Optimal Design of Single-Cell Experiments within Temporally Fluctuating Environments

Abstract

24Modern biological experiments are becoming increasingly complex, and designing these experi-25 ments to yield the greatest possible quantitative insight is an open challenge. Increasingly, compu-26 tational models of complex stochastic biological systems are being used to understand and predict 27 biological behaviors or to infer biological parameters. Such quantitative analyses can also help 28 to improve experiment designs for particular goals, such as to learn more about specific model 29 mechanisms or to reduce prediction errors in certain situations. A classic approach to experiment 30 design is to use the Fisher information matrix (FIM), which quantifies the expected information a 31 particular experiment will reveal about model parameters. The Finite State Projection based FIM 32 (FSP-FIM) was recently developed to compute the FIM for discrete stochastic gene regulatory 33 systems, whose complex response distributions do not satisfy standard assumptions of Gaussian 34 variations. In this work, we develop the FSP-FIM analysis for a stochastic model of stress response 35 genes in S. cerevisae under time-varying MAPK induction. We validate this FSP-FIM analysis 36 and use it to optimize the number of cells that should be quantified at particular times to learn as 37 much as possible about the model parameters. We then demonstrate how the FSP-FIM approach 38 can be extended to explore how different measurement times or genetic modifications can help to 39 minimize uncertainty in the sensing of extracellular environments, such as external salinity mod-40 ulations. This work demonstrates the potential of quantitative models to not only make sense of 41 modern biological data sets, but to close the loop between quantitative modeling and experimental 42 data collection. 44The standard approach to design experiments has been to rely entirely on expert knowl-45 edge and intuition. However, as experimental investigations become more complex and 46 seek to examine systems with more subtle non-linear interactions, it becomes much harder 47 to improve experimental designs using intuition alone. This issue has become especially 48 relevant in modern single-cell-single-molecule investigations of gene regulatory processes. 49Performing such powerful, yet complicated experiments involves the selection from among 50 a large number of possible experimental designs, and it is often not clear which designs 51 will provide the most relevant information. A systematic approach to solve this problem is 52 model-driven experiment design, in which one uses an assumed (and potentially incorrect) 53 mathematical model of the system to estimate and optimize the value of potential exper-54 imental settings. In recent years, model-driven experiment design has gained traction for 55 biological models of gene expression, whether in the Bayesian setting [1] or using Fisher 56 information for deterministic models [2], and even in the stochastic, single-cell setting [3-57 6]. Despite the promise and active development of model-driven e...