A Computational Systems Biology Software Platform for Multiscale Modeling and Simulation: Integrating Whole-Body Physiology, Disease Biology, and Molecular Reaction Networks

Today, in silico studies and trial simulations already complement experimental approaches in pharmaceutical R&D and have become indispensable tools for decision making and communication with regulatory agencies. While biology is multiscale by nature, project work, and software tools usually focus on isolated aspects of drug action, such as pharmacokinetics at the organism scale or pharmacodynamic interaction on the molecular level. We present a modeling and simulation software platform consisting of PK-Sim® and MoBi® capable of building and simulating models that integrate across biological scales. A prototypical multiscale model for the progression of a pancreatic tumor and its response to pharmacotherapy is constructed and virtual patients are treated with a prodrug activated by hepatic metabolization. Tumor growth is driven by signal transduction leading to cell cycle transition and proliferation. Free tumor concentrations of the active metabolite inhibit Raf kinase in the signaling cascade and thereby cell cycle progression. In a virtual clinical study, the individual therapeutic outcome of the chemotherapeutic intervention is simulated for a large population with heterogeneous genomic background. Thereby, the platform allows efficient model building and integration of biological knowledge and prior data from all biological scales. Experimental in vitro model systems can be linked with observations in animal experiments and clinical trials. The interplay between patients, diseases, and drugs and topics with high clinical relevance such as the role of pharmacogenomics, drug–drug, or drug–metabolite interactions can be addressed using this mechanistic, insight driven multiscale modeling approach

Penalized Variational Autoencoder for Molecular Design

Variational autoencoders have emerged as one of the most common approaches for automating molecular generation. We seek to learn a cross-domain latent space capturing chemical and biological information, simultaneously. To do so, we introduce the Penalized Variational Autoencoder which directly operates on SMILES, a linear string representation of molecules, with a weight penalty term in the decoder to address the imbalance in the character distribution of SMILES strings. We find that this greatly improves upon previous variational autoencoder approaches in the quality of the latent space and the generalization ability of the latent space to new chemistry. Next, we organize the latent space according to chemical and biological properties by jointly training the Penalized Variational Autoencoder with linear units. Extensive experiments on a range of tasks, including reconstruction, validity, and transferability demonstrates that the proposed methods here substantially outperform previous SMILES and graph-based methods, as well as introduces a new way to generate molecules from a set of desired properties, without prior knowledge of a chemical structure

Fair Value Pricing in Purchasing

Creating price transparency in product markets is one of the major tasks that purchasing departments have to manage. This paper introduces a new statistical approach to create price transparency, making use of nonlinear regression methods as well as artificial neuronal networks. The paper reveals the underlying mathematical models and shows an application example

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

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

Exemplary representation of derived distributions of correlation between the population parameters.

<p>The correlation of a pair of parameters along all individuals was calculated for each of the 500 subsamples of the posterior distribution. For each pair of parameters the histogram of all correlations is shown, representing the uncertainty of the respective correlation.</p

Comparison of visual predictive checks of population pharmacokinetics.

<p>(<b>a</b>) Visual predicive check (VPC) of the pharmacokinetic behavior using the posterior distributions based on the presented Bayesian population PBPK approach. The uncertainty in population parameters was included in the VPC. (<b>b</b>) Visual predicive check of the pharmacokinetic behavior using the prior distributions of all parameters. (<b>c</b>) Visual predicive check (VPC) of the pharmacokinetic behavior using the maximum posterior estimates of the posterior distribution based on the presented Bayesian population PBPK approach. Each VPC is presented in linear scale (left) and logarithmic scale (right). The VPCs were performed as described in the text. In each VPC, the 5% and 95% percentiles (black dotted lines) and the median (black line) of the experimental data (red dots) are compared against the 95% confidence intervals of the 5% and 95% percentile of the simulation (light blue area) and the median (blue area).</p

Comparison of characteristic parameters of the prior and posterior population distributions.

<p>Prior and posterior geometric mean values and coefficients of variations (CV) are shown for nine exemplary physiological parameters.</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

Comparison of marginal prior and posterior distributions of nine exemplary physiological parameters.

<p>For each parameter, the marginal posterior density estimate out of the full posterior (red line) is compared to the corresponding prior distribution (green dotted line). Limits on x axis represent physiological constraints as defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139423#pone.0139423.s004" target="_blank">S1 Table</a> (except for intP where the maximum x value was reduced by a factor of 20 and for specCL were the maximum x value was reduced by a factor of 2 for better visualization)</p