Mathematical modelling is an invaluable tool to describe dynamic cellular processes and to rationalise cell-to-cell variability within the population. This requires statistical methods to infer unknown model parameters from dynamic, multi-individual data accounting for heterogeneity caused by both intrinsic and extrinsic noise. Here we present PEPSDI, a scalable and flexible framework for Bayesian inference in state-space mixed-effects stochastic dynamic single-cell models. Unlike previous frameworks, PEPSDI imposes a few modelling assumptions when inferring unknown model parameters from time-lapse data. Specifically, it can infer 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. This allowed us to identify hexokinase activity as a source of extrinsic noise, and to deduce that sugar availability dictates cell-to-cell variability in the budding yeast Saccharomyces cerevisiae SNF1 nutrient sensing pathway.

Lithium salts are used in the treatment of mood disorders, cancer, and Alzheimer’s disease. It has been shown to prolong life span in several phyla; however, not yet in budding yeast. In our study, we investigate the influence of lithium on yeast cells’ viability by characterizing protein aggregate formation, cell volume, and molecular crowding in the context of stress adaptation. While our data suggest a concentration-dependent growth inhibition caused by LiCl, we show an extended long-term survival rate as an effect of lithium addition upon glucose deprivation. We show that caloric restriction mitigates the negative impact of LiCl on cellular survival. Therefore, we suggest that lithium could affect glucose metabolism upon caloric restriction, which could explain the extended long-term survival observed in our study. We find furthermore that lithium chloride did not affect an immediate salt-induced Hsp104-dependent aggregate formation but cellular adaptation to H2O2 and acute glucose starvation. We presume that different salt types and concentrations interfere with effective Hsp104 recruitment or its ATP-dependent disaggregase activity as a response to salt stress. This work provides novel details of Li+ effect on live eukaryotic cells which may also be applicable in further research on the treatment of cancer, Alzheimer’s, or other age-related diseases in humans.

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.