Abstract
Single-cell time-lapse studies have advanced the quantitative understanding of cellular pathways and their inherent cell-to-cell variability. However, parameters retrieved from individual experiments are model dependent and their estimation is limited, if based on solely one kind of experiment. Hence, methods to integrate data collected under different conditions are expected to improve model validation and information content. Here we present a multi-experiment nonlinear mixed effect modeling approach for mechanistic pathway models, which allows the integration of multiple single-cell perturbation experiments. We apply this approach to the translation of green fluorescent protein after transfection using a massively parallel read-out of micropatterned single-cell arrays. We demonstrate that the integration of data from perturbation experiments allows the robust reconstruction of cell-to-cell variability, i.e., parameter densities, while each individual experiment provides insufficient information. Indeed, we show that the integration of the datasets on the population level also improves the estimates for individual cells by breaking symmetries, although each of them is only measured in one experiment. Moreover, we confirmed that the suggested approach is robust with respect to batch effects across experimental replicates and can provide mechanistic insights into the nature of batch effects. We anticipate that the proposed multi-experiment nonlinear mixed effect modeling approach will serve as a basis for the analysis of cellular heterogeneity in single-cell dynamics.
Highlights
Living cells show molecular and phenotypic differences at the single-cell level even in isogenic populations.[1,2] Sources of cell-tocell variability include noisy cellular processes,[2] differences in cell cycle state,[3] the history of individual cells,[4] as well as spatiotemporal differences of the cell’s environment.[5]
1⁄2mRNAðtÞ 1⁄4 1⁄2mRNAðtÞ þ m0 application, the structural non-identifiability is problet ! t0; t
By analyzing single-cell trajectories from both we transform the model and reduced the parameter experiments in a consistent nonlinear mixed effect modeling vector to a set of parameters θ that consists of products of the approach, we demonstrate that both protein and mRNA degradation rates can be uniquely identified
Summary
Living cells show molecular and phenotypic differences at the single-cell level even in isogenic populations.[1,2] Sources of cell-tocell variability include noisy cellular processes,[2] differences in cell cycle state,[3] the history of individual cells,[4] as well as spatiotemporal differences of the cell’s environment.[5]. After a cell successfully internalizes mRNA lipoplexes, the corresponding mRNA molecules are translated reported that NLME is more robust than STS in settings with large parameter uncertainty, as it reduces uncertainty[26,28] and removes estimation bias.[25] into fluorescent proteins This translation processes can be described by biochemical rate equations (Fig. 1c).[21] The use of tubing systems allows for the observation of the translation. Previous studies have shown that the single-cell degradation rates of mRNAs and proteins are structurally non-identifiable when considering time-lapse microscopy measurements for a single protein.[10] This holds for the respective population average parameters, as long as no further assumptions are made.[24] For this estimation of protein translation parameters.
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