In recent years, epigenetic memory systems have been developed based on DNA methylation and positive feedback systems. Achieving a robust design for these systems is generally a challenging and multifactorial task. We developed and validated a novel mathematical model to describe methylation-based epigenetic memory systems that capture switching dynamics of methylation levels and methyltransferase amounts induced by different inputs. A bifurcation analysis shows that the system operates in the bistable range, but in its current setup is not robust to changes in parameters. An expansion of the model captures heterogeneity of cell populations by accounting for distributed cell division rates. Simulations predict that the system is highly sensitive to variations in temperature, which affects cell division and the efficiency of the zinc finger repressor. A moderate decrease in temperature leads to a highly heterogeneous response to input signals and bistability on a single-cell level. The predictions of our model were confirmed by flow cytometry experiments conducted in this study. Overall, the results of our study give insights into the functional mechanisms of methylation-based memory systems and demonstrate that the switching dynamics can be highly sensitive to experimental conditions.
Background:The description of intracellular processes based on chemical reaction kinetics has become a standard approach in the last decades, and parameter estimation poses several challenges. Sensitivity analysis is a powerful tool in model development that can aid model calibration in various ways. Results can for example be used to simplify the model by elimination or fixation of parameters that have a negligible influence on relevant model outputs. However, models are usually subject to rescaling and normalization to reference experiments, which changes the variance of the output. Thus, the results of the sensitivity analysis may change depending on the choice of these rescaling factors and reference experiments. Although it might intuitively be clear, this fact has not been addressed in the literature so far. Methods: In this study we investigate the effect of model rescaling and additional normalization to a reference experiment on the outcome of two different sensitivity analyses. Results are exemplified on a model for the MAPK pathway module in PC-12 cell lines. For this purpose we apply local sensitivity analysis and a global variance-based method based on Sobol sensitivity coefficients, and compare the results for differently scaled and normalized model versions. Results: Results indicate that both sensitivity analyses are invariant under simple rescaling of variables and parameters with constant factors, provided that sensitivity coefficients are normalized and that the parameter space is appropriately chosen for Sobol's method. By contrast, normalization to a reference experiment that also depends on parameters has a large impact on the results of any sensitivity analysis, and in particular complicates the interpretation. Conclusion: This work shows that, in order to perform sensitivity analysis, it is necessary to take into account the dependency on parameters of the reference condition when working with normalized model versions.
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