Determining fetal drug exposure (except at the time of birth) is not possible for both logistical and ethical reasons. Therefore, we developed a novel maternal-fetal physiologically based pharmacokinetic (m-f-PBPK) model to predict fetal exposure to drugs and populated this model with gestational age-dependent changes in maternal-fetal physiology. Then, we used this m-f-PBPK to: 1) perform a series of sensitivity analyses to quantitatively demonstrate the impact of fetoplacental metabolism and placental transport on fetal drug exposure for various drug-dosing regimens administered to the mother; 2) predict the impact of gestational age on fetal drug exposure; and 3) demonstrate that a single umbilical venous (UV)/maternal plasma (MP) ratio (even after multiple-dose oral administration to steady state) does not necessarily reflect fetal drug exposure. In addition, we verified the implementation of this m-f-PBPK model by comparing the predicted UV/MP and fetal/MP AUC ratios with those predicted at steady state after an intravenous infusion. Our simulations yielded novel insights into the quantitative contribution of fetoplacental metabolism and/or placental transport on gestational age-dependent fetal drug exposure. Through sensitivity analyses, we demonstrated that the UV/MP ratio does not measure the extent of fetal drug exposure unless obtained at steady state after an intravenous infusion or when there is little or no fluctuation in MP drug concentrations after multiple-dose oral administration. The proposed m-f-PBPK model can be used to predict fetal exposure to drugs across gestational ages and therefore provide the necessary information to assess the risk of drug toxicity to the fetus.

Achieving sufficient concentrations of antituberculosis (TB) drugs in pulmonary tissue at the optimum time is still a challenge in developing therapeutic regimens for TB. A physiologically based pharmacokinetic model incorporating a multicompartment permeability-limited lung model was developed and used to simulate plasma and pulmonary concentrations of seven drugs. Passive permeability of drugs within the lung was predicted using an in vitro-in vivo extrapolation approach. Simulated epithelial lining fluid (ELF):plasma concentration ratios showed reasonable agreement with observed clinical data for rifampicin, isoniazid, ethambutol, and erythromycin. For clarithromycin, itraconazole and pyrazinamide the observed ELF:plasma ratios were significantly underpredicted. Sensitivity analyses showed that changing ELF pH or introducing efflux transporter activity between lung tissue and ELF can alter the ELF:plasma concentration ratios. The described model has shown utility in predicting the lung pharmacokinetics of anti-TB drugs and provides a framework for predicting pulmonary concentrations of novel anti-TB drugs.

We analyze a simple linear triggering model of the T-cell receptor (TCR) within the framework of queuing theory, in which TCRs enter the queue upon full activation and exit by downregulation. We fit our model to four experimentally characterized threshold activation criteria and analyze their specificity and sensitivity: the initial calcium spike, cytotoxicity, immunological synapse formation, and cytokine secretion. Specificity characteristics improve as the time window for detection increases, saturating for time periods on the timescale of downregulation; thus, the calcium spike (30 s) has low specificity but a sensitivity to single-peptide MHC ligands, while the cytokine threshold (1 h) can distinguish ligands with a 30% variation in the complex lifetime. However, a robustness analysis shows that these properties are degraded when the queue parameters are subject to variation-for example, under stochasticity in the ligand number in the cell-cell interface and population variation in the cellular threshold. A time integration of the queue over a period of hours is shown to be able to control parameter noise efficiently for realistic parameter values when integrated over sufficiently long time periods (hours), the discrimination characteristics being determined by the TCR signal cascade kinetics (a kinetic proofreading scheme). Therefore, through a combination of thresholds and signal integration, a T cell can be responsive to low ligand density and specific to agonist quality. We suggest that multiple threshold mechanisms are employed to establish the conditions for efficient signal integration, i.e., coordinate the formation of a stable contact interface.

We present a simple proof of the formula for the free energy of the random energy model using a large deviation property which holds almost surely with respect to the randomness. This proof is extended to the case with external magnetic field leading to the solution of a model with higher-order ferromagnetic term. It is shown that this model is useful for Sourlas' application to error-correcting codes as was already pointed out in a recent letter by the authors.