Confidence intervals by constrained optimization-An algorithm and software package for practical identifiability analysis in systems biology.

Practical identifiability of Systems Biology models has received a lot of attention in recent scientific research. It addresses the crucial question for models' predictability: how accurately can the models' parameters be recovered from available experimental data. The methods based on profile likelihood are among the most reliable methods of practical identification. However, these methods are often computationally demanding or lead to inaccurate estimations of parameters' confidence intervals. Development of methods, which can accurately produce parameters' confidence intervals in reasonable computational time, is of utmost importance for Systems Biology and QSP modeling. We propose an algorithm Confidence Intervals by Constraint Optimization (CICO) based on profile likelihood, designed to speed-up confidence intervals estimation and reduce computational cost. The numerical implementation of the algorithm includes settings to control the accuracy of confidence intervals estimates. The algorithm was tested on a number of Systems Biology models, including Taxol treatment model and STAT5 Dimerization model, discussed in the current article. The CICO algorithm is implemented in a software package freely available in Julia (https://github.com/insysbio/LikelihoodProfiler.jl) and Python (https://github.com/insysbio/LikelihoodProfiler.py).

Comparison of asymptotic confidence sets for regression in small samples.

In case of small samples, asymptotic confidence sets may be inaccurate, with their actual coverage probability far from a nominal confidence level. In a single framework, we consider four popular asymptotic methods of confidence estimation. These methods are based on model linearization, F-test, likelihood ratio test, and nonparametric bootstrapping procedure. Next, we apply each of these methods to derive three types of confidence sets: confidence intervals, confidence regions, and pointwise confidence bands. Finally, to estimate the actual coverage of these confidence sets, we conduct a simulation study on three regression problems. A linear model and nonlinear Hill and Gompertz models are tested in conditions of different sample size and experimental noise. The simulation study comprises calculation of the actual coverage of confidence sets over pseudo-experimental datasets for each model. For confidence intervals, such metrics as width and simultaneous coverage are also considered. Our comparison shows that the F-test and linearization methods are the most suitable for the construction of confidence intervals, the F-test - for confidence regions and the linearization - for pointwise confidence bands.

Comprehensive study of the drug delivery properties of poly(l-lactide)-poly(ethylene glycol) nanoparticles in rats and tumor-bearing mice.

Nanoparticles made of polylactide-poly(ethylene glycol) block-copolymer (PLA-PEG) are promising vehicles for drug delivery due to their biodegradability and controllable payload release. However, published data on the drug delivery properties of PLA-PEG nanoparticles are heterogeneous in terms of nanoparticle characteristics and mostly refer to low injected doses (a few mg nanoparticles per kg body weight). We have performed a comprehensive study of the biodistribution of nanoparticle formulations based on PLA-PEG nanoparticles of ~100nm size at injected doses of 30 to 140mg/kg body weight in healthy rats and nude tumor-bearing mice. Nanoparticle formulations differed by surface PEG coverage and by release kinetics of the encapsulated model active pharmaceutical ingredient (API). Increase in PEG coverage prolonged nanoparticle circulation half-life up to ~20h in rats and ~10h in mice and decreased retention in liver, spleen and lungs. Circulation half-life of the encapsulated API grew monotonously as the release rate slowed down. Plasma and tissue pharmacokinetics was dose-linear for inactive nanoparticles, but markedly dose-dependent for the model therapeutic formulation, presumably because of the toxic effects of released API. A mathematical model of API distribution calibrated on the data for inactive nanoparticles and conventional API form correctly predicted the distribution of the model therapeutic formulation at the lowest investigated dose, but for higher doses the toxic action of the released API had to be explicitly modelled. Our results provide a coherent illustration of the ability of controllable-release PLA-PEG nanoparticles to serve as an effective drug delivery platform to alter API biodistribution. They also underscore the importance of physiological effects of released drug in determining the biodistribution of therapeutic drug formulations at doses approaching tolerability limits.