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Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace.

ABSTRACT: The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM and the closely-related multiple Bennett acceptance ratio (MBAR) method can be improved by using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution.

SUBMITTER: Zhang C

PROVIDER: S-EPMC4955632 | biostudies-literature | 2016

REPOSITORIES: biostudies-literature

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Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace.

Zhang Cheng C Lai Chun-Liang CL Pettitt B Montgomery BM

Molecular simulation 20160705 13

The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid converge ...[more]

PMID: 27453632

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Project description:Free energy perturbation (FEP) simulations have been widely applied to obtain predictions of the relative binding free energy for a series of congeneric ligands binding to the same receptor, which is an essential component for the lead optimization process in computer-aided drug discovery. In the case of several congeneric ligands forming a perturbation map involving a closed thermodynamic cycle, the summation of the estimated free energy change along each edge in the cycle using Bennett acceptance ratio (BAR) usually will deviate from zero due to systematic and random errors, which is the hysteresis of cycle closure. In this work, the advanced reweighting techniques binless weighted histogram analysis method (UWHAM) and locally weighted histogram analysis method (LWHAM) are applied to provide statistical estimators of the free energy change along each edge in order to eliminate the hysteresis effect. As an example, we analyze a closed thermodynamic cycle involving four congeneric ligands which bind to HIV-1 integrase, a promising target which has emerged for antiviral therapy. We demonstrate that, compared with FEP and BAR, more accurate and hysteresis-free estimates of free energy differences can be achieved by using UWHAM to find a single estimate of the density of states based on all of the data in the cycle. Furthermore, by comparison of LWHAM results obtained from the inclusion of different numbers of neighboring states with UWHAM estimation involving all the states, we show how to determine the optimal neighborhood size in the LWHAM analysis to balance the trade-offs between computational cost and accuracy of the free energy prediction. Even with the smallest neighborhood, LWHAM can improve the BAR free energy estimates using the same input data as BAR. We introduce an overlapping states matrix that is constructed by using the global jump formula of LWHAM and plot its heat map. The heat map provides a quantitative measure of the overlap between pairs of alchemical/thermodynamic states. We explain how to identify and improve the FEP calculations along the edges that most likely cause large systematic errors by using the heat map of the overlapping states matrix and by comparing the BAR and UWHAM estimates of the free energy change.

Project description:PurposeGlioblastoma and anaplastic astrocytoma represent the most commonly encountered high-grade-glioma (HGG) in adults. Although both neoplasms are very distinct entities in context of epidemiology, clinical course and prognosis, their appearance in conventional magnetic resonance imaging (MRI) is very similar. In search for additional information aiding the distinction of potentially confusable neoplasms, histogram analysis of apparent diffusion coefficient (ADC) maps recently proved to be auxiliary in a number of entities. Therefore, our present exploratory retrospective study investigated whether ADC histogram profile parameters differ significantly between anaplastic astrocytoma and glioblastoma, reflect the proliferation index Ki-67, or are associated with the prognostic relevant MGMT (methylguanine-DNA methyl-transferase) promotor methylation status.MethodsPre-surgical ADC volumes of 56 HGG patients were analyzed by histogram-profiling. Association between extracted histogram parameters and neuropathology including WHO-grade, Ki-67 expression and MGMT promotor methylation status was investigated due to comparative and correlative statistics.ResultsGrade IV gliomas were more heterogeneous than grade III tumors. More specifically, ADCmin and the lowest percentile ADCp10 were significantly lower, whereas ADCmax, ADC standard deviation and Skewness were significantly higher in the glioblastoma group. ADCmin, ADCmax, ADC standard deviation, Kurtosis and Entropy of ADC histogram were significantly correlated with Ki-67 expression. No significant difference could be revealed by comparison of ADC histogram parameters between MGMT promotor methylated and unmethylated HGG.ConclusionsADC histogram parameters differ significantly between glioblastoma and anaplastic astrocytoma and show distinct associations with the proliferative activity in both HGG. Our results suggest ADC histogram profiling as promising biomarker for differentiation of both, however, further studies with prospective multicenter design are wanted to confirm and further elaborate this hypothesis.

Project description:BackgroundThe incidence of chronic kidney disease (CKD) is high, and is easy to develop into end-stage renal disease (ESRD), which requires kidney dialysis or kidney transplantation. Therefore, we want to explore the clinical value of magnetic resonance quantitative histogram analysis based on spatial labeling with multiple inversion pulses (SLEEK) in assessing renal function in the early stage.MethodsOne hundred and twenty-nine patients underwent abdominal MRI examination, including a coronal SLEEK sequence. The patients were divided into the control group [CG, 47 cases, estimated glomerular filtration rate (eGFR) >90], the mild renal function impairment (mRI) group (48 cases, eGFR =60-90), and the moderate to severe renal function impairment (m-sRI) group (34 cases, eGFR <60). Two experienced radiologists delineated cortex and medulla regions of interest (ROIs) on SLEEK images to obtain cortex and medulla quantitative histogram parameters [Mean, Median, Percentiles (5th, 10th, 25th, 75th, and 90th), Skewness, Kurtosis, and Entropy] using FireVoxel. These histogram parameters were compared by proper statistical methods such as one-way analysis of variance, the χ2 test, and receiver operating characteristic (ROC) curve analysis.ResultsFour histogram parameters (Inhomogeneitycortex, Skewnesscortex, Kurtosismedulla, and Entropymedulla) differed significantly between the CG and the mRI group. One medulla (Entropymedulla) and nine cortex (Meancortex, Mediancortex, Kurtosiscortex, Entropycortex, and 5th, 10th, 25th, 75th, and 90th Percentilecortex) histogram parameters were significantly different between the m-RI and m-sRI groups. The most relevant parameter to eGFR was Inhomogenitycortex (r=-0.450, P<0.001). Inhomogeneitycortex had the largest area under the curve (AUC) for differentiating the mRI group from the CG (AUC =0.718; 95% CI: 0.616-0.806), while 25th Percentilecortex generated the largest AUC (AUC =0.786; 95% CI: 0.681-0.869) for differentiating the mRI and m-sRI groups.ConclusionsQuantitative histogram parameters based on a SLEEK sequence can be used to supplement renal dysfunction assessment. Cortex histogram parameters are more valuable for evaluating renal function than medulla histogram parameters.

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Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace.

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Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace.

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