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.

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SummarySingle-cell time-lapse studies have advanced the quantitative understanding of cell-to-cell variability. However, as the information content of individual experiments is limited, methods to integrate data collected under different conditions are required.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.

Using an analytical theory and detailed computational experiments, we predict surprising optical bistability behavior in various photonic crystal systems.Photonic crystals (PCs) provide extraordinary possibilities for molding the flow of light. Non-linear PCs thus exhibit novel physical effects useful for design of all-optical active devices. We solve the full non-linear Maxwell's equations numerically (with minimal physical approximations) to demonstrate unexpected optical bistability phenomena in various PC systems. Their highly nonlinear input/output power relations can be used to implement many applications (e.g. all-optical pulse reshaping, optical limiting, logic gates, etc.) We also develop analytical models that excellently describe the behavior of the systems.