Assessing the performance of QSP models: biology as the driver for validation.

Validation of a quantitative model is a critical step in establishing confidence in the model's suitability for whatever analysis it was designed. While processes for validation are well-established in the statistical sciences, the field of quantitative systems pharmacology (QSP) has taken a more piecemeal approach to defining and demonstrating validation. Although classical statistical methods can be used in a QSP context, proper validation of a mechanistic systems model requires a more nuanced approach to what precisely is being validated, and what role said validation plays in the larger context of the analysis. In this review, we summarize current thoughts of QSP validation in the scientific community, contrast the aims of statistical validation from several contexts (including inference, pharmacometrics analysis, and machine learning) with the challenges faced in QSP analysis, and use examples from published QSP models to define different stages or levels of validation, any of which may be sufficient depending on the context at hand.

Understanding the Dynamics of the Transient and Permanent Opening Events of the Mitochondrial Permeability Transition Pore with a Novel Stochastic Model.

The mitochondrial permeability transition pore (mPTP) is a non-selective pore in the inner mitochondrial membrane (IMM) which causes depolarization when it opens under conditions of oxidative stress and high concentrations of Ca2+. In this study, a stochastic computational model was developed to better understand the dynamics of mPTP opening and closing associated with elevated reactive oxygen species (ROS) in cardiomyocytes. The data modeled are from "photon stress" experiments in which the fluorescent dye TMRM (tetramethylrhodamine methyl ester) is both the source of ROS (induced by laser light) and sensor of the electrical potential difference across the IMM. Monte Carlo methods were applied to describe opening and closing of the pore along with the Hill Equation to account for the effect of ROS levels on the transition probabilities. The amplitude distribution of transient mPTP opening events, the number of transient mPTP opening events per minute in a cell, the time it takes for recovery after transient depolarizations in the mitochondria, and the change in TMRM fluorescence during the transition from transient to permanent mPTP opening events were analyzed. The model suggests that mPTP transient open times have an exponential distribution that are reflected in TMRM fluorescence. A second multiple pore model in which individual channels have no permanent open state suggests that 5-10 mPTP per mitochondria would be needed for sustained mitochondrial depolarization at elevated ROS with at least 1 mPTP in the transient open state.

Effect of crista morphology on mitochondrial ATP output: A computational study.

Folding of the mitochondrial inner membrane (IM) into cristae greatly increases the ATP-generating surface area, S IM, per unit volume but also creates diffusional bottlenecks that could limit reaction rates inside mitochondria. This study explores possible effects of inner membrane folding on mitochondrial ATP output, using a mathematical model for energy metabolism developed by the Jafri group and two- and three-dimensional spatial models for mitochondria, implemented on the Virtual Cell platform. Simulations demonstrate that cristae are micro-compartments functionally distinct from the cytosol. At physiological steady states, standing gradients of ADP form inside cristae that depend on the size and shape of the compartments, and reduce local flux (rate per unit area) of the adenine nucleotide translocase. This causes matrix ADP levels to drop, which in turn reduces the flux of ATP synthase. The adverse effects of membrane folding on reaction fluxes increase with crista length and are greater for lamellar than tubular crista. However, total ATP output per mitochondrion is the product of flux of ATP synthase and S IM which can be two-fold greater for mitochondria with lamellar than tubular cristae, resulting in greater ATP output for the former. The simulations also demonstrate the crucial role played by intracristal kinases (adenylate kinase, creatine kinase) in maintaining the energy advantage of IM folding.

Aging processes in systems with anomalous slow dynamics.

Recently, different numerical studies of coarsening in disordered systems have shown the existence of a crossover from an initial, transient, power-law domain growth to a slower, presumably logarithmic, growth. However, due to the very slow dynamics and the long-lasting transient regime, one is usually not able to fully enter the asymptotic regime when investigating the relaxation of these systems toward equilibrium. We here study two simple driven systems-the one-dimensional ABC model and a related domain model with simplified dynamics-that are known to exhibit anomalous slow relaxation where the asymptotic logarithmic growth regime is readily accessible. Studying two-times correlation and response functions, we focus on aging processes and dynamical scaling during logarithmic growth. Using the time-dependent growth length as the scaling variable, a simple aging picture emerges that is expected to also prevail in the asymptotic regime of disordered ferromagnets and spin glasses.