Bayesian Population Physiologically-Based Pharmacokinetic (PBPK) Approach for a Physiologically Realistic Characterization of Interindividual Variability in Clinically Relevant Populations

<div><p>Interindividual variability in anatomical and physiological properties results in significant differences in drug pharmacokinetics. The consideration of such pharmacokinetic variability supports optimal drug efficacy and safety for each single individual, e.g. by identification of individual-specific dosings. One clear objective in clinical drug development is therefore a thorough characterization of the physiological sources of interindividual variability. In this work, we present a Bayesian population physiologically-based pharmacokinetic (PBPK) approach for the mechanistically and physiologically realistic identification of interindividual variability. The consideration of a generic and highly detailed mechanistic PBPK model structure enables the integration of large amounts of prior physiological knowledge, which is then updated with new experimental data in a Bayesian framework. A covariate model integrates known relationships of physiological parameters to age, gender and body height. We further provide a framework for estimation of the <i>a posteriori</i> parameter dependency structure at the population level. The approach is demonstrated considering a cohort of healthy individuals and theophylline as an application example. The variability and co-variability of physiological parameters are specified within the population; respectively. Significant correlations are identified between population parameters and are applied for individual- and population-specific visual predictive checks of the pharmacokinetic behavior, which leads to improved results compared to present population approaches. In the future, the integration of a generic PBPK model into an hierarchical approach allows for extrapolations to other populations or drugs, while the Bayesian paradigm allows for an iterative application of the approach and thereby a continuous updating of physiological knowledge with new data. This will facilitate decision making e.g. from preclinical to clinical development or extrapolation of PK behavior from healthy to clinically significant populations.</p></div

PhysioSpace: Relating Gene Expression Experiments from Heterogeneous Sources Using Shared Physiological Processes

<div><p>Relating expression signatures from different sources such as cell lines, in vitro cultures from primary cells and biopsy material is an important task in drug development and translational medicine as well as for tracking of cell fate and disease progression. Especially the comparison of large scale gene expression changes to tissue or cell type specific signatures is of high interest for the tracking of cell fate in (trans-) differentiation experiments and for cancer research, which increasingly focuses on shared processes and the involvement of the microenvironment. These signature relation approaches require robust statistical methods to account for the high biological heterogeneity in clinical data and must cope with small sample sizes in lab experiments and common patterns of co-expression in ubiquitous cellular processes. We describe a novel method, called PhysioSpace, to position dynamics of time series data derived from cellular differentiation and disease progression in a genome-wide expression space. The PhysioSpace is defined by a compendium of publicly available gene expression signatures representing a large set of biological phenotypes. The mapping of gene expression changes onto the PhysioSpace leads to a robust ranking of physiologically relevant signatures, as rigorously evaluated via sample-label permutations. A spherical transformation of the data improves the performance, leading to stable results even in case of small sample sizes. Using PhysioSpace with clinical cancer datasets reveals that such data exhibits large heterogeneity in the number of significant signature associations. This behavior was closely associated with the classification endpoint and cancer type under consideration, indicating shared biological functionalities in disease associated processes. Even though the time series data of cell line differentiation exhibited responses in larger clusters covering several biologically related patterns, top scoring patterns were highly consistent with a priory known biological information and separated from the rest of response patterns. </p> </div

Detailed results of the differentiation time series analyses.

<p>(A) Line plots of most relevant PhysioScores for the three differentiation time series comparing scores from PhysioSpaces 1 and 3. Lines with names ending with “Lukk” correspond to the third PhysioSpace (Lukk et al. 2010 [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0077627#B18" target="_blank">18</a>], E-MTAB-62), other lines correspond to the first PhysioSpace (GSE7307). (B) Heart and ESC increasingly dominate leading PhysioScores in the cardiomyocyte differentiation time series. Depicted are the PhysioScores of the 5 strongest signatures from cardiomyocyte differentiation. Red (blue) colors correspond to positive (negative) PhysioScores. (C) Comparison of pluripotency (ESC) and lineage (fetal brain/placenta/heart) scores for the three differentiation time series exhibit different dynamics in PhysioSpace 1. The lineage score corresponds to the dominant lineage in each differentiation, i.e. fetal brain, placenta, and heart for the neural, trophoblast, and cardiomyocyte differentiation, respectively. (D) The matching score is used to compare the implemented PhysioSpace algorithm to a classical GSEA based algorithm, showing relatively strong differences between the two methods for the trophoblast and cardiomyocyte differentiations. The implemented PhysioSpace algorithm has generally a higher matching score.</p

Overview over the PhysioSpace algorithm.

<p>(A) Data from a new experiment is transformed to remove ellipticity and the resulting fold-change vector is compared to a compendium of signatures from prior experiments using a robust, rank-based scoring method. Graphical displays and the statistical validation allow to evaluate the position of the new experiment in the global PhysioSpace. (B, C) Illustration of the influence of non-sphericity on sample permutations. (B) In the presence of a strong ellipticity, sample permutation does not randomize directions in contrast to more spherically distributed samples as obtained through the spherical transformation approach (C).</p

Heatmap of PhysioScores combining selected signatures from three PhysioSpaces.

<p>The PhysioScores for all six investigated datasets are visualized in context for selected signatures. In order to evaluate the stability of the method, the signatures were derived from three different physiological databases resulting in PhysioSpaces 1-3. The results are depicted in a heatmap-like representation. The color scheme differs between datasets but is the same for the PhysioSpaces 1-3, ranging from negative values in blue and green to positive values in orange and red. The dendrogram represents a hierarchical clustering of the signatures according to a Pearson-correlation distance. Values within clusters are usually similar, e.g clusters of neural or immune signatures. The results corresponding to PhysioSpaces 1-3 show similar dynamics and consistent dominating signatures, while the absolute values are only approximately comparable.</p

Main steps of the PhysioSpace generation and mapping algorithms.

<p>Main steps of the PhysioSpace generation and mapping algorithms.</p

Schematic illustration of the presented Bayesian population PBPK approach.

<p>(A) A Bayesian framework is combined with a detailed mechanistic PBPK model, where a Markov chain Monte Carlo (MCMC) approach is considered to identify the high dimensional parameter distribution. (B) Prior population-specific anatomical and physiological information is integrated into an hierarchical model approach. (C) Individual-specific experimental data and physiological parameters are considered to parameterize the model and to generate individual model outputs. (D) Due to the model structure of the PBPK model, substance parameters can be differentiated from physiological parameters. This allows a global determination of the substance information, since it does not vary individually or from population to population.</p

Details of results from cancer progression.

<p>Ranking of PhysioScores comparing breast cancer samples of grade 1 to grade 2 or 3 (A) and lung samples from never smokers to former or current smokers (B). Apparently, grading differences in breast cancer are associated with more signatures from the PhysioSpace than differences in gene expression of smokers and non-smokers. Blue (red) colors depict negative (positive) PhysioScores. Filled bars indicate significant scores according to a sample-permutation FDR (Benjamini-Hochberg) cutoff of 0.1. </p

Individual-specific model simulations of theophylline venous plasma concentrations.

<p>For each of the 12 individuals the PBPK model was subsequently parameterized and simulated with each of 500 individual and independent parameter vectors out of the posterior distribution. The 95% confidence interval of all simulations (grey area) is shown together with the mean value curve (blue dotted line) and the experimental data (red circles). Dark grey dotted lines depict the upper and lower bound of the 95% confidence interval of all simulations including the inferred measurement error.</p