The Genomic Fabric Perspective on the Transcriptome Between Universal Quantifiers and Personalized Genomic Medicine

Abstract

Numerous groups race to discover the gene biomarker whose alteration alone is indicative of a particular disease in all humans. Biomarkers are selected from the most frequently altered genes in large population cohorts. However, thousands of other genes are simultaneously affected, and, in each person, the same disease results from a unique, never-repeatable combination of gene alterations. Therefore, our Genomic Fabric Paradigm (GFP) switches the focus from the alteration of one particular gene to the overall change in selected groups of functionally related genes. Biomarkers are of little therapeutic value, their high alterability indicating low protection by the homeostatic mechanisms as for minor players. Instead of these most alterable genes in all patients, GFP identifies in each patient the genes whose highly protected expression governs major functional pathways by controlling the expression of numerous other genes. Smart manipulation of such (commander) genes would have the maximum therapeutic benefit not for everybody but for the treated person. The genomic fabric is defined as the transcriptome associated with the most interconnected and stably expressed network of genes responsible for a particular functional pathway. The fabric exhibits specificity with respect to race/strain, sex, age, tissue/cell type, and lifestyle and environmental factors. It remodels during development, progression of a disease, and in response to external stimuli. GFP is powered by mathematically advanced analytical tools whose application is illustrated by reprocessing data from previously published gene expression experiments.

Appendices

Appendix 1: Significant Regulation of Gene Expression

Usually, a gene is considered as significantly regulated if the p value of the heteroscedastic t-test for the equality of the two distribution means is less than 0.05. The p-value can be adjusted for the occurrence of false positive results in multiple-testing using Benjamini and Hochberg (1995), Benjamini and Yekutieli (2001), Bonferroni (Duggal et al. 2008), Hochberg and Benjamini (1990), Holm (1979), or Hommel (Hommel and Bernhard 1994) correction. I choose to apply a Bonferroni-type correction only to the redundant group of spots probing the same gene (Iacobas et al. 2005). In addition to the p-value, some authors require also that the absolute expression ratio between the compared groups of samples exceeds an arbitrarily introduced cut-off (2× or 1.5×). I prefer a composite criterion in which the absolute expression ratio |x| of gene γ in condition C2 with respect to condition C1 exceeds the combined effect of technical noise and biological variability:

$$ \begin{aligned} & \left| {\left. {x_{\gamma }^{{(c_{1} \to c_{2} )}} } \right| > 1 + \sqrt {2\left( {\left( {CV_{\gamma }^{{(C_{2} )}} } \right)^{2} + \left( {CV_{\gamma }^{{(C_{1} )}} } \right)^{2} } \right)\quad \, {\text{and}}\, \quad p_{\gamma }^{{(C_{1} \to C_{2} )}} } } \right.\left| {_{\text{Bonferroni\,correction\,for\,redundancy\,group}} < 0.05} \right. \hfill \\ & {\text{where}}\;x_{\gamma }^{(C1 \to C2)} = \left\{ {\begin{array}{*{20}c} {\frac{{\upmu_{\gamma }^{{(C_{2} )}} }}{{\upmu_{\gamma }^{{(C_{1} )}} }}} & {if\;C_{1} \le C_{2} } \\ { - \frac{{\upmu_{\gamma }^{{(C_{1} )}} }}{{\upmu_{\gamma }^{{(C_{2} )}} }}} & {if\;C_{1} > C_{2} } \\ \end{array} } \right.\begin{array}{*{20}c} , & {\underbrace {{\upmu_{\gamma }^{(C)} \equiv \overline{{a_{\gamma }^{(C)} }} }}_{{{\text{average}}\,\,{\text{expression}}\,\,{\text{level}}}}} \\ \end{array} \begin{array}{*{20}c} , & {\underbrace {{CV_{\gamma }^{(C)} \equiv \frac{{stdev(a_{\gamma }^{(C)} )}}{{\upmu_{\gamma }^{(C)} }}}}_{{{\text{coefficient}}\,\,{\text{of}}\,{\text{variation}}}}} \\ \end{array} \hfill \\ \end{aligned} $$

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Appendix 2: Relative Expression Variability (REV)

REV is the mid-interval of the ε (usually 5 %) acceptable error Chi-square estimate of the transcript abundance coefficient of variation E. REV has a Bonferroni-type correction for the number R of spots on the microarray probing redundantly gene “γ”.

$$ REV_{\gamma }^{(C)} (\varepsilon ) = E_{\gamma }^{(C)} \frac{1}{2}\left( {\sqrt {\frac{{4R_{\gamma }^{(C)} - 1}}{{\chi^{2} (4R_{\gamma }^{(C)} - 1;\;1 - \varepsilon /2)}}} + \sqrt {\frac{{4R_{\gamma }^{(C)} - 1}}{{\chi^{2} \left( {4R_{\gamma }^{(C)} - 1;\;\varepsilon /2} \right)}}} } \right) \times 100\,\% $$

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Appendix 3: Gene Commanding Height (GCH) of Individual Genes and the Fabric Prominence Score (FPS)

$$ GCH_{\Gamma }^{(C)} (\upgamma ) \equiv \underbrace {{\left( {\frac{{\left\langle {\left. {REV^{(C)} (\upgamma )} \right\rangle_{\Gamma } } \right.}}{{REV^{(C)} (\upgamma )}}} \right)}}_{{{\text{relative}}\,\,\,{\text{control}}}}\exp \underbrace {{\left( {\frac{{\left( {\overline{{(\rho_{\upgamma ,\uplambda }^{(C)} )^{2} }} } \right)_{\uplambda \in \Gamma ,\upbeta \ne \upgamma } }}{{\left\langle {(\rho_{\upgamma ,\uplambda }^{(C)} )^{2} } \right\rangle_{\upgamma ,\uplambda \in \Gamma ,\upbeta \ne \upgamma } }} - 1} \right)}}_{{{\text{relative}}\,\,{\text{coordination}}}},\quad FPS^{(C)} \equiv \left( {\overline{{GCH_{\Gamma }^{(C)} (\upgamma )}} } \right)_{\uplambda \in \Gamma } $$

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where $\rho_{\gamma ,\lambda }^{(C)}$ is Pearson pair-wise correlation coefficient between the expression levels of genes γ and λ in condition C, $\left\langle X \right\rangle {\text{and}}\;\overline{X}$ denoting respectively the median and the average of the variable X in the indicated domains.

Appendix 4: Pair-Wise Relevance (PWR)

$$ PWR_{\gamma ,\lambda }^{(C)} \equiv \underbrace {{\frac{{\mu_{\gamma }^{(C)} }}{{\left\langle {\mu_{\gamma }^{(C)} } \right\rangle \varGamma }}}}_{\text{relative\,\,expression\,\,in}\,\,\varGamma \,} \times \frac{{\left\langle {REV^{(C)} (\gamma )_{\varGamma } } \right\rangle }}{{\underbrace {{REV^{(C)} (\gamma )}}_{\text{relative\,\,control\,\,in}\,\,\varGamma }}} \times \underbrace {{\left( {\rho_{\gamma ,\lambda }^{(C)} } \right)^{2} }}_{\text{coordination}} \times \frac{{\left\langle {REV^{(C)} (\lambda )} \right\rangle_{\varLambda } }}{{\underbrace {{REV^{(C)} (\lambda )}}_{\text{relative\,\,control\,\,in}\,\,\varLambda }}} \times \quad \frac{{\mu_{\lambda }^{(C)} }}{{\underbrace {{\left\langle {\mu_{\lambda }^{(C)} } \right\rangle_{\varLambda } }}_{\text{relative\,\,expression\,\,\,in}\,\,\varLambda }}}\quad \quad \left| {\begin{array}{*{20}c} {\gamma \in \varGamma ,\;\lambda \in \varLambda } \\ {\lambda \ne \gamma } \\ \end{array} } \right. $$

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Appendix 5: Transcriptomic Distance (TD)

$$ \begin{aligned} \left( {TD_{\varGamma }^{(C2,C1)} } \right)^{2} & = \frac{1}{[\varGamma ]}\sum\limits_{\gamma \in \varGamma } {\left( {\underbrace {{\left( {\exp \left| {\log \left( {\frac{{a_{\gamma }^{(C2)} }}{{a_{\gamma }^{(C1)} }}} \right)} \right| - 1} \right)^{2} \left( {1 - p_{\gamma }^{(C2,C1)} } \right)^{2} }}_{{\text{regulation{\kern 1pt} {\kern 1pt} of{\kern 1pt} expression{\kern 1pt} {\kern 1pt} level}}}} \right)} \\ & \quad + \frac{1}{[\varGamma ]}\sum\limits_{\gamma \in \varGamma } {\left( {\mathop {\underbrace {{\left\langle {REV_{\gamma }^{(C1)} } \right\rangle_{\varGamma }^{2} \left( {\frac{1}{{REV_{\gamma }^{C2} }} - \frac{1}{{REV_{\gamma }^{C1} }}} \right)}}_{{\text{regulation{\kern 1pt} {\kern 1pt} of{\kern 1pt} expression{\kern 1pt} {\kern 1pt} control}}}}\limits^{2} } \right)} + \frac{1}{[\varGamma ]}\sum\limits_{\gamma \in \varGamma } {\left( {\underbrace {{\frac{{\sum\limits_{\delta \in \varGamma ,\delta \ne \gamma } {(p_{\gamma ,\delta }^{(C2)} - p_{\gamma ,\delta }^{(C1)} )^{2} } }}{[\varGamma ] - 1}}}_{{\text{regulation{\kern 1pt} {\kern 1pt} of{\kern 1pt} networking}}}} \right)} \\ \end{aligned} $$

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