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• W4291448511 abstract "Article15 August 2022Open Access Transparent process Quantifying the phenotypic information in mRNA abundance Evan Maltz Evan Maltz Department of Chemistry and Biochemistry, UCLA, Los Angeles, CA, USA Institute of Quantitative and Computational Bioscience, UCLA, Los Angeles, CA, USA Contribution: Conceptualization, Software, Formal analysis, Validation, ​Investigation, Visualization, Methodology, Writing - original draft, Writing - review & editing Search for more papers by this author Roy Wollman Corresponding Author Roy Wollman [email protected] orcid.org/0000-0003-3865-2605 Department of Chemistry and Biochemistry, UCLA, Los Angeles, CA, USA Institute of Quantitative and Computational Bioscience, UCLA, Los Angeles, CA, USA Department of Integrative Biology and Physiology, UCLA, Los Angeles, CA, USA Contribution: Conceptualization, Formal analysis, Supervision, Funding acquisition, Validation, Methodology, Writing - original draft, Project administration, Writing - review & editing Search for more papers by this author Evan Maltz Evan Maltz Department of Chemistry and Biochemistry, UCLA, Los Angeles, CA, USA Institute of Quantitative and Computational Bioscience, UCLA, Los Angeles, CA, USA Contribution: Conceptualization, Software, Formal analysis, Validation, ​Investigation, Visualization, Methodology, Writing - original draft, Writing - review & editing Search for more papers by this author Roy Wollman Corresponding Author Roy Wollman [email protected] orcid.org/0000-0003-3865-2605 Department of Chemistry and Biochemistry, UCLA, Los Angeles, CA, USA Institute of Quantitative and Computational Bioscience, UCLA, Los Angeles, CA, USA Department of Integrative Biology and Physiology, UCLA, Los Angeles, CA, USA Contribution: Conceptualization, Formal analysis, Supervision, Funding acquisition, Validation, Methodology, Writing - original draft, Project administration, Writing - review & editing Search for more papers by this author Author Information Evan Maltz1,2 and Roy Wollman *,1,2,3 1Department of Chemistry and Biochemistry, UCLA, Los Angeles, CA, USA 2Institute of Quantitative and Computational Bioscience, UCLA, Los Angeles, CA, USA 3Department of Integrative Biology and Physiology, UCLA, Los Angeles, CA, USA *Corresponding author. Tel: 310 8254321; E-mail: [email protected] Molecular Systems Biology (2022)18:e11001https://doi.org/10.15252/msb.202211001 PDFDownload PDF of article text and main figures. Peer ReviewDownload a summary of the editorial decision process including editorial decision letters, reviewer comments and author responses to feedback. ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InMendeleyWechatReddit Figures & Info Abstract Quantifying the dependency between mRNA abundance and downstream cellular phenotypes is a fundamental open problem in biology. Advances in multimodal single-cell measurement technologies provide an opportunity to apply new computational frameworks to dissect the contribution of individual genes and gene combinations to a given phenotype. Using an information theory approach, we analyzed multimodal data of the expression of 83 genes in the Ca2+ signaling network and the dynamic Ca2+ response in the same cell. We found that the overall expression levels of these 83 genes explain approximately 60% of Ca2+ signal entropy. The average contribution of each single gene was 17%, revealing a large degree of redundancy between genes. Using different heuristics, we estimated the dependency between the size of a gene set and its information content, revealing that on average, a set of 53 genes contains 54% of the information about Ca2+ signaling. Our results provide the first direct quantification of information content about complex cellular phenotype that exists in mRNA abundance measurements. Synopsis The dependency of cellular signaling dynamics variability on transcriptional state was estimated by applying information theory estimation to paired multimodal measurements of mRNA abundances and cellular cytosolic Ca2+ dynamics response to ATP. Overall expression levels of 83 genes related to Ca2+ signaling explain 60% of the observed variability in Ca2+ signaling dynamics. Most of the information provided by any single gene is redundant with other genes. 54% of information about Ca2+ dynamics exists in the most informative set of 12 genes or a random set of 53 genes. Introduction Cellular phenotypes emerge from many regulated interactions between various components. Rates of synthesis and degradation determine the instantaneous abundances of different biological molecules. These kinetic rates are themselves a property of regulatory interactions between biomolecules creating multilayered feedback networks (El-Samad, 2021). Both the dynamic and instantaneous abundances of biomolecules are key determinants of cellular phenotypes, underlying their ability to make different decisions given the same stimulus (Perkins & Swain, 2009; Cheong et al, 2011; Purvis & Lahav, 2013). The ability to systematically measure the abundance of large sets of different biomolecules such as mRNA and proteins enables the determination of regulatory strengths across different nodes of these complex networks. Pioneering work in Escherichia coli based on instantaneous single-cell measurements of mRNA and protein copy numbers reveals a surprisingly low correlation coefficient of r = 0.01 ± 0.03 across 129 highly expressed genes (Taniguchi et al, 2010). The lack of correlation between mRNA and protein in E. coli might be due to their small size and magnitude of temporal fluctuation in mRNA levels. However, more recent advances in multimodal assays in mammalian cells also identified low correlations between the abundances of most proteins and corresponding mRNAs (Darmanis et al, 2016; Gong et al, 2017; Stoeckius et al, 2017; Schulz et al, 2018; Mair et al, 2020). This low correlation appears to contradict intuition that protein and mRNA levels should strongly correspond within cells because of the dependency suggested by the central dogma (Liu et al, 2016). An alternative hypothesis is that the majority of regulatory steps and phenotypically relevant information lie in posttranscriptional processes. Posttranscriptional regulation can modulate both protein activity and abundance via protein interactions, posttranslational modifications, RNA interactions/structure, and more. Stochastic processes also obscure the importance of molecular composition to phenotypic outcomes (Perkins & Swain, 2009; Balázsi et al, 2011; Cheong et al, 2011). Yet, many studies have pointed to differences in mRNA levels among clonal cells to explain differences in cellular phenotypes (Shaffer et al, 2020; Emert et al, 2021). These observations highlight a need for a better framework to address fundamental questions: Does mRNA abundance matter? What fraction of the information about cellular phenotype is determined by mRNA abundance, and what fraction is due to posttranscriptional regulation? Quantifying the information content in mRNA abundance about cellular phenotypes is technically and computationally challenging due to the many layers of complex interactions in cellular networks (Macaulay et al, 2017). Phenotypic information displayed in clonal cells is controlled by molecular composition, stochastic factors, intermediate regulation, and crosstalk (Azeloglu & Iyengar, 2015). Many approaches have been developed to disentangle these complex and distributed dependencies. Feature engineering has been one powerful tool to reveal interpretable characteristics of signaling dynamics, finding multiple motifs that encode information about stimulus dose and type (Nelson et al, 2004; Hafner et al, 2017; Zhang et al, 2017; Wong et al, 2019; Adelaja et al, 2021). However, these features do not capture all the information in complex dynamics, which are difficult to study and fully recapitulate in mechanistic models (Myers et al, 2021). Another common approach is to perform dimensionality reduction and/or clustering to integrate different modalities (Subramanian et al, 2020; Kinnunen et al, 2021). Several studies have clustered groups of genes or cells based on signal patterns to reveal general mechanisms of how signaling dynamics affect transcription (Hafner et al, 2017; Lane et al, 2017). However, it is still unknown how differences in arbitrary sets of transcripts relate to dynamic signals in the same cells. Signaling phenomena may emerge due to differences among many combinations of genes, which may be missed when simplified to either individual genes or gene clusters. Single-cell network states are notoriously difficult to fully measure, and insights into the relationships between many components require high-dimensional and multimodal data from the same cells (Spencer et al, 2009; Azeloglu & Iyengar, 2015; Macaulay et al, 2017; Adelaja et al, 2021). Although useful in many contexts, feature engineering, clustering, and dimensionality reduction are not guaranteed to capture all useful information. Directly quantifying the relationship between many transcripts and a phenotype via an information theoretic approach can provide a direct measure of the importance of mRNA abundance. However, three challenges prevent the general use of information theory in quantifying information content in RNA abundance. (i) Biological feedbacks entangle mRNA abundance and cellular phenotype. Cellular phenotypes that emerge over long timescale, for example, cellular differentiations, have a longer timescale than the lifetime of mRNA molecules that potentially determine the emerging phenotypes. In these cases, mRNA abundances themselves change dynamically adding additional complexities. (ii) Quantification of importance of mRNA abundance requires paired measurements of mRNA and the emerging cellular phenotype in question, measurements that are technically challenging due to the destructive nature of mRNA quantification methods. (iii) The statistical measures needed to answer these questions, entropy and mutual information, are notoriously hard to infer. Below, we discuss how these challenges could be addressed to provide direct quantification of the information content in mRNA abundance. Ca2+ signaling is a useful model system to quantify the dependency between mRNA abundance and emerging cellular phenotypes. Ca2+ signaling is a system in which the emerging phenotype is faster than changes in mRNA abundance. This timescale separation allows us to assume mRNA abundances are at a quasi-steady state and do not change significantly during the experiment. The dynamics of the Ca2+ signaling response to ATP is a well-studied model system for environmental sensing, featuring one of the most ubiquitous and multifunctional pathways across cell types. An important role of Ca2+ signaling is the coordination of responses to changes in extracellular environment. In the physiological context of tissues, cell lysis causes an unusual local increase in extracellular ATP, among other molecules. This type of damage sensing relies on the purinergic cell surface receptors, P1 and P2, which detect adenosine and ATP, respectively (Alves et al, 2018). The P2Y GPCR triggers a downstream signaling cascade via protein interactions. Gq-GTP is released from the P2Y receptor where it can then bind to and activate phospholipase C (PLCβ). PLCβ cleaves PIP2 into IP3 and DAG, which facilitate signaling by binding to their respective receptors, IP3R and DAGR. The IP3R is embedded in the membrane of the endoplasmic reticulum and functions as a gated Ca2+ channel that releases Ca2+ into the cytoplasm upon IP3 binding. Cytoplasmic Ca2+ concentrations are kept relatively low at 50–100 nM and spike up to 1uM during signaling with significant and rapid fluctuations producing unique dynamics in every cell (Bagur & Hajnóczky, 2017). Changes in cytoplasmic Ca2+ concentration over time (i.e., its signaling dynamics) have many emergent features such as oscillations caused by coupling between positive and negative feedback loops (Azeloglu & Iyengar, 2015). Studies have shown these dynamics specifically propagate relevant environmental and stimulus information (Selimkhanov et al, 2014). While in the cytoplasm, Ca2+ regulates many signaling molecules, for example, kinases and phosphatases, through direct binding to Ca2+ binding domains such as the EF-hand and through binding to calmodulin isoforms that enables it to activate kinases such as protein kinase C. These kinases affect many downstream transcriptional and protein-mediated responses that ultimately regulate cell behavior. The timescale of Ca2+ dynamics is significantly faster than the timescale of gene expression differentiation, allowing us to interpret a symmetric measure of dependency, such as mutual information, in a directed manner (Putney, 2012). Overall, the Ca2+ signaling pathway is a complex network with regulation at transcriptional and posttranscriptional levels, providing us with a great model system to dissect the phenotypic information content in mRNA abundances. Precise measurements of dynamic single-cell, multimodal data have been collected to address these questions. Studies featuring multiomic image-based measurements have mostly focused on fixed cell measurements such as immunofluorescence, spatial arrangement of cells in tissues, and chromatin structure (Wang et al, 2018; Liu et al, 2021; Zhang et al, 2021). Studies that have involved dynamic phenotypes were limited by the low sensitivity of scRNAseq (Lane et al, 2017) or had to focus on only a handful of genes (Lee et al, 2014). Nonetheless, methods are being developed to integrate live cell dynamics and reliable RNA quantification of hundreds of genes (Foreman & Wollman, 2020; Genshaft et al, 2021). Measuring the transcriptional state of the Ca2+ signaling pathway requires the quantification of the abundance of hundreds of genes. Multiplexed error-robust fluorescence in situ hybridization (MERFISH) has been developed as a high-throughput, single-cell method for accurately counting large numbers of transcripts (Moffitt et al, 2016). Because it is performed in situ, MERFISH can be combined with other imaging methods to create high-dimensional, multimodal data consisting of both dynamic and instantaneous measurements. Combining transcriptomic and live-cell data offers unique insights into the role of dynamic regulation and sources of phenotypic information. The challenge of collecting high-dimensional, single cell, paired transcriptomic, and signaling dynamics data has been successfully addressed in recent work (Foreman & Wollman, 2020). There, we demonstrated a single-cell method for collecting paired measurements of live Ca2+ signaling dynamics and relevant gene expression using MERFISH. In that work, nontransformed epithelial cells that express a Ca2+ biosensor were activated with extracellular ATP, imaged for 13 min, and fixed for mRNA abundance quantification using MERFISH. Pairing of cells between the two modalities of the experiment created a unique dataset of 5,128 cells with 314 timepoints of Ca2+ signaling dynamics and counts for 83 transcripts. This dataset was the basis for the work described here. New analytical frameworks have emerged for understanding complex dependencies in multimodal measurements with intractable data distributions. Information theory provides a powerful analytical framework for understanding the relationship between system structure and output (Brennan et al, 2012). Shannon's mutual information is a statistical approach for measuring the magnitude of shared, or symmetric, information between two random variables. This framework is powerful because it captures nonlinear relationships and measures true dependence in absolute terms, although it has been difficult to apply to biochemical systems without strict assumptions about the data distribution (Tostevin & ten Wolde, 2010; Uda et al, 2013). However, multiomic measurements of single cells often involve different data types that are difficult to relate, that is to define a joint probability distribution. In the case of Ca2+ signaling networks, signaling data are sampled from a continuous process, whereas RNA abundances are discrete. Many paradigms rely on separate analysis of each data type, often via dimensionality reduction or clustering, before relationships can be quantified (Welch et al, 2019; Lee et al, 2020; Fang et al, 2021). While other approaches (e.g., binning or kernel-density estimation) exist for defining a joint probability distribution over some data types, they fail to perform well outside of strict assumptions about the distributions (e.g., gaussianity) or limited dimensionality; a general, scalable approach is necessary to reduce the need for complex and highly specific analytical pipelines that have emerged (Gayoso et al, 2021; Zuo & Chen, 2021). Highly flexible neural networks have demonstrated their ability to estimate characteristics of these probability distributions to allow a deeper understanding of the statistical and information theoretic properties of the data. Deep learning has proven useful for classification of and feature generation from ERK and Akt signaling dynamics (Jacques et al, 2021). However, direct interpretation of latent embeddings in these neural network outputs is challenging. An alternative use of deep learning methodologies is a universal functional approximator where neural networks are used to approximate unknown functions to achieve different objective functions. This approach was codified within variational inference and has been proven very useful in probability estimates. For complex data of mixed types where mutual information is analytically intractable, optimization of neural network functional approximator could be used to find a lower bound. This approach was recently demonstrated under the name mutual information neural estimator (MINE), which uses a deep neural network to learn a function that can encode the data and find a tight lower bound on the mutual information (preprint: Belghazi et al, 2018). Briefly, MINE is a universal function approximator that searches for a mapping function T in a large space of encoder functions parameterized by θ . T maps the data consisting of mRNA counts and Ca2+ signal dynamics, G and Ca 2 + respectively, of arbitrary dimensionality such that T θ : G Ca 2 + → ℝ . Remarkably, the data require no significant transformations, MINE is simply trained on the raw data because all transformations required for an efficient mapping are theoretically learnable by a model with enough parameters and samples. Letting ℙ ≔ ℙ G , Ca 2 + represent the joint probability, that is, paired data, and ℚ ≔ ℙ G ⊗ ℙ Ca 2 + represent the product of the marginal probabilities, that is, independently sampled data, the mutual information between G and Ca 2 + is the distance between the joint and marginal distributions. This distance is measured using the Kullback–Leibler divergence ( D KL ), and a stronger relationship between G and Ca 2 + is equivalent to a greater distance between the joint and marginals: I G Ca 2 + = D KL ℙ ∥ ℚ . Using the Donsker-Varadhan representation of the D KL , the model parameters θ are optimal when gradient ascent has maximized E ℙ T θ − log E ℚ e T θ ≤ D KL ℙ ∥ ℚ , where E denotes the expected value.This estimate represents a lower bound on the mutual information. MINE is highly flexible because it makes almost no assumptions about the structure of the data. MINE searches through a large function space for the optimal transformation function to encode the data types assuming there are enough samples to constrain the model. The result is a lower-bound estimate of the mutual information between paired modalities of almost any dimensionality and complexity. The recent technological development in multiplexed single-cell measurements and machine learning approaches for the inference of mutual information could be integrated to provide direct quantification of the phenotypic information content of mRNA abundances. Here, we utilize these developments and focus on a model with timescale separation between an emerging phenotype and mRNA abundance. We relied on highly multiplexed FISH-based quantification of mRNA levels that is more accurate than sequencing-based approaches and also allows integration with other imaging modalities. Inference of mutual information was done using the Ca2+ signaling network as a model; we fit MINE on various subsets of 83 genes and 314 Ca2+ timepoints to quantify the contribution of transcript abundance to signaling dynamics. To establish a baseline, we first calculated the dependency between individual genes and Ca2+ signals. We then calculated the mutual information between gene pairs and Ca2+ signals to account for redundancy. Gene sets of all sizes were then sampled using various strategies to measure how information changes with set size. Using PCA, we evaluate how useful phenotypic information accounts for transcript-level variance. Overall, we demonstrate a new information theoretic framework for analyzing paired single-cell data that provide a quantification of the dependency between sets of mRNAs and an emergent cell-scale dynamic phenotype. Results To investigate the information content of transcript counts and dynamic Ca2+ signals, we first analyzed each modality on their own. Ca2+ signals display significant heterogeneity across cells (Fig 1A). Likewise, most transcripts had a large range of abundances across cells, although distributions varied depending on the transcript. Pairwise correlation coefficients were calculated for 83 genes across 5,128 cells (Fig 1B). The magnitude of the correlations for all gene pairs was relatively low with an average of r = 0.16 compared to just cell cycle genes at r = 0.44. Assuming most genes are generally informative, one interpretation of the low correlations and heterogeneous transcript distributions is that transcripts contain unique information. To test this hypothesis, we quantified the transcriptional information by performing PCA then calculating the differential entropy, a measure of information for continuous probability distributions, of the components (equation 2, Fig 1C–E). Because each principal component is an independent, weighted sum of the row vectors of the data, we can approximate the differential entropy among orthogonal components assuming normality via the central limit theorem. Differential entropy across principal components does not measure the information in absolute terms but can describe how the information is distributed relative to the explained variance. We found that six principal components explain 75% of the variance, but only 15% of the gene entropy. The contrast between Fig 1C and D appears contradictory in that few orthogonal components explain most of the variance, yet entropy is steadily added across components with no obvious plateau. This analysis shows that simple measures such as explained variance that are often used for dimensionality reduction are not necessarily appropriate proxies of information content. Accounting for relevant, phenotypic information could help resolve discrepancies between explained variance and differential entropy. To estimate the signal entropy, that is, information content in Ca2+ signaling, we took advantage of its dynamic patterns. Differential entropy of Ca2+ can be estimated using spectral entropy (equation 1), a scale-invariant measure of information (Burg, 1975). The periodogram shows a continuum of signal frequencies with apparently low variance (Fig 1F). Signal entropy can be calculated using this distribution of frequencies, which we found to be 4.2 bits or ~18 signaling states. The mutual information between mRNA abundance and Ca2+ signaling is bounded by the distribution with the lowest entropy. Thus, 4.2 bits provides a likely upper bound to the true mutual information between transcripts and Ca2+ signals. Figure 1. Structure of gene and Ca2+ data A. Representative examples of Ca2+ dynamics of four cells in the dataset. B. A histogram of the pairwise gene correlation matrix (tri-up) which highlights the relatively low correlations. C. Explained variance of mRNA transcript counts from PCA. D. Differential entropy of transcripts estimated by PCA. E. Plot of explained variance (panel C) vs differential entropy (panel D) with an increasing number of principal components. F. Dynamic Ca2+ signal periodogram (cropped to show only the lower wavelength, higher power frequencies). Ca2+ dynamic signals were found to contain a spectral entropy of 4.2 bits. Data information: Collectively, panels (C–E) show that most of the entropy comes from components that do not explain much of the variance. Download figure Download PowerPoint To quantify how useful phenotypic information is distributed across genes, we estimated mutual information between individual genes and Ca2+ signals (Fig 2A). To help choose hyperparameters and evaluate MINE's performance, we tested the model on multivariate gaussian distributions and found a mean residual of 0.37 bits with a Pearson's correlation coefficient of 0.97 to the ground truth (Appendix Fig S2). Applied to the experimental data, we measured the total mutual information between all genes and Ca2+ at 2.5 ± 0.4 bits. Most individual genes contain significant information about Ca2+ signals, an average of 0.7 bits, and the most informative gene accounts for 34% of the 4.2 bits of signal entropy. Cell cycle-associated genes were well distributed throughout the list, whereas genes coding for Ca2+ and/ or calmodulin-dependent proteins such as PPP3CA and CCDC47 were at the top of the list. If each gene contained completely unique information, then the sum of the phenotypic information in each gene should add up to the total of 2.5 ± 0.4 bits. Interestingly, this sum is significantly larger than the total I(G;Ca2+), indicating a high degree of redundancy (Fig 2B). The average mutual information between a single gene and Ca2+ signals is 0.7 bits, which is 17% of the signal entropy (Fig 2C). How the mutual information is shared across genes is not immediately clear. We further tested whether informative genes, that is, genes that have high average pairwise mutual information to other genes, are also informative about Ca2+ dynamics (Fig 2D). Overall, genes that are more informative about Ca2+ signaling are also more informative about the expression of other genes. These genes that are highly informative about Ca2+ and many other transcripts may be interpreted as summary genes containing redundant, but distributed information. The second most informative single gene, PPP1CA, exemplifies this effect, as it codes for a subunit of PP1 that interacts with >200 regulatory proteins involved in a myriad of critical cell processes. Notably, the top two most informative genes, PPP3CA and PPP1CA, are both broadly connected phosphatases; kinases and phosphatases were consistently informative and concentrated toward the top of the list. However, from this analysis alone, it is not clear how many genes contain redundant information and to what extent. Figure 2. Mutual information between individual genes and Ca2+ signals A. I(Gi;Ca2+) sorted from least to greatest. Error bars show standard deviation of three technical replicates, that is three independent runs of the MINE algorithms on the same data. B. The blue line shows the cumulative sum of I(Gi;Ca2+) from (A) sorted from greatest to least, and individual genes appear to contain a lot of information (56 bits) about Ca2+ signals. The black dashed line shows mutual information between all 83 genes and Ca2+ dynamics estimated to be 2.5 bits. C. Histogram of (A) showing the mean I(Gi;Ca2+) is 0.7 bits. D. I(Gi;Gj) represents the pairwise mutual information between genes, the information that genes have about each other. This plot shows that genes that are more informative about other genes tend to be more informative about Ca2+ dynamics. Download figure Download PowerPoint To better understand how the superfluous information in Fig 2B is distributed among genes, we calculated the synergy redundancy index (SRI) between gene pairs with respect to Ca2+ (Dietterich et al, 2002; Schneidman et al, 2003). SRI(Gi,Gj ¦ Ca2+) measures the information overlap between genes by subtracting I(Gi;Ca2+) and I(Gj;Ca2+) from I({Gi,Gj};Ca2+). A gene pair with negative SRI means that the sum of the mutual information between each gene and Ca2+ was greater than the gene pair, so the genes must contain some of the same information (redundant). A positive SRI indicates that there is more information about Ca2+ in the gene pair than in the sum of the individual genes (synergistic). An SRI of 0 describes a pair of genes that are either generally uninformative or are independent, containing unique and nonoverlapping information about Ca2+. Calculating SRI between all gene pairs reveals that most pairs are significantly redundant (Fig 3A and B). On average, gene pairs share 0.43 bits which accounts for 61% of the 0.7 bits of phenotypic information contained in the average individual gene. Furthermore, the more informative a gene is about Ca2+, the more redundant it is with other genes (Fig 3C). This finding supports that some genes aggregate information from many oth" @default.
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• W4291448511 title "Quantifying the phenotypic information in <scp>mRNA</scp> abundance" @default.
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