For this ongoing work, the bounds of the noise model were chosen as = ?0.1? and = 1.2? to allow for 2D incorporation data that is both higher and negative than the theoretical number of amides. Likelihood function The likelihood function (for each data point, scales the probability of generating the data point when the expected data point value 6-Carboxyfluorescein is A unimodal distribution was chosen as a prior for the uncertainty where the expected uncertainty 0 is derived from the standard deviation of 2D incorporation from observations at = 0; the heavy tail of the distribution allows for outliers. Sampling The main computational cost of the method consists of searching the space of exchange rates for each residue site. Bayesian method consisting of a forward model, noise model, probabilities prior, and a Monte Carlo sampling scheme. This method exploits a residue-resolved exponential rate model of HDX-MS data obtained from all peptides simultaneously, and models experimental error explicitly. The result is the best possible estimate of HDX significance and magnitude for each residue given the data. We demonstrate the method by revealing richer structural interpretation of HDX data on two nuclear receptors: vitamin D-receptor (VDR) and retinoic acid receptor gamma (ROR). The method is implemented in HDX Workbench and as a standalone module of the open source and of HDX in a macromolecule due to a perturbation event, such as ligand binding, point change or mutation in experimental conditions. Open in a separate window Figure 1 Method FlowchartExperimental: The method uses MS data that is analyzed by instrument-specific software, such as HDX Workbench, to produce 2D incorporation data vs. time. The resulting .csv files or modified .csv files are used as input into the Bayesian method. Bayesian Method: Step 1; Data (information) is gathered, including the HDX-MS 2D incorporation data for both apo and liganded (or perturbed) states as well an estimate for the error, 0, and deuterium saturation level, consists of the exchange rate constant for each backbone amide hydrogen {and prior information and = {of peptide after exchange time and approximated by a unimolecular first-order reaction. It is expressed as is the number of observable amides for peptide and are the beginning and ending residues of peptide is a delta function whose value is one if residue has an observable amide and zero if otherwise. Noise Model The theoretical deuterium incorporation at a given site is bound to be between 0 and 1, scaled by the fraction of deuterium in the exchange buffer, ? thus, we modeled the error in the experimental data using a truncated Gaussian, resulting in the probability of observing a single data point, for peptide at time and replicate is the point error estimate for peptide at timepoint = ({and are the bounds of the truncated Gaussian. For this ongoing 6-Carboxyfluorescein work, the bounds of the noise model were chosen as = ?0.1? and = 1.2? to allow for 2D incorporation data that is both negative and higher than the theoretical number of amides. Likelihood function The likelihood function (for each data point, scales the probability of generating the data point when the expected data point value is A unimodal distribution was chosen as a prior for the uncertainty where the expected uncertainty 0 is derived from the standard 6-Carboxyfluorescein deviation of 2D incorporation F3 from observations at 6-Carboxyfluorescein = 0; the heavy tail of the distribution allows for outliers. Sampling The main computational cost of the method consists of searching the space of exchange rates for each residue site. To reduce the complexity of the search, a finite grid of exchange rates is chosen with the minimum and maximum values of exchange determined from the range of experimental time points. For small systems (proteins with 30 exchangeable amides), the true number of available exchange states can be enumerated. In the full case of larger systems, sampling is performed by a Metropolis Monte Carlo (MC) algorithm35 to generate models of HD exchange rates, {and standard deviation for the log(in the peptide is calculated from the ensemble of best scoring models for each target state. The HDX is then reported as the difference between the mean values of each continuing state, while the significance can be reported using a two-sample Z-score: is the number of best scoring models chosen from each state. Alternatively, the total result can be transformed into a probability, , that the HDX observations for the two conditions are different by integrating along the normal distribution. = 10, followed by 50 steps each at = 4, 3, 2 and 1 and a production run of 5000 steps at = 1. The right time to complete each apo-ligand HDX dataset was 2C4 hours on two 2.2GHz processors (one for each independent run). From the combined ensemble of.
