SUMMARY: Dynamic models represent a powerful tool for studying complex biological processes, ranging from cell signalling to cell differentiation. Building such models often requires computationally demanding modelling workflows, such as model exploration and parameter estimation. We developed two Julia-based tools: SBMLImporter.jl, an SBML importer, and PEtab.jl, an importer for parameter estimation problems in the PEtab format, designed to streamline modelling processes. These tools leverage Julia's high-performance computing capabilities, including symbolic pre-processing and advanced ODE solvers. PEtab.jl aims to be a Julia-accessible toolbox that supports the entire modelling pipeline from parameter estimation to identifiability analysis. AVAILABILITY AND IMPLEMENTATION: SBMLImporter.jl and PEtab.jl are implemented in the Julia programming language. Both packages are available on GitHub (github.com/sebapersson/SBMLImporter.jl and github.com/sebapersson/PEtab.jl) as officially registered Julia packages, installable via the Julia package manager. Each package is continuously tested and supported on Linux, macOS, and Windows.

Understanding the inherited nature of how biological processes dynamically change over time and exhibit intra- and inter-individual variability, due to the different responses to environmental stimuli and when interacting with other processes, has been a major focus of systems biology. The rise of single-cell fluorescent microscopy has enabled the study of those phenomena. The analysis of single-cell data with mechanistic models offers an invaluable tool to describe dynamic cellular processes and to rationalise cell-to-cell variability within the population. However, extracting mechanistic information from single-cell data has proven difficult. This requires statistical methods to infer unknown model parameters from dynamic, multi-individual data accounting for heterogeneity caused by both intrinsic (e.g. variations in chemical reactions) and extrinsic (e.g. variability in protein concentrations) noise. Although several inference methods exist, the availability of efficient, general and accessible methods that facilitate modelling of single-cell data, remains lacking. Here we present a scalable and flexible framework for Bayesian inference in state-space mixed-effects single-cell models with stochastic dynamic. Our approach infers model parameters when intrinsic noise is modelled by either exact or approximate stochastic simulators, and when extrinsic noise is modelled by either time-varying, or time-constant parameters that vary between cells. We demonstrate the relevance of our approach by studying how cell-to-cell variation in carbon source utilisation affects heterogeneity in the budding yeast Saccharomyces cerevisiae SNF1 nutrient sensing pathway. We identify hexokinase activity as a source of extrinsic noise and deduce that sugar availability dictates cell-to-cell variability.