key: cord-0289871-f5w05rc2
authors: de Jong, Tristan; Guryev, Victor; Moshkin, Yury M.
title: Discovery of pharmaceutically-targetable pathways and prediction of survivorship for pneumonia and sepsis patients from the view point of ensemble gene noise
date: 2020-04-11
journal: bioRxiv
DOI: 10.1101/2020.04.10.035717
sha: cf05c74c5d0778e1f4c7868b13d5f0318407a351
doc_id: 289871
cord_uid: f5w05rc2

Finding novel biomarkers for human pathologies and predicting clinical outcomes for patients is rather challenging. This stems from the heterogenous response of individuals to disease which is also reflected in the inter-individual variability of gene expression responses. This in turn obscures differential gene expression analysis (DGE). In the midst of the COVID-19 pandemic, we wondered whether an alternative to DGE approaches could be applied to dissect the molecular nature of a host-response to infection exemplified here by an analysis of H1N1 influenza, community/hospital acquired pneumonia (CAP) and sepsis. To this end, we turned to the analysis of ensemble gene noise. Ensemble gene noise, as we defined it here, represents a variance within an individual for a collection of genes encoding for either members of known biological pathways or subunits of annotated protein complexes. From the law of total variance, ensemble gene noise depends on the stoichiometry of the ensemble genes’ expression and on their average noise (variance). Thus, rather than focusing on specific genes, ensemble gene noise allows for the holistic identification and interpretation of gene expression disbalance on the level of gene networks and systems. Comparing H1N1, CAP and sepsis patients we spotted common disturbances in a number of pathways/protein complexes relevant to the sepsis pathology which lead to an increase in the ensemble gene noise. Among others, these include mitochondrial respiratory chain complex I and peroxisomes which could be readily targeted for adjuvant treatment by methylene blue and 4-phenylbutyrate respectively. Finally, we showed that ensemble gene noise could be successfully applied for the prediction of clinical outcome, namely mortality, of CAP and sepsis patients. Thus, we conclude that ensemble gene noise represents a promising approach for the investigation of molecular mechanisms of a pathology through a prism of alterations in coherent expression of gene circuits.

Both viral and bacterial pneumonia may lead to a life-threatening condition, namely sepsis.

Most notable cases, in the public perception, include pandemic viral infections, such as the 2009 swine flu pandemic caused by H1N1 [1] and more recently, the 2019 coronavirus disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) [2] .

Like with any other annual severe acute respiratory infections (SARI), these pandemics resulted in a significant raise in patients with sepsis at intensive care units [3, 4] . Sepsis is a complex reaction of the host (human) to a systemic infection (viral or bacterial) often resulting in septic shock or death [5] [6] [7] . A problem of sepsis treatment, the prediction of patients' clinical outcomes and the risks of mortality relates to the highly heterogenous nature of sepsis [8] .

Thus, despite recent progress in identification of molecular biomarkers for sepsis [8] [9] [10] [11] [12] [13] [14] [15] , treatment remains mainly non-curative and clinical outcomes are mostly inferred from clinical signs [5] .

A canonical approach for the identification of disease biomarkers and their potential therapeutic targets relies on differential gene expression (DGE) analysis either on RNA or protein levels. This stems from a classical gene regulation Jacob-Monod model, which implies a specific gene expression response (up-or down-regulation) to a specific signal (see recent perspective on historical origins of the model in [16] . However, gene expression is a stochastic process and cellular responses to signals often trigger a cascade of changes in gene expression, making it difficult to discover specific targets and biomarkers for a disease.

The stochastic nature of gene expression implies a natural variation in RNA and protein copy numbers [17] . According to the fluctuation-response relationship [18, 19] , an amount of gene expression response to a signal (fluctuation) is proportional to its variance (or squared biological coefficient of variation -bcv 2 ) for log-scaled values of RNA copy number [20] .

Consequently, statistical inference of differentially expressed genes will be biased towards genes with high variance (bcv 2 ) ( Figure S1 ). This leads to a set of intrinsic problems with DGE analysis. 1) genes with increased variability in expression will strongly respond to any cellular signal aimed at them. However, these genes may not necessarily be causative for a diseased state. Even under normal circumstances they exhibit large fluctuations and, thus, are looseregulated. 2) In contrast, genes with a low variability will respond only modestly, but these genes are tight-regulated and any fluctuations in their expression might be causative for a diseased state.

Upon calling significantly changed genes, to make biological sense, these genes are mapped to known biological pathways, such as GO or KEGG [21, 22] , or to subunits of protein complexes annotated by CORUM or other interaction databases [23] . Thus, a second statistical test is required, namely gene set enrichment analysis (GSEA). However, this is not without its own caveats. The major one is that GSEA depends on the statistical inference of DGE and DGE cut-offs [24, 25] . As a result, biological interpretations from DGE might be drastically affected by pitfalls arising from the fluctuation-response relationship, DGE thresholding and the choice of statistical approach for GSEA.

To circumvent this, we reasoned that 1) genes do not function in isolation, but rather act as ensembles representing biological pathways and/or subunits of protein complexes. From the whole blood expression profiles of patients under intensive care treatment we estimated how ensemble gene noise corresponds to a pathological state, such as sepsis, community/hospital acquired pneumonia (CAP) or viral H1N1 pneumonia (H1N1). From this analysis we identified a number of pathways for which ensemble gene noise associated positively with an individual health/disease state treated as an ordinal variable (healthy < early H1N1 phase < late H1N1 phase and healthy < sepsis/CAP survived < sepsis/CAP deceased patients). Finally, we identified pathways and complexes where deregulation is associated with a poor prognosis and predicted the clinical outcome (survival/mortality) for CAP/sepsis patients based on ensemble gene noise with high accuracy. We concluded that the ensemble gene noise provides a powerful tool for the discovery of systemic disease biomarkers, pharmaceutically targetable pathways and the prediction of a disease clinical outcome.

Sepsis is thought to trigger a plethora of heterogenous host responses to a systemic infection [5, 8] . We reasoned that this heterogeneity might be reflected in the inter-individual gene expression variability (standard deviation - or variance - 2 ). Considering that a) RNA copy number is a mixed Poisson (e.g. negative binomial) random variable [26] and that b) logtransformed microarray hybridization signal intensities correlate with log-transformed RNAseq copy numbers [27] . It is easy to show that the variance of log gene expression approximates the biological coefficient of variation (bcv 2 ) [20] . From the first-order Taylor We estimated the dispersions for whole blood log gene expressions in CAP and sepsis patients (8826 genes), and H1N1 infected patients (7240 genes) from the two data sets GSE65682 and GSE21802 respectively (for a detailed description of cohorts see original studies and Methods) [8, 11, 28] . For CAP and sepsis patients we also accounted for age, including it as a random variable in the Generalized Additive Model for Location, Scale and Shape (GAMLSS) [29] , see Methods. On average, the dispersions in log gene expressions in CAP, sepsis and H1N1 patients were significantly higher as compared to healthy individuals ( Figure 1A ). To that, for CAP patents' dispersions in log gene expressions were significantly higher for deceased patients as compared to those survived. Likewise, for H1N1 patients, dispersions in log gene expressions further increased in the late phase of infection ( Figure 1A ). For sepsis patients, on average dispersions in log gene expressions were comparable between survived and deceased patients for all analysed genes ( Figure 1A ). However, for genes for which dispersions changed significantly between healthy individuals and sepsis patients (Bonferroni adjusted p ≤ 0.05), their dispersions on average were higher in the deceased patients as compared to the survived (p < 0.001). Together, these suggest that host response to infection increases the biological coefficients of variations in genes' RNA copy numbers (as σ ) and substantiates heterogeneity in the pathogenesis of sepsis [8] from the gene expression perspective.

Because of the fluctuation-response relationship [18] , absolute changes in the mean log gene expressions (||) in response to infection (CAP, H1N1) and sepsis correlated significantly with the variances of the log gene expressions ( Figure 1B) . Interestingly, we also noted significant correlations between the absolute changes in inter-individual gene expression variabilities (| 2 |) and the variances of log genes expressions ( Figure 1C ). Consequently, || and | 2 | were also correlated ( Figure 1D ). Thus, we conclude that H1N1, CAP and sepsis result in coordinated changes in both the mean and heterogeneity of the expression of genes and that magnitudes of these changes depend on genes' biological coefficients of variation.

Both the mean and variance relate to population (inter-individual) statistics reflecting distinct aspects of gene regulation. Changes in means fit the classical DGE view on gene response to a pathology and other biological processes, while changes in variances yield a view on heterogeneity of gene response. However, as we noted before (Figure 1 and S1), statistical inference of these changes is biased towards higher a significance for genes with a high biological coefficient of variation. Although changes in RNA copy number can serve in practical applications for diagnostics of a disease and clinical outcomes, inter-individual variability cannot be used for diagnosis. At the same time, stochastic fluctuations in gene expression remain attractive for the dissection of novel molecular mechanisms of a pathology.

Therefore, we expect that estimation of ensemble gene noise may provide additional benefits for diagnostics by quantifying fluctuations, while being informative for personalized treatment.

We define ensemble gene noise as the variance of log-transformed, normalized expression levels for a collection of genes , … , encoding for either proteins of a pathway or subunits of a protein complex. To this end, we mapped genes to the KEGG-annotated pathways and the CORUM-annotated protein complexes [22, 23] . From the law of total variance: We, then, correlated Var for ensembles with H1N1, CAP and sepsis disease states. For H1N1 viral infection, disease state can be clearly ranked: non-infected (healthy) < early phase < late phase of infection, thus it represents an ordinal variable [28] . For CAP and sepsis patients, we assumed that a condition of the deceased patients was worse than that of the survived. We considered that healthy < survived < deceased can also be represented as ordinal disease state variable. Circumstantially, this is supported by distinct blood gene expression endotypes [8] and an increased gene expression heterogeneity ( Figure 1A ). Kendall rank correlation identified a number of pathways and protein complexes for which ensemble gene noise was positively and significantly associated with the disease state in H1N1 (FDR ≤ 0.05), and CAP and sepsis patients (Bonferroni-adjusted p ≤ 0.05) ( Figure 2A ). None of the pathways or gene complexes were negatively associated with the disease state at the specified significance thresholds. We used different p value adjustment procedures (FDR -less conservative, and Bonferroni -more conservative) for H1N1, CAP and sepsis patents due to the large differences in sample sizes (number of patients) between these data sets.

Out of all gene ensembles, 13 of them proved to be consistent and correlated to the increased disease state in ensemble gene noise in all three disease conditions (Figure 2A , B, Table S1A ).

Most of these gene ensembles (pathways) are known to be involved in the pathology of sepsis through multiple experimental evidences (Table 1) , thus substantiating a power of ensemble gene noise analysis. However, ensemble gene noise yields novel insights into the molecular mechanisms of sepsis (H1N1, CAP or other-causes of sepsis) by suggesting a holistic misregulation in stoichiometry and gene noise for these gene ensembles.

We also identified 5 gene ensembles for which ensemble gene noise was positively and significantly correlated with the disease state in H1N1 and CAP patients ( Figure 2A , Table   S1B ). However, ensemble gene noise for these pathways was also significantly increased in sepsis patients (t-test, Bonferroni adjusted p < 0.01) despite insignificant rank correlation. To that, some of these pathways can be implicated in the pathology of sepsis (Table 1) . Two of these ensembles were represented by genes encoding mitochondrial respiratory chain complex I (Complex I) ( Figure 2C ). From the point of view of ensemble gene noise this suggests an altered stoichiometry and gene noise in the expression of the subunits of the Complex I which, as a result, might lead to its improper assembly and function in H1N1, CAP and sepsis patients.

Indeed, it has been established that the activity of the Complex I is decreased and correlates with the severity of sepsis [30] . Complex I is the first set of enzymes of the respiratory chain and it is the entry point for most electrons into the electron transport chain [31] . Interestingly, however, in case of the Complex I inhibition or deregulation, methylene blue (MB) can bypass it by acting as alternative redox mediator in the electron transport chain, thus, restoring mitochondrial respiration [32, 33] ( Figure 2D ). MB is also considered to be a promising therapeutic in treatment of septic shock [34, 35] . Thus, ensemble gene noise might provide a simple yet powerful explanatory shortcut, from the expression of thousands of genes to the function of gene ensembles and possible pharmaceutical targets.

Treatment of sepsis is challenging and mortality rates among sepsis patients are high. Yet, prediction of clinical outcome is also challenging due to heterogeneity in the pathology [8] and gene expression ( Figure 1A ). Recently, Molecular Diagnosis and Risk Stratification of Sepsis (MARS) consortium identified the Mars1 gene expression endotype which was significantly associated with acute (28-day) mortality, however, for other endotypes Mars2-4 poorly discriminated between the survival and mortality of patients [8] . Thus, we wondered whether the clinical outcome (mortality) could be predicted from the ensemble gene noise.

To this end, we trained binary logistic gradient boosted regression tree models using survival and acute mortality as a binary response variable for clinical outcome and patients' age and blood ensemble gene noise as models' features. The models were trained with XGBoost [36] . Overall, class-imbalance, noise due to the inter-individual heterogeneity and highdimensionality of model features are among the major problems of machine learning [37] . In part, ensemble gene noise leads to a reduction in inter-individual variability ( Figure S3) AUCs for the discovery and validation cohorts were 0.871 and 0.707 respectively, suggesting a reasonable accuracy of the model. However, from the model scores, and evaluation of the model specificity/sensitivity it appears that the model is biased towards the prediction of major class (survived) ( Figure 3A , Table 2 and Table S2A ). Thus, class prediction balanced accuracies (bACC = Specificity/2 + Sensitivity/2) were 0.799 and 0.701 for the discovery and validation cohorts respectively. Nonetheless, the survival probability for patients predicted to have a high risk of mortality was significantly lower than the survival probability of patients predicted to have low risk of mortality in both discovery and validation cohorts. To that, our model better predicts the risks of mortality as compared to the Mars1 endotype inferred from the log gene expression unsupervised learning ( Figure 3C ) [8] . Potentially, this could be due to a lower inter-individual variability of gene ensembles noise as compared to log gene expression ( Figure S3 ).

In an attempt to increase the prediction accuracy, we trained to separated gradient boosted tree models for CAP ( Figure 4 ) and sepsis ( Figure 5 ) patients. Indeed, in both cases the accuracy of the prediction of the minor class (deceased patients) increased (Table 2 and S2) in both discovery and validation cohorts. Likewise, AUCs for the validation cohorts were also higher as compared to the model predicting mortality for both (CAP and sepsis) type of patients (compare Figure 4B and 5B with Figure 3B ). To that, differences in AUCs between discovery and validation cohorts were lower for the models predicting mortality separately for CAP and sepsis patients as for the model trained on both type of patients. This was especially evident for the model predicting mortality for the CAP patients ( Figure 4B ). Thus, knowing the cause of sepsis improves the prediction accuracy of the models.

Finally, it has to be noted that both the feature selection and gradient boosted regression trees allow for the ranking of the model features' importance (Figures 3D, 4D, 5D and Table S3 ).

First, it turned out that a patients' age does not noticeably contribute to the prediction of mortality in CAP patients and it ranks low in the prediction of mortality of sepsis patients.

Second, high ranking gene ensembles (pathways) could be immediately associated with host response to infection and, thus, pathology of the sepsis. These include legionellosis (a pathway responsible for atypical pneumonia caused by Legionella bacteria), epithelial cell signalling in

Helicobacter pylori infection and leishmaniasis, and imbalances in these pathways either caused by corresponding infections or immune activation could lead to the sepsis [38] [39] [40] . To that, ensemble gene noise in immune pathways, such as rheumatoid arthritis and primary immunodeficiency, contribute to the prediction of clinical outcome in sepsis patients ( Figure   3D , 5D and Table S3 ). Thus, we conclude that the ensemble gene noise uncovers novel approaches and insights to the discovery of biomarkers, prediction of clinical outcome and to the molecular mechanisms of a pathology from the point of view of imbalances in stoichiometry and gene noise of expression in gene ensembles.

Here we attempted a dissection of molecular mechanisms of human pathology, exemplified by This approach offers an alternative, but non-mutually exclusive to the DGE interpretation of a molecular basis of disease and both have their own strengths and weaknesses.

We noted in the introduction that due to a fluctuation-response a statistical inference of DGE might be biased towards genes with a high inter-individual variability, i.e. "noisy" genes ( Figure S1 ) [18, 19] . However, the same applies to ensemble gene noise ( Figure S4 ). This imposes a certain problem to the interpretation of both DGE and ensemble gene noise. On one hand, it can be suggested that large deviations in expression of genes and ensembles, which are naturally prone to high fluctuations, might not be causative for a disease, as an organism is already adapted to such variations. On the other hand, these genes/ensembles themselves might play an important adaptive role [41] and their over-response could lead to a disease. At the moment it seems difficult to come to a resolution between these two possibilities, but they should be considered, specifically in identification of pharmaceutical targets: genes or gene ensembles (pathways, protein complexes).

As compared to DGE, ensemble gene noise provides a holistic interpretation to mis-regulation in gene expression under pathologic or other conditions. As it operates on the level of gene ensembles it does not require gene set enrichment analysis (GSEA), thus it circumvents potential pitfalls of GSEA associated with the cut-off problem of DGE [24, 25] . As any gene expression analysis ensemble gene noise relies on the quality and completeness of pathways and the protein complexes' annotation. Finally, we noted that inter-individual variability of ensemble gene noise is significantly less than that of individual gene expression ( Figure S3 ).

This, in turn, might improve the accuracy of diagnostic and clinical outcome models. Though it might come at the expense of less features being available for the selection and training of models. At the same time, in future studies, both DGE and ensemble gene noise could be combined.

In this study we applied the concept of ensemble gene noise to the analysis of critically ill H1N1, CAP and sepsis patients [8, 28] . We noted a large-scale gene response in two dimensions: on the level of mean gene expression and on the level of variance (inter-individual variability). Interestingly, both responses were correlated ( Figure 1D ) and both were dependent on gene variance suggesting that the fluctuation-response might drive changes in these two parameters of gene expression co-ordinately [18] . In all three cases (H1N1, CAP and sepsis), inter-individual variability was increased for a bulk of the genes. Consequently, we only identified pathways or gene complexes for which ensemble gene noise was significantly increased for H1N1, CAP and sepsis patients as compared to healthy individuals. This suggests that inter-individual gene expression variability is a prominent driver of ensemble gene noise in these patients.

it is difficult to identify a reasonably small set of either genes or gene ensembles for biological interpretation. Thus, we only focused on the pathways (protein complexes) for which ensemble gene noise increased in all three cases and correlated these with a disease state (Figure 2A ).

From this intersection we inferred 13 pathways most of which have been previously implicated in sepsis (Table 1 ). To that, 5 pathways (protein complexes) showed significant association of ensemble gene noise with H1N1 infection phase and CAP disease state and for which ensemble gene noise also increased significantly in sepsis patients ( Figure 2A) . Potentially, these pathways could be targeted for adjuvant treatment of sepsis. Especially, we consider mitochondrial respiratory chain complex I (Complex I) ( Figure 2D ) and peroxisome promising for pharmaceutical targeting. Increased ensemble gene noise for the Complex I would imply either altered stoichiometry, or increased gene expression noise for genes encoding subunits of the Complex I or both. As a result, this might lead to improper assembly of the Complex I and affecting its function. The impaired Complex I function can be bypassed by an alternative redox mediator, such as methylene blue [32, 33] . To that, methylene blue is a selective inhibitor of the nitric oxide-cyclic guanosine monophosphate (NO-cGMP) pathway [35] and increased NO levels is a hallmark of sepsis [42] . Some clinical studies have already indicated a beneficial role of methylene blue in the treatment of sepsis [34, 35] . Similar to mitochondrial respiration, peroxisomes also play an important role in the pathology of sepsis as the dysfunction of peroxisomes results in oxidative stress [43] . Again, an increased ensemble gene noise for peroxisome pathway indicates a potential mechanism for such dysfunction in H1N1, CAP and sepsis patients. Potentially peroxisome biogenesis could be restored by 4-phenylbutyrate and

there several studies indicating its positive role in treatment of sepsis [44, 45] . Considering future directions, it could be proposed that search for epigenetic modulators of ensemble gene noise might represent a novel pharmaceutical avenue for adjuvant treatments of sepsis.

Finally, we explored the possibility to use ensemble gene noise in the prediction of clinical outcomes. Previously some promising biomarkers and gene expression endotypes associated with septic shock and mortality have been identified based on DGE analysis [8, 9] . However, as already mentioned, ensemble gene noise looks at gene expression from a different, yet complementary, angle, thus enabling the identification of novel pathways and biomarkers for sepsis and other diseases. To that, models predicting pathology based on ensemble gene noise could potentially be more robust, as inter-individual variability for ensemble gene noise is lower than that for log gene expression ( Figure S3 ). Furthermore, Gradient boosted regression tree models trained on CAP and sepsis patients to predict their mortality had a good accuracy on validation cohort ( Figure 3 , Table 2 ). These outperformed predictions based on the Mars1 gene expression endotype, which was shown to associate with a poor prognosis [8] , both on the discovery and validation cohorts ( Figure 3C ). Interestingly, some ensemble gene noise features selected statistically for the models predicting mortality in both CAP/sepsis-, CAPand sepsis-patients couldimmediately be related to the host's response to infection. For example, increases in ensemble gene noise in legionellosis, epithelial cell signalling in of sepsis and its outcome.

In conclusion, here we showed a potential of ensemble gene noise in the biological interpretation of a disease, the identification of pharmaceutically targetable pathways, novel biomarkers, and the prediction of clinical outcome. Together, we believe that ensemble gene noise analysis could be broadly applied alongside with DGE to dissect molecular mechanisms of the pathology in two complementary dimensions: in Jacob-Monod dimension of specific gene regulation and in a novel dimension of holistic gene circuit regulation.

GSE65682 Affymetrix Human Genome U219 Array whole blood gene expression profiles were used for the analysis of community/hospital acquired pneumonia (CAP) and sepsis patients [8, 11] . In brief, the cohort consisted of 42 healthy individuals ( GSE21802 Illumina human-6 v2.0 expression bead-chip whole blood gene expression profiles were used for the analysis of H1N1 infected patients [28] . The cohort consisted of 4 healthy individuals and 19 H1N1 patients (8 in early and 11 in late phase of the disease). The early phase was defined as early, from the onset of symptoms -day 0 to day 8 , and late -from day 9 and above. The statistics of the cohorts is given in Table 1 of [28] , however neither sex nor age assignments were available for the patients from the GSE21802 series annotation.

GSE65682 microarrays signal intensities were pre-processed (background corrected and RMA-normalized) with the Bioconductor oligo package [46] . Lowly-expressed and outlier genes were identified in high dimensions using the spatial signs (sign2) algorithm of mvouliter R package with a critical value for outlier detection at 0.9.The robust principal components explained a variance of 0.95 [47] . GSE21802 signal intensities significantly above the background were quantile normalized [48] . Genes were annotated with Bioconductor hgu219.db and illuminaHumanv2.db database packages for GSE65682 (8826 genes) and GSE21802 (7240 genes) respectively.

Statistical analysis was done using R and R/Bioconductor packages [49] .

To estimate the inter-individual gene expression variability for healthy, CAP and sepsis patients we accounted for age as a random effect. To this end, we used Generalized Additive

Model for Location, Scale and Shape (GAMLSS) [20, 29] . In brief, for normally distributed [20] .

Gene ensemble lists were generated by the mapping of genes to the KEGG-annotated biological pathways or CORUM-annotated subunits of mammalian protein complexes [22, 23] . Their gene noise was estimated for each individual by calculating the variances of log-transformed expressions of genes for each ensemble ( Figure 1S ). Estimates of gene ensembles noise were correlated with the disease states (healthy < early phase < late phase for H1N1 and healthy < survived < deceased for CAP and sepsis) by Kendall rank correlation, treating the disease state as an ordinal variable. Linear trends between disease states and ensembles gene noise were estimated by rank-based regression [50] .

To predict the mortality of CAP and sepsis patients we trained gradient boosted regression tree models with a scalable tree boosting system XGBoost [36] using mortality within 28 days as a binary response variable, and ensemble gene noise and age as independent model features. To this end, we split individuals into discovery and validation cohorts following exactly the same partitioning as annotated in GSE65682 [8] . Then, we trained 3 models: 1) a model predicting mortality for CAP and sepsis patients, 2) a model predicting mortality for CAP patients, and 3) a model predicting mortality for sepsis patients. Models features were preselected using discovery cohorts by t test comparing ensembles gene noise for survived and deceased patients to maximize the accuracy of XGBoost training on the discovery data sets. For CAP and sepsis

(1), and sepsis (3) Mitochondrial disfunction resulting in reduced respiratory chain complex I activity and low ATP levels is a whole mark for sepsis. [30] KEGG: Osteoclast differentiation Mean expression of osteoclast differentiation genes is up-regulated in human septic shock. [66] KEGG: Tight junction Sepsis disrupts intestinal barrier which leads to a multiple organ dysfunction syndrome and alters the expression of tight junction proteins.

[67] Ensemble gene noise can be estimated from PCR without normalization to a reference gene. 

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We thank Oleg Derkatch who motivated this work and Dr. Laurent Schwartz, Olga and ErrolFontanellaz who pointed to a potential use of methylene blue. This work has been supported by the Russian Science Foundation grant: 20-14-00055 to YMM and Gene Learning Association.