Information processing by simple molecular motifs and susceptibility to noise

Network regulation meets substrate modification chemistry

Biochemical networks are at the heart of cellular information processing. These networks contain distinct facets: (i) processing of information from the environment via cascades/pathways along with network regulation and (ii) modification of substrates in different ways, to confer protein functionality, stability and processing. While many studies focus on these factors individually, how they interact and the consequences for cellular systems behaviour are poorly understood. We develop a systems framework for this purpose by examining the interplay of network regulation (canonical feedback and feed-forward circuits) and multisite modification, as an exemplar of substrate modification. Using computational, analytical and semi-analytical approaches, we reveal distinct and unexpected ways in which the substrate modification and network levels combine and the emergent behaviour arising therefrom. This has important consequences for dissecting the behaviour of specific signalling networks, tracing the origins of systems behaviour, inference of networks from data, robustness/evolvability and multi-level engineering of biomolecular networks. Overall, we repeatedly demonstrate how focusing on only one level (say network regulation) can lead to profoundly misleading conclusions about all these aspects, and reveal a number of important consequences for experimental/theoretical/data-driven interrogations of cellular signalling systems.

Molecular Origins of Transcriptional Heterogeneity in Diazotrophic Klebsiella oxytoca

Phenotypic heterogeneity in clonal bacterial batch cultures has been shown for a range of bacterial systems; however, the molecular origins of such heterogeneity and its magnitude are not well understood. Under conditions of extreme low-nitrogen stress in the model diazotroph Klebsiella oxytoca, we found remarkably high heterogeneity of nifHDK gene expression, which codes for the structural genes of nitrogenase, one key enzyme of the global nitrogen cycle. This heterogeneity limited the bulk observed nitrogen-fixing capacity of the population. Using dual-probe, single-cell RNA fluorescent in situ hybridization, we correlated nifHDK expression with that of nifLA and glnK-amtB, which code for the main upstream regulatory components. Through stochastic transcription models and mutual information analysis, we revealed likely molecular origins for heterogeneity in nitrogenase expression. In the wild type and regulatory variants, we found that nifHDK transcription was inherently bursty, but we established that noise propagation through signaling was also significant. The regulatory gene glnK had the highest discernible effect on nifHDK variance, while noise from factors outside the regulatory pathway were negligible. Understanding the basis of inherent heterogeneity of nitrogenase expression and its origins can inform biotechnology strategies seeking to enhance biological nitrogen fixation. Finally, we speculate on potential benefits of diazotrophic heterogeneity in natural soil environments. IMPORTANCE Nitrogen is an essential micronutrient for both plant and animal life and naturally exists in both reactive and inert chemical forms. Modern agriculture is heavily reliant on nitrogen that has been "fixed" into a reactive form via the energetically expensive Haber-Bosch process, with significant environmental consequences. Nitrogen-fixing bacteria provide an alternative source of fixed nitrogen for use in both biotechnological and agricultural settings, but this relies on a firm understanding of how the fixation process is regulated within individual bacterial cells. We examined the cell-to-cell variability in the nitrogen-fixing behavior of Klebsiella oxytoca, a free-living bacterium. The significance of our research is in identifying not only the presence of marked variability but also the specific mechanisms that give rise to it. This understanding gives insight into both the evolutionary advantages of variable behavior as well as strategies for biotechnological applications.

scGENA: A Single-Cell Gene Coexpression Network Analysis Framework for Clustering Cell Types and Revealing Biological Mechanisms

Single-cell RNA-sequencing (scRNA-seq) is a recent high-throughput technique that can measure gene expression, reveal cell heterogeneity, rare and complex cell populations, and discover cell types and their relationships. The analysis of scRNA-seq data is challenging because of transcripts sparsity, replication noise, and outlier cell populations. A gene coexpression network (GCN) analysis effectively deciphers phenotypic differences in specific states by describing gene–gene pairwise relationships. The underlying gene modules with different coexpression patterns partially bridge the gap between genotype and phenotype. This study presents a new framework called scGENA (single-cell gene coexpression network analysis) for GCN analysis based on scRNA-seq data. Although there are several methods for scRNA-seq data analysis, we aim to build an integrative pipeline for several purposes that cover primary data preprocessing, including data exploration, quality control, normalization, imputation, and dimensionality reduction of clustering as downstream of GCN analysis. To demonstrate this integrated workflow, an scRNA-seq dataset of the human diabetic pancreas with 1600 cells and 39,851 genes was implemented to perform all these processes in practice. As a result, scGENA is demonstrated to uncover interesting gene modules behind complex diseases, which reveal biological mechanisms. scGENA provides a state-of-the-art method for gene coexpression analysis for scRNA-seq data.

A mutual information-based in vivo monitoring of adaptive response to targeted therapies in melanoma

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In vivo dependencies should be quantified in adaptive resistance mechanistic studies

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Mutual information (MI) quantifies any type rather than just linear dependencies

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MI outperforms classic expression correlation coefficients

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Adaptive response to small-molecules inhibitors can be monitored in vivo using MI

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Strategies that prevent adaptive resistance can be monitored in vivo using MI

The mechanisms of adaptive resistance to genetic-based targeted therapies of solid malignancies have been the subject of intense research. These studies hold great promise for finding co-targetable hub/pathways which in turn would control the downstream non-genetic mechanisms of adaptive resistance. Many such mechanisms have been described in the paradigmatic BRAF-mutated melanoma model of adaptive response to BRAF inhibition. Currently, a major challenge for these mechanistic studies is to confirm in vivo, at the single-cell proteomic level, the existence of dependencies between the co-targeted hub/pathways and their downstream effectors. Moreover, the drug-induced in vivo modulation of these dependencies needs to be demonstrated. Here, we implement such single-cell-based in vivo expression dependency quantification using immunohistochemistry (IHC)-based analyses of sequential biopsies in two xenograft models. These mimic phase 2 and 3 trials in our own therapeutic strategy to prevent the adaptive response to BRAF inhibition. In this mechanistic model, the dependencies between the targeted Li₂CO₃-inducible hub HuR and the resistance effectors are more likely time-shifted and transient since the minority of HuR^Low cells, which act as a reservoir of adaptive plasticity, switch to a HuR^High state as they paradoxically proliferate under BRAF inhibition. Nevertheless, we show that a copula/kernel density estimator (KDE)-based quantification of mutual information (MI) efficiently captures, at the individual level, the dependencies between HuR and two relevant resistance markers pERK and EGFR, and outperforms classic expression correlation coefficients. Ultimately, the validation of MI as a predictive IHC-based metric of response to our therapeutic strategy will be carried in clinical trials.

Noise and the molecular processes underlying cell fate decision-making

Cell fate decision-making events involve the interplay of many molecular processes, ranging from signal transduction to genetic regulation, as well as a set of molecular and physiological feedback loops. Each aspect offers a rich field of investigation in its own right, but to understand the whole process, even in simple terms, we need to consider them together. Here we attempt to characterise this process by focussing on the roles of noise during cell fate decisions. We use a range of recent results to develop a view of the sequence of events by which a cell progresses from a pluripotent or multipotent to a differentiated state: chromatin organisation, transcription factor stoichiometry, and cellular signalling all change during this progression, and all shape cellular variability, which becomes maximal at the transition state.

An Ensemble Method to Reconstruct Gene Regulatory Networks Based on Multivariate Adaptive Regression Splines

Gene regulatory networks (GRNs) play a key role in biological processes. However, GRNs are diverse under different biological conditions. Reconstructing gene regulatory networks (GRNs) from gene expression has become an important opportunity and challenge in the past decades. Although there are a lot of existing methods to infer the topology of GRNs, such as mutual information, random forest, and partial least squares, the accuracy is still low due to the noise and high dimension of the expression data. In this paper, we introduce an ensemble Multivariate Adaptive Regression Splines (MARS) based method to reconstruct the directed GRNs from multifactorial gene expression data, called PBMarsNet. PBMarsNet incorporates part mutual information (PMI) to pre-weight the candidate regulatory genes and then uses MARS to detect the nonlinear regulatory links. Moreover, we apply bootstrap to run the MARS multiple times and average the outputs of each MARS as the final score of regulatory links. The results on DREAM4 challenge and DREAM5 challenge datasets show PBMarsNet has a superior performance and generalization over other state-of-the-art methods.

D3GRN: a data driven dynamic network construction method to infer gene regulatory networks

BACKGROUND

To infer gene regulatory networks (GRNs) from gene-expression data is still a fundamental and challenging problem in systems biology. Several existing algorithms formulate GRNs inference as a regression problem and obtain the network with an ensemble strategy. Recent studies on data driven dynamic network construction provide us a new perspective to solve the regression problem.

RESULTS

In this study, we propose a data driven dynamic network construction method to infer gene regulatory network (D3GRN), which transforms the regulatory relationship of each target gene into functional decomposition problem and solves each sub problem by using the Algorithm for Revealing Network Interactions (ARNI). To remedy the limitation of ARNI in constructing networks solely from the unit level, a bootstrapping and area based scoring method is taken to infer the final network. On DREAM4 and DREAM5 benchmark datasets, D3GRN performs competitively with the state-of-the-art algorithms in terms of AUPR.

CONCLUSIONS

We have proposed a novel data driven dynamic network construction method by combining ARNI with bootstrapping and area based scoring strategy. The proposed method performs well on the benchmark datasets, contributing as a competitive method to infer gene regulatory networks in a new perspective.

On Information Extraction and Decoding Mechanisms Improved by Noisy Amplification in Signaling Pathways

The cells need to process information about extracellular stimuli. They encode, transmit and decode the information to elicit an appropriate response. Studies aimed at understanding how such information is decoded in the signaling pathways to generate a specific cellular response have become essential. Eukaryotic cells decode information through two different mechanisms: the feed-forward loop and the promoter affinity. Here, we investigate how these two mechanisms improve information transmission. A detailed comparison is made between the stochastic model of the MAPK/ERK pathway and a stochastic minimal decoding model. The maximal amount of transmittable information was computed. The results suggest that the decoding mechanism of the MAPK/ERK pathway improve the channel capacity because it behaves as a noisy amplifier. We show a positive dependence between the noisy amplification and the amount of information extracted. Additionally, we show that the extrinsic noise can be tuned to improve information transmission. This investigation has revealed that the feed-forward loop and the promoter affinity motifs extract information thanks to processes of amplification and noise addition. Moreover, the channel capacity is enhanced when both decoding mechanisms are coupled. Altogether, these findings suggest novel characteristics in how decoding mechanisms improve information transmission.

Exploring the information transmission properties of noise-induced dynamics: application to glioma differentiation

Background

Cells operate in an uncertain environment, where critical cell decisions must be enacted in the presence of biochemical noise. Information theory can measure the extent to which such noise perturbs normal cellular function, in which cells must perceive environmental cues and relay signals accurately to make timely and informed decisions. Using multivariate response data can greatly improve estimates of the latent information content underlying important cell fates, like differentiation.

Results

We undertake an information theoretic analysis of two stochastic models concerning glioma differentiation therapy, an alternative cancer treatment modality whose underlying intracellular mechanisms remain poorly understood. Discernible changes in response dynamics, as captured by summary measures, were observed at low noise levels. Mitigating certain feedback mechanisms present in the signaling network improved information transmission overall, as did targeted subsampling and clustering of response dynamics.

Conclusion

Computing the channel capacity of noisy signaling pathways present great probative value in uncovering the prevalent trends in noise-induced dynamics. Areas of high dynamical variation can provide concise snapshots of informative system behavior that may otherwise be overlooked. Through this approach, we can examine the delicate interplay between noise and information, from signal to response, through the observed behavior of relevant system components.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2970-7) contains supplementary material, which is available to authorized users.

Gene Regulatory Network Inference from Single-Cell Data Using Multivariate Information Measures

While single-cell gene expression experiments present new challenges for data processing, the cell-to-cell variability observed also reveals statistical relationships that can be used by information theory. Here, we use multivariate information theory to explore the statistical dependencies between triplets of genes in single-cell gene expression datasets. We develop PIDC, a fast, efficient algorithm that uses partial information decomposition (PID) to identify regulatory relationships between genes. We thoroughly evaluate the performance of our algorithm and demonstrate that the higher-order information captured by PIDC allows it to outperform pairwise mutual information-based algorithms when recovering true relationships present in simulated data. We also infer gene regulatory networks from three experimental single-cell datasets and illustrate how network context, choices made during analysis, and sources of variability affect network inference. PIDC tutorials and open-source software for estimating PID are available. PIDC should facilitate the identification of putative functional relationships and mechanistic hypotheses from single-cell transcriptomic data.

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PIDC infers gene regulatory networks from single-cell transcriptomic data

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Multivariate information measures and context in PIDC improve network inference

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Heterogeneity in single-cell data carries information about gene-gene interactions

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Fast, efficient, open-source software is made freely available

Multidimensional biochemical information processing of dynamical patterns

Cells receive signaling molecules by receptors and relay information via sensory networks so that they can respond properly depending on the type of signal. Recent studies have shown that cells can extract multidimensional information from dynamical concentration patterns of signaling molecules. We herein study how biochemical systems can process multidimensional information embedded in dynamical patterns. We model the decoding networks by linear response functions, and optimize the functions with the calculus of variations to maximize the mutual information between patterns and output. We find that, when the noise intensity is lower, decoders with different linear response functions, i.e., distinct decoders, can extract much information. However, when the noise intensity is higher, distinct decoders do not provide the maximum amount of information. This indicates that, when transmitting information by dynamical patterns, embedding information in multiple patterns is not optimal when the noise intensity is very large. Furthermore, we explore the biochemical implementations of these decoders using control theory and demonstrate that these decoders can be implemented biochemically through the modification of cascade-type networks, which are prevalent in actual signaling pathways.

'Molecular habituation' as a potential mechanism of gradual homeostatic loss with age

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Constitutive signals indicate homeostatic dysregulation but their effect on signal transduction remains largely unexplored.

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A theoretical approach is undertaken to examine how oxidative stress may affect redox signal transduction.

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Constitutive signals can result in a ‘molecular habituation’ effect that interferes with information transmission.

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The robustness of such a theoretical observation to the underlying methodology hints at the generality of this principle.

The ability of reactive oxygen species (ROS) to cause molecular damage has meant that chronic oxidative stress has been mostly studied from the point of view of being a source of toxicity to the cell. However, the known duality of ROS molecules as both damaging agents and cellular redox signals implies another perspective in the study of sustained oxidative stress. This is a perspective of studying oxidative stress as a constitutive signal within the cell. In this work, we adopt a theoretical perspective as an exploratory and explanatory approach to examine how chronic oxidative stress can interfere with signal processing by redox signalling pathways in the cell. We report that constitutive signals can give rise to a ‘molecular habituation’ effect that can prime for a gradual loss of biological function. This is because a constitutive signal in the environment has the potential to reduce the responsiveness of a signalling pathway through the prolonged activation of negative regulators. Additionally, we demonstrate how this phenomenon is likely to occur in different signalling pathways exposed to persistent signals and furthermore at different levels of biological organisation.

Control mechanisms for stochastic biochemical systems via computation of reachable sets

Controlling the behaviour of cells by rationally guiding molecular processes is an overarching aim of much of synthetic biology. Molecular processes, however, are notoriously noisy and frequently nonlinear. We present an approach to studying the impact of control measures on motifs of molecular interactions that addresses the problems faced in many biological systems: stochasticity, parameter uncertainty and nonlinearity. We show that our reachability analysis formalism can describe the potential behaviour of biological (naturally evolved as well as engineered) systems, and provides a set of bounds on their dynamics at the level of population statistics: for example, we can obtain the possible ranges of means and variances of mRNA and protein expression levels, even in the presence of uncertainty about model parameters.

Modeling amplified p53 responses under DNA-PK inhibition in DNA damage response

During DNA double strand breaks (DSBs) repair, coordinated activation of phosphatidylinositol 3-kinase (PI3K)-like kinases can activate p53 signaling pathway. Recent findings have identified novel interplays among these kinases demonstrating amplified first p53 pulses under DNA-PK inhibition. However, no theoretical model has been developed to characterize such dynamics. In current work, we modeled the prolonged p53 pulses with DNA-PK inhibitor. We could identify a dose-dependent increase in the first pulse amplitude and width. Meanwhile, weakened DNA-PK mediated ATM inhibition was insufficient to reproduce such dynamic behavior. Moreover, the information flow was shifted predominantly to the first pulse under DNA-PK inhibition. Furthermore, the amplified p53 responses were relatively robust. Taken together, our model can faithfully replicate amplified p53 responses under DNA-PK inhibition and provide insights into cell fate decision by manipulating p53 dynamics.

Inferring extrinsic noise from single-cell gene expression data using approximate Bayesian computation

Background

Gene expression is known to be an intrinsically stochastic process which can involve single-digit numbers of mRNA molecules in a cell at any given time. The modelling of such processes calls for the use of exact stochastic simulation methods, most notably the Gillespie algorithm. However, this stochasticity, also termed “intrinsic noise”, does not account for all the variability between genetically identical cells growing in a homogeneous environment.

Despite substantial experimental efforts, determining appropriate model parameters continues to be a challenge. Methods based on approximate Bayesian computation can be used to obtain posterior parameter distributions given the observed data. However, such inference procedures require large numbers of simulations of the model and exact stochastic simulation is computationally costly.

In this work we focus on the specific case of trying to infer model parameters describing reaction rates and extrinsic noise on the basis of measurements of molecule numbers in individual cells at a given time point.

Results

To make the problem computationally tractable we develop an exact, model-specific, stochastic simulation algorithm for the commonly used two-state model of gene expression. This algorithm relies on certain assumptions and favourable properties of the model to forgo the simulation of the whole temporal trajectory of protein numbers in the system, instead returning only the number of protein and mRNA molecules present in the system at a specified time point. The computational gain is proportional to the number of protein molecules created in the system and becomes significant for systems involving hundreds or thousands of protein molecules.

Conclusions

We employ this simulation algorithm with approximate Bayesian computation to jointly infer the model’s rate and noise parameters from published gene expression data. Our analysis indicates that for most genes the extrinsic contributions to noise will be small to moderate but certainly are non-negligible.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0324-x) contains supplementary material, which is available to authorized users.

Robustness of MEK-ERK Dynamics and Origins of Cell-to-Cell Variability in MAPK Signaling

Cellular signaling processes can exhibit pronounced cell-to-cell variability in genetically identical cells. This affects how individual cells respond differentially to the same environmental stimulus. However, the origins of cell-to-cell variability in cellular signaling systems remain poorly understood. Here, we measure the dynamics of phosphorylated MEK and ERK across cell populations and quantify the levels of population heterogeneity over time using high-throughput image cytometry. We use a statistical modeling framework to show that extrinsic noise, particularly that from upstream MEK, is the dominant factor causing cell-to-cell variability in ERK phosphorylation, rather than stochasticity in the phosphorylation/dephosphorylation of ERK. We furthermore show that without extrinsic noise in the core module, variable (including noisy) signals would be faithfully reproduced downstream, but the within-module extrinsic variability distorts these signals and leads to a drastic reduction in the mutual information between incoming signal and ERK activity.

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Active MEK and ERK levels differ profoundly among genetically identical cells

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A statistical framework is developed to identify the causes of this variability

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Analysis shows that extrinsic noise upstream MEK-ERK module causes cell variability

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Within-module extrinsic variability distorts signals

Extending the dynamic range of transcription factor action by translational regulation

A crucial step in the regulation of gene expression is binding of transcription factor (TF) proteins to regulatory sites along the DNA. But transcription factors act at nanomolar concentrations, and noise due to random arrival of these molecules at their binding sites can severely limit the precision of regulation. Recent work on the optimization of information flow through regulatory networks indicates that the lower end of the dynamic range of concentrations is simply inaccessible, overwhelmed by the impact of this noise. Motivated by the behavior of homeodomain proteins, such as the maternal morphogen Bicoid in the fruit fly embryo, we suggest a scheme in which transcription factors also act as indirect translational regulators, binding to the mRNA of other regulatory proteins. Intuitively, each mRNA molecule acts as an independent sensor of the input concentration, and averaging over these multiple sensors reduces the noise. We analyze information flow through this scheme and identify conditions under which it outperforms direct transcriptional regulation. Our results suggest that the dual role of homeodomain proteins is not just a historical accident, but a solution to a crucial physics problem in the regulation of gene expression.