Data-driven mechanistic analysis method to reveal dynamically evolving regulatory networks

A toolkit for enhanced reproducibility of RNASeq analysis for synthetic biologists

Sequencing technologies, in particular RNASeq, have become critical tools in the design, build, test and learn cycle of synthetic biology. They provide a better understanding of synthetic designs, and they help identify ways to improve and select designs. While these data are beneficial to design, their collection and analysis is a complex, multistep process that has implications on both discovery and reproducibility of experiments. Additionally, tool parameters, experimental metadata, normalization of data and standardization of file formats present challenges that are computationally intensive. This calls for high-throughput pipelines expressly designed to handle the combinatorial and longitudinal nature of synthetic biology. In this paper, we present a pipeline to maximize the analytical reproducibility of RNASeq for synthetic biologists. We also explore the impact of reproducibility on the validation of machine learning models. We present the design of a pipeline that combines traditional RNASeq data processing tools with structured metadata tracking to allow for the exploration of the combinatorial design in a high-throughput and reproducible manner. We then demonstrate utility via two different experiments: a control comparison experiment and a machine learning model experiment. The first experiment compares datasets collected from identical biological controls across multiple days for two different organisms. It shows that a reproducible experimental protocol for one organism does not guarantee reproducibility in another. The second experiment quantifies the differences in experimental runs from multiple perspectives. It shows that the lack of reproducibility from these different perspectives can place an upper bound on the validation of machine learning models trained on RNASeq data.

Graphical Abstract

Efficient gradient-based parameter estimation for dynamic models using qualitative data

MOTIVATION

Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence.

RESULTS

Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data.

AVAILABILITY AND IMPLEMENTATION

The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Efficient gradient-based parameter estimation for dynamic models using qualitative data

Motivation

Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence.

Results

Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data.

Availability and implementation

The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

Supplementary information

Supplementary data are available at Bioinformatics online.

A Probabilistic Framework for Molecular Network Structure Inference by Means of Mechanistic Modeling

Ordinary differential equations (ODEs) provide a powerful formalism to model molecular networks mechanistically. However, inferring the model structure, given a set of time course measurements and a large number of alternative molecular mechanisms, is a challenging and open research question. Existing search heuristics are designed only for finding a single best model configuration and cannot account for the uncertainty in selecting the network components. In this study, we present a novel Markov chain Monte Carlo approach for performing Bayesian model structure inference over ODE models. We formulate a Metropolis algorithm that explores the model space efficiently and is suitable for obtaining probabilistic inferences about the network structure. The method and its special parallelization possibilities are demonstrated using simulated data. Furthermore, we apply the method to a time course RNA sequencing data set to infer the structure of the transiently evolving core regulatory network that steers the T helper 17 (Th17) cell differentiation. Our results are in agreement with the earlier finding that the Th17 lineage-specific differentiation program evolves in three sequential phases. Further, the analysis provides us with probabilistic predictions on the molecular interactions that are active in different phases of Th17 cell differentiation.

Condition-Specific Modeling of Biophysical Parameters Advances Inference of Regulatory Networks

Large-scale inference of eukaryotic transcription-regulatory networks remains challenging. One underlying reason is that existing algorithms typically ignore crucial regulatory mechanisms, such as RNA degradation and post-transcriptional processing. Here, we describe InfereCLaDR, which incorporates such elements and advances prediction in Saccharomyces cerevisiae. First, InfereCLaDR employs a high-quality Gold Standard dataset that we use separately as prior information and for model validation. Second, InfereCLaDR explicitly models transcription factor activity and RNA half-lives. Third, it introduces expression subspaces to derive condition-responsive regulatory networks for every gene. InfereCLaDR’s final network is validated by known data and trends and results in multiple insights. For example, it predicts long half-lives for transcripts of the nucleic acid metabolism genes and members of the cytosolic chaperonin complex as targets of the proteasome regulator Rpn4p. InfereCLaDR demonstrates that more biophysically realistic modeling of regulatory networks advances prediction accuracy both in eukaryotes and prokaryotes.

Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes

Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and, thus, gain novel biological insight. Several toolboxes can infer model parameters and structure for small- to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of the state-of-the-art methods for parameter and model inference, with an emphasis on scalability.

Parallelization and High-Performance Computing Enables Automated Statistical Inference of Multi-scale Models

Mechanistic understanding of multi-scale biological processes, such as cell proliferation in a changing biological tissue, is readily facilitated by computational models. While tools exist to construct and simulate multi-scale models, the statistical inference of the unknown model parameters remains an open problem. Here, we present and benchmark a parallel approximate Bayesian computation sequential Monte Carlo (pABC SMC) algorithm, tailored for high-performance computing clusters. pABC SMC is fully automated and returns reliable parameter estimates and confidence intervals. By running the pABC SMC algorithm for ∼10⁶ hr, we parameterize multi-scale models that accurately describe quantitative growth curves and histological data obtained in vivo from individual tumor spheroid growth in media droplets. The models capture the hybrid deterministic-stochastic behaviors of 10⁵-10⁶ of cells growing in a 3D dynamically changing nutrient environment. The pABC SMC algorithm reliably converges to a consistent set of parameters. Our study demonstrates a proof of principle for robust, data-driven modeling of multi-scale biological systems and the feasibility of multi-scale model parameterization through statistical inference.