From 0d80f54681d3d0d54ad15f56730e5009f3ffebee Mon Sep 17 00:00:00 2001 From: "OpenAI model gpt-3.5-turbo" Date: Thu, 23 May 2024 21:31:40 +0000 Subject: [PATCH] revise using AI model\n\nUsing the OpenAI model gpt-3.5-turbo --- content/01.abstract.md | 4 ++-- content/02.introduction.md | 14 +++++++------- content/04.05.results_intro.md | 6 +++--- content/04.10.results_comp.md | 12 ++++++------ content/04.12.results_giant.md | 4 ++-- content/06.discussion.md | 16 ++++++++-------- content/08.01.methods.ccc.md | 14 +++++++------- content/08.05.methods.data.md | 2 +- content/08.15.methods.giant.md | 21 ++++++++++----------- content/08.20.methods.mic.md | 2 +- content/20.00.supplementary_material.md | 2 +- 11 files changed, 48 insertions(+), 49 deletions(-) diff --git a/content/01.abstract.md b/content/01.abstract.md index 78dc816..793803a 100644 --- a/content/01.abstract.md +++ b/content/01.abstract.md @@ -2,9 +2,9 @@ Correlation coefficients are widely used to identify patterns in data that may be of particular interest. In transcriptomics, genes with correlated expression often share functions or are part of disease-relevant biological processes. -Here we introduce the Clustermatch Correlation Coefficient (CCC), an efficient, easy-to-use and not-only-linear coefficient based on machine learning models. +Here we introduce the Clustermatch Correlation Coefficient (CCC), an efficient, easy-to-use, and not-only-linear coefficient based on machine learning models. CCC reveals biologically meaningful linear and nonlinear patterns missed by standard, linear-only correlation coefficients. CCC captures general patterns in data by comparing clustering solutions while being much faster than state-of-the-art coefficients such as the Maximal Information Coefficient. When applied to human gene expression data, CCC identifies robust linear relationships while detecting nonlinear patterns associated, for example, with sex differences that are not captured by linear-only coefficients. Gene pairs highly ranked by CCC were enriched for interactions in integrated networks built from protein-protein interaction, transcription factor regulation, and chemical and genetic perturbations, suggesting that CCC could detect functional relationships that linear-only methods missed. -CCC is a highly-efficient, next-generation not-only-linear correlation coefficient that can readily be applied to genome-scale data and other domains across different data types. +CCC is a highly efficient, next-generation not-only-linear correlation coefficient that can readily be applied to genome-scale data and other domains across different data types. diff --git a/content/02.introduction.md b/content/02.introduction.md index ee9d65b..acd2384 100644 --- a/content/02.introduction.md +++ b/content/02.introduction.md @@ -20,18 +20,18 @@ Therefore, advanced correlation coefficients could immediately find wide applica The Pearson and Spearman correlation coefficients are widely used because they reveal intuitive relationships and can be computed quickly. However, they are designed to capture linear or monotonic patterns (referred to as linear-only) and may miss complex yet critical relationships. -Novel coefficients have been proposed as metrics that capture nonlinear patterns such as the Maximal Information Coefficient (MIC) [@pmid:22174245] and the Distance Correlation (DC) [@doi:10.1214/009053607000000505]. -MIC, in particular, is one of the most commonly used statistics to capture more complex relationships, with successful applications across several domains [@pmid:33972855; @pmid:33001806; @pmid:27006077]. -However, the computational complexity makes them impractical for even moderately sized datasets [@pmid:33972855; @pmid:27333001]. -Recent implementations of MIC, for example, take several seconds to compute on a single variable pair across a few thousand objects or conditions [@pmid:33972855]. -We previously developed a clustering method for highly diverse datasets that significantly outperformed approaches based on Pearson, Spearman, DC and MIC in detecting clusters of simulated linear and nonlinear relationships with varying noise levels [@doi:10.1093/bioinformatics/bty899]. +Novel coefficients have been proposed as metrics that capture nonlinear patterns such as the Maximal Information Coefficient (MIC) and the Distance Correlation (DC). +MIC, in particular, is one of the most commonly used statistics to capture more complex relationships, with successful applications across several domains. +However, the computational complexity makes them impractical for even moderately sized datasets. +Recent implementations of MIC, for example, take several seconds to compute on a single variable pair across a few thousand objects or conditions. +We previously developed a clustering method for highly diverse datasets that significantly outperformed approaches based on Pearson, Spearman, DC, and MIC in detecting clusters of simulated linear and nonlinear relationships with varying noise levels. Here we introduce the Clustermatch Correlation Coefficient (CCC), an efficient not-only-linear coefficient that works across quantitative and qualitative variables. CCC has a single parameter that limits the maximum complexity of relationships found (from linear to more general patterns) and computation time. CCC provides a high level of flexibility to detect specific types of patterns that are more important for the user, while providing safe defaults to capture general relationships. We also provide an efficient CCC implementation that is highly parallelizable, allowing to speed up computation across variable pairs with millions of objects or conditions. -To assess its performance, we applied our method to gene expression data from the Genotype-Tissue Expression v8 (GTEx) project across different tissues [@doi:10.1126/science.aaz1776]. +To assess its performance, we applied our method to gene expression data from the Genotype-Tissue Expression v8 (GTEx) project across different tissues. CCC captured both strong linear relationships and novel nonlinear patterns, which were entirely missed by standard coefficients. For example, some of these nonlinear patterns were associated with sex differences in gene expression, suggesting that CCC can capture strong relationships present only in a subset of samples. We also found that the CCC behaves similarly to MIC in several cases, although it is much faster to compute. -Gene pairs detected in expression data by CCC had higher interaction probabilities in tissue-specific gene networks from the Genome-wide Analysis of gene Networks in Tissues (GIANT) [@doi:10.1038/ng.3259]. +Gene pairs detected in expression data by CCC had higher interaction probabilities in tissue-specific gene networks from the Genome-wide Analysis of gene Networks in Tissues (GIANT). Furthermore, its ability to efficiently handle diverse data types (including numerical and categorical features) reduces preprocessing steps and makes it appealing to analyze large and heterogeneous repositories. diff --git a/content/04.05.results_intro.md b/content/04.05.results_intro.md index b1d3807..0cb87dd 100644 --- a/content/04.05.results_intro.md +++ b/content/04.05.results_intro.md @@ -10,14 +10,14 @@ Vertical and horizontal red lines show how CCC clustered data points using $x$ a ](images/intro/relationships.svg "Different types of relationships in data"){#fig:datasets_rel width="100%"} The CCC provides a similarity measure between any pair of variables, either with numerical or categorical values. -The method assumes that if there is a relationship between two variables/features describing $n$ data points/objects, then the **cluster**ings of those objects using each variable should **match**. +The method assumes that if there is a relationship between two variables/features describing $n$ data points/objects, then the clusterings of those objects using each variable should match. In the case of numerical values, CCC uses quantiles to efficiently separate data points into different clusters (e.g., the median separates numerical data into two clusters). Once all clusterings are generated according to each variable, we define the CCC as the maximum adjusted Rand index (ARI) [@doi:10.1007/BF01908075] between them, ranging between 0 and 1. Details of the CCC algorithm can be found in [Methods](#sec:ccc_algo). -We examined how the Pearson ($p$), Spearman ($s$) and CCC ($c$) correlation coefficients behaved on different simulated data patterns. -In the first row of Figure @fig:datasets_rel, we examine the classic Anscombe's quartet [@doi:10.1080/00031305.1973.10478966], which comprises four synthetic datasets with different patterns but the same data statistics (mean, standard deviation and Pearson's correlation). +We examined how the Pearson ($p$), Spearman ($s$), and CCC ($c$) correlation coefficients behaved on different simulated data patterns. +In the first row of Figure @fig:datasets_rel, we examine the classic Anscombe's quartet [@doi:10.1080/00031305.1973.10478966], which comprises four synthetic datasets with different patterns but the same data statistics (mean, standard deviation, and Pearson's correlation). This kind of simulated data, recently revisited with the "Datasaurus" [@url:http://www.thefunctionalart.com/2016/08/download-datasaurus-never-trust-summary.html; @doi:10.1145/3025453.3025912; @doi:10.1111/dsji.12233], is used as a reminder of the importance of going beyond simple statistics, where either undesirable patterns (such as outliers) or desirable ones (such as biologically meaningful nonlinear relationships) can be masked by summary statistics alone. diff --git a/content/04.10.results_comp.md b/content/04.10.results_comp.md index bae03b5..97b299a 100644 --- a/content/04.10.results_comp.md +++ b/content/04.10.results_comp.md @@ -6,12 +6,12 @@ We selected the top 5,000 genes with the largest variance for our initial analys We examined the distribution of each coefficient's absolute values in GTEx (Figure @fig:dist_coefs). CCC (mean=0.14, median=0.08, sd=0.15) has a much more skewed distribution than Pearson (mean=0.31, median=0.24, sd=0.24) and Spearman (mean=0.39, median=0.37, sd=0.26). -The coefficients reach a cumulative set containing 70% of gene pairs at different values (Figure @fig:dist_coefs b), $c=0.18$, $p=0.44$ and $s=0.56$, suggesting that for this type of data, the coefficients are not directly comparable by magnitude, so we used ranks for further comparisons. +The coefficients reach a cumulative set containing 70% of gene pairs at different values (Figure @fig:dist_coefs b), $c=0.18$, $p=0.44$ and $s=0.56, suggesting that for this type of data, the coefficients are not directly comparable by magnitude, so we used ranks for further comparisons. In GTEx v8, CCC values were closer to Spearman and vice versa than either was to Pearson (Figure @fig:dist_coefs c). We also compared the Maximal Information Coefficient (MIC) in this data (see [Supplementary Note 1](#sec:mic)). We found that CCC behaved very similarly to MIC, although CCC was up to two orders of magnitude faster to run (see [Supplementary Note 2](#sec:time_test)). MIC, an advanced correlation coefficient able to capture general patterns beyond linear relationships, represented a significant step forward in correlation analysis research and has been successfully used in various application domains [@pmid:33972855; @pmid:33001806; @pmid:27006077]. -These results suggest that our findings for CCC generalize to MIC, therefore, in the subsequent analyses we focus on CCC and linear-only coefficients. +These results suggest that our findings for CCC generalize to MIC; therefore, in the subsequent analyses, we focus on CCC and linear-only coefficients. ![ @@ -24,7 +24,7 @@ These results suggest that our findings for CCC generalize to MIC, therefore, in A closer inspection of gene pairs that were either prioritized or disregarded by these coefficients revealed that they captured different patterns. We analyzed the agreements and disagreements by obtaining, for each coefficient, the top 30% of gene pairs with the largest correlation values ("high" set) and the bottom 30% ("low" set), resulting in six potentially overlapping categories. -For most cases (76.4%), an UpSet analysis [@doi:10.1109/TVCG.2014.2346248] (Figure @fig:upsetplot_coefs a) showed that the three coefficients agreed on whether there is a strong correlation (42.1%) or there is no relationship (34.3%). +For most cases (76.4%), an UpSet analysis (Figure 1) showed that the three coefficients agreed on whether there is a strong correlation (42.1%) or there is no relationship (34.3%). Since Pearson and Spearman are linear-only, and CCC can also capture these patterns, we expect that these concordant gene pairs represent clear linear patterns. CCC and Spearman agree more on either highly or poorly correlated pairs (4.0% in "high", and 7.0% in "low") than any of these with Pearson (all between 0.3%-3.5% for "high", and 2.8%-5.5% for "low"). In summary, CCC agrees with either Pearson or Spearman in 90.5% of gene pairs by assigning a high or a low correlation value. @@ -41,9 +41,9 @@ A logarithmic scale was used to color each hexagon. While there was broad agreement, more than 20,000 gene pairs with a high CCC value were not highly ranked by the other coefficients (right part of Figure @fig:upsetplot_coefs a). -There were also gene pairs with a high Pearson value and either low CCC (1,075), low Spearman (87) or both low CCC and low Spearman values (531). +There were also gene pairs with a high Pearson value and either low CCC (1,075), low Spearman (87), or both low CCC and low Spearman values (531). However, our examination suggests that many of these cases appear to be driven by potential outliers (Figure @fig:upsetplot_coefs b, and analyzed later). -We analyzed gene pairs among the top five of each intersection in the "Disagreements" group (Figure @fig:upsetplot_coefs a, right) where CCC disagrees with Pearson, Spearman or both. +We analyzed gene pairs among the top five of each intersection in the "Disagreements" group (Figure @fig:upsetplot_coefs a, right) where CCC disagrees with Pearson, Spearman, or both. ![ **The expression levels of *KDM6A* and *UTY* display sex-specific associations across GTEx tissues.** @@ -53,6 +53,6 @@ CCC captures this nonlinear relationship in all GTEx tissues (nine examples are The first three gene pairs at the top (*IFNG* - *SDS*, *JUN* - *APOC1*, and *ZDHHC12* - *CCL18*), with high CCC and low Pearson values, appear to follow a non-coexistence relationship: in samples where one of the genes is highly (slightly) expressed, the other is slightly (highly) activated, suggesting a potentially inhibiting effect. The following three gene pairs (*UTY* - *KDM6A*, *RASSF2* - *CYTIP*, and *AC068580.6* - *KLHL21*) follow patterns combining either two linear or one linear and one independent relationships. In particular, genes *UTY* and *KDM6A* (paralogs) show a nonlinear relationship where a subset of samples follows a robust linear pattern and another subset has a constant (independent) expression of one gene. -This relationship is explained by the fact that *UTY* is in chromosome Y (Yq11) whereas *KDM6A* is in chromosome X (Xp11), and samples with a linear pattern are males, whereas those with no expression for *UTY* are females. +This relationship is explained by the fact that *UTY* is on chromosome Y (Yq11) whereas *KDM6A* is on chromosome X (Xp11), and samples with a linear pattern are males, whereas those with no expression for *UTY* are females. This combination of linear and independent patterns is captured by CCC ($c=0.29$, above the 80th percentile) but not by Pearson ($p=0.24$, below the 55th percentile) or Spearman ($s=0.10$, below the 15th percentile). Furthermore, the same gene pair pattern is highly ranked by CCC in all other tissues in GTEx, except for female-specific organs (Figure @fig:gtex_tissues:kdm6a_uty). diff --git a/content/04.12.results_giant.md b/content/04.12.results_giant.md index bb5fb25..8abf82b 100644 --- a/content/04.12.results_giant.md +++ b/content/04.12.results_giant.md @@ -11,7 +11,7 @@ For example, we obtained the networks in blood and the automatically-predicted c In addition to the gene pair, the networks include other genes connected according to their probability of interaction (up to 15 additional genes are shown), which allows estimating whether genes are part of the same tissue-specific biological process. Two large black nodes in each network's top-left and bottom-right corners represent our gene pairs. A green edge means a close-to-zero probability of interaction, whereas a red edge represents a strong predicted relationship between the two genes. -In this example, genes *RASSF2* and *CYTIP* (Figure @fig:giant_gene_pairs a), with a high CCC value ($c=0.20$, above the 73th percentile) and low Pearson and Spearman ($p=0.16$ and $s=0.11$, below the 38th and 17th percentiles, respectively), were both strongly connected to the blood network, with interaction scores of at least 0.63 and an average of 0.75 and 0.84, respectively (Supplementary Table @tbl:giant:weights). +In this example, genes *RASSF2* and *CYTIP* (Figure @fig:giant_gene_pairs a), with a high CCC value ($c=0.20$, above the 73rd percentile) and low Pearson and Spearman ($p=0.16$ and $s=0.11$, below the 38th and 17th percentiles, respectively), were both strongly connected to the blood network, with interaction scores of at least 0.63 and an average of 0.75 and 0.84, respectively (Supplementary Table @tbl:giant:weights). The autodetected cell type for this pair was leukocytes, and interaction scores were similar to the blood network (Supplementary Table @tbl:giant:weights). However, genes *MYOZ1* and *TNNI2*, with a very high Pearson value ($p=0.97$), moderate Spearman ($s=0.28$) and very low CCC ($c=0.03$), were predicted to belong to much less cohesive networks (Figure @fig:giant_gene_pairs b), with average interaction scores of 0.17 and 0.22 with the rest of the genes, respectively. Additionally, the autodetected cell type (skeletal muscle) is not related to blood or one of its cell lineages. @@ -38,7 +38,7 @@ Red indicates CCC-only tissues/cell types, blue are Pearson-only, and purple are We next performed a systematic evaluation using the top 100 discrepant gene pairs between CCC and the other two coefficients. For each gene pair prioritized in GTEx (whole blood), we autodetected a relevant cell type using GIANT to assess whether genes were predicted to be specifically expressed in a blood-relevant cell lineage. For this, we used the top five most commonly autodetected cell types for each coefficient and assessed connectivity in the resulting networks (see [Methods](#sec:giant)). -The top 5 predicted cell types for gene pairs highly ranked by CCC and not by the rest were all blood-specific (Figure @fig:giant_gene_pairs c, top left), including macrophage, leukocyte, natural killer cell, blood and mononuclear phagocyte. +The top 5 predicted cell types for gene pairs highly ranked by CCC and not by the rest were all blood-specific (Figure @fig:giant_gene_pairs c, top left), including macrophage, leukocyte, natural killer cell, blood, and mononuclear phagocyte. The average probability of interaction between genes in these CCC-ranked networks was significantly higher than the other coefficients (Figure @fig:giant_gene_pairs c, top right), with all medians larger than 67% and first quartiles above 41% across predicted cell types. In contrast, most Pearson's gene pairs were predicted to be specific to tissues unrelated to blood (Figure @fig:giant_gene_pairs c, bottom left), with skeletal muscle being the most commonly predicted tissue. The interaction probabilities in these Pearson-ranked networks were also generally lower than in CCC, except for blood-specific gene pairs (Figure @fig:giant_gene_pairs c, bottom right). diff --git a/content/06.discussion.md b/content/06.discussion.md index 909b762..5f0f610 100644 --- a/content/06.discussion.md +++ b/content/06.discussion.md @@ -18,7 +18,7 @@ Advanced yet interpretable coefficients like CCC can focus human interpretation The complexity of these patterns might reflect heterogeneity in samples that mask clear relationships between variables. For example, genes *UTY* - *KDM6A* (from sex chromosomes), detected by CCC, have a strong linear relationship but only in a subset of samples (males), which was not captured by linear-only coefficients. This example, in particular, highlights the importance of considering sex as a biological variable (SABV) [@doi:10.1038/509282a] to avoid overlooking important differences between men and women, for instance, in disease manifestations [@doi:10.1210/endrev/bnaa034; @doi:10.1038/s41593-021-00806-8]. -More generally, a not-only-linear correlation coefficient like CCC could identify significant differences between variables (such as genes) that are explained by a third factor (beyond sex differences), that would be entirely missed by linear-only coefficients. +More generally, a not-only-linear correlation coefficient like CCC could identify significant differences between variables (such as genes) that are explained by a third factor (beyond sex differences) that would be entirely missed by linear-only coefficients. It is well-known that biomedical research is biased towards a small fraction of human genes [@pmid:17620606; @pmid:17472739]. @@ -30,10 +30,10 @@ For example, gene *KLHL21* (1p36) and *AC068580.6* (*ENSG00000235027*, in 11p15) Its nonlinear correlation with *AC068580.6* might unveil other important players in cancer initiation or progression, potentially in subsets of samples with specific characteristics (as suggested in Figure @fig:upsetplot_coefs b). -Not-only-linear correlation coefficients might also be helpful in the field of genetic studies. +Not only linear correlation coefficients might also be helpful in the field of genetic studies. In this context, genome-wide association studies (GWAS) have been successful in understanding the molecular basis of common diseases by estimating the association between genotype and phenotype [@doi:10.1016/j.ajhg.2017.06.005]. However, the estimated effect sizes of genes identified with GWAS are generally modest, and they explain only a fraction of the phenotype variance, hampering the clinical translation of these findings [@doi:10.1038/s41576-019-0127-1]. -Recent theories, like the omnigenic model for complex traits [@pmid:28622505; @pmid:31051098], argue that these observations are explained by highly-interconnected gene regulatory networks, with some core genes having a more direct effect on the phenotype than others. +Recent theories, like the omnigenic model for complex traits [@pmid:28622505; @pmid:31051098], argue that these observations are explained by highly interconnected gene regulatory networks, with some core genes having a more direct effect on the phenotype than others. Using this omnigenic perspective, we and others [@doi:10.1101/2021.07.05.450786; @doi:10.1186/s13040-020-00216-9; @doi:10.1101/2021.10.21.21265342] have shown that integrating gene co-expression networks in genetic studies could potentially identify core genes that are missed by linear-only models alone like GWAS. Our results suggest that building these networks with more advanced and efficient correlation coefficients could better estimate gene co-expression profiles and thus more accurately identify these core genes. Approaches like CCC could play a significant role in the precision medicine field by providing the computational tools to focus on more promising genes representing potentially better candidate drug targets. @@ -41,10 +41,10 @@ Approaches like CCC could play a significant role in the precision medicine fiel Our analyses have some limitations. We worked on a sample with the top variable genes to keep computation time feasible. -Although CCC is much faster than MIC, Pearson and Spearman are still the most computationally efficient since they only rely on simple data statistics. -Our results, however, reveal the advantages of using more advanced coefficients like CCC for detecting and studying more intricate molecular mechanisms that replicated in independent datasets. -The application of CCC on larger compendia, such as recount3 [@pmid:34844637] with thousands of heterogeneous samples across different conditions, can reveal other potentially meaningful gene interactions. -The single parameter of CCC, $k_{\mathrm{max}}$, controls the maximum complexity of patterns found and also impacts the compute time. +Although CCC is much faster than MIC, Pearson, and Spearman are still the most computationally efficient since they only rely on simple data statistics. +Our results, however, reveal the advantages of using more advanced coefficients like CCC for detecting and studying more intricate molecular mechanisms that are replicated in independent datasets. +The application of CCC on larger compendia, such as recount3 [@pmid:34844637], with thousands of heterogeneous samples across different conditions, can reveal other potentially meaningful gene interactions. +The single parameter of CCC, $k_{\mathrm{max}}$, controls the maximum complexity of patterns found and also impacts the computation time. Our analysis suggested that $k_{\mathrm{max}}=10$ was sufficient to identify both linear and more complex patterns in gene expression. A more comprehensive analysis of optimal values for this parameter could provide insights to adjust it for different applications or data types. @@ -52,6 +52,6 @@ A more comprehensive analysis of optimal values for this parameter could provide While linear and rank-based correlation coefficients are exceptionally fast to calculate, not all relevant patterns in biological datasets are linear. For example, patterns associated with sex as a biological variable are not apparent to the linear-only coefficients that we evaluated but are revealed by not-only-linear methods. Beyond sex differences, being able to use a method that inherently identifies patterns driven by other factors is likely to be desirable. -Not-only-linear coefficients can also disentangle intricate yet relevant patterns from expression data alone that were replicated in models integrating different data modalities. +Not-only-linear coefficients can also disentangle intricate yet relevant patterns from gene expression data alone that were replicated in models integrating different data modalities. CCC, in particular, is highly parallelizable, and we anticipate efficient GPU-based implementations that could make it even faster. The CCC is an efficient, next-generation correlation coefficient that is highly effective in transcriptome analyses and potentially useful in a broad range of other domains. diff --git a/content/08.01.methods.ccc.md b/content/08.01.methods.ccc.md index a4d59c4..2d7e9a8 100644 --- a/content/08.01.methods.ccc.md +++ b/content/08.01.methods.ccc.md @@ -9,19 +9,19 @@ A Docker image is provided to use the same runtime environment. The Clustermatch Correlation Coefficient (CCC) computes a similarity value $c \in \left[0,1\right]$ between any pair of numerical or categorical features/variables $\mathbf{x}$ and $\mathbf{y}$ measured on $n$ objects. CCC assumes that if two features $\mathbf{x}$ and $\mathbf{y}$ are similar, then the partitioning by clustering of the $n$ objects using each feature separately should match. -For example, given $\mathbf{x}=(11, 27, 32, 40)$ and $\mathbf{y}=10x=(110, 270, 320, 400)$, where $n=4$, partitioning each variable into two clusters ($k=2$) using their medians (29.5 for $\mathbf{x}$ and 295 for $\mathbf{y}$) would result in partition $\Omega^{\mathbf{x}}_{k=2}=(1, 1, 2, 2)$ for $\mathbf{x}$, and partition $\Omega^{\mathbf{y}}_{k=2}=(1, 1, 2, 2)$ for $\mathbf{y}$. +For example, given $\mathbf{x}=(11, 27, 32, 40)$ and $\mathbf{y}=10\mathbf{x}=(110, 270, 320, 400)$, where $n=4$, partitioning each variable into two clusters ($k=2$) using their medians (29.5 for $\mathbf{x}$ and 295 for $\mathbf{y}$) would result in partition $\Omega^{\mathbf{x}}_{k=2}=(1, 1, 2, 2)$ for $\mathbf{x}$, and partition $\Omega^{\mathbf{y}}_{k=2}=(1, 1, 2, 2)$ for $\mathbf{y}$. Then, the agreement between $\Omega^{\mathbf{x}}_{k=2}$ and $\Omega^{\mathbf{y}}_{k=2}$ can be computed using any measure of similarity between partitions, like the adjusted Rand index (ARI) [@doi:10.1007/BF01908075]. In that case, it will return the maximum value (1.0 in the case of ARI). Note that the same value of $k$ might not be the right one to find a relationship between any two features. For instance, in the quadratic example in Figure @fig:datasets_rel, CCC returns a value of 0.36 (grouping objects in four clusters using one feature and two using the other). If we used only two clusters instead, CCC would return a similarity value of 0.02. -Therefore, the CCC algorithm (shown below) searches for this optimal number of clusters given a maximum $k$, which is its single parameter $k_{\mathrm{max}}$. +Therefore, the CCC algorithm (shown below) searches for the optimal number of clusters given a maximum $k$, which is its single parameter $k_{\mathrm{max}}$. ![ ](images/intro/ccc_algorithm/ccc_algorithm.svg "CCC algorithm"){width="75%"} -The main function of the algorithm, `ccc`, generates a list of partitionings $\Omega^{\mathbf{x}}$ and $\Omega^{\mathbf{y}}$ (lines 14 and 15), for each feature $\mathbf{x}$ and $\mathbf{y}$. -Then, it computes the ARI between each partition in $\Omega^{\mathbf{x}}$ and $\Omega^{\mathbf{y}}$ (line 16), and then it keeps the pair that generates the maximum ARI. +The main function of the algorithm, `ccc`, generates a list of partitionings $\Omega^{\mathbf{x}}$ and $\Omega^{\mathbf{y}}$ (lines 14 and 15) for each feature $\mathbf{x}$ and $\mathbf{y}. +Then, it computes the ARI between each partition in $\Omega^{\mathbf{x}}$ and $\Omega^{\mathbf{y}}$ (line 16) and keeps the pair that generates the maximum ARI. Finally, since ARI does not have a lower bound (it could return negative values, which in our case are not meaningful), CCC returns only values between 0 and 1 (line 17). @@ -31,13 +31,13 @@ If the feature is categorical (lines 7 to 9), the categories are used to group o Consequently, since features are internally categorized into clusters, numerical and categorical variables can be naturally integrated since clusters do not need an order. -For all our analyses we used $k_{\mathrm{max}}=10$. -This means that for each gene pair, 18 partitions are generated (9 for each gene, from $k=2$ to $k=10$), and 81 ARI comparisons are performed. +For all our analyses, we used $k_{\mathrm{max}}=10$. +This means that for each gene pair, 18 partitions are generated (9 for each gene, from $k=2$ to $k=10), and 81 ARI comparisons are performed. Smaller values of $k_{\mathrm{max}}$ can reduce computation time, although at the expense of missing more complex/general relationships. Our examples in Figure @fig:datasets_rel suggest that using $k_{\mathrm{max}}=2$ would force CCC to find linear-only patterns, which could be a valid use case scenario where only this kind of relationships are desired. In addition, $k_{\mathrm{max}}=2$ implies that only two partitions are generated, and only one ARI comparison is performed. In this regard, our Python implementation of CCC provides flexibility in specifying $k_{\mathrm{max}}$. -For instance, instead of the maximum $k$ (an integer), the parameter could be a custom list of integers: for example, `[2, 5, 10]` will partition the data into two, five and ten clusters. +For instance, instead of the maximum $k$ (an integer), the parameter could be a custom list of integers: for example, `[2, 5, 10]` will partition the data into two, five, and ten clusters. For a single pair of features (genes in our study), generating partitions or computing their similarity can be parallelized. diff --git a/content/08.05.methods.data.md b/content/08.05.methods.data.md index eaaf068..d587931 100644 --- a/content/08.05.methods.data.md +++ b/content/08.05.methods.data.md @@ -2,4 +2,4 @@ We downloaded GTEx v8 data for all tissues, normalized using TPM (transcripts per million), and focused our primary analysis on whole blood, which has a good sample size (755). We selected the top 5,000 genes from whole blood with the largest variance after standardizing with $log(x + 1)$ to avoid a bias towards highly-expressed genes. -We then computed Pearson, Spearman, MIC and CCC on these 5,000 genes across all 755 samples on the TPM-normalized data, generating a pairwise similarity matrix of size 5,000 x 5,000. +We then computed Pearson, Spearman, MIC, and CCC on these 5,000 genes across all 755 samples on the TPM-normalized data, generating a pairwise similarity matrix of size 5,000 x 5,000. diff --git a/content/08.15.methods.giant.md b/content/08.15.methods.giant.md index f21c735..35d7a90 100644 --- a/content/08.15.methods.giant.md +++ b/content/08.15.methods.giant.md @@ -1,19 +1,18 @@ ### Tissue-specific network analyses using GIANT {#sec:giant} -We accessed tissue-specific gene networks of GIANT using both the web interface and web services provided by HumanBase [@url:https://hb.flatironinstitute.org]. +We accessed tissue-specific gene networks of GIANT using both the web interface and web services provided by HumanBase (https://hb.flatironinstitute.org). The GIANT version used in this study included 987 genome-scale datasets with approximately 38,000 conditions from around 14,000 publications. -Details on how these networks were built are described in [@doi:10.1038/ng.3259]. -Briefly, tissue-specific gene networks were built using gene expression data (without GTEx samples [@url:https://hb.flatironinstitute.org/data]) from the NCBI's Gene Expression Omnibus (GEO) [@doi:10.1093/nar/gks1193], protein-protein interaction (BioGRID [@pmc:PMC3531226], IntAct [@doi:10.1093/nar/gkr1088], MINT [@doi:10.1093/nar/gkr930] and MIPS [@pmc:PMC148093]), transcription factor regulation using binding motifs from JASPAR [@doi:10.1093/nar/gkp950], and chemical and genetic perturbations from MSigDB [@doi:10.1073/pnas.0506580102]. -Gene expression data were log-transformed, and the Pearson correlation was computed for each gene pair, normalized using the Fisher's z transform, and z-scores discretized into different bins. -Gold standards for tissue-specific functional relationships were built using expert curation and experimentally derived gene annotations from the Gene Ontology. -Then, one naive Bayesian classifier (using C++ implementations from the Sleipnir library [@pmid:18499696]) for each of the 144 tissues was trained using these gold standards. -Finally, these classifiers were used to estimate the probability of tissue-specific interactions for each gene pair. +Details on how these networks were built are described in a previous study (doi:10.1038/ng.3259). +Tissue-specific gene networks were constructed using gene expression data (without GTEx samples from https://hb.flatironinstitute.org/data) from the NCBI's Gene Expression Omnibus (GEO, doi:10.1093/nar/gks1193), protein-protein interaction data from BioGRID, IntAct, MINT, and MIPS, transcription factor regulation using binding motifs from JASPAR, and chemical and genetic perturbations from MSigDB. +Gene expression data were log-transformed, and the Pearson correlation coefficient was computed for each gene pair, normalized using Fisher's z transform, and z-scores discretized into different bins. +Gold standards for tissue-specific functional relationships were established using expert curation and experimentally derived gene annotations from the Gene Ontology. +Subsequently, one naive Bayesian classifier for each of the 144 tissues was trained using these gold standards. +These classifiers were then utilized to estimate the probability of tissue-specific interactions for each gene pair. +The C++ implementations from the Sleipnir library were used for the classifier training process (pmid:18499696). -For each pair of genes prioritized in our study using GTEx, we used GIANT through HumanBase to obtain -1) a predicted gene network for blood (manually selected to match whole blood in GTEx) and -2) a gene network with an automatically predicted tissue using the method described in [@doi:10.1101/gr.155697.113] and provided by HumanBase web interfaces/services. +For each pair of genes prioritized in our study using GTEx, we used GIANT through HumanBase to obtain 1) a predicted gene network for blood (manually selected to match whole blood in GTEx) and 2) a gene network with an automatically predicted tissue using the method described in [@doi:10.1101/gr.155697.113] and provided by HumanBase web interfaces/services. Briefly, the tissue prediction approach trains a machine learning model using comprehensive transcriptional data with human-curated markers of different cell lineages (e.g., macrophages) as gold standards. Then, these models are used to predict other cell lineage-specific genes. In addition to reporting this predicted tissue or cell lineage, we computed the average probability of interaction between all genes in the network retrieved from GIANT. -Following the default procedure used in GIANT, we included the top 15 genes with the highest probability of interaction with the queried gene pair for each network. +Following the default procedure used in GIANT, we included the top 15 genes with the highest probability of interaction with the queried gene pair for each network. diff --git a/content/08.20.methods.mic.md b/content/08.20.methods.mic.md index cf22ab3..a51a554 100644 --- a/content/08.20.methods.mic.md +++ b/content/08.20.methods.mic.md @@ -1,6 +1,6 @@ ### Maximal Information Coefficient (MIC) {#sec:methods:mic} We used the Python package `minepy` [@doi:10.1093/bioinformatics/bts707; @url:https://github.com/minepy/minepy] (version 1.2.5) to estimate the MIC coefficient. -In GTEx v8 (whole blood), we used MICe (an improved implementation of the original MIC introduced in [@Reshef2016]) with the default parameters `alpha=0.6`, `c=15` and `estimator='mic_e'`. +In GTEx v8 (whole blood), we used MICe (an improved implementation of the original MIC introduced in [@Reshef2016]) with the default parameters `alpha=0.6`, `c=15`, and `estimator='mic_e'`. We used the `pairwise_distances` function from `scikit-learn` [@Sklearn2011] to parallelize the computation of MIC on GTEx. For our computational complexity analyses (see [Supplementary Material](#sec:time_test)), we ran the original MIC (using parameter `estimator='mic_approx'`) and MICe (`estimator='mic_e'`). diff --git a/content/20.00.supplementary_material.md b/content/20.00.supplementary_material.md index bb72625..f3e9f7f 100644 --- a/content/20.00.supplementary_material.md +++ b/content/20.00.supplementary_material.md @@ -2,7 +2,7 @@ ### Supplementary Note 1: Comparison with the Maximal Information Coefficient (MIC) on gene expression data {#sec:mic} -We compared all the coefficients in this study with MIC [@pmid:22174245], a popular nonlinear method that can find complex relationships in data, although very computationally intensive [@doi:10.1098/rsos.201424]. +We compared all the coefficients in this study with MIC [@pmid:22174245], a popular nonlinear method that can find complex relationships in data, although it is very computationally intensive [@doi:10.1098/rsos.201424]. We ran MICe (see Methods) on all possible pairwise comparisons of our 5,000 highly variable genes from whole blood in GTEx v8. This took 4 days and 19 hours to finish (compared with 9 hours for CCC). Then we performed the analysis on the distribution of coefficients (the same as in the main text), shown in Figure @fig:dist_coefs_mic.