Identification of Gene Regulation Models from Single-Cell Data

Abstract

Abstract. In quantitative analyses of biological processes, one may use many different scales of models (e.g., spatial or non-spatial, deterministic or stochastic, time varying or at steady state) or many different approaches to match models to experimental data (e.g., model fitting or parameter uncertainty/sloppiness quantification with different experiment designs). These different analyses can lead to surprisingly different results, even when applied to the same data and the same model. We use a simplified gene regulation model to illustrate many of these concerns, especially for ODE analyses of deterministic processes, chemical master equation and finite state projection analyses of heterogeneous processes, and stochastic simulations. For each analysis, we employ Matlab and Python software to consider a time-dependent input signal (e.g., a kinase nuclear translocation) and several model hypotheses, along with simulated single-cell data. We illustrate different approaches (e.g., deterministic and stochastic) to identify the mechanisms and parameters of the same model from the same simulated data. For each approach, we explore how uncertainty in parameter space varies with respect to the chosen analysis approach or specific experiment design. We conclude with a discussion of how our simulated results relate to the integration of experimental and computational investigations to explore signal-activated gene expression models in yeast [1] and human cells [2] ‡.

A Growing Toolbox to Image Gene Expression in Single Cells: Sensitive Approaches for Demanding Challenges

“…It seems therefore accurate to devise more complex models including more states or regulatory reactions (Nicolas et al, 2017; see below). However, particular attention should be paid that the model complexity is justified by the available data to avoid overfitting (Patange et al, 2018;Weber et al, 2018). It is also important to use strategies that select the most appropriate model, and ideally a model can be verified by predicting experimentally testable outcomes, or by correlating the impact of experimental perturbations to the different model states (Weber et al, 2018).…”

“…However, particular attention should be paid that the model complexity is justified by the available data to avoid overfitting (Patange et al, 2018;Weber et al, 2018). It is also important to use strategies that select the most appropriate model, and ideally a model can be verified by predicting experimentally testable outcomes, or by correlating the impact of experimental perturbations to the different model states (Weber et al, 2018). Bridging the Gap between Imaging and Biochemistry Recent genome-wide experiments revealed a variety of complexes forming on core promoters (Krebs et al, 2017;Shao and Zeitlinger, 2017).…”

Special Function Methods for Bursty Models of Transcription

“…Finally, technical challenges in single-cell transcriptomics, such as sparsity of sampling in sequencing [56] and noise in fluorescence microscopy [57], have resulted in alternative competing explanations for qualitative features of observed biomolecule distributions, such as heavy-tailed laws [25,27] and apparent dropouts [58][59][60][61]. We anticipate that intrinsic degeneracies, as well as aleatory effects, in mapping from a model parameter space to an observable space preclude the unambiguous identification of underlying biophysical schema: the presence of parameter equivalence classes, even in inference of simple models, is well-characterized [62][63][64][65]. Nevertheless, we also anticipate that the development of analytical solutions, as well as numerical solvers, for a diversity of transcriptional mechanisms, sampling behaviors, and multimodal observables will aid in making inference sufficiently robust for design and extrapolation.…”

Bayesian inference of Stochastic reaction networks using Multifidelity Sequential Tempered Markov Chain Monte Carlo

“…The present work is concerned with the selection, parameter estimation, and uncertainty propagation of these reaction network models within the Bayesian framework. Bayesian methods are a powerful tool for system identification for SRN models because they provide rigorous uncertainty quantification by identifying a probability distribution over plausible model parameters instead of selecting a single model that may fit the data well [11][12][13][14][15]. This distribution over the models given the data is called the posterior distribution.…”