Conserved Machine Learning Rankings of Myc Gene Combinations Across Different Sensitivity Methods Connote Existence of Biological Synergy

1. Significance

A search engine was used to reveal and prioritise gene combinations, by adapting the code from a recently published work. Rankings of combinations were observed to be conserved across the different sensitivity methods (used to estimate the influence of components of a combination). This points to possible existence of synergy between genes at biological level. Presented here are rankings of experimentally established combinations of MYC-X for CRC treated with ETC-1922159 and rankings that are unexplored. These point to efficacy and potential of the search engine. The engine is effective for ranking combinations of any gene of choice.

2. Introduction

2.1. Combinatorial Search Problem and a Possible Solution

A recent design of a machine learning based search engine was published [1], that ranks combinations of genes that might be working synergistically in cells in various processes. To demostrate its efficacy in real life scenario, the data set containing recordings of up/down regulated genes generated from colorectal cancer (CRC) cells treated with PROCN-WNT inhibitor drug ETC-1922159 was taken [2]. The regulation of the genes were recorded individually, but in many cases, it is still not known which higher (≥ 2) order gene combinations might be playing a greater role in CRC. Here, I demonstrate that the rankings assigned to gene combinations at 2^nd order, by the search engine are conserved across the different sensitivity methods (and kernels/variants). This conservation points to the possible existance of the synergy between genes at the biological level. Readers are requested to go through the adaptation of the above mentioned work for gaining deeper insight into the working of the pipeline and its use of published data set generated after administration of ETC-1922159, [3].

2.2. Insight Behind the Work

Across all search engines has the fundamental principle remains the same i.e to capture the pattern available in the data and based on that pattern, rank a list of queries. Different algorithms can be applied, however if the fundamental pattern is captured accurately, then the rankings will remain approximately the same, with slight variations, across the different kinds of search engines used. I use one search engine, however, vary the way the patterns are captured via use of different sensitivity methods. Each sensitivity method uses a different flavour/mathematical formulation to compute the sensitivity indices to estimate the influence of the involved factors. These involved factors are genes that play a role in cell biology, in the above research. The insight is that all methods will capture the sensitivity of the involved factors based on their recorded regulations and the search engine will rank the combination of factors based on these sensitivity indices. Since the role of involved factors are captured properly, the search engine will give appropriate rankings to the combinations, thus capturing which gene combinations might be playing significantly in a biological phenomena. The above work shows rankings for experimentally confirmed combinations as well as unexplored/untested combinations. These rankings are not just numbers. They point to the existence of biological synergy in the form of gene combinations, whether tested in wet lab or unexplored till now. Finally, the findings suggest that the rankings are conserved across the different sensitivity methods used.

2.3. PORCN-WNT Inhibitors

The regulation of the Wnt pathway is dependent on the production and secretion of the WNT proteins. Thus, the inhibition of a causal factor like PORCN which contributes to the WNT secretion has been proposed to be a way to interfere with the Wnt cascade, which might result in the growth of tumor. Several groups have been engaged in such studies and known PORCN-WNT inhibitors that have been made available till now are IWP-L6 [4,5], C59 [6], LGK974 [7] and ETC-1922159 [8]. In this study, the focus of the attention is on the implications of the ETC-1922159, after the drug has been administered. The drug is a enantiomer with a nanomolar activity and excellent bioavailability as claimed in [8].

2.4. MYC

c-MYC (MYC) is a gene that encodes for transcription factor. It belongs to the family of MYC genes which includes B-MYC, N-MYC, L-MYC and S-MYC. Mutations in c-MYC have been found to be involved in various kinds of cancers. MYC (or v-myc avian myelocytomatosis viral oncogene homolog) contains a helix-loop-helix (HLH) and leucine zipper (LZ) domain that helps it to bind to interact with DNA and form a complex with MAX [9], respectively. A good introductory review on c-MYC can be found in [10] which covers topics on transcription factors and binding sites, transcriptional properties, MYC affected genes and finally role of MYC in cell cycle, apoptosis [11] and metabolism [12]. A lot of work has been done in MYC at various levels as it is implicated in various types of cancer. Additionally, MYC has been found to have influence on the chromatin structure also [13]. In colon cancer, c-MYC has been found to be highly expressed [14,15]. In colorectal cancer cells treated with ETC-1922159, MYC was found to be down regulated along with other genes. In this study, I use MYC as a choice of gene because it is induced by mitogenic signals and regulates downstream cellular responses. Overexpressed MYC promotes malignant transformation and modulates expression of a range of genes in experimental systems, however only a few are proven direct targets.

For curating experimentally established combinations of MYC, I use the list tabulated by [16]. They present a large-scale screen for MYC-binding sites in live human cells by identifying genes directly bound by MYC through the consensus E-box element CACGTG. Their strategy was based on the preselection of candidate sites with bioinformatic tools, which was followed by the experimental analysis of a large number of individual sites with a quantitative ChIP assay. They identify 257 genes within the high-affinity group of MYC-targets and assign them to a functional category. The genes qualify as high-affinity targets in all cell lines tested.

3. Tools of Study

Sensitivity analysis and its relevance in systems biology have been covered in a recently published article [17], which forms the foundation for this work. In this work, the sensitivity indices are computed for all factors or combination of factors affecting the pathway. Ranking using support vector machines (SVM) are then employed using these sensitivity indices. The work uses SVM package by [18] in https://www.cs.cornell.edu/people/tj/svm_light/svm_rank.html. I use the adaptation of the above engine to rank 2^nd order gene combinations.

3.1. Sensitivity Analysis

For completeness, a part of [17] has been reproduced below.

3.1.1. Variance Based Sobol Method

Seminal work by Russian mathematician [19] lead to development as well as employment of SA methods to study various complex systems where it was tough to measure the contribution of various input parameters in the behaviour of the output. A recent unpublished review on the global SA methods by [20] categorically delineates these methods with the following functionality • screening for sorting influential measures ([21] method, Group screening in [22,23], Iterated factorial design in [24], Sequential bifurcation design in [25,26]), • quantitative indicies for measuring the importance of contributing input factors in linear models ([27,28,29,30]) and nonlinear models ([31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47]) and • exploring the model behaviour over a range on input values ([48,49,50,51]). [20] also provide various criteria in a flowchart for adapting a method or a combination of the methods for sensitivity analysis.

The general idea for variance based Sobol method is as follows - A model could be represented as a mathematical function with a multidimensional input vector where each element of a vector is an input factor. This function needs to be defined in a unit dimensional cube. Based on ANOVA decomposition, the function can then be broken down into $f_0$ and summands of different dimensions, if $f_0$ is a constant and integral of summands with respect to their own variables is 0. This implies that orthogonality follows in between two functions of different dimensions, if at least one of the variables is not repeated. By applying these properties, it is possible to show that the function can be written into a unique expansion. Next, assuming that the function is square integrable variances can be computed. The ratio of variance of a group of input factors to the variance of the total set of input factors constitute the sensitivity index of a particular group.

3.1.2. Density Based HSIC Method

Besides the above [19]’s variance based indicies, more recent developments regarding new indicies based on density, derivative and goal-oriented can be found in [52,53,54], respectively. In a latest development, [55] propose new class of indicies based on density ratio estimation [52] that are special cases of dependence measures. This in turn helps in exploiting measures like distance correlation [56] and Hilbert-Schmidt independence criterion [57] as new sensitivity indicies. The framework of these indicies is based on use of [58] f-divergence, concept of dissimilarity measure and kernel trick [59]. Finally, [55] propose feature selection as an alternative to screening methods in sensitivity analysis. The main issue with variance based indicies [19] is that even though they capture importance information regarding the contribution of the input factors, they • do not handle multivariate random variables easily and • are only invariant under linear transformations. In comparison to these variance methods, the newly proposed indicies based on density estimations [52] and dependence measures are more robust.

The general idea for density based HSIC method is as follows - The sensitivity index is actually a distance correlation which incorporates the kernel based Hilbert-Schmidt Information Criterion between two input vectors in higher dimension. The criterion is nothing but the Hilbert-Schmidt norm of cross-covariance operator which generalizes the covariance matrix by representing higher order correlations between the input vectors through nonlinear kernels. For every operator and provided the sum converges, the Hilbert-Schmidt norm is the dot product of the orthonormal bases. For a finite dimensional input vectors, the Hilbert-Schmidt Information Criterion estimator is a trace of product of two kernel matrices (or the Gram matrices) with a centering matrix such that HSIC evalutes to a summation of different kernel values.

It is this strength of the kernel methods that HSIC is able to capture the deep nonlinearities in the biological data and provide reasonable information regarding the degree of influence of the involved factors within the pathway. Improvements in variance based methods also provide ways to cope with these nonlinearities but do not exploit the available strength of kernel methods. Results in the later sections provide experimental evidence for the same.

3.1.3. Sensitivity Package in R

The sensitivity package by [60] was used to develop the search engine pipeline. The current research uses the Hilbert Schmidt Independence Criterion (HSIC) and SOBOL method, implemented in the sensitivity package mentioned above. I use three different kernels under the HSIC method namely, • laplace, • linear and • rbf. For SOBOL method, I use • sobol-2002, and • sobol-jansen. Each of these variants or kernels have been implemented in the sensitivity package and option has been provided in the search engine code to generate the rankings for a particular gene, using a choice of a kernel/variant at a time. Technical details about the variants and kernels can be found in references cited in [60].

4. Static Data by [2]

Data used in this research work was released in a publication by [2]. The ETC-1922159 was released in Singapore in July 2015 under the flagship of the Agency for Science, Technology and Research (A*STAR) and Duke-National University of Singapore Graduate Medical School (Duke-NUS). Note that the ETC-1922159 data show numerical point measurements that is as [2] quote - "List of differentially expressed genes identified at three days after the start of ETC-159 treatment of colorectal tumors. Log2 fold-changes between untreated (vehicle, VEH) and ETC-159 treated (ETC) tumors are reported." The numerical point measurements of differentially expressed genes were recorded using the following formulation of fold changes in equation 1 (see [61,62,63]).

$${log}_2{\displaystyle \frac{VE{H}_{avg}}{ET{C}_{avg}}}$$

(1)

5. Methodology

5.1. Revealing Higher Order Biological Hypotheses via Sensitivity Analysis and Insilico Ranking Algorithm

In the trial experiments on ETC-1922159 [2], a list of genes ($2500\pm$) have been reported to be up and down regulated after the drug treatment and a time buffer of 3 days. Some of the transcript levels of these genes have been recorded and the experimental design is explained elaborately in the same manuscript. In the list are also available unknown or uncharacterised proteins that have been recorded after the drug was administered. These have been marked as "- -" in the list (Note - In this manuscript these uncharacterised proteins have been marked as "XXM", were $M=1,2,3,...$). The aim of this work is to reveal unknown/unexplored/untested biological hypotheses that form higher order combinations. For example, it is known that the combinations of WNT-FZD or RSPO-LGR-RNF play significant roles in the Wnt pathway. But the $n\ge 2,3,...$-order combinations out of $N(>n)$ genes forms a vast combinatorial search forest that is extremely tough to investigate due to the humongous amount of combinations. Currently, a major problem in biology is to cherry pick the combinations based on expert advice, literature survey or random choices to investigate a particular combinatorial hypothesis. The current work aims to reveal these unknown/unexplored/untested combinations by prioritising these combinations using a potent support vector ranking algorithm [18]. This cuts down the cost in time/energy/investment for any investigation concerning a biological hypothesis in a vast search space.

The pipleline works by computing sensitivity indicies for each of these combinations and then vectorising these indices to connote and form discriminative feature vector for each combination. The ranking algorithm is then applied to a set of combinations/sensitivity index vectors and a ranking score is generated. Sorting these scores leads to prioritization of the combinations. Note that these combinations are now ranked and give the biologists a chance to narrow down their focus on crucial biological hypotheses in the form of combinations which the biologists might want to test. Analogous to the webpage search engine, where the click of a button for a few key-words leads to a ranked list of web links, the pipeline uses sensitivity indices as an indicator of the strength of the influence of factors or their combinations, as a criteria to rank the combinations.

5.2. Design for Static Data from [2]

The procedure begins with the listing of all $C_k^n$ combinations for k number of genes from a total of n genes. Here n can be the choice of the biologist. k is $\ge 2$ and $\le (n-1)$. Each of the combination of order k represent a unique set of interaction between the involved genetic factors. Note that the ETC-1922159 data show numerical point measurements that is as [2] quote "List of differentially expressed genes identified at three days after the start of ETC-159 treatment of colorectal tumors. Log2 fold-changes between untreated (vehicle, VEH) and ETC-159 treated (ETC) tumors are reported." Since the sensitivity analysis methods require a sample for a particular observation, a steep gaussian distribution was generated with a jitter (noise) added to the deviation from the reported point measurement of 0.005. In this experiment, the distribution contained 10 measurements (including the point of measurement under consideration). This is repeated for each point of measurement.

To have an averaged ranking, the experiment was designed to run for 50 iterations. In each iteration, the datasets are combined in a specifed format which go as input as per the requirement of a particular sensitivity analysis method. Thus for each $p^{th}$ combination in $C_k^n$ combinations, the dataset is prepared in a required format (See .R code in mainscript-2-2.R). Details of formatting the data have not been presented in the article to maintain the fluidity and brevity. Interested readers can find examples of formating the data in the sensitivity analysis package in R. After the data has been transformed, vectorized programming is employed for density based sensitivity analysis and looping is employed for variance based sensitivity analysis to compute the required sensitivity indices for each of the p combinations.

After the above sensitivity indices have been stored for each of the $p^{th}$ combination, for a chosen sensitivity analysis method, the next step in the design of experiment is conducted. Here, the indices are averaged per combination to have a mean index value. These index values form the discriminative features for a particular combination. For a $k^{th}$ order combination, a vector of k elements or indices forms a feature vector. Thus for $C_k^n$ combinations there will be $C_k^n$ vectors, each containing k elements. Next, $SV{M}_{learn}^{Rank}$ [18] is used to generate a model on default value C value of 20. In the current experiment on toy model C value has not been tunned. The training set helps in the generation of the model as the different gene combinations are numbered in order which are used as rank indices. The model is then used to generate score on the observations in the testing set using the $SV{M}_{classify}^{Rank}$ [18]. This is followed by sorting of these scores along with the rank indices already assigned to the gene combinations. The end result is a sorted order of the gene combinations based on the ranking score learned by the $SV{M}^{Rank}$ algorithm.

Note that the following is the order in which the files should be executed in R, in order, for obtaining the desired results (Note that the code will not be explained here) - • use source("extractETCdata.R") • use source("mainScript-2-2.R") • use source("SVMRank-Results-S-mean.R").

6. Results & Discussion

6.1. How to Interpret the Ranking?

In each of the sections below, one will find two tables.

The first table lists the rankings of a particular gene combination based on these kernels. Based on majority voting, a combination is decided to be low ranked or high ranked. So, for example, if majority rankings point to low numerical value (i.e below the half way mark of approximately 2500 gene combinations), then the combination is possibly not highly ranked in colorectal cancer cells AFTER the ETC-1922159 treatment. Looking at it in another way, this low ranking suggests that the combination might have been up regulated in colorectal cancer cells BEFORE the ETC-1922159 treatment. This points to the inference that the combination of the two genes/proteins was working synergistically in colorectal cancer, while being up regulated and before ETC-1922159 treatment. The ETC-1922159 administration had caused a down regulation of genes in colorectal cancer cells and what is available as data by [2] points to down regulated recordings of genes/proteins taken individually.

The second table uses the majority voting mentioned above, to filter out which combinations need to be further tests in the wet lab. These combinations recorded in the second table are inferences/pointers to existence of possible synergistic combinations that might be working in the cell, in a particular scenario (here colorectal cancer cells). Additionally, one will see two inferences - • based on the experimentally tested and established synergies in any other pathological/normal cell, if recorded in colorectal cancer cells treated with ETC-1922159, these combinations will ranked by the engine appropriately (or note - there might be a possibility that the experimentally tested combination established in a different scenario, might not get an approprate rank by the search engine in the colorectal cancer cells treated with ETC-1922159.) and • based on the cues from previous point, there will be combinations ranked by the engine, that point to new synergies that have not been explored/tested in wet lab.

Further, in a list of approximately 2500 genes that were up/down regulated after ETC-1922159 treatment, for the second order combinations there will be 2499 combinations. The engine generates the ranking for all these 2499 combinations. However, it is not possible to report the ranking of all 2499 combinations in a single article, for a particular gene under investigation. The full set of rankings reveal a prioritized list of new combinations that emerge as plausible biological hypotheses that might be working synergistically in colorectal cancer cells. These require further tests. For transperancy and reproducibility, one can download the code of search engine in R language and run it on the data made available by [2], to get a full list of some 2499, 2^nd order combinations for a particular gene of choice. Higher order combinations can also be generated using this engine.

Finally, we also see how the rankings behave across the different sensitivity methods and how they are conserved across the same. This conservation points to existence of biological synergy between the components of a combination (i.e either experimentally established or is unexplored/untested).

6.2. Conserved Rankings of Experimentally Established and Unexplored/Untested, MYC - X Combinations

NOTE - X denotes a particular gene/protein of interest.

[16] divide the MYC target genes into diverse functional categories. I use the same categories (the below sections) and present rankings of those combinations that were recorded in CRC cells treated with ETC-1922159. Further, rankings of unexplored/untested combinations for genes that might be related to family of X are also presented. Note that I present rankings of combinations of genes that were down regulated after the ETC-1922159 treatment. Also, bold MYC - X means the target genes mentioned in [16] were also found/recorded in CRC treated with ETC-1922159. Conserved rankings for these bolster confirmatory experimental results.

6.2.1. Adehesion / Matrix / Tissue Remodeling (AMT)

Under this functional category in [16], the following MYC-target genes are reported - integrin subunit beta 1 (ITGB1), integrin subunit alpha 6 (ITGA6), collagen type IV alpha (1/2) chain (COL4A-1/2), serpin family E member 1 (SERPINE1) and acid phosphatase 5, tartrate resistant (ACP5).

Table 1 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 2 generated from analysis of the ranks in Table 1. The Table 1 shows rankings w.r.t MYC. For genes related to Integrins (i.e ITGA9, ITGB3BP and ITGAE); Collagen (i.e COL9A3); Serpin family (i.e SERPINF2); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to Collagen (i.e COL18A1 and COL27A1); Acid phosphatase (i.e ACP1 and ACP6); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 1 graphically, in Table 2.

6.2.2. Ligand / Receptor (LR)

Under this functional category in [16], the following MYC-target genes are reported - fibroblast growth factor receptor 4 (FGFR4), G protein-coupled receptor 4 (GPR4), Interleukin (IL-2/11RA/13), cholinergic receptor nicotinic beta 1 subunit (CHRNB1), NOTCH4 and transforming growth factor beta (TGFB-1/2/3).

Table 3 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 4 generated from analysis of the ranks in Table 3. The Table 3 shows rankings w.r.t MYC. For genes related to Fibroblast growth factor receptor (i.e FGFR4); G protein-coupled receptor (i.e GPR63 and GPRC5B); Interleukin (i.e IL33, IL17RB and IL17D); Cholinergic receptors nicotinic subunits (i.e CHRNA5); NOTCH (i.e NOTCH1) and Transforming growth factor beta (i.e TGFBR3) all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to G protein-coupled receptor (i.e GPR68, GPR137C and GPR19); Interleukin (i.e IL17RD and IL1RL2); NOTCH (i.e NOTCH4) and Transforming growth factor beta (i.e TGFB1 and TGFBRAP1); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 3 graphically, in Table 4.

6.2.3. Structural (STR)

Under this functional category in [16], the following MYC-target genes are reported - erythrocyte membrane protein band 4.2 (EPB42), laminin subunit beta 2 (LAMB2), lamin A/C (LMNA) and stathmin 1/oncoprotein 18 (STMN1).

Table 5 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 6 generated from analysis of the ranks in Table 5. The Table 5 shows rankings w.r.t MYC. For genes related to Erythrocyte membrane protein band (EPB41L4A); Lamin (i.e LMNB1 and LMNB2) and Stathmin 1/oncoprotein 18 (i.e STMN1); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to Laminin subunit beta (i.e LAMB1); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 5 graphically, in Table 6.

6.2.4. Channels / Components (CC)

Under this functional category in [16], the following MYC-target genes are reported - solute carrier family 4 member 2 (SLC4A2).

Table 7 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 8 generated from analysis of the ranks in Table 7. The Table 7 shows rankings w.r.t MYC. For genes related to Solute carrier family 4 (SLC4A7); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

One can also interpret the results of the Table 7 graphically, in Table 8.

6.2.5. Chaperone / Protein Folding (CPF)

Under this functional category in [16], the following MYC-target genes are reported - heat shock protein family (HSPA8, HSPE1, HSPD1 and HSPCAL3).

Table 9 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 10 generated from analysis of the ranks in Table 9. The Table 9 shows rankings w.r.t MYC. For genes related to Heat shock protein family (i.e HSPB6, HSPE1, HSPD1, HSPA4L and HSPA9); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to Heat shock protein family (i.e HSPA4); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 9 graphically, in Table 10.

6.2.6. Translation / Ribosomal Protein (TRP)

Under this functional category in [16], the following MYC-target genes are reported - eukaryotic translation initiation factor (EIF-4A1/4E/5A2); Poly(A)-binding protein (PABP); ribosomal protein S (RPS-19/6) and ribosomal protein L (RPL-13A/19/22/27A).

Table 11 and shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 13 generated from analysis of the ranks in Table 11 and Table 12. The Table 11 shows rankings w.r.t MYC. For genes related to Eukaryotic translation initiation factor (i.e EIF2B3 and EIF2D); Poly(A)-binding protein (i.e PABPC1L); and Ribosomal protein S (i.e RPSA, RPS2, RPS2P46, RPS3A, RPS18, RPS9 and RPS23) all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to Eukaryotic translation initiation factor (i.e EIF3L, EIF2B1, EIF2AK4, EIF4B, EIF3E, EIF3F, EIF2B5 and EIF4EBP1); Poly(A)-binding protein (i.e PABPC4) and Ribosomal protein S (i.e RPS5, RPS11, RPS27, RPS4X, RPS3, RPS6KL1, RPS27A, RPS14, RPS21, RPS24, RPS16, RPS19, RPS20, RPS13, RPS7, RPS12, RPS8, RPS29, RPS25 and RPS23); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

The Table 12 shows rankings w.r.t MYC. For genes related to Ribosomal protein L (i.e RPL22, RPL5, RPL7L1, RPL21, RPL10A, RPL15, RPL19, RPL41, RPL23, RPL13A, RPL4 and RPL3) all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to Ribosomal protein L (i.e RPL24, RPL39, RPL30, RPL27A, RPL35A, RPL7, RPL7A, RPL38, RPL26, RPL23A, RPL14, RPL6, RPL11, RPL27, RPL12, RPL37A, RPL39L, RPL37, RPL36A, RPL31, RPL9, RPL35, RPL18A, RPL32, RPL34 and RPL13); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 11 and Table 12 graphically, in Table 13.

6.2.7. Vesicle Protein / Trafficking (VPT)

Under this functional category in [16], the following MYC-target genes are reported - peroxisomal biogenesis factor (PEX3).

Table 14 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 15 generated from analysis of the ranks in Table 14. The Table 14 shows rankings w.r.t MYC. For genes related to peroxisomal biogenesis factor (i.e PEX5 and PEX6); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to peroxisomal biogenesis factor (i.e PEX3); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 14 graphically, in Table 15.

6.2.8. Carbohydrate (CH)

Under this functional category in [16], the following MYC-target genes are reported - aldehyde dehydrogenases (ALDH2); solute carrier family 2 facilitated glucose transporter (SLC2A4) and aldo-keto reductase family (AKR1A).

Table 16 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 17 generated from analysis of the ranks in Table 16. The Table 16 shows rankings w.r.t MYC. For genes related to aldehyde dehydrogenases (i.e ALDH1B1, ALDH7A1 and ALDH5A1); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to aldehyde dehydrogenases (i.e ALDH3A2, ALDH9A1 and ALDH3A1); solute carrier family 2 facilitated glucose transporter (i.e SLC2A11) and aldo-keto reductase family (i.e AKR1C4); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 16 graphically, in Table 17.

6.2.9. Energy Metabolism (EM)

Under this functional category in [16], the following MYC-target genes are reported - uncoupling protein/solute carrier family 25 mitochondrial carrier (UCP/SLC25A71 and UCP3/SLC25A9).

Table 18 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 19 generated from analysis of the ranks in Table 18. The Table 18 shows rankings w.r.t MYC. For genes related to uncoupling protein/solute carrier family 25 mitochondrial carrier (i.e SLC25A27 (UCP4), SLC25A26, SLC25A8 (UCP2), SLC25A19 and SLC25A35); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to uncoupling protein/solute carrier family 25 mitochondrial carrier (i.e SLC25A38, SLC25A14 (UCP5), SLC25A40, SLC25A15 and SLC25A32); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 18 graphically, in Table 19.

6.2.10. Lipid (LPD)

Under this functional category in [16], the following MYC-target genes are reported - Acyl-CoA dehydrogenase family (ACADM).

Table 20 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 21 generated from analysis of the ranks in Table 20. The Table 20 shows rankings w.r.t MYC. For genes related to Acyl-CoA dehydrogenase family (i.e ACADM and ACADSB); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to Acyl-CoA dehydrogenase family (i.e ACAD8); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 20 graphically, in Table 21.

6.2.11. Nucleotide (NTD)

Under this functional category in [16], the following MYC-target genes are reported - phosphoribosylaminoimidazole carboxylase and phosphoribosylaminoimidazolesuccinocarboxamide synthase (PAICS); phosphoribosyl pyrophosphate amidotransferase (PPAT); and deoxycytidine kinase (DCK).

Table 22 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 23 generated from analysis of the ranks in Table 22. The Table 22 shows rankings w.r.t MYC. For genes related to phosphoribosylaminoimidazole carboxylase and phosphoribosylaminoimidazolesuccinocarboxamide synthase (PAICS); and phosphoribosyl pyrophosphate amidotransferase (PPAT); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to deoxycytidine kinase (DCK); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 22 graphically, in Table 23.

6.2.12. Signal Transduction (STD)

Under this functional category in [16], the following MYC-target genes are reported - cyclophilin peptidylprolyl isomerases (PPID); and phospholipases (PLA2G4A).

Table 24 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 25 generated from analysis of the ranks in Table 24. The Table 24 shows rankings w.r.t MYC. For genes related to cyclophilin peptidylprolyl isomerases (i.e PPIA, PPID, PPIL1 and PPIH); and phospholipases (i.e PLCB4); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to cyclophilin peptidylprolyl isomerases (i.e PPIL3); and phospholipases (i.e PLA2G4A, PLA2G3, PLCG1, PLCB2 and PLCH1); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 24 graphically, in Table 25.

6.2.13. Nuclear Regulatory Factors (NRF)

Under this functional category in [16], the following MYC-target genes are reported - canonical high mobility group (HMGN2); sirtuins (SIRT1); and OZF (ZNF146).

Table 26 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 27 generated from analysis of the ranks in Table 26. The Table 26 shows rankings w.r.t MYC. For genes related to canonical high mobility group (i.e HMGN3, HMGB2, HMGB3 and HMGB1); and Sirtuins (i.e SIRT3); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to canonical high mobility group (i.e HMGN2 and HMGN5); and OZF (i.e ZNF146); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 26 graphically, in Table 27.

6.2.14. Nucleolus / RNA-Binding Protein (NRBP)

Under this functional category in [16], the following MYC-target genes are reported - dyskerin pseudouridine synthase 1 (DKC1); stem-loop histone mRNA binding protein (SLBP); nucleolin (NCL); surfeit (SURF6); nucleolar protein (NOL1); heterogeneous nuclear ribonucleoprotein (HNRPA1 and HNRNPA2B1); and RNA binding motif protein (RBM3).

Table 28 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 29 generated from analysis of the ranks in Table 28. The Table 28 shows rankings w.r.t MYC. For genes related to dyskerin pseudouridine synthase 1 (i.e DKC1); nucleolin (i.e NCL); nucleolar protein (i.e NOL8 and NOL6); heterogeneous nuclear ribonucleoprotein (i.e HNRNPA3, HNRNPA1L2, HNRNPA1 and HNRNPD); and RNA binding motif protein (i.e RBMX); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to stem-loop histone mRNA binding protein (i.e SLBP); surfeit (i.e SURF6); nucleolar protein (i.e NOL10, NOL9 and NOL11); heterogeneous nuclear ribonucleoprotein (i.e HNRNPM, HNRNPC, HNRNPA0, HNRNPH3 and HNRNPR); and RNA binding motif protein (i.e RBM19, RBM28 and RBM26); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 28 graphically, in Table 29.

6.2.15. Transcription Factors (TF)

Under this functional category in [16], the following MYC-target genes are reported - achaete-scute family bHLH transcription factor 2 (ASCL2); ETS proto-oncogene 2, transcription factor (ETS2); MYB proto-oncogene (MYBL2); E2F transcription factor (E2F1); transcription factor (TCF12); HOXL subclass homeoboxes (HOXD13); NME/NM23 nucleoside diphosphate kinase (NME1); and forkhead boxes (FOXM1).

Table 30 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 31 generated from analysis of the ranks in Table 30. The Table 30 shows rankings w.r.t MYC. For genes related to achaete-scute family bHLH transcription factor 2 (i.e ASCL2); ETS proto-oncogene 2, transcription factor (i.e ETS2); MYB proto-oncogene (i.e MYBL2, MYB and MYBL1); E2F transcription factor (i.e E2F2, E2F7, E2F1 and E2F8); transcription factor (i.e TCF19 and TCF7); HOXL subclass homeoboxes (i.e HOXB9, HOXB8, HOXB5 and HOXA9); NME/NM23 nucleoside diphosphate kinase (i.e NME1); and forkhead boxes (i.e FOXM1); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to E2F transcription factor (i.e E2F5); transcription factor (i.e TCFL5 and TCF3); HOXL subclass homeoboxes (i.e HOXB7, HOXB3, HOXB13, HOXA11 and HOXB4); NME/NM23 nucleoside diphosphate kinase (i.e NME4); and forkhead boxes (i.e FOXA2 and FOXJ1); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 30 graphically, in Table 31.

6.2.16. DNA Maintenance / Repair (DMR)

Under this functional category in [16], the following MYC-target genes are reported - apurinic/ apyrimidinic endodeoxyribonuclease (APEX1); telomerase reverse transcriptase (TERT); prothymosin alpha (PTMA); DNA polymerases (POLB and POLD2); H2A histones (H2AZ); minichromosome maintenance complex component (MCM7); BRCA1/BRCA2-containing complex (BRCA2); and DNA topoisomerase (TOP1).

Table 32 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 33 generated from analysis of the ranks in Table 32. The Table 32 shows rankings w.r.t MYC. For genes related to apurinic/apyrimidinic endodeoxyribonuclease (i.e APEX1); DNA polymerases (i.e POLQ, POLE2, POLA1, POLD1, POLG2, POLE3, POLA2 and POLD2); H2A histones (i.e H2AFV, H2AFZ and H2AFX); minichromosome maintenance complex component (i.e MCM4, MCM8, MCM3, MCM10, MCM2, MCM5, MCM6 and MCM7); BRCA1/BRCA2-containing complex (i.e BRCA1 and BRCA2); and DNA topoisomerase (i.e TOP2A and TOP1MT); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to telomerase reverse transcriptase (i.e TERT); prothymosin alpha transcription factor (i.e PTMA); DNA polymerases (i.e POLB); and DNA topoisomerase (i.e TOP2B); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 32 graphically, in Table 33.

Additionally, since members of DNA polymerases are MYC targets, I also analysed rankings of combinations of members of DNA-dependent RNA polymerase (POLR), with MYC.

Table 34 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 35 generated from analysis of the ranks in Table 34. The Table 34 shows rankings w.r.t MYC. For genes related to DNA-dependent RNA polymerase (i.e POLR1D, POLR3K, POLR1E, POLR1B, POLR2G, POLR2K, POLR3E, POLR3A and POLR1C); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to DNA-dependent RNA polymerase (i.e POLR2D, POLR2F and POLR1A); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 34 graphically, in Table 35.

6.2.17. Other (OT)

Under this functional category in [16], the following MYC-target genes are reported - epoxide hydrolase (EPHX1); inositol monophosphatase (IMPA2); pyruvate dehydrogenase (PDHA1); microsomal glutathione S-transferase (MGST1); and solute carrier family 19 (SLC19A1).

Table 36 shows rankings of these combinations. Followed by this is the unexplored combinatorial hypotheses in Table 37 generated from analysis of the ranks in Table 36. The Table 36 shows rankings w.r.t MYC. For genes related to epoxide hydrolase (i.e EPHX2); inositol monophosphatase (i.e IMPA2); pyruvate dehydrogenase (i.e PDHA1); microsomal glutathione S-transferase (i.e MGST1); and solute carrier family 19 (i.e SLC19A1 and SLC19A3); all show majority low rankings (below half way mark) across the SA methods. That is, the low rankings indicate that a combination is weakly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in up regulated manner in CRC BEFORE the drug treatment.

On the other hand, genes related to microsomal glutathione S-transferase (i.e MGST2); all show majority high rankings (above half way mark). That is, the high rankings indicate that a combination is strongly down regulated after ETC-1922159 treatment. Thus, they might be working synergistically in down regulated manner in CRC AFTER the drug treatment.

One can also interpret the results of the Table 36 graphically, in Table 37.

7. Conclusion

Findings of this work point to conserved machine learning rankings of gene combinations across different sensitivity methods. These findings point to the existence of biological synergy among the genes, for experimentally tested combinations as well as those that have to be explored/tested. Results for MYC related combinations in CRC cells treated with ETC-1922159, are presented. A theoretically sound and a practical framework has been developed to prioritize higher order combinations of regulated genes after the administration of ETC-1922159 PORCN-WNT inhibitor in cancer cells. The prioritization uses advanced sensitivity methods that exploit nonlinear relations in reproducing kernel hilbert spaces via kernel trick and support vector ranking method to rank and reveal various combinations of identified and unidentified factors that are affected after the drug treatment. This gives medical specialists/oncologists/biologists a way to navigate in a guided manner in a vast combinatorial search forest, thus cutting down cost in time/investment/energy as well as avoid cherry picking unknown biological hypotheses. Biologists/oncologists would not have to struggle to search for gene combinations of interest, which they might want to test in wet lab.