Bayesian Model Averaging for Ensemble-Based Estimates of Solvation-Free Energies

Ensemble deep learning models for prediction and uncertainty quantification of ground magnetic perturbation

Geomagnetically Induced Currents are one of the most hazardous effects caused by geomagnetic storms. In the past literature, the variations in ground magnetic fields over time, dB/dt were used as a proxy value for GIC. Machine Learning (ML) techniques have emerged as a preferred methodology to predict dB/dt. However, space weather data are highly dynamic in nature, and the data distribution is subject to change over time due to environmental variability. The ML models developed are prone to the uncertainty in the input data and therefore suffer from high variance. In addition, a part of an ML architecture performance is conditional on the variables used to model the system in focus. Therefore, a single algorithm may not generate the required accuracy for a given dataset. In this work, a Bayesian Ensemble ML model has been developed to predict the variations over time of the local ground magnetic horizontal component, dBH/dt. The Ensemble methodology combines multiple ML models in the prediction process to predict dBH/dt. Bayesian statistics allow the estimation of model parameters and output as probability distributions, where the variance quantifies the uncertainty. The input data consists of solar-wind data from OmniWeb for the years 2001–2010. The local ground horizontal magnetic components for the corresponding time were calculated using SuperMAG data for the Ottawa ground magnetometer station for the years mentioned above. The years 2011–2015 were selected for model testing, as it encompasses the 5 August 2011 and 17 March 2015 geomagnetic storms. Five different accuracy metrics were considered; namely, Root Mean Squared Error (RMSE), Probability of Detection (POD), Probability of False Detection (PFD), Proportion Correct (PC), and Heidke Skills Score (HSS). The parameter uncertainty of the models is quantified, and the mean predicted dBH/dt is generated with a 95% credible interval. It can be observed that different models perform better with different datasets and the ensemble model has an accuracy comparable to the models with a relatively strong performance.

An Immune-Gene-Based Classifier Predicts Prognosis in Patients With Cervical Squamous Cell Carcinoma

Objective: Immunity plays a vital role in the human papilloma virus (HPV) persistent infection, and closely associates with occurrence and development of cervical squamous cell carcinoma (CSCC). Herein, we performed an integrated bioinformatics analysis to establish an immune-gene signature and immune-associated nomogram for predicting prognosis of CSCC patients. Methods: The list of immunity-associated genes was retrieved from ImmPort database. The gene and clinical information of CSCC patients were obtained from The Cancer Genome Atlas (TCGA) website. The immune gene signature for predicting overall survival (OS) of CSCC patients was constructed using the univariate Cox-regression analysis, random survival forests, and multivariate Cox-regression analysis. This signature was externally validated in GSE44001 cohort from Gene Expression Omnibus (GEO). Then, based on the established signature and the TCGA cohort with the corresponding clinical information, a nomogram was constructed and evaluated via Cox regression analysis, concordance index (C-index), receiver operating characteristic (ROC) curves, calibration plots and decision curve analyses (DCAs). Results: A 5-immune-gene prognostic signature for CSCC was established. Low expression of ICOS, ISG20 and high expression of ANGPTL4, SBDS, LTBR were risk factors for CSCC prognosis indicating poor OS. Based on this signature, the OS was significantly worse in high-risk group than in low-risk group (p-value < 0.001), the area under curves (AUCs) for 1-, 3-, 5-years OS were, respectively, 0.784, 0.727, and 0.715. A nomogram incorporating the risk score of signature and the clinical stage was constructed. The C-index of this nomogram was 0.76. AUC values were 0.811, 0.717, and 0.712 for 1-, 3-, 5-years OS. The nomogram showed good calibration and gained more net benefits than the 5-immune-gene signature and the clinical stage. Conclusion: The 5-immune-gene signature may serve as a novel, independent predictor for prognosis in patients with CSCC. The nomogram incorporating the signature risk score and clinical stage improved the predictive performance than the signature and clinical stage alone for predicting 1-year OS.

Validation of Free Energy Methods in AMBER

Herein we provide high-precision validation tests of the latest GPU-accelerated free energy code in AMBER. We demonstrate that consistent free energy results are obtained in both the gas phase and in solution. We first show, in the context of thermodynamic integration (TI), that the results are invariant with respect to "split" (e.g., stepwise decharge-vdW-recharge) versus "unified" protocols. This brought to light a subtle inconsistency in previous versions of AMBER that was traced to the improper treatment of 1-4 vdW and electrostatic interactions involving atoms across the softcore boundary. We illustrate that under the assumption that the ensembles produced by different legs of the alchemical transformation between molecules A and B in the gas phase and aqueous phase are very small, the inconsistency in the relative hydration free energy ΔΔG_hydr[A → B] = ΔG_aq[A → B] - ΔG_gas[A → B] is minimal. However, for general cases where the ensembles are shown to be substantially different, as expected in ligand-protein binding applications, these errors can be large. Finally, we demonstrate that results for relative hydration free energy simulations are independent of TI or multistate Bennett's acceptance ratio (MBAR) analysis, invariant to the specific choice of the softcore region, and in agreement with results derived from absolute hydration free energy values.

Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is underdetermined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a new method for quantifying this uncertainty in implicit solvation calculations of small molecules using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space requires compressed sensing combined with an iterative rotation method to enhance problem sparsity. We demonstrate the application of the method by presenting results for the uncertainties in small molecule solvation energies based on these approaches. The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parametrization problems, including those beyond continuum solvation calculations. The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters.