Casein kinase-1(α1/δ /γ1) & 2α1 (CSNK) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

Casein kinase-1(α1/δ/γ1) & 2α1 (CSNK) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells shriprakash sinha Independent Researcher; Orcid ID : 0000-0001-7027-5788 Address : 104-Madhurisha Heights Phase 1, Risali, Bhilai-490006, India Corresponding author email : [email protected] Abstract Casein kinase (CSNK) are serine/threonine-selective protein kinase, which selectively modifies other proteins by covalently adding phosphates to them (phosphorylation) as opposed to kinases which modify lipids, carbohydrates, or other molecules. Gujral and MacBeath [1] provides a quantitative, and dynamic study of WNT3A-mediated stimulation of HEK 293 cells, where they record time based expression profiles of several response genes which correlated significantly with proliferation and migration. By monitoring the dynamics of gene expression using self-organizing maps, they identified clusters of genes that exhibit similar expression dynamics and uncovered previously unrecognized positive and negative feedback loops. However, their study depicts/uses singular measurements of individual gene expression at different time snapshots/points to infer the system wide analysis of the pathway. At any particular time point, it is often the case that genes are working synergistically in combinations, even though their expression measurements are singular in nature. Here, I •enumerate and rank all 2415 CSNK (family member) related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for CSNK-X-X combinations, which point to existence of biological synergy of some of these combinations across the different sensitivity methods; and •study the behaviour of some of these combinations related to WNT3A response genes that are ranked by the machine learning search engine (Sinha [2]) in time. Patterns of combinations emerge, some of which have been tested in wet lab, while others require further wet lab analysis. Keywords: Sensitivity analysis, Support vector ranking, Hilbert Schmidt Independence Criterion indices (HSIC) and Sobol indicies, WNT3A ITime behavioural study of 3-odr CSNK comb. in WNT3A stimulated cells 1Aspects of unpublished work were presented in a poster session at Cell Symposia: Technology. Biology. Data Science, 9-11 October 2016, Berkeley, California, USA. Preprint submitted to Preprint March 26, 2025 1. Significance Sinha [2] recently demonstrated the use of machine learning based search engine to rank/reveal gene combinations at 2nd order for the time series data by Gujral and MacBeath [1] and showed how it is possible to locate combinations of priority that might be working synergistically, using sensitivity methods and powerful support vector ranking algorithm. However, the problem explodes combinatorially with even a small set of 71 recorded genes in the study by Gujral and MacBeath [1], when one steps to explore 3rd order combinations. With the total number of 71C3(= 57155) combinations, it becomes nearly impossible for any biologist to study the system wide dynamics of any pathway. Also, the amount of time usually needed to search for and test a combination is far more than the search down by the machine learning based search engine. Here, I extend the research work by Sinha [2] to conduct a behavioral study of 3rd order FOXN1 related combinations using individual gene expressions measured in time, in WNT3A stimulated HEK 293 cells. 2. Introduction The details of the machine learning based search engine has been recently published in Sinha [2] and deployed to explore the 2nd order combinations of genes in the data set provided by Gujral and MacBeath [1]. Nevertheless, here, I point to the fundamentals of the published work for completeness. 2.1. A combinatorial problem Sensitivity analysis plays a major role in computing the strength of the influence of involved factors in any phenomena under investigation. When applied to expression profiles of various intra/extracellular factors that form an integral part of a signaling pathway, the variance and density based analysis yields a range of sensitivity indices for individual as well as various combinations of factors. These combinations denote the higher order interactions among the involved factors. Computation of higher order interactions is often time consuming but it gives a chance to explore the various combinations that might be of interest in the working mechanism of the pathway. For example, in a range of fourth order combinations among the various factors of the Wnt pathway, it would be easy to assess the influence of the destruction complex formed by APC, AXIN, CSKI and GSK3 interaction. But the effect of these combinations vary over time as measurements of fold changes and deviations in fold changes vary. So it is imperative to know how an interaction or a combination of the involved factors behave in time and Sinha [2] develops a procedure to track the behaviour by exploiting the influences of these involved factors. 2.2. A possible solution In this work, after estimating the individual effects of factors for a higher order combination, the individual indices are considered as discriminative features. A combination, 2 then, is a feature set in higher order (≥2 ,i.e multivariate). With an excessively large number of factors involved in the pathway, it is difficult to search for important combinations in a wide search space over different orders. Exploiting the analogy with the issues of prioritizing webpages using ranking algorithms, for a particular order, a full set of combinations of interactions can then be prioritized based on these features using a powerful ranking algorithm via support vectors Joachims [3]. Recording the changing rankings of the combinations over time reveals how higher order interactions behave within the pathway and when an intervention might be necessary to influence the interaction within the pathway. 2.3. The earliest research using Casein A phosphoprotein is a protein that is post-translationally modified by the attachment of either a single phosphate group, or a complex molecule such as 5’-phospho-DNA, through a phosphate group. In eukaryotes, the target amino acid is mostly serine, threonine, or tyrosine residues,while in prokaryotes, it is aspartic acid or histidine residues. Cozzone [4] summarizes and documents the phosphorylation of proteins, as a major regulatory mechanism in cells. In rat liver mitochondria, Burnett and Kennedy [5] discovered an enzyme capable of catalyzing the transfer of phosphate from ATP to protein. Of a number of proteins tested, they observed that only casein was phosphorylated at an appreciable rate. αcasein was observed to phosphorylate at about 4 times the rate of β-casein. Further, nearly all of the radioactivity transferred from ATP labeled with P32 to casein could be accounted for as radioactive phosphoserine in acid hydrolysates of the casein. Free phosphoserine did not appear to be an intermediate in the reaction. Casein is a family of related phosphoproteins, known in the form of α-S1 (encoded by CSN1S1), α-S2 (encoded by CSN1S2), β(encoded by CSN2) and κ(encoded by CSN3), casein. Fujiwara et al. [6] isolated and characterized 5 yeast artificial chromosome (YAC) clones containing the human casein gene family, to study the control mechanisms for the expression of these genes. They performed, partial restriction analysis in conjunction with the chromosomal fragmentation method and fluorescence in situ hybridization (FISH) analysis, to construct a detailed physical map of the casein gene family and determined the chromosomal localization of these genes. The isolated YAC clones 748F3, 882G11, 886B3 and 960D2 contained the entire casein gene family, while the κ-casein gene was absent in 750D11. The human αS1-, βand κ-casein genes were found to be closely linked and arranged in the order αS1-β-κ. The casein gene family was localized to chromosome 4q21.1 by FISH analysis. 2.4. Casein kinase (CSNK) The Casein kinase family of protein kinases are serine/threonine-selective enzymes, which selectively modifies other proteins by covalently adding phosphates to them (i.e phosphorylation, Cohen [7]) as opposed to kinases which modify lipids, carbohydrates, or other molecules. In the Golgi apparatus of lactating rat mammary gland, Bingham and Farrell Jr [8] found a casein kinase that catalyzed the phosphorylation of dephosphorylated α-S13 casein by ATP. They report that dephosphorylated βand κ-caseins were also phosphorylated by this enzyme, while other milk proteins (β-lactoglobulin, α-lactalbumin, native α-S1-, β-, and κ-casein, and proteins of the fat globule membrane) were phosphorylated to a limited extent. They observed that the optimum pH for phosphate incorporation into dephosphorylated casein was 7.6; the Kmfor dephosphorylated αS1-casein was 12 µm (.27 mg per ml), whereas the Kmfor ATP was 80 µm. Further, the casein kinase required a divalent cation for maximum activity (both Ca2+and Mg2+ could satisfy this requirement). These findings suggested that the phosphorylation of casein (a food protein), was quite different from the phosphorylation of cellular enzymes, which required cyclic AMP, was inhibited by Ca2+and was involved in control mechanisms. Hanks and Hunter [9] carried out a monumental task of analyzing and collating the amino acid sequences of all protein kinases and defining the conserved structural features that characterize the portion of these proteins that is responsible for catalytic activity. In their review, they present information about the eukaryotic protein kinases (a large superfamily of homologous proteins), which are related by their kinase domains (also known as catalytic domains), which consist of ≈250-300 amino acid residues. They observe that the kinase domains that define this group of enzymes contain 12 conserved subdomains that fold into a common catalytic core structure, as revealed by the 3-dimensional structures of severed proteinserine kinases. There are two main sub-divisions within the superfamily: the protein-serine/threonine kinases and the protein-tyrosine kinases. Further, they suggest that a classification scheme can be founded on a kinase domain phylogeny, which reveals families of enzymes that have related substrate specificities and modes of regulation. 2.4.1. Casein kinase 1 (CSNK1 / CK1) CSNK1A1 - Tapia et al. [10] isolated and sequenced, a cDNA clone coding for human protein kinase CK1 (casein kinase 1), thus demonstrating that it corresponded to a homolog of the CK1α(CSNK1A1) form found in bovine brain. Using this cDNA sequence and PCR amplification, they further isolated YAC genomic clones that contain this human CK1αsequence. These YACs were used for fluorescent in situ hybridization in order to localize the human CK1αgene to chromosome 13q13. Fish et al. [11] reported the cloning and characterization of a novel isoform of CKI from a human placental cDNA library. The cDNA for this isoform, hCKIε(CSNK1E), predicted a basic polypeptide of 416 amino acids and a molecular mass of 47.3 kDa. They observed that it encoded a core kinase domain of 285 amino acids and a carboxylterminal tail of 123 amino acids. The kinase domain was 53-98% identical to the kinase domains of other CKI family members and was most closely related to the δisoform. Localization of the hCKIεgene to chromosome 22q12-13 and the hCKIδ(CSNK1D) gene to chromosome 17q25 confirmed that these were distinct genes in the CKI family. In summary, hCKIεwas a novel CKI isoform with properties that overlapped those of previously described CKI isoforms. CSNK1D - Rowles et al. [12] purified casein kinase I (CKI) over 6000-fold from bovine thymus and sequenced seven tryptic peptides that accounted for nearly 25% of the primary sequence of the enzyme. They isolated partial cDNAs encoding CKI and 4 a related enzyme (CKIδ), by using PCR. Further, they used the CKI PCR product to probe a bovine brain cDNA library from which cDNAs corresponding to CKI (CKIα) and two homologous enzymes (CKIβand CKIγ) were identified. Their finding of the existence of least four CKI-like enzymes suggested that CKI activity in tissues/cell extracts may be composed of multiple related but distinct protein kinases. Based on this, they suggest that this group of enzymes was not similar to any other known protein kinases and may, therefore, represent an additional branch of the protein kinase family. Graves et al. [13] reported the molecular cloning and characterization of a 49-kDa form of casein kinase I from rat testis. A cDNA clone encoding the enzyme, designated casein kinase I δ(CSNK1D), contained an open reading frame of 1284 nucleotides that predicted a polypeptide of 428 amino acids with a Mr, of 49,121. The predicted amino acid sequence shared 76% identity with casein kinase I α, a 37-kDa form that was cloned from bovine brain by Rowles et al. [12]. Further, expression of the casein kinase IδcDNA in Escherichia coli resulted in active enzyme that phosphorylated casein, phosvitin, and the peptide substrate DDDDVASLPGLRRR. They observed taht Casein kinase I δrepresented a separate member of the casein kinase I family distinguished by its larger size and unique kinetic behavior with respect to heparin. Kusuda et al. [14] isolated and sequenced a cDNA clone coding for human casein kinase I (CK1). They found that the entire amino acid sequence of human CK1 was 97% homologous to that of rat CK1δ, and their sequences in the kinase domain (284 amino acid residues) were completely identical, thus predicting that the obtained cDNA was for a human homolog of the CK1δisoform (CSNK1D). The human CK1δ gene was mapped to chromosome 17q25.2q25.3 by fluorescencein situhybridization and polymerase chain reaction analysis of the human/rodent hybrid cell panels. CSNK1G1 - Kusuda et al. [15] isolated two types of cDNA for human casein kinase 1 γ1 (hCK1 γ1). They found hCK1γ1S to encode a polypeptide consisting of 393 amino acids, which was highly homologous with already reported rat CK1γ1 (rCK1γ1), while the other type of cDNA (hCK1γ1L) encoded a polypeptide consisting of 422 amino acids, which was quite identical in the kinase domain, but different in the C-terminal sequence from hCK1γ1S. Further, hCK1γ1L had a characteristic sequence of 50 amino acids at the C-terminal end and this motif was shown to be shared by the casein kinase γ2 and γ3 from rat and human, thus suggesting that it was a signature sequence of the gamma-isoforms. RT-PCR analysis revealed that hCK1γ1S mRNA was predominantly present in the testis, whereas the abundance of hCK1γ1L mRNA was nearly the same in the twelve tissues examined. Finally, the human hCK1γ1 gene (CSNK1G1) was mapped to chromosome 15q22.1–>q22.31 by fluorescence in situ hybridization. 2.4.2. Casein kinase 2 (CSNK2 / CK2) By immunological screening of λgt11 expression libraries, Saxena et al. [16] isolated cloned cDNAs encoding both subunits of Drosophila melanogaster casein kinase II, and the complete amino acid sequence of both polypeptides was deduced by DNA sequencing. The alpha cDNA contained an open reading frame of 336 amino acid residues and the expected semi-invariant residues present in the catalytic domain of previously sequenced protein kinases, confirming that it was the catalytic subunit of the 5 enzyme. On the other hand, the beta subunit was derived from an open reading frame of 215 amino acid residues and exhibited no extensive homology to other proteins whose sequences were known at the time of this research. Using a Drosophila casein kinase II cDNA probe, Meisner et al. [17] isolated a human cDNA encoding the alpha subunit of casein kinase II and a partial cDNA encoding the rat homologue. The Drosophila enzyme sequence was found to be 90% identical with the human casein kinase II sequence, and there was only a single amino acid difference between the published partial bovine sequence and the human sequence. These results were consistent with the possibility that two genes could encode the alpha subunits. Casein kinase II holoenzyme appears to be a tetramer, containing two αor α’ subunits (or one of each) and two beta subunits. Study by Lozeman et al. [18], show that there are two distinct catalytic subunits for casein kinase II (alpha and alpha’) and that the sequence of these subunits was largely conserved between the bovine and the human. Yang-Feng et al. [19] localized the human CKII-αDNA sequence to two loci: 11p15.5p15.4 and 20p13, using a combination of segregation analysis of rodent-human hybrid cells and chromosomal in situ hybridization. In contrast, they mapped the CKllα’ gene to chromosome 16, by somatic cell hybrid analysis. Taken together with their previous assignment of the CKII regulatory β-subunit gene to 6p12p21, these results indicated that although the products of these genes formed a single biological complex, they were encoded on different human chromosomes. CSNK2A1 - Finally, Wirkner et al. [20] isolated and characterized a 18.9-kb genomic clone representing a central portion of the human casein kinase II (CKII) subunit αgene (CSNK2A1). Using the whole clone as a probe, the gene was localized on chromosome 20p13. The clone contained eight exons whose sequences comprised bases 102 to 824 of the coding region of the human CKIIαand the exon/intron splice junctions conformed to the gt/ag rule. Three of the nine introns were located at positions corresponding to those in the CKIIαgene of the nematode Caenorhabditis elegans. The introns contained eight complete and eight incomplete Alu repeats. Some of the Alu sequences were arranged in tandems of two or three, which seemed to originate from insertions of younger Alu sequences into the poly(A) region of previously integrated Alu sequences, as indicated by flanking direct repeats. I present 3rd order combinations of CSNK with other genes, that the machine learning based search engine points to, as possible synergistic combinations that might be working in time. 3. Methods Please refer to sections of Sinha [2] for methods, design of study and analysis of data for 2nd order combinations. The same method and design of study is used to generate results for 3rd order combinations presented in this study. 6 4. Time series data Gujral and MacBeath [1] present a set of 71 WNT-related gene expression values for 6 different times points over a range of 24-hour period using qPCR. The changes represent the fold-change in the expression levels of genes in 200 ng/mL WNT3A-stimulated HEK 293 cells in time relative to their levels in unstimulated, serum-starved cells at 0hour. Gujral and MacBeath [1] state that qPCR data are the means of three biological replicates. Only genes whose mean transcript levels changed by more than two-fold at one or more time points during the 24-hour time course were considered significant. Positive (negative) numbers represent up (down) -regulation. We have already covered the issues related to these data sets in detail in Sinha [21]. Readers are requested to go through them in the pointed reference. The tools of study which are used here have been published in another foundational work in Sinha [21]. 5. Design of experiment 5.1. Pipeline for time series data For the case of time series data, interactions among the contributing factors are studied by comparing triplets of fold-changes at single time points. The prodecure begins with the generation of distribution around measurements at single time points with added noise is done to estimate the indices. A distribution is generated for the fold changes at single time points. Then for every gene, there is a vector of values representing fold changes as well as deviations in fold changes for different time points and durations between time points, respectively. Next a listing of all Cn kcombinations for knumber of genes from a total of ngenes is generated. kis ≥2 and ≤(n−1). Each of the combination of order krepresents a unique set of interaction between the involved genetic factors. After this, 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 pth combination in Cn kcombinations, the dataset is prepared in the required format from the distributions for two separate cases which have been discussed above. (See .R code in mainScript-1-1.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 pcombinations. This procedure is done for different kinds of sensitivity analysis methods. After the above sensitivity indices have been stored for each of the pth combination, the next step in the design of experiment is conducted. Since there is only one recording of sensitivity index per combination, each combination forms a training example which is alloted a training index and the sensitivity indices of the individual genetic factors form the training example. Thus there are Cn ktraining examples for kth order interaction. Using this training set SVMRank learn Joachims [3] is used to generate a model on default value Cvalue of 20. In the current experiment on toy model Cvalue 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 7 model is then used to generate score on the observations in the testing set using the SV MRank classi f y Joachims [3]. Note that due to availability of only one example per combination, after the model has been built, the same training data is used as test data to generates the scores. This procedure is executed for each and every sensitivity analysis method. This is followed by sorting of these scores along with the rank indices (i.e the training 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 MRank algorithm. Finally, this entire procedure is computed for sensitivity indices generated for each and every fold change at time point and deviations in fold change at different durations. Observing the changing rank of a particular combination at different times and different time periods will reveal how a combination is behaving. 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(”mainScript-1-1.R”) with arguments for Dynamic data •source(”SVMRankResults-D.R”), to rank the interactions (again this needs to be done separately for different kinds of SA methods), •use source(”Combine-Time-files.R”), if computing indices separately via previous file, •source(”Sort-n-Plot-D.R”) to sort the interactions. Note that the sorting is chages the interaction ranking in time. Thus •use source(”Interaction-Priority-Intime.R”) to find the prioritized ranking of each and every interaction over the different time points and finally •use source(”Print-RankingAND-Interaction-Rank.R”) to print individual ranking of the required input factor with other interaction factors. 6. Results & Discussion 6.1. Time series data by Gujral and MacBeath [1] NOTE - Ranking was assigned on scores that were sorted in DECREASING values. So, 1 was assigned to highest score and vice versa. Results for the 3rd order interactions are presented here. The results first discuss the behaviour of interactions across the snapshots of time using the computed sensitivities on fold change measurements per time snapshot. The analysis was done using 4 different sensitivity indices. Out of the 71C3combinations, I consider/present only those combinations that show a ranking within first 10,000 out of 57,155. This choice is liberal and biologists/oncologists can have a more stricter choice as per need. Two observations are made, •the ranking of a particular combination is conserved (i.e within the 10,000 range) in a particular time point or in the early phase or late phase of WNT3A stimulation, across the majority of the four sensitivity methods, which is a strict criteria of assessment or •the ranking of a particular combination is conserved across time points/phase (i.e they are within the 10,000 range) and the majority of the four sensitivity methods, which is relaxed criteria of assessment. Applying this filter helps reveal important combinations of interest that might be working synergistically at a higher order level in the cell. Regarding technical points of implementation, the rankings were generated without scaling/normalizing the time series data provided by Gujral and MacBeath [1]. 8 For estimating the sensitivity indices, a small gaussian distribution using the function rnorm that generates a vector of normally distributed random variables given a vector length n (here 9, the 10th one is the mean/recorded gene regulation itself), a population mean µand population standard deviation σ. The syntax for using rnorm is as follows: rnorm(n, mean, sd). Further, I use the jitter funtion to add a little bit of noise to the data. This helps to see if the generated rankings are robust or not. 6.2. Enumeration and ranking of 2415 CSNK1A1-X-X combinations from Gujral and MacBeath [1] In the supplementary section, I present four files, each containing the rankings of 3rd order combinations, that wary in time (shown for 5 time points). Each file represents the rankings computed using a particular sensitivity method. The changing rankings in time for a particular combination represents the importance of contribution/role that combination plays in the cell stimulated with WNT3A. The sensitivity methods used are Hilbert Schmidt Independence Criterion indices (HSIC) indices (with rbf and linear kernel in Da Veiga [22]) and Sobol indicies (with 2002 implementation in Saltelli [23] and martinez implementation in Martinez [24] and Baudin et al. [25]). 6.3. Conserved machine learning rankings for tested CSNK1A1-XX combinations A total of 2415, 3rd order combinations involving CSNK1A1 were obtained from a full set of 71C3= 57155 combinations. Further, from this selected set, using the above criteria for conserved rankings, I report/tabulate the meaningful combinations that might be working synergistically. Tables 2, 3 and 4 show the rankings for the same combinations as in table 1, but using rbf kernel for HSIC, 2002 implementation for SOBOL and martinez implementation for SOBOL, respectively. As one tallies the rankings of across these tables for a particular combination, one finds that the role of the combination of interest is conserved. This conservation points to the existence of the biological synergy, whether the combination has been tested or unexplored/untested. 6.3.1. Examining the behaviour of DVL-CSNK1A1-X combinations Dishevelled (DVL) protein plays a central role in WNT pathway by transducing the signal from the Wnt receptor complex to the β-catenin destruction complex. DVL also plays a pivotal role in the planar cell polarity pathway that involves the c-JUN N-terminal kinase (JNK). JNKs were originally identified as kinases that bind and phosphorylate c-JUN on Ser-63 and Ser-73 within its transcriptional activation domain. Cong et al. [26] found that casein kinase I (CKI), a positive regulator of WNT signaling, stimulated DVL activity in the WNT pathway, but dramatically inhibited DVL activity in the JNK pathway. Consistent with this, they observed that overexpression of CKI in Drosophila melanogaster stimulated WNT signaling and disrupted planar cell polarity. Furthermore, by using RNA interference, they demonstrated that the Drosophila CKI homologue double time positively regulated the β-catenin pathway via DVL and negatively regulated the DVL-induced JNK pathway. They thus suggested that CKI 9 directly for, β-catenin. The structural and biochemical data suggested a novel model for how APC functions in β-catenin degradation. Looking at the tables above, one finds the following combinations for APC along with CSNK1A1, to be prominent at 3rd order level - APC-CSNK1A1-DAAM1, APCCSNK1A1-TCF7L1, APC-CSNK1A1-WNT2, APC-BCL9-CSNK1A1, APC-CSNK1A1DKK1, APC-CSNK1A1-FBXW11, APC-CSNK1A1-SENP2, APC-CSNK1A1-TCF7, APC-CSNK1A1-FBXW4, APC-CSNK1A1-FZD1, APC-CSNK1A1-FZD8, APC-CSNK1A1GSK3B and APC-CSNK1A1-FRZB. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 6.4. Conserved machine learning rankings for tested CSNK1D-X-X combinations A total of 2415, 3rd order combinations involving CSNK were obtained from a full set of 71C3= 57155 combinations. Further, from this selected set, using the above criteria for conserved rankings, I report/tabulate the meaningful combinations that might be working synergistically. Tables 6, 7 and 8 show the rankings for the same combinations as in table 5, but using rbf kernel for HSIC, 2002 implementation for SOBOL and martinez implementation for SOBOL, respectively. As one tallies the rankings of across these tables for a particular combination, one finds that the role of the combination of interest is conserved. This conservation points to the existence of the biological synergy, whether the combination has been tested or unexplored/untested. NOTE - We consider the same factors which acted in combination for CSNK1A1, in the previous sections, as we have evidence of literature that have verified the existence of combinatorial synergy with CSNK1A1. Here we see if there exists combinations for CSNK1D, or not. 6.4.1. Examining the behaviour of DVL-CSNK1D-X combinations Looking at the tables above, one finds the following combinations for members of DVL family along with CSNK1D, to be prominent at 3rd order level - BCL9-CSNK1DDVL1 and CSNK1D-DVL2-LEF1. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 6.4.2. Examining the behaviour of TCF-CSNK1D-X combinations Looking at the tables above, one finds the following combinations for members of TCF family along with CSNK1D, to be prominent at 3rd order level - CSNK1D-FGF4TCF7L1, CSNK1D-FGF4-TCF7, CSNK1D-PORCN-TCF7, CSNK1D-PPP2R1A-TCF7L1, CSNK1D-PPP2R1A-TCF7, CSNK1D-FOXN1-TCF7L1, CSNK1D-JUN-TCF7L1, CSNK1DFOXN1-TCF7, CSNK1D-JUN-TCF7, CSNK1D-GSK3A-TCF7L1 and CSNK1D-LRP6TCF7. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 16 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CSNK1D-FGF4-SENP2 12 15434 36642 38886 8419 CSNK1D-FGF4-FOSL1 30 6054 51426 42593 32863 CSNK1D-FGF4-TCF7L1 44 18859 55201 32920 17618 CSNK1D-FGF4-WNT5A 59 12095 43366 47094 42796 CSNK1D-FGF4-WNT3A 62 3435 29950 56252 22054 CSNK1D-FGF4-LRP5 68 8358 23265 46644 15156 CSNK1D-FGF4-PPP2R1A 72 17401 22364 53716 30729 CSNK1D-FGF4-WNT2B 82 23581 20638 52449 10903 CSNK1D-FGF4-WNT4 98 6482 43663 41124 12062 CSNK1D-FGF4-SFRP1 103 1452 48498 52465 14299 CSNK1D-FGF4-TCF7 114 16725 32161 19689 28545 CSNK1D-FGF4-SFRP4 120 325 44939 34338 20617 CSNK1D-FGF4-RHOU 137 7470 45846 49163 20155 CSNK1D-FGF4-FRAT1 154 4058 50213 49903 6296 CSNK1D-FGF4-NLK 182 13641 35785 54873 12126 CSNK1D-FGF4-GSK3B 194 12598 37191 52378 26164 CSNK1D-FGF4-LEF1 219 1576 38743 22056 7921 CSNK1D-FGF4-FZD7 220 17662 38625 44699 22997 CSNK1D-PORCN-SENP2 254 26488 43944 21480 22511 CSNK1D-SFRP1-WNT2B 268 48716 36593 46538 17001 AES-AXIN1-CSNK1D 336 51649 23870 47953 1427 CSNK1D-FOXN1-LEF1 437 1005 10226 23334 20989 CSNK1D-FGF4-FZD8 505 12071 27989 37578 9827 CSNK1D-FZD2-LEF1 522 392 1270 40271 30141 CSNK1D-FGF4-KREMEN1 529 10037 50110 50880 28493 CSNK1D-FSHB-LEF1 553 21733 36403 3295 16135 CSNK1D-FOSL1-FZD1 568 999 47773 10250 51091 CSNK1D-PORCN-WNT2B 573 51683 44617 47981 16208 CSNK1D-FOXN1-SENP2 624 4830 5783 7469 36423 CSNK1D-GSK3A-LEF1 723 313 2418 21648 1291 CSNK1D-FGF4-WNT3 740 18961 36184 50414 8143 CSNK1D-FGF4-TLE1 799 22825 47823 41761 7069 CSNK1D-JUN-LEF1 823 6859 47543 11454 29458 CSNK1D-PPP2R1A-WNT5A 992 931 1207 30631 56811 FZD5-CCND3-CSNK1D 1013 2704 4480 48146 19 CSNK1D-PORCN-TLE2 1050 41629 52347 39317 20436 CSNK1D-FGF4-FZD6 1063 5699 37365 32586 26789 CSNK1D-PORCN-TCF7 1115 16160 38935 28820 29405 CSNK1D-FOXN1-KREMEN1 1122 3656 11331 13933 38262 CSNK1D-PPP2R1A-TCF7L1 1128 12625 3602 38061 56712 CSNK1D-FOXN1-PPP2CA 1252 17427 16752 21509 34632 CSNK1D-CXXC4-FZD1 1263 2919 24873 24770 29960 CSNK1D-FOXN1-WNT2B 1328 17615 2986 7052 5219 CSNK1D-CTNNB1-T 1338 17969 13628 49746 36181 CSNK1D-FOXN1-FZD8 1359 10239 4066 27563 3347 CSNK1D-PPP2R1A-TCF7 1430 4169 153 38743 7414 CSNK1D-FGF4-LRP6 1476 6459 24160 48759 14140 CSNK1D-PORCN-SLC9A3R1 1596 41508 51420 34746 16992 CSNK1D-FGF4-SLC9A3R1 1680 16334 34504 26928 33064 CSNK1D-FOXN1-TCF7L1 1701 17694 5920 17923 11937 CSNK1D-TLE1-TLE2 1724 21275 41549 44598 15361 CSNK1D-WNT1-WNT2B 1760 3377 3805 17345 50447 CSNK1D-FOXN1-FZD7 1784 13446 5253 17028 40495 CSNK1D-FOXN1-MYC 1836 2577 20627 16019 40465 CSNK1D-SFRP1-SFRP4 1855 34480 36277 39100 23037 CSNK1D-PORCN-SFRP1 1945 41776 54231 29005 26519 CSNK1D-FGF4-PPP2CA 2103 20756 11349 39534 15407 CSNK1D-FOXN1-SLC9A3R1 2107 11939 2569 12418 40459 CSNK1D-PORCN-FBXW4 2224 25065 31330 23189 19480 CSNK1D-JUN-TCF7L1 2260 26231 56724 39559 1567 CSNK1D-FOXN1-FZD1 2304 904 14917 34472 44382 CSNK1D-FGF4-FSHB 2441 17927 45150 34061 11599 CSNK1D-FZD6-SFRP4 2540 1448 2060 26618 40843 FZD5-CCND2-CSNK1D 2569 50084 31913 44030 55296 CSNK1D-GSK3A-SFRP4 2717 1830 17275 20425 6307 CSNK1D-WNT3-WNT3A 2727 49625 22336 55596 44252 CSNK1D-JUN-WNT3A 2740 3878 56083 44551 46162 CSNK1D-CXXC4-FRAT1 2744 18327 34701 8594 2661 CSNK1D-NLK-WNT4 2750 2726 9906 45186 25621 CSNK1D-WNT1-WNT2 2884 830 8568 25186 5895 CSNK1D-FOXN1-RHOU 2891 4517 7734 29359 18640 CSNK1D-PORCN-PPP2R1A 2896 17111 34991 43683 19157 CSNK1D-PORCN-WNT5A 2899 17376 34214 55252 32946 CSNK1D-FGF4-PYGO1 2967 23307 41918 28164 3925 CSNK1D-GSK3A-SENP2 3013 17698 1355 31846 6960 CSNK1D-FOXN1-TCF7 3058 2324 2856 25009 48032 CSNK1D-FGF4-PITX2 3093 11417 24874 53815 30793 CSNK1D-FGF4-WIF1 3202 18099 34798 40988 22019 CSNK1D-FOXN1-LRP5 3219 4054 11922 50036 24583 CSNK1D-JUN-TCF7 3439 2738 31647 25028 51027 CSNK1D-FOSL1-FRZB 3460 9515 54696 17041 40782 CSNK1D-GSK3A-WNT2B 3478 33755 3658 52438 24593 CSNK1D-FRAT1-FZD1 3569 4219 52992 30046 47083 CSNK1D-WNT1-WNT4 3618 317 9161 25363 16241 CSNK1D-NLK-WNT3A 3672 3466 7618 26301 5357 CSNK1D-GSK3A-WNT2 3764 1816 4728 34640 8679 CSNK1D-FOXN1-PITX2 3778 6280 4678 21772 36345 CSNK1D-FOXN1-LRP6 3780 5416 14616 20732 36025 CSNK1D-JUN-WNT2B 3782 39855 36594 49047 2280 BCL9-CSNK1D-DVL1 3917 28513 23552 3666 9410 FZD5-CSNK1D-WNT5A 3923 32577 23307 47873 6444 CSNK1D-JUN-PYGO1 3934 1849 39438 23725 46933 CSNK1D-SFRP1-WNT5A 3998 16473 29590 51130 13720 CSNK1D-JUN-SENP2 4050 19615 50185 29822 41231 CSNK1D-GSK3A-PPP2CA 4064 22624 794 37163 9946 CSNK1D-FOXN1-GSK3B 4159 13828 5801 31044 53930 CSNK1D-GSK3A-KREMEN1 4185 9426 5865 52232 3987 CCND3-CSNK1D-FGF4 4247 56969 5553 44696 25096 BCL9-CSNK1D-FOSL1 4412 39895 11612 3219 55102 CSNK1D-FZD2-PPP2CA 4453 21686 1861 42323 46897 CSNK1D-SFRP1-WNT3A 4551 19558 52514 48069 19184 CSNK1D-LRP6-RHOU 4592 17007 12476 52979 3340 CSNK1D-CTBP2-LEF1 4610 223 28103 22239 7005 BCL9-CSNK1D-SENP2 4632 37058 3181 4534 51855 CSNK1D-FOXN1-WNT3A 4647 1495 8738 24005 46405 CSNK1D-DVL2-LEF1 4662 5034 10825 440 37937 CSNK1D-JUN-TLE2 4736 22202 35404 30933 11826 CCND3-CSNK1D-WNT5A 4753 43030 22446 46977 51854 CSNK1D-FOSL1-FZD7 4768 31561 48499 37364 37254 CSNK1D-NLK-SENP2 4773 12377 9957 43796 3597 CSNK1D-SFRP1-TLE2 4922 46547 38030 46678 31499 CSNK1D-GSK3A-TCF7L1 5032 24389 11966 40967 20883 CSNK1D-PITX2-SFRP4 5096 37446 11233 10582 41257 CSNK1D-FZD2-LRP5 5122 962 3101 54072 26208 CSNK1D-GSK3A-RHOU 5141 8223 4832 44949 10510 CSNK1D-CTNNB1-FRZB 5197 24993 56239 40597 28537 CSNK1D-FGF4-MYC 5235 14215 44901 39123 23202 CSNK1D-JUN-WNT4 5251 20001 51942 21538 52316 BCL9-CSNK1D-EP300 5259 34971 18070 4629 41428 CSNK1D-FOXN1-PPP2R1A 5317 3754 8571 14144 18670 FZD5-CCND1-CSNK1D 5355 24059 52933 18167 50576 CSNK1D-FZD2-SFRP4 5362 1855 17483 13582 54971 CSNK1D-FOXN1-WNT4 5440 3392 11967 26112 53280 APC-BTRC-CSNK1D 5442 10883 12646 22647 6204 CSNK1D-CTBP2-SFRP4 5542 334 31924 37036 44498 CSNK1D-LRP6-TCF7 5593 12297 32989 31678 26667 Table 5: Rankings of CSNK1D-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear 6.4.3. Examining the behaviour of PP2A-CSNK1D-X combinations Looking at the tables above, one finds the following combinations for members of PPP2A family along with CSNK1D, to be prominent at 3rd order level - CSNK1DFGF4-PPP2R1A, CSNK1D-FOXN1-PPP2CA, CSNK1D-FGF4-PPP2CA, CSNK1D17 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CSNK1D-FGF4-SENP2 2542 27165 19967 35638 32914 CSNK1D-FGF4-FOSL1 3694 6645 6799 4138 45840 CSNK1D-FGF4-TCF7L1 4541 25809 20278 40264 36271 CSNK1D-FGF4-WNT5A 16991 26760 1497 11585 17580 CSNK1D-FGF4-WNT3A 866 6634 43990 20734 56058 CSNK1D-FGF4-LRP5 8844 18263 430 12232 23605 CSNK1D-FGF4-PPP2R1A 3004 29048 12442 15684 23801 CSNK1D-FGF4-WNT2B 2842 20288 7801 35728 43120 CSNK1D-FGF4-WNT4 2044 17655 11902 17351 48590 CSNK1D-FGF4-SFRP1 17187 352 5460 18719 36092 CSNK1D-FGF4-TCF7 2578 13286 34 28753 54402 CSNK1D-FGF4-SFRP4 6151 154 43125 29798 22993 CSNK1D-FGF4-RHOU 3836 6390 11977 25185 40250 CSNK1D-FGF4-FRAT1 4624 3572 29726 25608 46279 CSNK1D-FGF4-NLK 5343 27561 8638 8497 51980 CSNK1D-FGF4-GSK3B 2870 6165 39093 37995 35649 CSNK1D-FGF4-LEF1 16885 889 16278 22379 29256 CSNK1D-FGF4-FZD7 3708 1492 23721 12408 17016 CSNK1D-PORCN-SENP2 5664 26748 24402 26200 37885 CSNK1D-SFRP1-WNT2B 7873 54928 11692 34070 52974 AES-AXIN1-CSNK1D 33513 47832 7845 51708 6743 CSNK1D-FOXN1-LEF1 6150 3755 45826 20298 28446 CSNK1D-FGF4-FZD8 1068 28301 13813 37144 30865 CSNK1D-FZD2-LEF1 38842 5216 13377 4337 12007 CSNK1D-FGF4-KREMEN1 2147 22653 25065 18882 43497 CSNK1D-FSHB-LEF1 55374 14244 35230 8216 18460 CSNK1D-FOSL1-FZD1 14359 1015 37515 5753 14234 CSNK1D-PORCN-WNT2B 8595 53305 9816 26691 42121 CSNK1D-FOXN1-SENP2 1289 8520 39455 7070 25852 CSNK1D-GSK3A-LEF1 6720 14350 53714 3942 23987 CSNK1D-FGF4-WNT3 2419 18531 38096 22623 37111 CSNK1D-FGF4-TLE1 1651 32994 23493 5014 41934 CSNK1D-JUN-LEF1 20901 8723 38740 12713 27687 CSNK1D-PPP2R1A-WNT5A 27528 4279 14277 4265 42405 FZD5-CCND3-CSNK1D 4293 24482 51150 40471 36385 CSNK1D-PORCN-TLE2 12595 39793 26325 7235 43651 CSNK1D-FGF4-FZD6 6737 6408 6417 30228 39254 CSNK1D-PORCN-TCF7 4035 1408 266 23788 31209 CSNK1D-FOXN1-KREMEN1 3060 1922 41865 30003 8137 CSNK1D-PPP2R1A-TCF7L1 34388 5648 48876 25681 52823 CSNK1D-FOXN1-PPP2CA 677 25144 54449 22625 44186 CSNK1D-CXXC4-FZD1 7144 1734 27303 7250 11481 CSNK1D-FOXN1-WNT2B 2477 5135 39962 11954 23525 CSNK1D-CTNNB1-T 51919 2142 9666 39801 16008 CSNK1D-FOXN1-FZD8 484 13507 45944 36021 49258 CSNK1D-PPP2R1A-TCF7 34317 14103 3740 45791 33515 CSNK1D-FGF4-LRP6 18101 5680 13351 25149 10621 CSNK1D-PORCN-SLC9A3R1 26693 34397 22670 453 31614 CSNK1D-FGF4-SLC9A3R1 10617 29302 26992 4647 42618 CSNK1D-FOXN1-TCF7L1 1853 19094 49475 40364 5085 CSNK1D-TLE1-TLE2 28280 37833 12666 39269 5835 CSNK1D-WNT1-WNT2B 3674 5014 26127 3017 32922 CSNK1D-FOXN1-FZD7 2580 12602 43323 15316 39137 CSNK1D-FOXN1-MYC 463 3569 42774 40411 28606 CSNK1D-SFRP1-SFRP4 5865 32490 29157 40625 43609 CSNK1D-PORCN-SFRP1 36889 38723 2444 15209 50430 CSNK1D-FGF4-PPP2CA 3187 47005 13018 23779 39413 CSNK1D-FOXN1-SLC9A3R1 9628 8268 42958 15342 21726 CSNK1D-PORCN-FBXW4 5373 20376 20328 22365 50987 CSNK1D-JUN-TCF7L1 22113 18400 27177 33962 5630 CSNK1D-FOXN1-FZD1 186 1437 42030 14270 8269 CSNK1D-FGF4-FSHB 8876 10878 93 40281 25736 CSNK1D-FZD6-SFRP4 28948 9871 56626 33341 10920 FZD5-CCND2-CSNK1D 2174 48901 29308 29035 26999 CSNK1D-GSK3A-SFRP4 3312 9861 54850 25114 31433 CSNK1D-WNT3-WNT3A 4832 51374 56476 26830 11649 CSNK1D-JUN-WNT3A 3991 7790 52423 12387 1862 CSNK1D-CXXC4-FRAT1 14134 8276 23947 22453 12908 CSNK1D-NLK-WNT4 1538 21775 47534 6449 28873 CSNK1D-WNT1-WNT2 3841 8374 55936 27925 28491 CSNK1D-FOXN1-RHOU 3693 1529 28226 32793 21419 CSNK1D-PORCN-PPP2R1A 16940 28022 22571 2476 54099 CSNK1D-PORCN-WNT5A 17071 12074 1312 10487 50936 CSNK1D-FGF4-PYGO1 35224 24194 35705 42726 4974 CSNK1D-GSK3A-SENP2 679 19695 54356 47357 23687 CSNK1D-FOXN1-TCF7 526 3006 24338 37412 29080 CSNK1D-FGF4-PITX2 21808 22200 7826 55044 47261 CSNK1D-FGF4-WIF1 2570 27850 35517 16644 26870 CSNK1D-FOXN1-LRP5 3643 4399 15957 9681 3346 CSNK1D-JUN-TCF7 19796 346 649 20621 7941 CSNK1D-FOSL1-FRZB 19966 5694 21191 35654 5540 CSNK1D-GSK3A-WNT2B 537 38319 50713 23870 15104 CSNK1D-FRAT1-FZD1 30515 10291 41362 5174 7792 CSNK1D-WNT1-WNT4 2475 13139 28187 2712 22029 CSNK1D-NLK-WNT3A 12770 9632 43802 42949 37641 CSNK1D-GSK3A-WNT2 1633 16051 53761 28401 27543 CSNK1D-FOXN1-PITX2 11143 1695 49037 55776 7145 CSNK1D-FOXN1-LRP6 13480 3544 42500 13963 13814 CSNK1D-JUN-WNT2B 36826 33885 13766 40492 6501 BCL9-CSNK1D-DVL1 43892 32546 30461 1264 19067 FZD5-CSNK1D-WNT5A 10782 25515 25535 29067 55122 CSNK1D-JUN-PYGO1 46732 424 46278 41608 30058 CSNK1D-SFRP1-WNT5A 7931 18053 3281 19001 33260 CSNK1D-JUN-SENP2 2653 23718 38996 40186 21869 CSNK1D-GSK3A-PPP2CA 1046 40897 47094 14850 34061 CSNK1D-FOXN1-GSK3B 1758 13445 40737 47921 44449 CSNK1D-GSK3A-KREMEN1 1238 5197 49343 17131 39680 CCND3-CSNK1D-FGF4 53833 56236 13403 31362 5509 BCL9-CSNK1D-FOSL1 47904 42624 47654 3433 45846 CSNK1D-FZD2-PPP2CA 3053 36451 19189 15273 40108 CSNK1D-SFRP1-WNT3A 1694 2663 18831 24025 39031 CSNK1D-LRP6-RHOU 9238 26733 38518 37191 35303 CSNK1D-CTBP2-LEF1 8883 17823 28631 13435 18163 BCL9-CSNK1D-SENP2 44308 43457 33874 30051 32611 CSNK1D-FOXN1-WNT3A 174 2450 50841 26734 14997 CSNK1D-DVL2-LEF1 53540 4763 36760 14495 51756 CSNK1D-JUN-TLE2 17254 7221 33658 28649 27279 CCND3-CSNK1D-WNT5A 26184 41606 8103 12634 19595 CSNK1D-FOSL1-FZD7 39520 47576 23109 9945 26122 CSNK1D-NLK-SENP2 2789 23569 46292 12953 16278 CSNK1D-SFRP1-TLE2 13034 42315 14660 41421 27119 CSNK1D-GSK3A-TCF7L1 789 29786 54140 26077 36093 CSNK1D-PITX2-SFRP4 4175 45358 33459 4847 37993 CSNK1D-FZD2-LRP5 31249 14000 540 14876 15989 CSNK1D-GSK3A-RHOU 557 7015 53157 22185 43573 CSNK1D-CTNNB1-FRZB 15856 15227 48531 37431 9414 CSNK1D-FGF4-MYC 4085 24182 15055 21582 25623 CSNK1D-JUN-WNT4 23623 7470 42887 14337 2015 BCL9-CSNK1D-EP300 52623 25888 25234 6007 31047 CSNK1D-FOXN1-PPP2R1A 783 2341 30370 5693 20193 FZD5-CCND1-CSNK1D 4682 17735 35223 18136 46595 CSNK1D-FZD2-SFRP4 8632 6917 25028 10001 13916 CSNK1D-FOXN1-WNT4 712 1876 41088 1961 29254 APC-BTRC-CSNK1D 2236 12178 36083 5029 45903 CSNK1D-CTBP2-SFRP4 5497 10895 29317 34539 10978 CSNK1D-LRP6-TCF7 5176 36559 1881 36347 12983 Table 6: Rankings of CSNK1D-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf GSK3A-PPP2CA, CSNK1D-PPP2R1A-WNT5A, CSNK1D-PPP2R1A-TCF7L1, CSNK1DPPP2R1A-TCF7, CSNK1D-PORCN-PPP2R1A, CSNK1D-FZD2-PPP2CA and CSNK1DFOXN1-PPP2R1A. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 18 RANKING @tiUSING SOBOL - 2002 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CSNK1D-FGF4-SENP2 45011 27585 30267 41354 22081 CSNK1D-FGF4-FOSL1 31433 17351 34702 49796 3779 CSNK1D-FGF4-TCF7L1 25851 23703 28531 9955 26240 CSNK1D-FGF4-WNT5A 27276 41074 28302 22360 34593 CSNK1D-FGF4-WNT3A 26097 37629 27746 14081 26558 CSNK1D-FGF4-LRP5 2955 43397 25413 16078 42368 CSNK1D-FGF4-PPP2R1A 16041 36350 23034 23038 36186 CSNK1D-FGF4-WNT2B 28074 51541 15533 12033 30048 CSNK1D-FGF4-WNT4 31095 19365 29428 42965 30788 CSNK1D-FGF4-SFRP1 17254 46015 24945 24496 39736 CSNK1D-FGF4-TCF7 47373 33208 33019 35060 24479 CSNK1D-FGF4-SFRP4 39876 11006 32217 32622 17395 CSNK1D-FGF4-RHOU 12115 29224 26900 15818 35002 CSNK1D-FGF4-FRAT1 43307 19656 33814 44501 13085 CSNK1D-FGF4-NLK 11305 41185 24087 8932 35872 CSNK1D-FGF4-GSK3B 4128 7853 22532 14175 38412 CSNK1D-FGF4-LEF1 35712 40912 31537 37596 9192 CSNK1D-FGF4-FZD7 38718 29241 32518 33630 10048 CSNK1D-PORCN-SENP2 26180 49740 24174 6964 30394 CSNK1D-SFRP1-WNT2B 14464 28189 8702 8326 25216 AES-AXIN1-CSNK1D 17614 20399 2658 23007 32892 CSNK1D-FOXN1-LEF1 18416 22419 26392 15687 40976 CSNK1D-FGF4-FZD8 10015 39491 25159 24198 38526 CSNK1D-FZD2-LEF1 31519 19029 30167 30946 20994 CSNK1D-FGF4-KREMEN1 21369 16424 25622 19556 47905 CSNK1D-FSHB-LEF1 17557 28861 26741 15958 23463 CSNK1D-FOSL1-FZD1 33939 40307 29863 45255 32407 CSNK1D-PORCN-WNT2B 39627 20751 32331 36708 28715 CSNK1D-FOXN1-SENP2 22145 41275 26967 5135 47598 CSNK1D-GSK3A-LEF1 36973 16169 28985 41996 5916 CSNK1D-FGF4-WNT3 29097 5562 41695 44969 27058 CSNK1D-FGF4-TLE1 31338 33282 28628 47096 30909 CSNK1D-JUN-LEF1 25658 26247 28008 9195 29514 CSNK1D-PPP2R1A-WNT5A 26135 44357 28294 20860 36948 FZD5-CCND3-CSNK1D 46351 3330 50103 35023 9366 CSNK1D-PORCN-TLE2 40721 9512 29575 32383 21204 CSNK1D-FGF4-FZD6 18376 27935 24677 23494 47063 CSNK1D-PORCN-TCF7 10132 38975 27387 12057 30165 CSNK1D-FOXN1-KREMEN1 31821 16389 28671 30403 11306 CSNK1D-PPP2R1A-TCF7L1 25967 41054 27430 10798 32868 CSNK1D-FOXN1-PPP2CA 18148 46116 27668 8407 45131 CSNK1D-CXXC4-FZD1 15838 20986 27843 15827 35450 CSNK1D-FOXN1-WNT2B 34971 36541 30580 44435 4295 CSNK1D-CTNNB1-T 42761 39366 30573 52126 13625 CSNK1D-FOXN1-FZD8 31892 7178 33756 49005 20364 CSNK1D-PPP2R1A-TCF7 41472 28978 28805 36435 24561 CSNK1D-FGF4-LRP6 54180 13585 31741 41058 14672 CSNK1D-PORCN-SLC9A3R1 22475 41256 24969 21096 28384 CSNK1D-FGF4-SLC9A3R1 43276 13827 31871 40076 15155 CSNK1D-FOXN1-TCF7L1 35334 23957 30050 36064 4998 CSNK1D-TLE1-TLE2 19455 40358 5030 19470 26781 CSNK1D-WNT1-WNT2B 42719 30480 50555 50603 27505 CSNK1D-FOXN1-FZD7 25311 49876 23413 8098 36669 CSNK1D-FOXN1-MYC 44307 29810 29915 52115 22248 CSNK1D-SFRP1-SFRP4 32021 30603 35439 41782 29994 CSNK1D-PORCN-SFRP1 30977 7376 32969 50220 26759 CSNK1D-FGF4-PPP2CA 45504 35247 32816 42764 13525 CSNK1D-FOXN1-SLC9A3R1 23368 50212 27896 7855 37916 CSNK1D-PORCN-FBXW4 40912 20587 30104 44920 20175 CSNK1D-JUN-TCF7L1 40981 24954 29837 33199 13509 CSNK1D-FOXN1-FZD1 36474 18523 28735 38842 16102 CSNK1D-FGF4-FSHB 37586 23188 30054 39574 14949 CSNK1D-FZD6-SFRP4 37025 20562 29540 31061 17840 FZD5-CCND2-CSNK1D 39639 19905 41415 55029 16947 CSNK1D-GSK3A-SFRP4 38998 40109 29848 46577 10900 CSNK1D-WNT3-WNT3A 36262 46174 50463 43303 12247 CSNK1D-JUN-WNT3A 41685 14518 29055 33675 22133 CSNK1D-CXXC4-FRAT1 34042 35885 29812 41264 26139 CSNK1D-NLK-WNT4 41521 25413 31966 31421 31114 CSNK1D-WNT1-WNT2 14398 26421 6595 6539 29319 CSNK1D-FOXN1-RHOU 31392 16873 29114 44729 3759 CSNK1D-PORCN-PPP2R1A 38585 10367 29409 42259 26713 CSNK1D-PORCN-WNT5A 33173 15133 30807 39641 18354 CSNK1D-FGF4-PYGO1 41090 20740 34158 34168 20857 CSNK1D-GSK3A-SENP2 45946 48851 30360 53837 19511 CSNK1D-FOXN1-TCF7 21839 33109 27126 21035 52156 CSNK1D-FGF4-PITX2 45761 16034 33072 48233 21295 CSNK1D-FGF4-WIF1 34683 24427 28639 39649 25219 CSNK1D-FOXN1-LRP5 38778 34796 30801 41436 16166 CSNK1D-JUN-TCF7 16160 32149 27332 23912 43544 CSNK1D-FOSL1-FRZB 31318 38355 31685 44774 22524 CSNK1D-GSK3A-WNT2B 9527 37019 28419 11178 37958 CSNK1D-FRAT1-FZD1 20960 29768 28275 10710 43347 CSNK1D-WNT1-WNT4 20721 8116 11826 6782 37040 CSNK1D-NLK-WNT3A 15647 31281 25207 25693 26652 CSNK1D-GSK3A-WNT2 37628 15354 32710 30271 18583 CSNK1D-FOXN1-PITX2 18384 31000 27911 15993 34137 CSNK1D-FOXN1-LRP6 12836 27102 27262 5010 34889 CSNK1D-JUN-WNT2B 35800 33697 28958 34580 16565 BCL9-CSNK1D-DVL1 5169 2531 9866 16638 46496 FZD5-CSNK1D-WNT5A 21298 15129 1430 366 40105 CSNK1D-JUN-PYGO1 24772 39437 27678 10274 47704 CSNK1D-SFRP1-WNT5A 11269 25479 3686 15976 27188 CSNK1D-JUN-SENP2 19786 39894 26516 17689 39326 CSNK1D-GSK3A-PPP2CA 38964 24815 30788 42585 4984 CSNK1D-FOXN1-GSK3B 33934 15919 31085 51592 27046 CSNK1D-GSK3A-KREMEN1 20093 40861 28185 15145 51111 CCND3-CSNK1D-FGF4 25501 41888 19350 4356 36845 BCL9-CSNK1D-FOSL1 10419 8445 20713 5953 54355 CSNK1D-FZD2-PPP2CA 40401 31133 29816 40542 23445 CSNK1D-SFRP1-WNT3A 19952 32710 12566 7366 35990 CSNK1D-LRP6-RHOU 34637 26415 30562 44183 17446 CSNK1D-CTBP2-LEF1 35436 36626 30114 35212 1936 BCL9-CSNK1D-SENP2 7894 55225 16856 28157 9757 CSNK1D-FOXN1-WNT3A 36731 14201 28962 47587 13902 CSNK1D-DVL2-LEF1 37733 42004 32019 35022 16190 CSNK1D-JUN-TLE2 35323 15737 30487 31236 19521 CCND3-CSNK1D-WNT5A 26753 51792 5466 20864 48578 CSNK1D-FOSL1-FZD7 25294 25065 27511 18532 28438 CSNK1D-NLK-SENP2 40143 16432 28881 34696 27936 CSNK1D-SFRP1-TLE2 14852 25401 8318 13409 27386 CSNK1D-GSK3A-TCF7L1 23592 41249 27328 22703 35101 CSNK1D-PITX2-SFRP4 26609 44292 24260 17256 33381 CSNK1D-FZD2-LRP5 21506 19923 24132 16640 35889 CSNK1D-GSK3A-RHOU 11202 8387 26821 3303 37553 CSNK1D-CTNNB1-FRZB 35537 12277 40549 47197 15377 CSNK1D-FGF4-MYC 24133 31913 27203 19416 39013 CSNK1D-JUN-WNT4 24170 35809 26365 15414 39425 BCL9-CSNK1D-EP300 3311 5825 20711 3984 45817 CSNK1D-FOXN1-PPP2R1A 39046 11003 29491 48744 12072 FZD5-CCND1-CSNK1D 14887 40746 19201 997 4727 CSNK1D-FZD2-SFRP4 35660 24193 30365 46109 21000 CSNK1D-FOXN1-WNT4 23873 38225 27206 12028 40601 APC-BTRC-CSNK1D 42702 43953 47146 33780 8438 CSNK1D-CTBP2-SFRP4 35574 12520 29543 31811 17639 CSNK1D-LRP6-TCF7 14059 30348 28213 14212 32048 Table 7: Rankings of CSNK1D-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - SOBOL; Implementation - 2002 6.4.4. Examining the behaviour of LRP-CSNK1D-X combinations Looking at the tables above, one finds the following combinations for members of LRP family along with CSNK1D, to be prominent at 3rd order level - CSNK1D-FGF4LRP6, CSNK1D-FOXN1-LRP5, CSNK1D-FGF4-LRP5, CSNK1D-FOXN1-LRP6, CSNK1D19 RANKING @tiUSING SOBOL - MARTINEZ 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CSNK1D-FGF4-SENP2 55119 28784 753 23302 53897 CSNK1D-FGF4-FOSL1 39220 16866 389 23848 23132 CSNK1D-FGF4-TCF7L1 40859 12468 13114 42874 33245 CSNK1D-FGF4-WNT5A 39875 34325 26022 14242 1408 CSNK1D-FGF4-WNT3A 11042 19248 28222 21505 8886 CSNK1D-FGF4-LRP5 44011 14327 27863 30216 18989 CSNK1D-FGF4-PPP2R1A 32236 18431 4861 24170 28783 CSNK1D-FGF4-WNT2B 11099 33067 21662 18628 9514 CSNK1D-FGF4-WNT4 30931 24624 1645 40905 44453 CSNK1D-FGF4-SFRP1 24988 7332 20614 11103 14523 CSNK1D-FGF4-TCF7 56903 23341 587 8096 54144 CSNK1D-FGF4-SFRP4 51948 20558 476 17213 54793 CSNK1D-FGF4-RHOU 25547 26286 25711 24726 4948 CSNK1D-FGF4-FRAT1 56865 12006 918 21628 54532 CSNK1D-FGF4-NLK 33940 4625 12426 23698 5080 CSNK1D-FGF4-GSK3B 37094 8199 21044 25936 22668 CSNK1D-FGF4-LEF1 50110 29395 2034 27280 54041 CSNK1D-FGF4-FZD7 54587 3593 2262 16940 46019 CSNK1D-PORCN-SENP2 1456 4258 8869 32822 29157 CSNK1D-SFRP1-WNT2B 45504 25704 37754 9982 35219 AES-AXIN1-CSNK1D 35852 3680 25566 9981 7313 CSNK1D-FOXN1-LEF1 32374 24326 23110 46046 3210 CSNK1D-FGF4-FZD8 23206 13656 45564 35305 9821 CSNK1D-FZD2-LEF1 29724 23302 1126 4556 23508 CSNK1D-FGF4-KREMEN1 24857 20786 27757 39745 8714 CSNK1D-FSHB-LEF1 19222 39228 21058 21493 6562 CSNK1D-FOSL1-FZD1 41680 37855 2054 46155 46394 CSNK1D-PORCN-WNT2B 54547 33746 2831 17934 52535 CSNK1D-FOXN1-SENP2 38843 9650 25689 48746 11032 CSNK1D-GSK3A-LEF1 27984 32214 780 18412 15578 CSNK1D-FGF4-WNT3 27141 43301 10716 18079 36761 CSNK1D-FGF4-TLE1 30313 3293 20586 21005 55995 CSNK1D-JUN-LEF1 36389 9478 48851 37502 3819 CSNK1D-PPP2R1A-WNT5A 34799 46397 27927 38367 6548 FZD5-CCND3-CSNK1D 24425 35427 11357 16458 13140 CSNK1D-PORCN-TLE2 53642 34642 1349 6256 56564 CSNK1D-FGF4-FZD6 25549 14281 21210 22546 3415 CSNK1D-PORCN-TCF7 25748 22359 21805 36766 4140 CSNK1D-FOXN1-KREMEN1 32146 2230 14527 12211 48112 CSNK1D-PPP2R1A-TCF7L1 1420 17934 41275 37855 4684 CSNK1D-FOXN1-PPP2CA 35792 53371 27044 46895 15279 CSNK1D-CXXC4-FZD1 28112 48535 48166 35007 4846 CSNK1D-FOXN1-WNT2B 40727 20657 11342 28759 54605 CSNK1D-CTNNB1-T 55697 37457 1377 24186 53282 CSNK1D-FOXN1-FZD8 40606 42498 22468 13908 52376 CSNK1D-PPP2R1A-TCF7 50128 22951 5812 8544 53759 CSNK1D-FGF4-LRP6 56364 10127 2296 23831 56682 CSNK1D-PORCN-SLC9A3R1 15731 15687 5737 23413 32643 CSNK1D-FGF4-SLC9A3R1 52818 9841 830 24865 56433 CSNK1D-FOXN1-TCF7L1 51221 5285 6459 25508 51438 CSNK1D-TLE1-TLE2 42315 43646 33134 2508 54333 CSNK1D-WNT1-WNT2B 31537 11063 42528 38828 9460 CSNK1D-FOXN1-FZD7 33029 31601 24563 26553 33641 CSNK1D-FOXN1-MYC 50924 26721 3557 20447 56671 CSNK1D-SFRP1-SFRP4 21268 21314 35721 28006 9257 CSNK1D-PORCN-SFRP1 18994 35477 42 21142 50577 CSNK1D-FGF4-PPP2CA 55329 26273 1032 21669 55925 CSNK1D-FOXN1-SLC9A3R1 33119 17256 36353 44743 32463 CSNK1D-PORCN-FBXW4 54457 32031 1944 26924 56516 CSNK1D-JUN-TCF7L1 48658 28221 1848 12654 36298 CSNK1D-FOXN1-FZD1 55202 51315 557 15388 55873 CSNK1D-FGF4-FSHB 53386 36653 4663 24262 56290 CSNK1D-FZD6-SFRP4 51105 5714 720 31166 44306 FZD5-CCND2-CSNK1D 7223 27121 23185 31108 21218 CSNK1D-GSK3A-SFRP4 47899 34099 4951 23576 49750 CSNK1D-WNT3-WNT3A 11520 29889 44430 29706 9625 CSNK1D-JUN-WNT3A 49779 33157 919 18538 52334 CSNK1D-CXXC4-FRAT1 18469 1863 38915 19191 36580 CSNK1D-NLK-WNT4 55088 4562 19617 29935 54873 CSNK1D-WNT1-WNT2 40567 28297 16569 6336 51007 CSNK1D-FOXN1-RHOU 34252 18639 2074 27005 35628 CSNK1D-PORCN-PPP2R1A 46494 24460 5959 26920 56966 CSNK1D-PORCN-WNT5A 22402 4216 2288 18135 42734 CSNK1D-FGF4-PYGO1 53782 7577 1845 21026 56561 CSNK1D-GSK3A-SENP2 52934 31036 1324 14474 42126 CSNK1D-FOXN1-TCF7 32381 26851 38448 50093 9452 CSNK1D-FGF4-PITX2 44579 43462 767 11821 46293 CSNK1D-FGF4-WIF1 43363 48941 1472 39959 56626 CSNK1D-FOXN1-LRP5 52584 42034 6817 14398 37913 CSNK1D-JUN-TCF7 22295 36468 17276 29939 515 CSNK1D-FOSL1-FRZB 41028 37740 6910 31880 54766 CSNK1D-GSK3A-WNT2B 28987 44289 19857 45245 10158 CSNK1D-FRAT1-FZD1 35866 8723 28263 47919 5986 CSNK1D-WNT1-WNT4 4934 23696 3275 40685 48358 CSNK1D-NLK-WNT3A 30261 5484 6297 36145 38245 CSNK1D-GSK3A-WNT2 44075 10874 7758 16421 56183 CSNK1D-FOXN1-PITX2 39725 19950 32730 49412 6271 CSNK1D-FOXN1-LRP6 42807 7879 23909 46855 44003 CSNK1D-JUN-WNT2B 41000 35594 890 25093 56672 BCL9-CSNK1D-DVL1 13131 24654 56866 21285 11397 FZD5-CSNK1D-WNT5A 22240 8729 8905 8361 14874 CSNK1D-JUN-PYGO1 5673 24084 17393 28564 30653 CSNK1D-SFRP1-WNT5A 46232 40726 39677 8395 43436 CSNK1D-JUN-SENP2 31303 34385 30502 38156 4556 CSNK1D-GSK3A-PPP2CA 49948 27496 4120 13149 30348 CSNK1D-FOXN1-GSK3B 44857 1620 1103 5943 42753 CSNK1D-GSK3A-KREMEN1 8331 36538 18893 45935 39059 CCND3-CSNK1D-FGF4 33645 25729 11171 4259 2969 BCL9-CSNK1D-FOSL1 6994 56975 54633 36841 20797 CSNK1D-FZD2-PPP2CA 49236 39754 539 34368 52220 CSNK1D-SFRP1-WNT3A 36490 53621 5052 7047 50254 CSNK1D-LRP6-RHOU 34336 2691 1633 17028 44197 CSNK1D-CTBP2-LEF1 48968 10726 6135 22249 56309 BCL9-CSNK1D-SENP2 7818 31418 33113 7222 1844 CSNK1D-FOXN1-WNT3A 47715 2711 5484 26364 53183 CSNK1D-DVL2-LEF1 49081 18658 2603 29361 56933 CSNK1D-JUN-TLE2 55996 3817 12011 19143 52700 CCND3-CSNK1D-WNT5A 36336 364 51360 31612 43178 CSNK1D-FOSL1-FZD7 32946 26115 27641 53780 8204 CSNK1D-NLK-SENP2 54274 1758 35987 36243 51006 CSNK1D-SFRP1-TLE2 41155 46372 37122 5380 40515 CSNK1D-GSK3A-TCF7L1 2372 2561 26389 42919 28709 CSNK1D-PITX2-SFRP4 783 12794 45331 28854 43563 CSNK1D-FZD2-LRP5 4958 19633 32139 50415 4916 CSNK1D-GSK3A-RHOU 16007 10231 17105 47130 31183 CSNK1D-CTNNB1-FRZB 51258 45759 3242 19204 39592 CSNK1D-FGF4-MYC 27747 53740 29653 32287 2134 CSNK1D-JUN-WNT4 28813 34671 41857 33835 1136 BCL9-CSNK1D-EP300 37357 52675 55940 48065 6089 CSNK1D-FOXN1-PPP2R1A 53170 6227 2620 23711 53082 FZD5-CCND1-CSNK1D 31474 38575 10040 10604 7111 CSNK1D-FZD2-SFRP4 51918 14988 1412 33035 37704 CSNK1D-FOXN1-WNT4 40130 54610 25402 49876 4689 APC-BTRC-CSNK1D 56835 26515 42490 50974 18375 CSNK1D-CTBP2-SFRP4 49397 12922 932 7503 56132 CSNK1D-LRP6-TCF7 31280 19096 22465 41381 4029 Table 8: Rankings of CSNK1D-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - SOBOL; Implementation - martinez LRP6-RHOU, CSNK1D-FZD2-LRP5, and CSNK1D-LRP6-TCF7. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 20 6.4.5. Examining the behaviour of CTNNB1-CSNK1D-X combinations Looking at the tables above, one finds the following combinations for CTNNB1 along with CSNK1D, to be prominent at 3rd order level - CSNK1D-CTNNB1-T and CSNK1DCTNNB1-FRZB. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 6.4.6. Examining the behaviour of APC-CSNK1D-X combinations Looking at the tables above, one finds the following combinations for APC along with CSNK1D, to be prominent at 3rd order level - APC-BTRC-CSNK1D. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 6.5. Conserved machine learning rankings for tested CSNK1G1-XX combinations A total of 2415, 3rd order combinations involving CSNK1G1 were obtained from a full set of 71C3= 57155 combinations. Further, from this selected set, using the above criteria for conserved rankings, I report/tabulate the meaningful combinations that might be working synergistically. Tables 10, 11 and 12 show the rankings for the same combinations as in table 9, but using rbf kernel for HSIC, 2002 implementation for SOBOL and martinez implementation for SOBOL, respectively. As one tallies the rankings of across these tables for a particular combination, one finds that the role of the combination of interest is conserved. This conservation points to the existence of the biological synergy, whether the combination has been tested or unexplored/untested. NOTE - We consider the same factors which acted in combination for CSNK1A1, in the previous sections, as we have evidence of literature that have verified the existence of combinatorial synergy with CSNK1A1. Here we see if there exists combinations for CSNK1G1, or not. 6.5.1. Examining the behaviour of DVL-CSNK1G1-X combinations Looking at the tables above, one finds the following combinations for members of DVL family along with CSNK1G1, to be prominent at 3rd order level - CSNK1G1-DVL2WNT2, CSNK1G1-DVL2-TCF7, CSNK1G1-DVL2-FBXW11, CSNK1G1-DVL2-TCF7L1, CSNK1G1-DVL2-TLE2, CSNK1G1-DVL2-SENP2, CSNK1G1-DVL2-FOSL1, CSNK1G1DVL2-FZD1 and CSNK1G1-DVL2-FRZB. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 6.5.2. Examining the behaviour of TCF-CSNK1G1-X combinations Looking at the tables above, one finds the following combinations for members of TCF family along with CSNK1G1, to be prominent at 3rd order level - CSNK1G1DVL2-TCF7, CSNK1G1-NKD1-TCF7L1, CSNK1G1-FOXN1-TCF7L1, CSNK1G1DVL2-TCF7L1, CSNK1G1-FZD1-TCF7L1, CSNK1G1-FGF4-TCF7L1, CSNK1G1FOXN1-TCF7, CSNK1G1-NLK-TCF7L1, CSNK1G1-CTNNBIP1-TCF7L1, CSNK1G121 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CSNK1G1-NLK-SENP2 74 35675 3308 48520 19328 CSNK1G1-FOXN1-TLE2 226 3994 5316 18517 42187 CSNK1G1-NLK-WNT4 321 20710 3312 50831 31403 CSNK1G1-FOXN1-KREMEN1 390 10815 10745 12917 12924 CSNK1G1-FOXN1-SLC9A3R1 395 1314 2366 9985 14166 CSNK1G1-PORCN-SENP2 410 36322 35831 12245 17913 CSNK1G1-FZD2-SENP2 430 26396 20526 35632 16355 CSNK1G1-FSHB-LEF1 506 19332 10676 684 44215 CSNK1G1-DVL2-WNT2 512 22400 27124 6214 39864 CSNK1G1-FSHB-SFRP4 577 21679 6780 1575 25615 CSNK1G1-FZD2-TLE2 600 1430 44384 54164 52337 CSNK1G1-DVL2-SENP2 708 9805 19546 23999 8201 CSNK1G1-LRP5-SENP2 821 46576 17464 17352 30361 CSNK1G1-JUN-SENP2 855 23957 55112 11084 3256 CSNK1G1-NKD1-PPP2CA 926 17356 35232 35369 12912 CSNK1G1-FZD2-FZD7 944 16232 24487 55399 23887 CSNK1G1-FOXN1-PPP2R1A 960 4562 8931 10045 26824 CSNK1G1-CTNNBIP1-TCF7L1 999 13063 17121 18913 53234 CSNK1G1-FGF4-TLE2 1023 22382 54317 54503 47054 CSNK1G1-FZD2-SFRP4 1035 1065 32773 38790 38245 CSNK1G1-FSHB-SENP2 1054 47479 13640 1228 8996 CSNK1G1-DVL2-FOSL1 1061 14048 12622 34641 48959 CSNK1G1-DVL2-TCF7 1070 8709 15200 25653 4958 CSNK1G1-FZD2-PPP2CA 1082 23722 6311 56537 35909 CSNK1G1-JUN-WNT2 1087 1305 52762 5894 31347 CSNK1G1-CXXC4-FOSL1 1094 46700 26853 25310 54546 CSNK1G1-CTNNBIP1-DKK1 1133 14650 36806 5792 53273 CSNK1G1-JUN-TCF7L1 1134 10933 47748 13909 25134 CSNK1G1-FZD2-WNT2B 1144 10281 11030 49965 37172 CSNK1G1-CTNNBIP1-TLE2 1189 14302 22595 16694 56930 CSNK1G1-NKD1-TCF7L1 1194 9892 6186 28656 13545 CSNK1G1-FOXN1-FBXW4 1201 11491 20301 17590 26677 CSNK1G1-DVL2-FBXW11 1204 11366 47774 39156 34516 CSNK1G1-GSK3B-SLC9A3R1 1210 17915 3146 1251 20930 CSNK1G1-FGF4-KREMEN1 1239 30116 44329 46230 30098 CSNK1G1-NKD1-SENP2 1257 16631 15972 26700 19860 CSNK1G1-FOXN1-TCF7L1 1281 8663 5550 16139 11644 CSNK1G1-T-TLE2 1289 7716 26938 1980 47468 CSNK1G1-PORCN-TLE2 1291 31155 47884 19907 37757 CSNK1G1-PORCN-RHOU 1299 27191 33972 15284 20376 CSNK1G1-JUN-TLE2 1365 2675 25875 17296 52928 CSNK1G1-NKD1-SFRP4 1474 513 13103 24557 6931 CSNK1G1-FSHB-PPP2CA 1518 8523 49087 1235 27660 CSNK1G1-FOXN1-FRZB 1549 4678 4300 19697 7337 CSNK1G1-JUN-KREMEN1 1571 14622 52390 27682 7035 CSNK1G1-FOXN1-RHOU 1587 4796 8477 31603 16974 CSNK1G1-DVL2-TCF7L1 1594 26605 24282 21676 30138 CSNK1G1-SFRP1-WNT5A 1618 12629 47126 54603 30299 CSNK1G1-CTNNB1-KREMEN1 1675 48319 35467 28250 6432 CSNK1G1-SFRP1-TLE2 1712 35952 51589 41916 56964 CSNK1G1-JUN-FBXW4 1720 14629 26207 15285 48296 CSNK1G1-FZD1-SENP2 1791 37257 52309 26522 36929 CSNK1G1-PORCN-SLC9A3R1 1815 10503 40046 19851 14743 CSNK1G1-CTNNB1-SENP2 1823 48308 39023 36622 2971 CSNK1G1-CTNNB1-FBXW11 1832 37454 31263 43989 30890 CSNK1G1-CTNNB1-DAAM1 1863 29150 40706 29346 30532 CSNK1G1-JUN-RHOU 1898 1165 55257 34817 23988 CSNK1G1-DVL2-FZD1 1899 31769 26103 8981 50719 CSNK1G1-FZD1-TCF7L1 1928 14834 43931 28975 44251 CSNK1G1-FGF4-FOSL1 1936 28205 33826 36195 48093 CSNK1G1-FZD2-WNT4 1942 1607 11956 46269 29169 CSNK1G1-FZD2-LEF1 1947 1417 8944 51456 47383 CSNK1G1-GSK3A-TLE2 1958 19247 20416 54079 54261 CSNK1G1-FOXN1-FZD6 1966 10515 13241 17759 18874 CSNK1G1-JUN-PPP2R1A 1986 10228 52696 13904 47706 CSNK1G1-JUN-PYGO1 2002 4879 55264 32395 18429 CSNK1G1-DVL2-TLE2 2047 13079 24517 18237 55667 CSNK1G1-PORCN-TCF7L1 2073 14966 30891 15229 14200 CSNK1G1-FGF4-SENP2 2112 49038 53530 48190 17709 CSNK1G1-JUN-TCF7 2167 22852 38657 32689 6608 CSNK1G1-JUN-PPP2CA 2194 17201 31808 2244 24092 CSNK1G1-FZD1-FZD7 2236 8972 51512 19066 10647 CSNK1G1-CSNK2A1-MYC 2268 42433 43512 35352 51992 CSNK1G1-PORCN-FBXW4 2284 27821 27627 9377 23266 CSNK1G1-FGF4-TCF7L1 2285 10862 41090 54745 25393 CSNK1G1-FGF4-FBXW4 2297 23073 41204 39779 38778 CSNK1G1-FOXN1-TCF7 2327 21226 4505 21767 3917 CSNK1G1-NKD1-RHOU 2328 3565 14141 34128 1880 CSNK1G1-FZD2-FZD8 2338 18572 33760 38917 40049 CSNK1G1-JUN-WNT2B 2402 5466 39576 33692 34944 CSNK1G1-NLK-TCF7L1 2409 13940 8988 50696 40050 CSNK1G1-FZD2-SLC9A3R1 2430 12072 31728 53760 44963 CSNK1G1-GSK3B-LRP6 2470 3965 12186 1024 16413 CSNK1G1-PORCN-WNT2B 2472 8559 45236 34464 18734 CSNK1G1-CXXC4-DKK1 2488 45829 37872 27388 55403 CSNK1G1-CXXC4-FRAT1 2496 24384 49297 7946 49881 CSNK1G1-FGF4-PPP2R1A 2535 19539 51865 57137 46652 CSNK1G1-WIF1-WNT2B 2561 1995 24404 34807 53934 CSNK1G1-WIF1-WNT4 2582 628 24563 33380 53761 CSNK1G1-DIXDC1-WNT2B 2602 9079 34225 44850 51306 CSNK1G1-T-WNT2B 2676 4730 9390 14824 25293 CSNK1G1-T-TCF7L1 2695 8773 21250 845 15712 CSNK1G1-PORCN-PPP2R1A 2697 18740 49826 20704 24737 CSNK1G1-PORCN-WNT5A 2747 5935 22657 45224 29673 CSNK1G1-PORCN-SFRP1 2795 18557 36114 17627 42050 CSNK1G1-DVL2-FRZB 2830 11776 15278 32095 12867 CSNK1G1-JUN-SLC9A3R1 2848 7013 49399 24901 32991 CSNK1G1-JUN-WNT4 2974 622 48857 6464 4596 CSNK1G1-FSHB-MYC 2987 47541 16749 1201 23454 CSNK1G1-NLK-WNT2B 3057 20612 364 49392 38971 CSNK1G1-JUN-WNT5A 3068 8191 56989 38952 10438 CSNK1G1-SFRP1-WNT2B 3077 12559 37776 32807 54829 CSNK1G1-FGF4-FRAT1 3087 3833 51164 49600 29524 CSNK1G1-CTNNB1-FRZB 3107 38284 22901 35739 3612 CSNK1G1-CTBP2-DKK1 3146 194 46088 31304 49535 CSNK1G1-GSK3B-RHOU 3190 3405 4726 1433 8406 CSNK1G1-CTBP2-SLC9A3R1 3240 166 52122 36860 45086 CSNK1G1-DIXDC1-RHOU 3247 13611 55894 17887 29476 CSNK1G1-GSK3A-RHOU 3261 12094 4223 43874 25027 CSNK1G1-FZD2-WNT5A 3333 14640 38705 56952 5899 CSNK1G1-CTNNBIP1-FOSL1 3338 21173 6659 21711 53461 CSNK1G1-FSHB-WNT2B 3357 9060 28997 6593 37362 APC-CSNK1G1-FZD1 3390 30189 28290 1457 54900 CSNK1G1-PORCN-WNT2 3410 20366 30313 12508 34531 CSNK1G1-CTNNBIP1-FBXW11 3415 22265 9012 12002 52077 CSNK1G1-DIXDC1-DKK1 3474 22358 26349 38523 54006 CSNK1G1-FOXN1-FZD1 3475 2066 8269 14457 23102 CSNK1G1-FGF4-SFRP1 3511 22139 54017 39144 48180 CSNK1G1-NKD1-WNT2 3527 1109 9218 26094 482 CSNK1G1-JUN-SFRP4 3548 4317 53039 9482 18106 CSNK1G1-FGF4-SLC9A3R1 3554 8200 55502 49949 42703 CSNK1G1-PYGO1-TLE2 3565 24569 56894 5227 16188 CSNK1G1-FGF4-WNT4 3583 9743 47387 43850 34383 CSNK1G1-FOXN1-WNT3A 3634 7199 9792 30313 10861 CSNK1G1-FSHB-T 3636 19798 35345 312 15515 CSNK1G1-GSK3A-SENP2 3671 35222 2760 48687 25616 Table 9: Rankings of CSNK1G1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear JUN-TCF7L1, CSNK1G1-PORCN-TCF7L1, CSNK1G1-JUN-TCF7 and CSNK1G1T-TCF7L1. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 22 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CSNK1G1-NLK-SENP2 34480 34469 25805 4202 8014 CSNK1G1-FOXN1-TLE2 3512 4562 37294 11299 13219 CSNK1G1-NLK-WNT4 37117 32429 26444 1650 27288 CSNK1G1-FOXN1-KREMEN1 7103 1710 43024 36832 31611 CSNK1G1-FOXN1-SLC9A3R1 4227 955 39936 15459 33468 CSNK1G1-PORCN-SENP2 13585 41454 10606 1967 17443 CSNK1G1-FZD2-SENP2 16568 22383 10213 6975 36119 CSNK1G1-FSHB-LEF1 46458 5148 44690 1362 34271 CSNK1G1-DVL2-WNT2 26581 25977 21694 30622 18019 CSNK1G1-FSHB-SFRP4 49673 9604 39425 16774 51741 CSNK1G1-FZD2-TLE2 14214 390 12996 12800 24140 CSNK1G1-DVL2-SENP2 10060 33044 6346 24081 29517 CSNK1G1-LRP5-SENP2 14135 47074 22615 10563 18356 CSNK1G1-JUN-SENP2 2057 43819 27038 14070 17638 CSNK1G1-NKD1-PPP2CA 8799 37693 42013 33688 15900 CSNK1G1-FZD2-FZD7 21108 3606 11500 6373 21026 CSNK1G1-FOXN1-PPP2R1A 3415 1125 22606 474 39586 CSNK1G1-CTNNBIP1-TCF7L1 43171 9916 19650 22573 25909 CSNK1G1-FGF4-TLE2 12643 19305 27429 4012 34111 CSNK1G1-FZD2-SFRP4 27829 5976 9290 19601 31081 CSNK1G1-FSHB-SENP2 41253 35360 30966 2443 33408 CSNK1G1-DVL2-FOSL1 24608 32567 25022 2699 31491 CSNK1G1-DVL2-TCF7 15740 15189 43760 1824 49105 CSNK1G1-FZD2-PPP2CA 21192 37740 25191 13344 44898 CSNK1G1-JUN-WNT2 10147 5580 32401 33214 37290 CSNK1G1-CXXC4-FOSL1 18872 46435 17556 11771 54033 CSNK1G1-CTNNBIP1-DKK1 45274 12532 2085 28807 30170 CSNK1G1-JUN-TCF7L1 827 11310 28918 27910 3674 CSNK1G1-FZD2-WNT2B 31344 5642 34740 5475 23273 CSNK1G1-CTNNBIP1-TLE2 43515 18510 14805 25265 22352 CSNK1G1-NKD1-TCF7L1 6006 22577 49200 31622 30401 CSNK1G1-FOXN1-FBXW4 6456 4971 6852 14306 22075 CSNK1G1-DVL2-FBXW11 14851 14553 29808 12160 18195 CSNK1G1-GSK3B-SLC9A3R1 24505 22540 7318 7896 7232 CSNK1G1-FGF4-KREMEN1 12312 33122 8653 27029 51700 CSNK1G1-NKD1-SENP2 4079 7354 54740 12528 13804 CSNK1G1-FOXN1-TCF7L1 2258 13561 45680 37954 10050 CSNK1G1-T-TLE2 15349 28608 40369 17566 47898 CSNK1G1-PORCN-TLE2 25416 24850 21439 2281 53031 CSNK1G1-PORCN-RHOU 18456 21677 26712 34529 54262 CSNK1G1-JUN-TLE2 3633 15390 39684 2796 27092 CSNK1G1-NKD1-SFRP4 10332 8994 35937 45547 19919 CSNK1G1-FSHB-PPP2CA 50070 6934 23453 5427 21042 CSNK1G1-FOXN1-FRZB 4205 5593 40227 150 17600 CSNK1G1-JUN-KREMEN1 6491 2240 25073 41585 18357 CSNK1G1-FOXN1-RHOU 5126 2277 43717 34280 32087 CSNK1G1-DVL2-TCF7L1 8430 32795 20312 16548 46597 CSNK1G1-SFRP1-WNT5A 26848 12013 30115 7944 48214 CSNK1G1-CTNNB1-KREMEN1 12259 40883 18405 45871 37363 CSNK1G1-SFRP1-TLE2 38330 13700 14458 10263 44078 CSNK1G1-JUN-FBXW4 6418 15849 3058 18441 29387 CSNK1G1-FZD1-SENP2 32058 40787 30927 4374 20821 CSNK1G1-PORCN-SLC9A3R1 33423 29599 9114 6260 50642 CSNK1G1-CTNNB1-SENP2 8473 45202 18386 8358 20498 CSNK1G1-CTNNB1-FBXW11 8081 32056 33348 27118 24593 CSNK1G1-CTNNB1-DAAM1 13837 35555 36581 34030 48851 CSNK1G1-JUN-RHOU 2915 263 26104 42711 34946 CSNK1G1-DVL2-FZD1 5036 24181 26002 2834 17734 CSNK1G1-FZD1-TCF7L1 26757 20001 35110 22673 40307 CSNK1G1-FGF4-FOSL1 30497 29781 8021 11753 43558 CSNK1G1-FZD2-WNT4 13040 11367 14247 4325 36477 CSNK1G1-FZD2-LEF1 37628 651 37780 9885 25711 CSNK1G1-GSK3A-TLE2 21880 3846 34786 4128 44853 CSNK1G1-FOXN1-FZD6 9597 4725 31350 6692 33022 CSNK1G1-JUN-PPP2R1A 2410 8342 5954 20586 31871 CSNK1G1-JUN-PYGO1 17775 1546 36260 46060 22759 CSNK1G1-DVL2-TLE2 25707 7774 19195 28772 13026 CSNK1G1-PORCN-TCF7L1 19446 5592 14959 30431 50377 CSNK1G1-FGF4-SENP2 4616 45273 3041 10902 17063 CSNK1G1-JUN-TCF7 2531 27001 37335 13108 9426 CSNK1G1-JUN-PPP2CA 3740 31530 16470 29436 25461 CSNK1G1-FZD1-FZD7 42202 2356 44114 48791 35670 CSNK1G1-CSNK2A1-MYC 46238 56607 42725 857 38125 CSNK1G1-PORCN-FBXW4 10477 26670 1604 31235 52570 CSNK1G1-FGF4-TCF7L1 3125 11336 9840 33926 40511 CSNK1G1-FGF4-FBXW4 20873 40154 1525 33082 24319 CSNK1G1-FOXN1-TCF7 6103 15997 49902 11757 46472 CSNK1G1-NKD1-RHOU 7968 13163 45029 45281 48042 CSNK1G1-FZD2-FZD8 22757 27942 6185 40310 30385 CSNK1G1-JUN-WNT2B 7913 15753 39919 50228 16435 CSNK1G1-NLK-TCF7L1 38665 6811 44713 7792 48500 CSNK1G1-FZD2-SLC9A3R1 28704 8977 9734 10319 26207 CSNK1G1-GSK3B-LRP6 44943 8879 13860 8331 10201 CSNK1G1-PORCN-WNT2B 15765 2688 26141 22189 56019 CSNK1G1-CXXC4-DKK1 18870 49739 2762 48160 29218 CSNK1G1-CXXC4-FRAT1 10676 6045 28407 52045 39223 CSNK1G1-FGF4-PPP2R1A 8938 29139 2598 16353 38899 CSNK1G1-WIF1-WNT2B 38910 5666 25272 47015 36127 CSNK1G1-WIF1-WNT4 16896 27273 7830 48279 26589 CSNK1G1-DIXDC1-WNT2B 56105 5718 34204 36658 46240 CSNK1G1-T-WNT2B 7308 15374 20596 23413 32785 CSNK1G1-T-TCF7L1 2357 14811 41736 25166 36605 CSNK1G1-PORCN-PPP2R1A 16024 19421 9392 5370 55173 CSNK1G1-PORCN-WNT5A 8541 17540 20517 6560 46815 CSNK1G1-PORCN-SFRP1 27236 23068 16848 13318 54516 CSNK1G1-DVL2-FRZB 11203 3943 12156 18643 14086 CSNK1G1-JUN-SLC9A3R1 8199 8824 12860 16832 13385 CSNK1G1-JUN-WNT4 3575 5 23478 28885 6190 CSNK1G1-FSHB-MYC 43747 46283 35580 1289 17413 CSNK1G1-NLK-WNT2B 53434 5922 42619 33337 50690 CSNK1G1-JUN-WNT5A 1627 9471 37716 21278 33763 CSNK1G1-SFRP1-WNT2B 46506 17719 30569 35787 55375 CSNK1G1-FGF4-FRAT1 3622 6775 28403 42516 41038 CSNK1G1-CTNNB1-FRZB 9877 40304 14569 3677 31442 CSNK1G1-CTBP2-DKK1 12379 37559 2412 41433 4051 CSNK1G1-GSK3B-RHOU 31434 1254 24292 12304 14579 CSNK1G1-CTBP2-SLC9A3R1 25333 8891 16800 22800 25629 CSNK1G1-DIXDC1-RHOU 49459 11518 16506 41618 49774 CSNK1G1-GSK3A-RHOU 19387 9576 34864 29016 31935 CSNK1G1-FZD2-WNT5A 20419 29433 26502 7708 18760 CSNK1G1-CTNNBIP1-FOSL1 35395 8179 16803 17088 24295 CSNK1G1-FSHB-WNT2B 43414 19138 41449 6694 6668 APC-CSNK1G1-FZD1 7749 26824 42227 42495 14246 CSNK1G1-PORCN-WNT2 21543 32722 24973 9534 56929 CSNK1G1-CTNNBIP1-FBXW11 40429 22735 27221 29186 11089 CSNK1G1-DIXDC1-DKK1 26769 29764 1454 44361 36145 CSNK1G1-FOXN1-FZD1 1030 2372 37367 366 6405 CSNK1G1-FGF4-SFRP1 15656 24142 6725 14523 42132 CSNK1G1-NKD1-WNT2 6387 6428 51082 8449 39348 CSNK1G1-JUN-SFRP4 6927 6984 24622 46197 4920 CSNK1G1-FGF4-SLC9A3R1 10241 16030 4176 25778 44518 CSNK1G1-PYGO1-TLE2 21495 24434 29013 7562 53728 CSNK1G1-FGF4-WNT4 8298 17662 14155 26871 50395 CSNK1G1-FOXN1-WNT3A 7916 4786 40233 7694 33821 CSNK1G1-FSHB-T 51659 22786 44198 2191 56498 CSNK1G1-GSK3A-SENP2 17955 35543 38041 9692 22046 Table 10: Rankings of CSNK1G1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf 6.5.3. Examining the behaviour of PPP2A-CSNK1G1-X combinations Looking at the tables above, one finds the following combinations for members of PPP2A family along with CSNK1G1, to be prominent at 3rd order level - CSNK1G1NKD1-PPP2CA, CSNK1G1-FOXN1-PPP2R1A, CSNK1G1-FSHB-PPP2CA, CSNK1G1JUN-PPP2R1A, CSNK1G1-JUN-PPP2CA, CSNK1G1-FGF4-PPP2R1A, CSNK1G123 RANKING @tiUSING SOBOL - 2002 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CSNK1G1-NLK-SENP2 14817 11675 2225 15674 28868 CSNK1G1-FOXN1-TLE2 21537 42757 2336 15141 32041 CSNK1G1-NLK-WNT4 7646 8437 104 10192 43063 CSNK1G1-FOXN1-KREMEN1 12568 9848 1206 5693 56612 CSNK1G1-FOXN1-SLC9A3R1 29604 29598 56041 56960 9679 CSNK1G1-PORCN-SENP2 43281 37454 56745 49095 6460 CSNK1G1-FZD2-SENP2 11142 28642 7792 15597 42963 CSNK1G1-FSHB-LEF1 38254 27148 47701 53981 4899 CSNK1G1-DVL2-WNT2 27910 12643 15697 4994 46665 CSNK1G1-FSHB-SFRP4 49169 3805 44567 32085 3551 CSNK1G1-FZD2-TLE2 42543 28177 42687 36354 12646 CSNK1G1-DVL2-SENP2 22798 50683 12430 15447 46966 CSNK1G1-LRP5-SENP2 20952 26227 18132 5105 9267 CSNK1G1-JUN-SENP2 49955 51075 54767 43231 2180 CSNK1G1-NKD1-PPP2CA 2818 12720 1066 16639 39238 CSNK1G1-FZD2-FZD7 7158 42378 658 9668 56103 CSNK1G1-FOXN1-PPP2R1A 26102 33906 21109 71 51037 CSNK1G1-CTNNBIP1-TCF7L1 28112 7321 13375 27783 55812 CSNK1G1-FGF4-TLE2 38171 54018 38464 53649 27611 CSNK1G1-FZD2-SFRP4 23075 10268 7269 4789 48739 CSNK1G1-FSHB-SENP2 47318 7617 44202 35329 27387 CSNK1G1-DVL2-FOSL1 13304 16111 11364 20166 55668 CSNK1G1-DVL2-TCF7 22581 2224 18751 13174 56823 CSNK1G1-FZD2-PPP2CA 7371 1821 2940 12583 54147 CSNK1G1-JUN-WNT2 43215 54139 50622 48011 1250 CSNK1G1-CXXC4-FOSL1 25168 1437 11571 16056 25721 CSNK1G1-CTNNBIP1-DKK1 12140 38448 9541 5556 54479 CSNK1G1-JUN-TCF7L1 6017 14337 20145 21380 48232 CSNK1G1-FZD2-WNT2B 43957 8905 55685 37469 3334 CSNK1G1-CTNNBIP1-TLE2 25127 3237 10881 7849 46732 CSNK1G1-NKD1-TCF7L1 44067 52737 54968 47023 15857 CSNK1G1-FOXN1-FBXW4 27569 27578 1117 197 47485 CSNK1G1-DVL2-FBXW11 32525 55485 49860 43897 62 CSNK1G1-GSK3B-SLC9A3R1 17837 1282 3936 19428 55642 CSNK1G1-FGF4-KREMEN1 49711 51438 57107 44900 43052 CSNK1G1-NKD1-SENP2 8054 22379 116 14940 56704 CSNK1G1-FOXN1-TCF7L1 24011 53828 1796 3138 42955 CSNK1G1-T-TLE2 33761 15546 56982 41993 4590 CSNK1G1-PORCN-TLE2 7372 47733 19657 27924 17147 CSNK1G1-PORCN-RHOU 13901 19785 413 8056 50675 CSNK1G1-JUN-TLE2 6833 1066 4928 11587 56004 CSNK1G1-NKD1-SFRP4 10766 6807 490 4170 32258 CSNK1G1-FSHB-PPP2CA 45864 55377 47231 36646 7302 CSNK1G1-FOXN1-FRZB 16921 42333 17206 26037 35243 CSNK1G1-JUN-KREMEN1 6923 4884 26325 13483 55790 CSNK1G1-FOXN1-RHOU 22734 36628 1885 6243 38820 CSNK1G1-DVL2-TCF7L1 34613 54955 38410 43971 335 CSNK1G1-SFRP1-WNT5A 30598 12429 52931 54526 8133 CSNK1G1-CTNNB1-KREMEN1 8399 6622 8923 3958 38591 CSNK1G1-SFRP1-TLE2 36104 28241 56956 55279 6687 CSNK1G1-JUN-FBXW4 13976 51841 1693 18282 49989 CSNK1G1-FZD1-SENP2 46940 54887 56179 52112 3649 CSNK1G1-PORCN-SLC9A3R1 33650 47676 46612 33574 30645 CSNK1G1-CTNNB1-SENP2 47712 45420 46499 43561 3144 CSNK1G1-CTNNB1-FBXW11 1940 20675 21938 18791 49322 CSNK1G1-CTNNB1-DAAM1 12750 37186 12892 1955 43684 CSNK1G1-JUN-RHOU 7215 6024 2384 13893 54958 CSNK1G1-DVL2-FZD1 35203 16601 30820 51262 6952 CSNK1G1-FZD1-TCF7L1 13950 21245 2033 8324 25283 CSNK1G1-FGF4-FOSL1 8963 28835 12476 27024 48361 CSNK1G1-FZD2-WNT4 7022 898 12245 15373 35027 CSNK1G1-FZD2-LEF1 13090 29157 20896 15256 44016 CSNK1G1-GSK3A-TLE2 43557 47135 32471 29032 1778 CSNK1G1-FOXN1-FZD6 15112 29912 14213 23427 38252 CSNK1G1-JUN-PPP2R1A 17390 9694 2316 9148 46335 CSNK1G1-JUN-PYGO1 39719 47416 54841 47973 10949 CSNK1G1-DVL2-TLE2 36214 52629 39421 48657 6369 CSNK1G1-PORCN-TCF7L1 8742 30765 16154 23864 24961 CSNK1G1-FGF4-SENP2 2157 16345 1663 19346 36353 CSNK1G1-JUN-TCF7 43538 48608 50508 47527 4924 CSNK1G1-JUN-PPP2CA 49728 12194 55667 43794 1187 CSNK1G1-FZD1-FZD7 42817 7109 51146 49529 157 CSNK1G1-CSNK2A1-MYC 18695 1708 3446 13091 35254 CSNK1G1-PORCN-FBXW4 23515 9545 10526 23569 26078 CSNK1G1-FGF4-TCF7L1 47918 55844 55366 54508 35878 CSNK1G1-FGF4-FBXW4 44225 4355 54630 48647 959 CSNK1G1-FOXN1-TCF7 34219 34310 44976 35510 7051 CSNK1G1-NKD1-RHOU 40596 5950 54719 48495 7475 CSNK1G1-FZD2-FZD8 50007 14985 56494 47469 1059 CSNK1G1-JUN-WNT2B 12092 24688 5587 16813 56343 CSNK1G1-NLK-TCF7L1 44331 44573 53183 44188 4910 CSNK1G1-FZD2-SLC9A3R1 21480 38407 5615 17975 40405 CSNK1G1-GSK3B-LRP6 6438 18957 418 9590 54912 CSNK1G1-PORCN-WNT2B 8407 8013 15451 27068 11666 CSNK1G1-CXXC4-DKK1 29722 16090 47827 56588 1654 CSNK1G1-CXXC4-FRAT1 27618 3778 3433 676 48257 CSNK1G1-FGF4-PPP2R1A 48874 4935 46376 33919 6326 CSNK1G1-WIF1-WNT2B 13733 56852 4680 24169 53252 CSNK1G1-WIF1-WNT4 53996 12035 47320 37468 7141 CSNK1G1-DIXDC1-WNT2B 12114 7749 26029 14404 44639 CSNK1G1-T-WNT2B 39877 28951 37196 37502 2391 CSNK1G1-T-TCF7L1 33501 6689 34325 48942 815 CSNK1G1-PORCN-PPP2R1A 15949 51267 916 23706 44599 CSNK1G1-PORCN-WNT5A 10356 8876 25975 28454 18185 CSNK1G1-PORCN-SFRP1 7246 7363 14462 20174 36420 CSNK1G1-DVL2-FRZB 30588 38887 41771 49656 1919 CSNK1G1-JUN-SLC9A3R1 43202 5406 55467 38845 7125 CSNK1G1-JUN-WNT4 33107 46065 50016 51102 7862 CSNK1G1-FSHB-MYC 10008 29873 20279 26881 48302 CSNK1G1-NLK-WNT2B 49065 6850 56800 44447 6716 CSNK1G1-JUN-WNT5A 21479 39247 6333 24156 52648 CSNK1G1-SFRP1-WNT2B 34525 31075 56473 56358 3840 CSNK1G1-FGF4-FRAT1 23308 12898 577 6288 40499 CSNK1G1-CTNNB1-FRZB 11010 41399 10677 9362 28958 CSNK1G1-CTBP2-DKK1 36737 50084 41906 46380 7431 CSNK1G1-GSK3B-RHOU 41655 54814 54139 46702 874 CSNK1G1-CTBP2-SLC9A3R1 2953 39509 10302 16583 49929 CSNK1G1-DIXDC1-RHOU 16058 1799 7780 18030 48278 CSNK1G1-GSK3A-RHOU 47412 26494 53128 51332 7632 CSNK1G1-FZD2-WNT5A 50135 56267 44911 41731 22635 CSNK1G1-CTNNBIP1-FOSL1 28695 47395 40486 51217 12008 CSNK1G1-FSHB-WNT2B 6562 41743 11739 18943 50322 APC-CSNK1G1-FZD1 32683 26130 40629 37958 20743 CSNK1G1-PORCN-WNT2 50216 4601 38088 29252 9325 CSNK1G1-CTNNBIP1-FBXW11 27997 6997 10059 3785 44390 CSNK1G1-DIXDC1-DKK1 5009 2538 5529 18100 16388 CSNK1G1-FOXN1-FZD1 11929 3765 872 10484 55805 CSNK1G1-FGF4-SFRP1 54991 41009 55503 37797 21039 CSNK1G1-NKD1-WNT2 15676 18894 5930 17029 46372 CSNK1G1-JUN-SFRP4 42953 29268 37702 44736 6880 CSNK1G1-FGF4-SLC9A3R1 7617 19617 897 10351 45255 CSNK1G1-PYGO1-TLE2 17136 9155 11518 17890 32040 CSNK1G1-FGF4-WNT4 18545 9815 5216 15463 13843 CSNK1G1-FOXN1-WNT3A 18175 14967 2698 926 50456 CSNK1G1-FSHB-T 6318 9942 3904 6835 49975 CSNK1G1-GSK3A-SENP2 9667 52049 9371 22981 45654 Table 11: Rankings of CSNK1G1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - SOBOL; Implementation - 2002 PORCN-PPP2R1A and CSNK1G1-FZD2-PPP2CA. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 24 RANKING @tiUSING SOBOL - MARTINEZ 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CSNK1G1-NLK-SENP2 1023 28963 23752 12006 13662 CSNK1G1-FOXN1-TLE2 4073 26473 32009 15332 6483 CSNK1G1-NLK-WNT4 9882 34667 14911 20141 31237 CSNK1G1-FOXN1-KREMEN1 4187 16379 10411 17376 49738 CSNK1G1-FOXN1-SLC9A3R1 11281 33656 17132 33702 26731 CSNK1G1-PORCN-SENP2 15610 15039 24692 32268 17031 CSNK1G1-FZD2-SENP2 23323 8023 15244 20763 9314 CSNK1G1-FSHB-LEF1 8757 48545 39614 32449 13625 CSNK1G1-DVL2-WNT2 2134 29301 54842 50984 15101 CSNK1G1-FSHB-SFRP4 39476 50249 41873 33694 14579 CSNK1G1-FZD2-TLE2 21805 41649 20523 9228 19247 CSNK1G1-DVL2-SENP2 2829 8071 56530 44158 5270 CSNK1G1-LRP5-SENP2 430 22598 40400 16862 29795 CSNK1G1-JUN-SENP2 53562 32056 34894 40476 27708 CSNK1G1-NKD1-PPP2CA 19784 21076 9213 14040 31099 CSNK1G1-FZD2-FZD7 20133 14733 25644 20740 34303 CSNK1G1-FOXN1-PPP2R1A 2180 53719 33104 7285 38261 CSNK1G1-CTNNBIP1-TCF7L1 5806 12198 11262 5166 48378 CSNK1G1-FGF4-TLE2 8296 22216 32082 2863 23370 CSNK1G1-FZD2-SFRP4 3975 35697 43472 32265 3691 CSNK1G1-FSHB-SENP2 32972 50887 28581 8306 20113 CSNK1G1-DVL2-FOSL1 8083 52720 54665 44734 52383 CSNK1G1-DVL2-TCF7 1931 11355 48637 47697 45338 CSNK1G1-FZD2-PPP2CA 6902 15684 9374 21259 4565 CSNK1G1-JUN-WNT2 26112 36147 34970 53598 32760 CSNK1G1-CXXC4-FOSL1 3540 41011 53892 1277 30939 CSNK1G1-CTNNBIP1-DKK1 3286 20741 29442 46391 49878 CSNK1G1-JUN-TCF7L1 20659 31359 42235 11222 25258 CSNK1G1-FZD2-WNT2B 16988 38740 33148 19223 15749 CSNK1G1-CTNNBIP1-TLE2 3609 28632 45678 10368 21084 CSNK1G1-NKD1-TCF7L1 25433 42313 19013 1420 12490 CSNK1G1-FOXN1-FBXW4 2305 4668 32121 14002 38175 CSNK1G1-DVL2-FBXW11 18902 31099 45042 20063 7907 CSNK1G1-GSK3B-SLC9A3R1 13151 10808 29139 7865 15618 CSNK1G1-FGF4-KREMEN1 23388 19547 27651 18744 8543 CSNK1G1-NKD1-SENP2 5658 19388 11502 16684 22979 CSNK1G1-FOXN1-TCF7L1 20619 35523 15458 17164 22105 CSNK1G1-T-TLE2 21536 24813 30561 665 19587 CSNK1G1-PORCN-TLE2 23956 39888 45808 29516 4037 CSNK1G1-PORCN-RHOU 156 28220 17621 19760 27625 CSNK1G1-JUN-TLE2 3654 15612 6612 7680 23323 CSNK1G1-NKD1-SFRP4 3477 44788 33518 12420 52257 CSNK1G1-FSHB-PPP2CA 40612 43508 22826 3439 25861 CSNK1G1-FOXN1-FRZB 757 4827 23287 8957 51220 CSNK1G1-JUN-KREMEN1 21900 17437 22609 16420 7910 CSNK1G1-FOXN1-RHOU 2715 42081 23816 12990 28784 CSNK1G1-DVL2-TCF7L1 35932 38409 51352 32104 7019 CSNK1G1-SFRP1-WNT5A 18728 41171 27916 27826 21302 CSNK1G1-CTNNB1-KREMEN1 7668 39456 50237 10228 44604 CSNK1G1-SFRP1-TLE2 30635 31136 34280 5452 10126 CSNK1G1-JUN-FBXW4 35891 19352 22587 4046 48570 CSNK1G1-FZD1-SENP2 44823 32702 37344 23873 20064 CSNK1G1-PORCN-SLC9A3R1 9278 49182 53553 52071 36096 CSNK1G1-CTNNB1-SENP2 42637 17246 37340 28255 10424 CSNK1G1-CTNNB1-FBXW11 47591 47761 24648 52706 42288 CSNK1G1-CTNNB1-DAAM1 640 14671 43332 53397 11882 CSNK1G1-JUN-RHOU 22504 10065 14728 48707 5692 CSNK1G1-DVL2-FZD1 29822 52079 42226 21023 15435 CSNK1G1-FZD1-TCF7L1 3657 17738 32058 2877 3452 CSNK1G1-FGF4-FOSL1 3966 11339 26512 6277 5337 CSNK1G1-FZD2-WNT4 10410 34283 49819 8764 3839 CSNK1G1-FZD2-LEF1 25439 42050 48188 18015 7710 CSNK1G1-GSK3A-TLE2 15953 48553 26146 34236 29429 CSNK1G1-FOXN1-FZD6 465 20038 14379 3608 44811 CSNK1G1-JUN-PPP2R1A 23606 19004 7535 6758 46881 CSNK1G1-JUN-PYGO1 15049 21562 26708 38509 8167 CSNK1G1-DVL2-TLE2 25461 39155 51026 50993 10360 CSNK1G1-PORCN-TCF7L1 22705 5536 55332 52452 7332 CSNK1G1-FGF4-SENP2 15585 3966 9710 959 24750 CSNK1G1-JUN-TCF7 24936 47488 33304 8067 17856 CSNK1G1-JUN-PPP2CA 52121 39360 27268 41319 22355 CSNK1G1-FZD1-FZD7 23551 51418 20988 43171 26341 CSNK1G1-CSNK2A1-MYC 816 53067 52527 17682 54911 CSNK1G1-PORCN-FBXW4 5765 9868 51683 56209 13206 CSNK1G1-FGF4-TCF7L1 41064 41146 28605 3115 12570 CSNK1G1-FGF4-FBXW4 24615 51440 29249 42766 24693 CSNK1G1-FOXN1-TCF7 28811 39294 26956 517 23711 CSNK1G1-NKD1-RHOU 13195 46913 28099 45919 38961 CSNK1G1-FZD2-FZD8 55692 33791 38801 40579 16150 CSNK1G1-JUN-WNT2B 6543 12806 10942 2276 34250 CSNK1G1-NLK-TCF7L1 25249 40044 11018 25277 24236 CSNK1G1-FZD2-SLC9A3R1 72 11838 29010 16078 46306 CSNK1G1-GSK3B-LRP6 38011 14409 17563 26578 29511 CSNK1G1-PORCN-WNT2B 28382 5688 53042 54668 30496 CSNK1G1-CXXC4-DKK1 21335 46326 26057 31544 22681 CSNK1G1-CXXC4-FRAT1 2838 20322 35155 3949 37439 CSNK1G1-FGF4-PPP2R1A 51350 42511 16585 6456 20879 CSNK1G1-WIF1-WNT2B 2279 53121 35371 56846 2011 CSNK1G1-WIF1-WNT4 56789 43140 52845 54585 19132 CSNK1G1-DIXDC1-WNT2B 40930 25751 23698 20111 41840 CSNK1G1-T-WNT2B 41593 45959 12146 13197 24503 CSNK1G1-T-TCF7L1 18966 48845 25610 157 14816 CSNK1G1-PORCN-PPP2R1A 503 35730 3044 6124 43150 CSNK1G1-PORCN-WNT5A 46413 14655 30449 49521 13435 CSNK1G1-PORCN-SFRP1 28402 40020 24656 8442 10906 CSNK1G1-DVL2-FRZB 19883 55733 37226 45418 8700 CSNK1G1-JUN-SLC9A3R1 29086 31057 29189 10809 56936 CSNK1G1-JUN-WNT4 7327 52583 35808 38813 18150 CSNK1G1-FSHB-MYC 16803 10241 15398 7414 1214 CSNK1G1-NLK-WNT2B 51130 36723 22493 41024 14440 CSNK1G1-JUN-WNT5A 90 18823 34308 8819 39419 CSNK1G1-SFRP1-WNT2B 25407 48375 4565 5611 20190 CSNK1G1-FGF4-FRAT1 17863 11935 14252 19547 33993 CSNK1G1-CTNNB1-FRZB 2473 1895 48867 55068 18412 CSNK1G1-CTBP2-DKK1 9933 53999 48020 51075 12322 CSNK1G1-GSK3B-RHOU 12634 48456 37726 40555 19173 CSNK1G1-CTBP2-SLC9A3R1 10860 22491 33788 2639 39302 CSNK1G1-DIXDC1-RHOU 37350 50752 24433 17248 3736 CSNK1G1-GSK3A-RHOU 38032 48019 31225 42299 34354 CSNK1G1-FZD2-WNT5A 47509 40249 19979 4150 23159 CSNK1G1-CTNNBIP1-FOSL1 11949 32749 12277 6351 7950 CSNK1G1-FSHB-WNT2B 24679 21316 37424 4944 42965 APC-CSNK1G1-FZD1 21185 37153 44 28557 44726 CSNK1G1-PORCN-WNT2 44086 52040 53679 46699 15576 CSNK1G1-CTNNBIP1-FBXW11 8978 49664 28961 11257 11947 CSNK1G1-DIXDC1-DKK1 32455 51113 13061 32408 39336 CSNK1G1-FOXN1-FZD1 5809 24046 13888 4092 54967 CSNK1G1-FGF4-SFRP1 54217 40967 27315 4034 12736 CSNK1G1-NKD1-WNT2 584 24793 8285 23891 20671 CSNK1G1-JUN-SFRP4 18558 44438 31265 34955 26920 CSNK1G1-FGF4-SLC9A3R1 3812 15818 13512 15179 25323 CSNK1G1-PYGO1-TLE2 6707 43365 50722 55108 11091 CSNK1G1-FGF4-WNT4 2235 6629 11645 21643 241 CSNK1G1-FOXN1-WNT3A 8675 49134 21528 19393 15926 CSNK1G1-FSHB-T 25656 40734 22557 25924 2702 CSNK1G1-GSK3A-SENP2 8587 27952 42504 7797 12650 Table 12: Rankings of CSNK1G1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - SOBOL; Implementation - martinez 6.5.4. Examining the behaviour of LRP-CSNK1G1-X combinations Looking at the tables above, one finds the following combinations for members of LRP family along with CSNK1G1, to be prominent at 3rd order level - CSNK1G1-LRP5SENP2 and CSNK1G1-GSK3B-LRP6. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 25 Acknowledgments Special thanks to Mrs. Rita Sinha and late Mr. Prabhat Sinha for supporting the author financially, without which this work could not have been made possible. Supplementary The following files (ending with .txt and can be opened in R or in simple text processing program) with these names are made available with this manuscript. For CSNK, (1) -3-odr-TP-ranking-linear.txt, (2) -3-odr-TP-ranking-rbf.txt, (3) -3-odrTP-ranking-2002.txt, and (4) -3-odr-TP-ranking-martinez.txt, contain rankings for 3rd order combinations across each time point for, HSIC (linear kernel), HSIC (rbf kernel), SOBOL (2002 implementation) and SOBOL (martinez implementation), respectively. References [1] T. S. Gujral, G. MacBeath, A system-wide investigation of the dynamics of wnt signaling reveals novel phases of transcriptional regulation, PloS one 5 (2010) e10024. [2] S. Sinha, Machine learning ranking of plausible (un) explored synergistic gene combinations using sensitivity indices of time series measurements of wnt signaling pathway, Integrative Biology 16 (2024) zyae020. [3] T. Joachims, Training linear svms in linear time, in: Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining, ACM, 2006, pp. 217–226. [4] A. J. Cozzone, Protein phosphorylation in prokaryotes, Annual Reviews in Microbiology 42 (1988) 97–125. [5] G. Burnett, E. P. Kennedy, The enzymatic phosphorylation of proteins. (1954). [6] Y. Fujiwara, M. Miwa, M. Nogami, K. Okumura, T. Nobori, T. Suzuki, M. Ueda, Genomic organization and chromosomal localization of the human casein gene family, Human genetics 99 (1997) 368–373. [7] P. Cohen, The origins of protein phosphorylation, Nature cell biology 4 (2002) E127–E130. [8] E. W. Bingham, H. M. Farrell Jr, Casein kinase from the golgi apparatus of lactating mammary gland, Journal of Biological Chemistry 249 (1974) 3647–3651. [9] S. K. Hanks, T. Hunter, The eukaryotic protein kinase superfamily: kinase (catalytic) domain structure and classification 1, The FASEB journal 9 (1995) 576–596. [10] C. Tapia, T. Featherstone, C. G´ omez, P. Taillon-Miller, C. C. Allende, J. E. Allende, Cloning and chromosomal localization of the gene coding for human protein kinase ck1, FEBS letters 349 (1994) 307–312. [11] K. J. Fish, A. Cegielska, M. E. Getman, G. M. Landes, D. M. Virshup, Isolation and characterization of human casein kinase iε(cki), a novel member of the cki gene family (), Journal of Biological Chemistry 270 (1995) 14875–14883. [12] J. Rowles, C. Slaughter, C. Moomaw, J. Hsu, M. H. Cobb, Purification of casein kinase i and isolation of cdnas encoding multiple casein kinase i-like enzymes., Proceedings of the National Academy of Sciences 88 (1991) 9548–9552. [13] P. R. Graves, D. Haas, C. Hagedorn, A. DePaoli-Roach, P. Roach, Molecular cloning, expression, and characterization of a 49-kilodalton casein kinase i isoform from rat testis., Journal of Biological Chemistry 268 (1993) 6394–6401. 32 [14] J. Kusuda, N. Hidari, M. Hirai, K. Hashimoto, Sequence analysis of the cdna for the human casein kinase i δ (csnk1d) gene and its chromosomal localization, Genomics 32 (1996) 140–143. [15] J. Kusuda, M. Hirai, R. Tanuma, K. Hashimoto, Cloning, expression analysis and chromosome mapping of human casein kinase 1 γ1 (csnk1g1): Identification of two types of cdna encoding the kinase protein associated with heterologous carboxy-terminal sequences, Cytogenetics and cell genetics 90 (2000) 298–302. [16] A. Saxena, R. Padmanabha, C. V. Glover, Isolation and sequencing of cdna clones encoding alpha and beta subunits of drosophila melanogaster casein kinase ii, Molecular and cellular biology 7 (1987) 3409–3417. [17] H. Meisner, R. Heller-Harrison, J. Buxton, M. P. Czech, Molecular cloning of the human casein kinase ii. alpha. subunit, Biochemistry 28 (1989) 4072–4076. [18] F. J. Lozeman, D. W. Litchfield, C. Piening, K. Takio, K. A. Walsh, E. G. Krebs, Isolation and characterization of human cdna clones encoding the. alpha. and the. alpha.’subunits of casein kinase ii, Biochemistry 29 (1990) 8436–8447. [19] T. Yang-Feng, K. Zheng, I. Kopatz, T. Naiman, D. Canaani, Mapping of the human caseis kinase ii catalytic subunit genes: two loci carrying the homologues sewquences for the αsubunit, Nucleic acids research 19 (1991) 7125–7129. [20] U. Wirkner, H. Voss, P. Lichter, W. Ansorge, W. Pyerin, The human gene (csnk2a1) coding for the casein kinase ii subunit αis located on chromosome 20 and contains tandemly arranged alu repeats, Genomics 19 (1994) 257–265. [21] S. Sinha, Hilbert-schmidt and sobol sensitivity indices for static and time series wnt signaling measurements in colorectal cancer-part a, BMC systems biology 11 (2017) 120. [22] S. Da Veiga, Global sensitivity analysis with dependence measures, Journal of Statistical Computation and Simulation 85 (2015) 1283–1305. [23] A. Saltelli, Making best use of model evaluations to compute sensitivity indices, Computer physics communications 145 (2002) 280–297. [24] J. Martinez, Analyse de sensibilite globale par decomposition de la variance, Presentation in Journ´ ee des GdR Ondes & Mascot 13 (2011) 207. [25] M. Baudin, K. Boumhaout, T. Delage, B. Iooss, J.-M. Martinez, Numerical stability of sobol’indices estimation formula, in: Proceedings of the 8th International Conference on Sensitivity Analysis of Model Output (SAMO 2016), volume 30, 2016, pp. 50–51. [26] F. Cong, L. Schweizer, H. Varmus, Casein kinase iεmodulates the signaling specificities of dishevelled, Molecular and cellular biology 24 (2004) 2000–2011. [27] E. Lee, A. Salic, M. W. Kirschner, Physiological regulation of β-catenin stability by tcf3 and ck1ε, Journal of Cell Biology 154 (2001) 983–994. [28] Z.-H. Gao, J. M. Seeling, V. Hill, A. Yochum, D. M. Virshup, Casein kinase i phosphorylates and destabilizes the β-catenin degradation complex, Proceedings of the National Academy of Sciences 99 (2002) 1182–1187. [29] G. Davidson, W. Wu, J. Shen, J. Bilic, U. Fenger, P. Stannek, A. Glinka, C. Niehrs, Casein kinase 1 γcouples wnt receptor activation to cytoplasmic signal transduction, Nature 438 (2005) 867–872. [30] S. Amit, A. Hatzubai, Y. Birman, J. S. Andersen, E. Ben-Shushan, M. Mann, Y. Ben-Neriah, I. Alkalay, Axinmediated cki phosphorylation of β-catenin at ser 45: a molecular switch for the wnt pathway, Genes & development 16 (2002) 1066–1076. [31] N.-C. Ha, T. Tonozuka, J. L. Stamos, H.-J. Choi, W. I. Weis, Mechanism of phosphorylation-dependent binding of apc to β-catenin and its role in β-catenin degradation, Molecular cell 15 (2004) 511–521. 33