The Local Edge Machine: inference of dynamic models of gene regulation

Inferring gene regulatory networks using transcriptional profiles as dynamical attractors

Genetic regulatory networks (GRNs) regulate the flow of genetic information from the genome to expressed messenger RNAs (mRNAs) and thus are critical to controlling the phenotypic characteristics of cells. Numerous methods exist for profiling mRNA transcript levels and identifying protein-DNA binding interactions at the genome-wide scale. These enable researchers to determine the structure and output of transcriptional regulatory networks, but uncovering the complete structure and regulatory logic of GRNs remains a challenge. The field of GRN inference aims to meet this challenge using computational modeling to derive the structure and logic of GRNs from experimental data and to encode this knowledge in Boolean networks, Bayesian networks, ordinary differential equation (ODE) models, or other modeling frameworks. However, most existing models do not incorporate dynamic transcriptional data since it has historically been less widely available in comparison to "static" transcriptional data. We report the development of an evolutionary algorithm-based ODE modeling approach (named EA) that integrates kinetic transcription data and the theory of attractor matching to infer GRN architecture and regulatory logic. Our method outperformed six leading GRN inference methods, none of which incorporate kinetic transcriptional data, in predicting regulatory connections among TFs when applied to a small-scale engineered synthetic GRN in Saccharomyces cerevisiae. Moreover, we demonstrate the potential of our method to predict unknown transcriptional profiles that would be produced upon genetic perturbation of the GRN governing a two-state cellular phenotypic switch in Candida albicans. We established an iterative refinement strategy to facilitate candidate selection for experimentation; the experimental results in turn provide validation or improvement for the model. In this way, our GRN inference approach can expedite the development of a sophisticated mathematical model that can accurately describe the structure and dynamics of the in vivo GRN.

A general model-based causal inference method overcomes the curse of synchrony and indirect effect

To identify causation, model-free inference methods, such as Granger Causality, have been widely used due to their flexibility. However, they have difficulty distinguishing synchrony and indirect effects from direct causation, leading to false predictions. To overcome this, model-based inference methods that test the reproducibility of data with a specific mechanistic model to infer causality were developed. However, they can only be applied to systems described by a specific model, greatly limiting their applicability. Here, we address this limitation by deriving an easily testable condition for a general monotonic ODE model to reproduce time-series data. We built a user-friendly computational package, General ODE-Based Inference (GOBI), which is applicable to nearly any monotonic system with positive and negative regulations described by ODE. GOBI successfully inferred positive and negative regulations in various networks at both the molecular and population levels, unlike existing model-free methods. Thus, this accurate and broadly applicable inference method is a powerful tool for understanding complex dynamical systems.

Experimental guidance for discovering genetic networks through hypothesis reduction on time series

Large programs of dynamic gene expression, like cell cyles and circadian rhythms, are controlled by a relatively small "core" network of transcription factors and post-translational modifiers, working in concerted mutual regulation. Recent work suggests that system-independent, quantitative features of the dynamics of gene expression can be used to identify core regulators. We introduce an approach of iterative network hypothesis reduction from time-series data in which increasingly complex features of the dynamic expression of individual, pairs, and entire collections of genes are used to infer functional network models that can produce the observed transcriptional program. The culmination of our work is a computational pipeline, Iterative Network Hypothesis Reduction from Temporal Dynamics (Inherent dynamics pipeline), that provides a priority listing of targets for genetic perturbation to experimentally infer network structure. We demonstrate the capability of this integrated computational pipeline on synthetic and yeast cell-cycle data.

RSNET: inferring gene regulatory networks by a redundancy silencing and network enhancement technique

Background

Current gene regulatory network (GRN) inference methods are notorious for a great number of indirect interactions hidden in the predictions. Filtering out the indirect interactions from direct ones remains an important challenge in the reconstruction of GRNs. To address this issue, we developed a redundancy silencing and network enhancement technique (RSNET) for inferring GRNs.

Results

To assess the performance of RSNET method, we implemented the experiments on several gold-standard networks by using simulation study, DREAM challenge dataset and Escherichia coli network. The results show that RSNET method performed better than the compared methods in sensitivity and accuracy. As a case of study, we used RSNET to construct functional GRN for apple fruit ripening from gene expression data.

Conclusions

In the proposed method, the redundant interactions including weak and indirect connections are silenced by recursive optimization adaptively, and the highly dependent nodes are constrained in the model to keep the real interactions. This study provides a useful tool for inferring clean networks.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04696-w.

Conservation of dynamic characteristics of transcriptional regulatory elements in periodic biological processes

Background

Cell and circadian cycles control a large fraction of cell and organismal physiology by regulating large periodic transcriptional programs that encompass anywhere from 15 to 80% of the genome despite performing distinct functions. In each case, these large periodic transcriptional programs are controlled by gene regulatory networks (GRNs), and it has been shown through genetics and chromosome mapping approaches in model systems that at the core of these GRNs are small sets of genes that drive the transcript dynamics of the GRNs. However, it is unlikely that we have identified all of these core genes, even in model organisms. Moreover, large periodic transcriptional programs controlling a variety of processes certainly exist in important non-model organisms where genetic approaches to identifying networks are expensive, time-consuming, or intractable. Ideally, the core network components could be identified using data-driven approaches on the transcriptome dynamics data already available.

Results

This study shows that a unified set of quantified dynamic features of high-throughput time series gene expression data are more prominent in the core transcriptional regulators of cell and circadian cycles than in their outputs, in multiple organism, even in the presence of external periodic stimuli. Additionally, we observe that the power to discriminate between core and non-core genes is largely insensitive to the particular choice of quantification of these features.

Conclusions

There are practical applications of the approach presented in this study for network inference, since the result is a ranking of genes that is enriched for core regulatory elements driving a periodic phenotype. In this way, the method provides a prioritization of follow-up genetic experiments. Furthermore, these findings reveal something unexpected—that there are shared dynamic features of the transcript abundance of core components of unrelated GRNs that control disparate periodic phenotypes.

Inferring causality in biological oscillators

MOTIVATION

Fundamental to biological study is identifying regulatory interactions. The recent surge in time-series data collection in biology provides a unique opportunity to infer regulations computationally. However, when components oscillate, model-free inference methods, while easily implemented, struggle to distinguish periodic synchrony and causality. Alternatively, model-based methods test the reproducibility of time series given a specific model but require inefficient simulations and have limited applicability.

RESULTS

We develop an inference method based on a general model of molecular, neuronal and ecological oscillatory systems that merges the advantages of both model-based and model-free methods, namely accuracy, broad applicability and usability. Our method successfully infers the positive and negative regulations within various oscillatory networks, e.g. the repressilator and a network of cofactors at the pS2 promoter, outperforming popular inference methods.

AVAILABILITY AND IMPLEMENTATION

We provide a computational package, ION (Inferring Oscillatory Networks), that users can easily apply to noisy, oscillatory time series to uncover the mechanisms by which diverse systems generate oscillations. Accompanying MATLAB code under a BSD-style license and examples are available at https://github.com/Mathbiomed/ION. Additionally, the code is available under a CC-BY 4.0 License at https://doi.org/10.6084/m9.figshare.16431408.v1.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Inference of Gene Regulatory Network Uncovers the Linkage between Circadian Clock and Crassulacean Acid Metabolism in Kalanchoë fedtschenkoi

The circadian clock drives time-specific gene expression, enabling biological processes to be temporally controlled. Plants that conduct crassulacean acid metabolism (CAM) photosynthesis represent an interesting case of circadian regulation of gene expression as stomatal movement is temporally inverted relative to stomatal movement in C3 plants. The mechanisms behind how the circadian clock enabled physiological differences at the molecular level is not well understood. Recently, the rescheduling of gene expression was reported as a mechanism to explain how CAM evolved from C3. Therefore, we investigated whether core circadian clock genes in CAM plants were re-phased during evolution, or whether networks of phase-specific genes were simply re-wired to different core clock genes. We identified candidate core clock genes based on gene expression features and then applied the Local Edge Machine (LEM) algorithm to infer regulatory relationships between this new set of core candidates and known core clock genes in Kalanchoë fedtschenkoi. We further inferred stomata-related gene targets for known and candidate core clock genes and constructed a gene regulatory network for core clock and stomata-related genes. Our results provide new insight into the mechanism of circadian control of CAM-related genes in K. fedtschenkoi, facilitating the engineering of CAM machinery into non-CAM plants for sustainable crop production in water-limited environments.

Warm nights disrupt transcriptome rhythms in field-grown rice panicles

In rice, a small increase in nighttime temperature reduces grain yield and quality. How warm nighttime temperatures (WNT) produce these detrimental effects is not well understood, especially in field conditions where the typical day-to-night temperature fluctuation exceeds the mild increase in nighttime temperature. We observed genome-wide disruption of gene expression timing during the reproductive phase in field-grown rice panicles acclimated to 2 to 3 °C WNT. Transcripts previously identified as rhythmically expressed with a 24-h period and circadian-regulated transcripts were more sensitive to WNT than were nonrhythmic transcripts. The system-wide perturbations in transcript levels suggest that WNT disrupt the tight temporal coordination between internal molecular events and the environment, resulting in reduced productivity. We identified transcriptional regulators whose predicted targets are enriched for sensitivity to WNT. The affected transcripts and candidate regulators identified through our network analysis explain molecular mechanisms driving sensitivity to WNT and identify candidates that can be targeted to enhance tolerance to WNT.

Using extremal events to characterize noisy time series

Experimental time series provide an informative window into the underlying dynamical system, and the timing of the extrema of a time series (or its derivative) contains information about its structure. However, the time series often contain significant measurement errors. We describe a method for characterizing a time series for any assumed level of measurement error [Formula: see text] by a sequence of intervals, each of which is guaranteed to contain an extremum for any function that [Formula: see text]-approximates the time series. Based on the merge tree of a continuous function, we define a new object called the normalized branch decomposition, which allows us to compute intervals for any level [Formula: see text]. We show that there is a well-defined total order on these intervals for a single time series, and that it is naturally extended to a partial order across a collection of time series comprising a dataset. We use the order of the extracted intervals in two applications. First, the partial order describing a single dataset can be used to pattern match against switching model output (Cummins et al. in SIAM J Appl Dyn Syst 17(2):1589-1616, 2018), which allows the rejection of a network model. Second, the comparison between graph distances of the partial orders of different datasets can be used to quantify similarity between biological replicates.

Gene Regulatory Network Inference: An Introductory Survey

Gene regulatory networks are powerful abstractions of biological systems. Since the advent of high-throughput measurement technologies in biology in the late 1990s, reconstructing the structure of such networks has been a central computational problem in systems biology. While the problem is certainly not solved in its entirety, considerable progress has been made in the last two decades, with mature tools now available. This chapter aims to provide an introduction to the basic concepts underpinning network inference tools, attempting a categorization which highlights commonalities and relative strengths. While the chapter is meant to be self-contained, the material presented should provide a useful background to the later, more specialized chapters of this book.

Layers of regulation of cell-cycle gene expression in the budding yeast Saccharomyces cerevisiae

In the budding yeast Saccharomyces cerevisiae, transcription factors (TFs) regulate the periodic expression of many genes during the cell cycle, including gene products required for progression through cell-cycle events. Experimental evidence coupled with quantitative models suggests that a network of interconnected TFs is capable of regulating periodic genes over the cell cycle. Importantly, these dynamical models were built on transcriptomics data and assumed that TF protein levels and activity are directly correlated with mRNA abundance. To ask whether TF transcripts match protein expression levels as cells progress through the cell cycle, we applied a multiplexed targeted mass spectrometry approach (parallel reaction monitoring) to synchronized populations of cells. We found that protein expression of many TFs and cell-cycle regulators closely followed their respective mRNA transcript dynamics in cycling wild-type cells. Discordant mRNA/protein expression dynamics was also observed for a subset of cell-cycle TFs and for proteins targeted for degradation by E3 ubiquitin ligase complexes such as SCF (Skp1/Cul1/F-box) and APC/C (anaphase-promoting complex/cyclosome). We further profiled mutant cells lacking B-type cyclin/CDK activity ( clb1-6) where oscillations in ubiquitin ligase activity, cyclin/CDKs, and cell-cycle progression are halted. We found that a number of proteins were no longer periodically degraded in clb1-6 mutants compared with wild type, highlighting the importance of posttranscriptional regulation. Finally, the TF complexes responsible for activating G1/S transcription (SBF and MBF) were more constitutively expressed at the protein level than at periodic mRNA expression levels in both wild-type and mutant cells. This comprehensive investigation of cell-cycle regulators reveals that multiple layers of regulation (transcription, protein stability, and proteasome targeting) affect protein expression dynamics during the cell cycle.

Reconciling conflicting models for global control of cell-cycle transcription

Models for the control of global cell-cycle transcription have advanced from a CDK-APC/C oscillator, a transcription factor (TF) network, to coupled CDK-APC/C and TF networks. Nonetheless, current models were challenged by a recent study that concluded that the cell-cycle transcriptional program is primarily controlled by a CDK-APC/C oscillator in budding yeast. Here we report an analysis of the transcriptome dynamics in cyclin mutant cells that were not queried in the previous study. We find that B-cyclin oscillation is not essential for control of phase-specific transcription. Using a mathematical model, we demonstrate that the function of network TFs can be retained in the face of significant reductions in transcript levels. Finally, we show that cells arrested at mitotic exit with non-oscillating levels of B-cyclins continue to cycle transcriptionally. Taken together, these findings support a critical role of a TF network and a requirement for CDK activities that need not be periodic.