Challenges in the calibration of large-scale ordinary differential equation models

A quantitative systems pharmacology workflow toward optimal design and biomarker stratification of atopic dermatitis clinical trials

BACKGROUND

The development of atopic dermatitis (AD) drugs is challenged by many disease phenotypes and trial design options, which are hard to explore experimentally.

OBJECTIVE

We aimed to optimize AD trial design using simulations.

METHODS

We constructed a quantitative systems pharmacology model of AD and standard of care (SoC) treatments and generated a phenotypically diverse virtual population whose parameter distribution was derived from known relationships between AD biomarkers and disease severity and calibrated using disease severity evolution under SoC regimens.

RESULTS

We applied this workflow to the immunomodulator OM-85, currently being investigated for its potential use in AD, and calibrated the investigational treatment model with the efficacy profile of an existing trial (thereby enriching it with plausible marker levels and dynamics). We assessed the sensitivity of trial outcomes to trial protocol and found that for this particular example the choice of end point is more important than the choice of dosing regimen and patient selection by model-based responder enrichment could increase the expected effect size. A global sensitivity analysis revealed that only a limited subset of baseline biomarkers is needed to predict the drug response of the full virtual population.

CONCLUSIONS

This AD quantitative systems pharmacology workflow built around knowledge of marker-severity relationships as well as SoC efficacy can be tailored to specific development cases to optimize several trial protocol parameters and biomarker stratification and therefore has promise to become a powerful model-informed AD drug development and personalized medicine tool.

Mini-batch optimization enables training of ODE models on large-scale datasets

Quantitative dynamic models are widely used to study cellular signal processing. A critical step in modelling is the estimation of unknown model parameters from experimental data. As model sizes and datasets are steadily growing, established parameter optimization approaches for mechanistic models become computationally extremely challenging. Mini-batch optimization methods, as employed in deep learning, have better scaling properties. In this work, we adapt, apply, and benchmark mini-batch optimization for ordinary differential equation (ODE) models, thereby establishing a direct link between dynamic modelling and machine learning. On our main application example, a large-scale model of cancer signaling, we benchmark mini-batch optimization against established methods, achieving better optimization results and reducing computation by more than an order of magnitude. We expect that our work will serve as a first step towards mini-batch optimization tailored to ODE models and enable modelling of even larger and more complex systems than what is currently possible.

Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

The increasing complexity of advanced devices and systems increases the scale of mathematical models used in computer simulations. Multiparametric analysis and study on long-term time intervals of large-scale systems are computationally expensive. Therefore, efficient numerical methods are required to reduce time costs. Recently, semi-explicit and semi-implicit Adams–Bashforth–Moulton methods have been proposed, showing great computational efficiency in low-dimensional systems simulation. In this study, we examine the numerical stability of these methods by plotting stability regions. We explicitly show that semi-explicit methods possess higher numerical stability than the conventional predictor–corrector algorithms. The second contribution of the reported research is a novel algorithm to generate an optimized finite-difference scheme of semi-explicit and semi-implicit Adams–Bashforth–Moulton methods without redundant computation of predicted values that are not used for correction. The experimental part of the study includes the numerical simulation of the three-body problem and a network of coupled oscillators with a fixed and variable integration step and finely confirms the theoretical findings.

Benchmarking of numerical integration methods for ODE models of biological systems

Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when unknown parameters need to be inferred. This renders efficient and reliable numerical integration methods essential. However, these methods depend on various hyperparameters, which strongly impact the ODE solution. Despite this, and although hundreds of published ODE models are freely available in public databases, a thorough study that quantifies the impact of hyperparameters on the ODE solver in terms of accuracy and computation time is still missing. In this manuscript, we investigate which choices of algorithms and hyperparameters are generally favorable when dealing with ODE models arising from biological processes. To ensure a representative evaluation, we considered 142 published models. Our study provides evidence that most ODEs in computational biology are stiff, and we give guidelines for the choice of algorithms and hyperparameters. We anticipate that our results will help researchers in systems biology to choose appropriate numerical methods when dealing with ODE models.

Model reduction of genome-scale metabolic models as a basis for targeted kinetic models

Constraint-based, genome-scale metabolic models are an essential tool to guide metabolic engineering. However, they lack the detail and time dimension that kinetic models with enzyme dynamics offer. Model reduction can be used to bridge the gap between the two methods and allow for the integration of kinetic models into the Design-Built-Test-Learn cycle. Here we show that these reduced size models can be representative of the dynamics of the original model and demonstrate the automated generation and parameterisation of such models. Using these minimal models of metabolism could allow for further exploration of dynamic responses in metabolic networks.