Editorial

Editoria

Gelman-Rubin Convergence Statistics for each aEARM calibration.

The Gelman-Rubin convergence statistics for the aEARM parameters for each calibration scenario were tabulated. This table can be loaded from https://doi.org/10.5281/zenodo.7007655. (XLSX)</p

Objective functions and the role of a measurement model.

Mechanistic models of biological processes are typically encoded as systems of (ordinary) differential equations (Eq 1). Model calibration relies on an objective function (Eq 6)—or in a Bayesian setting, a likelihood function (Eq 7)—quantifies the degree of dissimilarity or similarity between model variables and corresponding measurements. Note, the objective or likelihood function uses an implied measurement model (Eq 6) which converts modeled variables x(t) to a quantity y(ti, θ) that can be compared to data . In physics and engineering, where measurements are typically quantitative, this implicit measurement model suffices. For nonquantitative measurements and observations, the measurement model must be defined explicitly in consideration of the nonquantitative measurements’ properties.</p

Co-clustering of descriptors and odors.

<p> Overview of method used for defining a bicluster (see text for definition). A column of (descriptors), and the corresponding row of (odors) are rank ordered. The indices derived from the rank-ordering are used to re-order rows and columns of (accomplished by computing the outer product between the rank-ordered column of and rank-ordered row of ), producing a submatrix with high correlation among both odors and descriptors. By the nature of the sorting procedure, these matrices – biclusters – will have their largest values in the upper-left corner. For purposes of visualization, biclusters were convolved with an averaging filter. The 10 biclusters defined by NMF on odor perceptual data.</p

Predicted Bid truncation dynamics of aEARM trained to nominal and ordinal datasets.

A.) Nominal cell death (x) vs survival (o) outcomes data for cells treated with 10ng/mL (orange) and 50ng/mL (grey) of TRAIL and with known relative values of DISC formation (x-axis). The 95% credible region (shaded region) of posterior predictions of tBID dynamics of aEARM calibrated to nominal data (right plot). The median prediction (solid-line) and true (dotted line) are also plotted. B.) Ordinal measurements for initiator caspase-DISC colocalization (IC-DISC) at 300s intervals (left plot). The 95% credible region (shaded region) of posterior predictions of tBID dynamics of aEARM calibrated to ordinal IC-DISC data (right plot), and C.) of aEARM calibrated to nominal and ordinal IC-DISC data. The median prediction (solid-line) and true (dotted line) were also plotted. The fit to IC-DISC data is shown in Fig G S1 Text.</p

Posterior predictions of aEARM trained to published fractional cell death data.

A. Fractional cell death in WT (blue) and high- and low- expression of dominant negative FADD (green and orange respectively) in HeLa cells treated with 0 to 200ng/mL TRAIL. These data come from Wajant et al. 1998 [29]. The aEARM and accompanying measurement model were calibrated to these data. B. The posterior predictions of the Gaussian process modeled mean fractional cell death values for WT and high- and low- expression of dominant negative FADD in HeLa cell treated with 0 to 200ng/mL TRAIL. C. Posterior predictions of the Gaussian process modeled mean fractional cell death values for WT and BID overexpressed (TAT-Bid) HeLa cells treated with and without 100ng/mL TRAIL. Fractional cell death predictions for these experimental conditions, which were excluded from our training dataset, correspond to fractional cell death measurements by Orzechowska et al [30]. The 95% credible region of the posterior prediction (D.) of tBID dynamics in cells treated with 25g/mL TRAIL. (E.) Posterior distributions of the weight for each feature extracted from tBID dynamics.</p

Predicted Bid truncation dynamics of aEARM trained to different sized ordinal datasets.

Multiple Bayesian optimizations were run on the A.) abridged Extrinsic Apoptosis Reaction Model (aEARM) using different sized ordinal dataset to probe how dataset size influenced certainty of aEARM predictions. B.) Initiator caspase reporter (IC-RP) fluorescence time-course measurements (at 180s intervals) were measured (top left) as a proxy for truncated tBid (data from Albeck et al21). The plot shows the mean (dotted orange line) ± 1 standard deviation (shaded region) for each time point. The 95% credible region (top right) of posterior predictions (shaded region) for tBID concentration in aEARM, calibrated to fluorescence measurements of IC-RP and EC-RP (See also Fig C in S1 Text). The median prediction (solid-line) and ground truth (dotted line) tBID concentration trajectories are shown. In the next four rows (from top to bottom), Ordinal measurements of tBID (left) at every 1500, 300, 180 and 60s interval, respectively. The 95% credible region of predictions (shaded region), median prediction (solid line) and true (dotted line) tBID dynamics for aEARM calibrated to ordinal measurements of tBID and cPARP occurring at every 1500, 300, 180 and 60s timepoint are plotted in plots on the right. The plots for cPARP ordinal measurements and predictions are found in Fig A in S1 Text.</p

Supporting Information file containing Tables A-E and Figs A-T.

The supporting information provides method details. Tables A-E describe parameters and reactions included in the aEARM. The following figures describe the prior and posterior distributions of aEARM parameters calibrated to using different dataset and measurement models. Also included (Figs A, G, K and R) are various posterior predictions for aEARM variables. This file contains a table of contents for further details. (DOCX)</p

Visualization of odors expressed in coordinates of the new basis.

<p> The weight matrix, , discovered by NMF. Columns of (each column corresponds to a different odor), are normalized and sorted into groups defined by peak coordinate (1–10). Plot of all 144 odors (each point is a column of ) in the space spanned by the first 3 basis vectors, and . Black, red, and blue points are those with peak coordinates in dimensions 1, 2, and 3 respectively. Gray points are all remaining odors. Chemical structures of representative odorants from the second and seventh diagonal blocks of the sorted matrix (panel ).</p

Predicted Bid truncation dynamics of aEARM trained to ordinal data using different measurement model parameterizations.

A.) and B.) The 95% credible region of posterior predictions (shaded region) of tBID dynamics for aEARM calibrated to ordinal measurements two fixed parameterizations for the measurement model (see Table C in S1 Text). The adjacent panels plot the measurement models predicted probability of class membership (x-axis) as a function of normalized tBID concentration (y-axis). C.) D.) and E.) The 95% credible region of posterior predictions (shaded region) of tBID dynamics of aEARM calibrated to ordinal measurements uniform, Cauchy (scale = 0.05) and Cauchy (scale = 0.005) prior distributions for the parameterizations of θj (the distance between offset βj and the preceding offset βj−1) for the measurement model, respectively. In each, the median prediction (solid line) and true (dotted line) tBID dynamics are also shown. The adjacent panels give the 95% credible region of posterior predictions of the probability of class membership (x-axis) as a function of normalized tBID concentration (y-axis). The left and their adjacent panels share the y-axis (normalized tBID concentration) Four accompanying plots show the prior (blue), posterior (orange) and true (dashed line) values of measurement model parameters.</p