a function of income percentile takes the shape of the letter, V, inspiring the name victory tax, where the middle class has the lowest ETR.
In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about ...data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference.
Identifying mechanisms that control molecular function is a significant challenge in pharmaceutical science and molecular engineering. Here, we present a novel projection pursuit recurrent neural ...network to identify functional mechanisms in the context of iterative supervised machine learning for discovery-based design optimization. Molecular function recognition is achieved by pairing experiments that categorize systems with digital twin molecular dynamics simulations to generate working hypotheses. Feature extraction decomposes emergent properties of a system into a complete set of basis vectors. Feature selection requires signal-to-noise, statistical significance, and clustering quality to concurrently surpass acceptance levels. Formulated as a multivariate description of differences and similarities between systems, the data-driven working hypothesis is refined by analyzing new systems prioritized by a discovery-likelihood. Utility and generality are demonstrated on several benchmarks, including the elucidation of antibiotic resistance in TEM-52 beta-lactamase. The software is freely available, enabling turnkey analysis of massive data streams found in computational biology and material science.
Principal component analysis (PCA) is commonly applied to the atomic trajectories of biopolymers to extract essential dynamics that describe biologically relevant motions. Although application of PCA ...is straightforward, specialized software to facilitate workflows and analysis of molecular dynamics simulation data to fully harness the power of PCA is lacking. The Java Essential Dynamics inspector (JEDi) software is a major upgrade from the previous JED software.
Employing multi-threading, JEDi features a user-friendly interface to control rapid workflows for interrogating conformational motions of biopolymers at various spatial resolutions and within subregions, including multiple chain proteins. JEDi has options for Cartesian-based coordinates (cPCA) and internal distance pair coordinates (dpPCA) to construct covariance (Q), correlation (R), and partial correlation (P) matrices. Shrinkage and outlier thresholding are implemented for the accurate estimation of covariance. The effect of rare events is quantified using outlier and inlier filters. Applying sparsity thresholds in statistical models identifies latent correlated motions. Within a hierarchical approach, small-scale atomic motion is first calculated with a separate local cPCA calculation per residue to obtain eigenresidues. Then PCA on the eigenresidues yields rapid and accurate description of large-scale motions. Local cPCA on all residue pairs creates a map of all residue-residue dynamical couplings. Additionally, kernel PCA is implemented. JEDi output gives high quality PNG images by default, with options for text files that include aligned coordinates, several metrics that quantify mobility, PCA modes with their eigenvalues, and displacement vector projections onto the top principal modes. JEDi provides PyMol scripts together with PDB files to visualize individual cPCA modes and the essential dynamics occurring within user-selected time scales. Subspace comparisons performed on the most relevant eigenvectors using several statistical metrics quantify similarity/overlap of high dimensional vector spaces. Free energy landscapes are available for both cPCA and dpPCA.
JEDi is a convenient toolkit that applies best practices in multivariate statistics for comparative studies on the essential dynamics of similar biopolymers. JEDi helps identify functional mechanisms through many integrated tools and visual aids for inspecting and quantifying similarity/differences in mobility and dynamic correlations.
Le Châtelier's principle is the cornerstone of our understanding of chemical equilibria. When a system at equilibrium undergoes a change in concentration or thermodynamic state (i.e., temperature, ...pressure, etc.), La Châtelier's principle states that an equilibrium shift will occur to offset the perturbation and a new equilibrium is established. We demonstrate that the effects of stabilizing mutations on the rigidity ⇔ flexibility equilibrium within the native state ensemble manifest themselves through enthalpy-entropy compensation as the protein structure adjusts to restore the global balance between the two. Specifically, we characterize the effects of mutation to single chain fragments of the anti-lymphotoxin-β receptor antibody using a computational Distance Constraint Model. Statistically significant changes in the distribution of both rigidity and flexibility within the molecular structure is typically observed, where the local perturbations often lead to distal shifts in flexibility and rigidity profiles. Nevertheless, the net gain or loss in flexibility of individual mutants can be skewed. Despite all mutants being exclusively stabilizing in this dataset, increased flexibility is slightly more common than increased rigidity. Mechanistically the redistribution of flexibility is largely controlled by changes in the H-bond network. For example, a stabilizing mutation can induce an increase in rigidity locally due to the formation of new H-bonds, and simultaneously break H-bonds elsewhere leading to increased flexibility distant from the mutation site via Le Châtelier. Increased flexibility within the VH β4/β5 loop is a noteworthy illustration of this long-range effect.
Objective The Supera stent (Abbott Laboratories, Abbott Park, Ill) has a unique biomimetic design allowing axial and longitudinal flexibility and fracture resistance. The aim of this retrospective ...study was to assess the midterm patency of Supera stents used to treat patients with superficial femoral and popliteal arterial disease by a single practice. Methods From April 2010 to December 2011, 53 patients and 59 limbs with symptomatic femoropopliteal lesions underwent angioplasty and stenting with the Supera stent. Five patients had no follow-up and were excluded. Demographics of the patients, radiographic images, morphologic features of the lesions, procedural reports, reinterventions, and follow-up clinical visit notes were reviewed. Primary patency was defined as clinical resolution of symptoms with no secondary interventions. Primary and secondary patency rates at 12, 24, and 36 months were estimated by Kaplan-Meier analysis. Results A total of 48 patients (42 men, six women; 54 limbs; mean age, 64.3 years range, 51-87) received Supera stents and had at least one follow-up visit as part of their treatment for femoropopliteal disease. Primary indications for intervention included claudication, rest pain, and tissue loss, at rates of 54% (29 of 54), 26% (14 of 54), and 20% (11 of 54), respectively; 22% of lesions were TransAtlantic Inter-Society Consensus type A or B and 78% were type C or D. Mean lesion length was 24.0 cm (range, 3-51). Mean follow-up was 27.5 months (range, 1-45). The ankle-brachial index increased from 0.58 ± 0.20 preoperatively to 0.77 ± 0.18 postoperatively ( P = .00004). Primary, primary assisted, and secondary patency rates at latest follow-up were 79.6%, 88.9%, and 92.3%, respectively. Cumulative primary patency rates by Kaplan-Meier analysis at 12, 24, and 36 months were 85.6%, 83.1%, and 76.7%, respectively. Secondary patency rates by Kaplan-Meier estimates at 12, 24, and 36 months were 93.8%, 93.8%, and 89.3%, respectively. No stent fractures were found at the time of any reinterventions. Long lesions >30 cm (n = 18) showed equivalent patency to lesions of 1 to 15 cm (n = 18) and lesions 15 to 30 cm in length (n = 18). Conclusions Our midterm results show that Supera stents are durable in treating femoropopliteal lesions, with notably high patency rates in patients with long lesion lengths.
The beta-lactamase enzyme provides effective resistance to beta-lactam antibiotics due to substrate recognition controlled by point mutations. Recently, extended-spectrum and inhibitor-resistant ...mutants have become a global health problem. Here, the functional dynamics that control substrate recognition in TEM beta-lactamase are investigated using all-atom molecular dynamics simulations. Comparisons are made between wild-type TEM-1 and TEM-2 and the extended-spectrum mutants TEM-10 and TEM-52, both in apo form and in complex with four different antibiotics (ampicillin, amoxicillin, cefotaxime and ceftazidime). Dynamic allostery is predicted based on a quasi-harmonic normal mode analysis using a perturbation scan. An allosteric mechanism known to inhibit enzymatic function in TEM beta-lactamase is identified, along with other allosteric binding targets. Mechanisms for substrate recognition are elucidated using multivariate comparative analysis of molecular dynamics trajectories to identify changes in dynamics resulting from point mutations and ligand binding, and the conserved dynamics, which are functionally important, are extracted as well. The results suggest that the H10-H11 loop (residues 214-221) is a secondary anchor for larger extended spectrum ligands, while the H9-H10 loop (residues 194-202) is distal from the active site and stabilizes the protein against structural changes. These secondary non-catalytically-active loops offer attractive targets for novel noncompetitive inhibitors of TEM beta-lactamase.
Atherectomy has become increasingly used as an endovascular treatment of lower extremity atherosclerotic disease in the United States. However, concerns and controversies about its indications and ...outcomes exist. The goal of the present systematic review and meta-analysis was to investigate the outcomes and complications related to atherectomy to treat femoropopliteal atherosclerotic disease.
A systematic review in accordance with the recommendations from the PRISMA (preferred reporting items for systematic reviews and meta-analyses) statement was performed. Four major scientific repositories (MEDLINE, Embase, the Cochrane Library, and Thompson Web of Sciences) were queried from their inception to April 5, 2020. We reviewed and entered the data in a dedicated dataset. The outcomes included the patency rates, clinical and hemodynamic improvement, and morbidity and mortality associated with atherectomy interventions.
Twenty-four studies encompassing 1900 patients met the inclusion criteria for the present study. Of the 1900 patients, 74.3% had presented with Rutherford class 1 to 3 and 25.7% presented with Rutherford class 4 to 6; 1445 patients had undergone atherectomy, and 455 patients had been treated without atherectomy. The atherectomy group had undergone directional atherectomy (n = 851), rotational atherectomy (n = 851), laser atherectomy (n = 201), and orbital atherectomy (n = 78). Most of these patients had also received adjunct treatments, which varied across the studies and included a combination of stenting, balloon angioplasty, or drug-coated balloon angioplasty. Technical success was achieved in 92.3% of the cases. Distal embolization, vessel perforation, and dissection occurred in 3.4%, 1.9%, and 4% of the cases, respectively. The initial patency was 95.4%. At the 12-month median follow-up, the primary patency was 72.6%. The ankle brachial index had improved from a preoperative mean of 0.6 to a postoperative mean of 0.84. The incidence of major amputation and mortality during the follow-up period was 2.2% and 3.4%, respectively.
The results from our review of the reported data suggest that femoropopliteal atherectomy can be completed safely, modestly improving the ankle brachial index and maintaining the 1-year patency in nearly three of four patients. However, these findings were based on heterogeneous studies that skewed the generalizable conclusions about atherectomy's efficacy. Atherectomy places a high cost burden on the healthcare system and is used in the United States at a higher rate than in other countries. Our review of the literature did not demonstrate clear atherectomy superiority to alternatives that would warrant the pervasive and increasing use of this costly technology. Future work should focus on developing high-quality randomized controlled trials to determine the specific patient and lesion characteristics for which atherectomy can add value.
We investigate changes in human c-type lysozyme flexibility upon mutation via a Distance Constraint Model, which gives a statistical mechanical treatment of network rigidity. Specifically, two ...dynamical metrics are tracked. Changes in flexibility index quantify differences within backbone flexibility, whereas changes in the cooperativity correlation quantify differences within pairwise mechanical couplings. Regardless of metric, the same general conclusions are drawn. That is, small structural perturbations introduced by single point mutations have a frequent and pronounced affect on lysozyme flexibility that can extend over long distances. Specifically, an appreciable change occurs in backbone flexibility for 48% of the residues, and a change in cooperativity occurs in 42% of residue pairs. The average distance from mutation to a site with a change in flexibility is 17-20 Å. Interestingly, the frequency and scale of the changes within single point mutant structures are generally larger than those observed in the hen egg white lysozyme (HEWL) ortholog, which shares 61% sequence identity with human lysozyme. For example, point mutations often lead to substantial flexibility increases within the β-subdomain, which is consistent with experimental results indicating that it is the nucleation site for amyloid formation. However, β-subdomain flexibility within the human and HEWL orthologs is more similar despite the lowered sequence identity. These results suggest compensating mutations in HEWL reestablish desired properties.
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