nemo like kinase (NLK) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

nemo like kinase (NLK) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells shriprakash sinha Independent Researcher; Orcid ID : orcid.org/0000-0001-7027-5788 104-Madhurisha Heights Phase 1, Risali, Bhilai-490006, India Abstract Nemo-Like Kinase (NLK) is a serine/threonine protein kinase , Nemo (NMO) being the Drosophila ortholog of the mammalian NLK gene. Its activation mechanism and downstream targets are still not well characterized. 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 NLK related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for NLK-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 NLK comb. in WNT3A stimulated cells Email address: [email protected] (shriprakash sinha) 1Aspects of unpublished work were presented in a poster session at Cell Symposia: Technology.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 February 27, 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 NLK 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. nemo like kinase (NLK) The Drosophila eye consists of a reiterative hexagonal array of photoreceptor cell clusters, the ommatidia. During normal morphogenesis, the clusters in the dorsal or ventral halves of the disc rotate 90◦in opposite directions, forming mirror images across a dorsoventral equator. In the mutant nemo (NMO), there is an initial turning of approximately 45◦, but further rotation is blocked. Choi and Benzer [4] indicate that the NMO acts upon each cluster as a whole; normal nmo function in one or more photoreceptor cells appears to be sufficient to induce full rotation. The NMO gene sequence is required to initiate the second step of rotation, via and an encoded serine/threonine protein kinase homolog. They show that in another mutant, roulette, excessive rotation through varying angles occurs in many ommatidia, which is suppressed by NMO, thus indicating that NMO acts upstream in a rotation-regulating pathway. Extracellular-signal regulated kinases/microtubule-associated protein kinases (ERK/MAPKs) and cyclin-directed kinases (CDKs) are key regulators of many aspects of cell growth and division, as well as apoptosis. Brott et al. [5] cloned NLK, where the NLK amino acid sequence is 54.5% similar and 41.7% identical to murine ERK2, and 49.6% similar and 38.4% identical to human CDC2. A feature that distinguishes NLK from ERL/MAPKs, CDKs, and also NMO, is its extended amino-terminal domain, that is very rich in glutamine, alanine, proline, and histidine. Mutation of the ATP-binding Lys-155 to methionine abolishes its ability to autophosphorylate, as does mutation of a putative activating threonine in kinase domain VIII, to valine, aspartic, or glutamic acid. NLK and NMO may be the first members of a family of kinases with homology to both ERK/MAPKs and CDKs. Mitogen-activated protein (MAP) kinases are a family of serine/threonine kinases that transduce extracellular cues into a variety of intracellular responses ranging from lineage specification to cell division and adaptation. Coulombe and Meloche [6] classify MAP kinases into conventional or atypical enzymes, based on their ability to get phosphorylated and activated by the MAP kinase kinase (MAPKK)/MEK family. Conventional MAP kinases comprise ERK1/ERK2, p38s, JNKs, and ERK5, which are all substrates of MAPKKs, while atypical MAP kinases include ERK3/ERK4, NLK and ERK7. Much less is known about the regulation, substrate specificity and physiological functions of atypical MAP kinases. Considering the structure of NLK, its C-terminal extension is conserved from worm to human (45% identity between LIT-1 and human NLK) and may contribute to the interaction of the kinase with specific substrates or targets as shown by Ishitani et al. [7]. The WNT signalling pathway regulates many developmental processes through 3 a complex of β-catenin and the T-cell factor/ lymphoid enhancer factor (TCF/LEF) family. WNT stabilizes cytosolic β-catenin, which then binds to TCF and activates gene transcription. In Caenorhabditis elegans, the proteins MOM4 and LIT1 regulate WNT signalling to polarize responding cells during embryogenesis as shown by Meneghini et al. [8]. MOM4 and LIT1 are homologous to TAK1 (a kinase activated by transforming growth factor-β) mitogenactivated protein-kinase-kinase kinase (MAP3K) and MAPK-related NLK, respectively, in mammalian cells. Ishitani et al. [7] hypothesize the possibility that TAK1 and NLK are also involved in WNT signalling in mammalian cellsand show that TAK1 activation stimulates NLK activity and downregulates transcriptional activation mediated by β-catenin and TCF. They demostrate that injection of NLK suppresses the induction of axis duplication by microinjected βcatenin in Xenopus embryos. NLK phosphorylates TCF/LEF factors and inhibits the interaction of the β-catenin-TCF complex with DNA. Thus, the TAK1-NLK-MAPKlike pathway negatively regulates the WNT signalling pathway. Yamada et al. [9] and Yamada et al. [10], also show similar results of NLK interaction with TCF/LEF family members. More specifically, c-myb proto-oncogene (c-MYB) regulates both the proliferation and apoptosis of hematopoietic cells by inducing the transcription of a group of target genes. Kanei-Ishii et al. [11] report that c-MYB protein is phosphorylated and degraded by WNT1 signal via the pathway involving TGF-β-activated kinase (TAK1), homeodomain-interacting protein kinase 2(HIPK2), and NLK. They show that WNT1 signal causes the nuclear entry of TAK1, which then activates HIPK2 and NLK. Further, NLK binds directly to c-MYB together with HIPK2, which results in the phosphorylation of c-MYB at multiple sites, followed by its ubiquitination and proteasomedependent degradation. Furthermore, overexpression of NLK in M1 cells abrogated the ability of c-MYB to maintain the undifferentiated state of these cells. Finally, Ishitani et al. [12] show that phosphorylation of TCF4 by NLK inhibited DNA binding by the β-catenin-TCF4 complex. These results suggested that NLK phosphorylation on these sites contributed to the down-regulation of LEF1/TCF transcriptional activity. Ishitani and Ishitani [13] summarize the current understanding of the function and regulation of NLK and discuss the aspects of NLK regulation that remain to be resolved. In this research work, I present 3rd order combinations of NLK 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. 4 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 [14]. 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 [14]. 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 5 model is then used to generate score on the observations in the testing set using the SVMRank 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 SVMRank 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]. 6 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 NLK-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 [15]) and Sobol indicies (with 2002 implementation in Saltelli [16] and martinez implementation in Martinez [17] and Baudin et al. [18]). 6.3. Conserved machine learning rankings for tested NLK-X-X combinations A total of 2415, 3rd order combinations involving NLK 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 WNT-NLK-X combinations Kanei-Ishii et al. [11] report that c-MYB protein is phosphorylated and degraded by WNT1 signal via the pathway involving TGF-β-activated kinase (TAK1), homeodomaininteracting protein kinase 2 (HIPK2), and NLK. They show that WNT1 signal causes the nuclear entry of TAK1, which then activates HIPK2 and NLK. Looking at the tables above, one finds the following combinations for members of the WNT family along with NLK, to be prominent at 3rd order level - LRP5-NLK-WNT4, FOSL1-NLKWNT4, CXXC4-NLK-WNT4, CTNNBIP1-NLK-WNT5A, NLK-PORCN-WNT2B, NLKPORCN-WNT2, LRP5-NLK-WNT2B, NLK-SFRP1-WNT5A, NLK-SFRP1-WNT2, NLK-SFRP1-WNT3, DIXDC1-NLK-WNT4, FRZB-NLK-WNT4, CSNK1G1-NLKWNT2B, FZD1-NLK-WNT5A, CTNNBIP1-NLK-WNT2B, LRP5-NLK-WNT5A, NLKFBXW4-WNT3A, FZD5-NLK-WNT4, FGF4-NLK-WNT2B, CSNK1G1-NLK-WNT4, NLK-WIF1-WNT2, FRAT1-NLK-WNT4, NLK-WIF1-WNT2B, FRAT1-NLK-WNT3A, 7 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 FZD1-NLK-SENP2 66 7254 6519 12561 16204 CSNK1G1-NLK-SENP2 74 35675 3308 48520 19328 LRP5-NLK-SENP2 99 17426 20510 156 54321 NLK-SFRP1-TCF7 125 43152 40831 35451 28596 LRP5-NLK-WNT4 173 5427 19931 576 56700 CSNK1D-FGF4-NLK 182 13641 35785 54873 12126 FRAT1-NLK-SENP2 308 14795 5137 12639 16597 CSNK1G1-NLK-WNT4 321 20710 3312 50831 31403 NLK-PORCN-PPP2CA 339 30605 43435 41734 4166 NLK-PORCN-SFRP4 368 53128 52278 37793 4619 FOSL1-NLK-WNT4 378 3397 2566 2260 40025 NLK-WIF1-WNT2 431 13840 49796 35119 6813 CXXC4-NLK-WNT4 491 167 4767 2069 15953 FRAT1-NLK-WNT4 534 1131 4271 13789 39755 CXXC4-NLK-FBXW4 591 19400 24702 2318 5774 CCND1-FGF4-NLK 650 37617 39188 40111 26729 BTRC-GSK3A-NLK 685 15173 52709 30778 8565 NLK-PORCN-SENP2 751 51440 56864 21216 6122 NLK-FBXW4-SLC9A3R1 760 5112 22367 45665 21602 FZD1-NLK-FBXW4 834 6168 26326 20481 40535 CTNNBIP1-NLK-WNT5A 840 10869 21909 56571 16909 LRP5-NLK-FBXW4 847 9156 37860 589 53712 CTNNBIP1-NLK-SFRP1 852 523 6419 55912 26165 NLK-WIF1-WNT2B 877 15574 29869 50706 14922 FZD1-NLK-SFRP1 923 208 3403 10308 46968 NLK-SFRP1-SFRP4 967 54433 34929 9753 40373 NLK-TLE1-TLE2 993 36487 34168 46840 34475 FRAT1-NLK-WNT3A 1005 19771 7884 9479 10249 NLK-PORCN-WNT2B 1006 26349 37659 35498 4512 FBXW2-FGF4-NLK 1060 19103 48572 41780 1397 LRP5-NLK-SFRP1 1066 2 18438 235 53114 NLK-PORCN-SLC9A3R1 1108 35858 56545 26507 3768 FZD1-NLK-TLE1 1147 12376 4310 27950 16973 NLK-PORCN-TCF7 1154 48490 41769 34836 12221 FBXW11-FGF4-NLK 1172 27458 51060 40627 25175 CSNK1G1-NLK-TLE1 1270 15559 1608 53075 20188 DKK1-NLK-SENP2 1343 20532 9328 35918 23556 FOSL1-NLK-WNT2B 1425 3331 440 49507 31594 CXXC4-NLK-TLE2 1467 3249 13379 2815 22591 FOSL1-NLK-WNT3A 1512 2335 4160 3374 12963 CXXC4-NLK-SFRP1 1520 3860 3645 1038 15312 DKK1-FGF4-NLK 1530 30108 32527 40415 19377 NLK-PORCN-WNT2 1557 46116 57071 36752 14418 FRAT1-NLK-FBXW4 1570 6400 25113 13146 24103 DAAM1-FGF4-NLK 1615 51287 55713 52792 17270 NLK-PORCN-TLE2 1657 49377 56092 39434 12430 LRP5-NLK-WNT2B 1725 4903 8642 34617 54453 NLK-PORCN-WNT4 1742 49908 50644 30880 6042 AES-AXIN1-NLK 1775 49282 47808 50035 53907 FZD1-NLK-WNT2B 1840 1616 1306 53698 22012 FOSL1-NLK-SFRP1 1846 2471 1853 521 54004 FZD7-NLK-WNT3A 1957 2219 4173 15212 30086 NLK-SFRP1-WNT5A 2032 55480 32725 47613 26430 FGF4-NLK-WNT4 2033 3044 4724 33423 28154 NLK-SFRP1-WNT2 2043 53015 46284 12054 33556 DVL2-JUN-NLK 2045 6588 32911 20097 18489 NLK-SFRP1-WNT3 2049 43102 31587 4584 28785 FZD8-NLK-WNT2B 2126 25291 1834 45776 56354 DIXDC1-NLK-WNT4 2128 13920 3978 2846 15403 CXXC4-NLK-WNT2B 2202 5290 1484 56489 12898 CTNNB1-NLK-TLE1 2322 31661 2654 17390 15058 FZD8-NLK-SFRP1 2340 2987 4568 21448 52792 CTBP1-FGF4-NLK 2373 24017 40861 28523 25856 NLK-PORCN-TCF7L1 2400 38016 56402 27460 3015 CSNK1G1-NLK-TCF7L1 2409 13940 8988 50696 40050 DVL1-FGF4-NLK 2505 55303 42133 41000 49492 FRZB-NLK-WNT4 2520 1556 5592 7221 22356 FRAT1-NLK-TLE2 2530 6281 12625 8358 38149 DVL2-FGF4-NLK 2539 9068 35433 35003 33783 FZD5-FGF4-NLK 2548 25184 37573 26783 23902 AES-EP300-NLK 2549 52374 48380 27425 55437 CSNK1D-NLK-WNT4 2750 2726 9906 45186 25621 BCL9-FGF4-NLK 2765 16506 49200 35441 40551 CXXC4-FGF4-NLK 2780 22054 41988 28791 40205 FBXW11-FOXN1-NLK 2897 3423 17764 15937 45601 FSHB-FZD2-NLK 3007 15229 33503 42544 8088 CSNK1G1-NLK-WNT2B 3057 20612 364 49392 38971 FZD1-NLK-PPP2R1A 3063 6647 16715 10003 26509 GSK3B-NLK-TLE1 3123 28197 2579 41126 15983 LRP5-NLK-SFRP4 3199 217 20954 446 56950 FZD1-NLK-WNT5A 3220 14961 17555 36449 16975 CTNNBIP1-NLK-FBXW4 3223 10049 26324 48138 19000 CTNNBIP1-NLK-WNT2B 3262 12256 1539 46850 31899 CSNK1A1-NLK-TLE1 3280 2505 5178 30696 38811 LRP5-NLK-WNT5A 3296 15243 30086 6594 47805 CTNNBIP1-NLK-RHOU 3322 501 7291 43407 48933 NLK-PORCN-TLE1 3414 46190 49745 10954 11706 DIXDC1-NLK-FBXW4 3436 6471 26909 5680 17650 FBXW2-JUN-NLK 3505 12581 49210 43684 51663 CTNNBIP1-NLK-WNT4 3546 4416 6989 50022 30148 FZD5-NLK-SENP2 3647 23886 4036 3124 1472 CSNK1D-NLK-WNT3A 3672 3466 7618 26301 5357 LRP5-NLK-PPP2R1A 3749 6866 25722 95 55900 CSNK1G1-NLK-PPP2R1A 3754 21618 10600 22928 48421 NLK-FBXW4-WNT3A 3762 18958 12589 35118 5530 CXXC4-NLK-TCF7L1 3843 4771 10375 1945 20127 FZD5-NLK-WNT4 3897 19032 2692 1966 40749 EP300-GSK3A-NLK 3902 24187 13268 22163 37611 CCND1-FRAT1-NLK 3929 35214 17635 44956 38660 CXXC4-NLK-WNT5A 3932 2627 16679 25816 15722 NLK-SFRP1-TLE2 3952 54493 39629 26154 50386 DKK1-GSK3A-NLK 3968 22383 24849 47754 29762 FGF4-NLK-WNT2B 3978 2527 804 55492 27607 FOSL1-NLK-SFRP4 3991 8084 2347 4123 43458 FRAT1-NLK-RHOU 4074 18571 5441 22722 18400 FRAT1-NLK-PPP2R1A 4096 7150 14882 4380 42041 CTNNBIP1-NLK-PPP2R1A 4168 17696 21970 43414 47292 NLK-PYGO1-WNT2 4229 27445 40800 13988 7354 AXIN1-FZD2-NLK 4347 26298 10959 26949 9217 NLK-WIF1-WNT4 4406 21046 38575 49983 13952 NLK-SFRP1-FBXW4 4416 23473 46584 11984 39379 GSK3A-JUN-NLK 4439 45904 37849 40408 18195 AXIN1-FOXN1-NLK 4448 7290 24395 14630 18096 FZD1-NLK-SFRP4 4509 3076 5015 18937 38268 CXXC4-NLK-RHOU 4522 5467 5985 8707 24421 DVL1-FOXN1-NLK 4529 51079 27843 11249 56056 FZD1-NLK-TCF7L1 4642 24230 11921 14016 23504 CCND3-FGF4-NLK 4644 49910 36053 48791 53135 DAAM1-FRAT1-NLK 4668 52014 25172 20469 49769 NLK-WIF1-WNT3A 4697 36349 45660 34357 1641 CTNNB1-NLK-WIF1 4707 9899 6192 11981 1923 FOSL1-NLK-TCF7L1 4743 4810 5264 1752 28982 CSNK1D-NLK-SENP2 4773 12377 9957 43796 3597 CSNK1A1-NLK-WIF1 4795 14710 6213 20851 31609 FRAT1-NLK-TCF7 4821 5072 6111 23919 29394 CCND1-NLK-WNT2B 4835 38149 1102 53863 38938 Table 1: Rankings of NLK-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear FOSL1-NLK-WNT2B, FOSL1-NLK-WNT3A, NLK-PORCN-WNT4, FZD1-NLK-WNT2B, FZD7-NLK-WNT3A, FGF4-NLK-WNT4, FZD8-NLK-WNT2B, CXXC4-NLK-WNT2B, CSNK1D-NLK-WNT4, CTNNBIP1-NLK-WNT4, CSNK1D-NLK-WNT3A, CXXC48 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 FZD1-NLK-SENP2 4216 33313 50995 20046 16713 CSNK1G1-NLK-SENP2 34480 34469 25805 4202 8014 LRP5-NLK-SENP2 28404 31921 48677 23545 26406 NLK-SFRP1-TCF7 8841 43619 30305 17506 12968 LRP5-NLK-WNT4 34513 16387 35220 5468 37281 CSNK1D-FGF4-NLK 5343 27561 8638 8497 51980 FRAT1-NLK-SENP2 47712 35472 55874 27952 35046 CSNK1G1-NLK-WNT4 37117 32429 26444 1650 27288 NLK-PORCN-PPP2CA 6640 37879 19229 30844 45007 NLK-PORCN-SFRP4 26548 54453 3595 31340 34837 FOSL1-NLK-WNT4 46914 7268 50547 1274 44200 NLK-WIF1-WNT2 40307 10226 11647 34273 29809 CXXC4-NLK-WNT4 22955 3089 37410 121 47163 FRAT1-NLK-WNT4 32436 4345 56234 697 36071 CXXC4-NLK-FBXW4 36361 6924 5576 32715 39457 CCND1-FGF4-NLK 23150 32232 22665 42559 12440 BTRC-GSK3A-NLK 8965 2718 45185 45189 49869 NLK-PORCN-SENP2 25839 52725 11882 9881 37272 NLK-FBXW4-SLC9A3R1 56671 1861 38594 29352 5573 FZD1-NLK-FBXW4 20283 8207 32619 27566 30042 CTNNBIP1-NLK-WNT5A 43965 11033 40662 17048 49376 LRP5-NLK-FBXW4 48704 10826 12482 34528 35402 CTNNBIP1-NLK-SFRP1 33298 2286 54426 26390 24484 NLK-WIF1-WNT2B 20533 18090 8143 25594 25892 FZD1-NLK-SFRP1 24451 9305 49446 19196 22902 NLK-SFRP1-SFRP4 25125 53640 1360 15834 31791 NLK-TLE1-TLE2 54439 46207 309 27068 8231 FRAT1-NLK-WNT3A 51049 30143 52377 44271 42168 NLK-PORCN-WNT2B 30300 3466 8133 31316 44880 FBXW2-FGF4-NLK 1671 979 163 29649 18596 LRP5-NLK-SFRP1 38815 3342 52455 23786 33500 NLK-PORCN-SLC9A3R1 39803 20122 9428 9998 42527 FZD1-NLK-TLE1 32959 8717 41662 33327 32893 NLK-PORCN-TCF7 14350 41604 26400 15610 37827 FBXW11-FGF4-NLK 2114 16567 7954 26999 37518 CSNK1G1-NLK-TLE1 51469 19124 38302 32990 19686 DKK1-NLK-SENP2 2831 28851 33433 831 12425 FOSL1-NLK-WNT2B 20492 705 35136 30860 53018 CXXC4-NLK-TLE2 21331 11904 46279 1885 30976 FOSL1-NLK-WNT3A 51755 5242 44005 49978 52983 CXXC4-NLK-SFRP1 49331 4153 49861 27131 33193 DKK1-FGF4-NLK 3129 15113 40241 34444 48762 NLK-PORCN-WNT2 44692 38504 8829 1995 53685 FRAT1-NLK-FBXW4 50800 21515 31927 26376 27004 DAAM1-FGF4-NLK 1482 50392 22580 43523 38010 NLK-PORCN-TLE2 41691 54802 745 25237 46608 LRP5-NLK-WNT2B 28396 1960 19941 23600 55297 NLK-PORCN-WNT4 33383 45823 7542 34942 49961 AES-AXIN1-NLK 32068 45433 3161 29821 53403 FZD1-NLK-WNT2B 28935 4414 27054 36546 52981 FOSL1-NLK-SFRP1 34233 941 55096 25592 35663 FZD7-NLK-WNT3A 23365 3018 51679 44843 19133 NLK-SFRP1-WNT5A 22263 52123 16817 33554 46452 FGF4-NLK-WNT4 4835 2733 36815 3654 11745 NLK-SFRP1-WNT2 33812 54135 6702 29330 45088 DVL2-JUN-NLK 17072 6052 41009 20313 44474 NLK-SFRP1-WNT3 51886 35916 3457 20064 40670 FZD8-NLK-WNT2B 50248 4499 42098 23442 25585 DIXDC1-NLK-WNT4 5010 8900 42377 1999 3181 CXXC4-NLK-WNT2B 28869 300 28004 21112 54426 CTNNB1-NLK-TLE1 55950 22712 28147 35986 13653 FZD8-NLK-SFRP1 54470 72 56582 18335 33221 CTBP1-FGF4-NLK 3746 33288 10452 55841 49146 NLK-PORCN-TCF7L1 31569 44836 10175 2151 43393 CSNK1G1-NLK-TCF7L1 38665 6811 44713 7792 48500 DVL1-FGF4-NLK 2306 54597 5405 53929 25428 FRZB-NLK-WNT4 6001 9443 53325 4130 50442 FRAT1-NLK-TLE2 26675 24348 52446 8545 15016 DVL2-FGF4-NLK 2327 15184 45235 14257 45259 FZD5-FGF4-NLK 2239 33059 12033 52334 51042 AES-EP300-NLK 38886 52106 1233 23736 42435 CSNK1D-NLK-WNT4 1538 21775 47534 6449 28873 BCL9-FGF4-NLK 6693 29487 24244 44096 45853 CXXC4-FGF4-NLK 1507 4569 5986 44776 54536 FBXW11-FOXN1-NLK 345 17553 4941 12084 9525 FSHB-FZD2-NLK 17474 18226 16777 16181 28351 CSNK1G1-NLK-WNT2B 53434 5922 42619 33337 50690 FZD1-NLK-PPP2R1A 20834 8886 52092 12766 24248 GSK3B-NLK-TLE1 45736 20255 50690 4684 15971 LRP5-NLK-SFRP4 42299 6001 52599 18512 34951 FZD1-NLK-WNT5A 28100 15641 23012 14962 49066 CTNNBIP1-NLK-FBXW4 44996 19802 33841 25211 38562 CTNNBIP1-NLK-WNT2B 23541 1910 34449 30631 55521 CSNK1A1-NLK-TLE1 16274 1109 56566 37347 24936 LRP5-NLK-WNT5A 33250 14809 24503 18293 46276 CTNNBIP1-NLK-RHOU 20208 392 56468 42238 24576 NLK-PORCN-TLE1 37435 39499 5549 31543 47543 DIXDC1-NLK-FBXW4 25837 3880 29684 25017 18802 FBXW2-JUN-NLK 29577 33489 631 40952 3561 CTNNBIP1-NLK-WNT4 27403 2923 45312 850 52767 FZD5-NLK-SENP2 9566 34294 49065 9629 25330 CSNK1D-NLK-WNT3A 12770 9632 43802 42949 37641 LRP5-NLK-PPP2R1A 22739 10079 12169 17484 38120 CSNK1G1-NLK-PPP2R1A 35195 9424 21823 20710 43474 NLK-FBXW4-WNT3A 26514 5505 28475 52773 4096 CXXC4-NLK-TCF7L1 38206 4994 56442 3145 46853 FZD5-NLK-WNT4 18569 6862 45684 649 46844 EP300-GSK3A-NLK 1488 36811 54049 43805 46079 CCND1-FRAT1-NLK 26521 15175 17461 50164 8676 CXXC4-NLK-WNT5A 46697 2350 52931 39870 42513 NLK-SFRP1-TLE2 44300 56949 757 34474 28195 DKK1-GSK3A-NLK 28 36037 55819 40750 50385 FGF4-NLK-WNT2B 13475 808 24001 38421 32951 FOSL1-NLK-SFRP4 56020 1030 45227 15474 45886 FRAT1-NLK-RHOU 52049 4579 56808 43475 33170 FRAT1-NLK-PPP2R1A 47257 5675 39028 27369 25057 CTNNBIP1-NLK-PPP2R1A 27842 23336 43647 19091 40032 NLK-PYGO1-WNT2 7759 3583 13307 7257 24124 AXIN1-FZD2-NLK 17740 18892 23208 35290 20140 NLK-WIF1-WNT4 27894 29051 3153 6969 7790 NLK-SFRP1-FBXW4 21614 5912 9190 38148 35118 GSK3A-JUN-NLK 12859 53370 40655 43079 36718 AXIN1-FOXN1-NLK 9541 19853 27767 42655 28011 FZD1-NLK-SFRP4 28087 13170 30488 13854 38484 CXXC4-NLK-RHOU 43136 740 51616 39219 36924 DVL1-FOXN1-NLK 3090 52566 51110 49483 15813 FZD1-NLK-TCF7L1 6486 13405 43996 6473 42827 CCND3-FGF4-NLK 277 51087 6136 52041 3116 DAAM1-FRAT1-NLK 48108 52925 26046 49813 10162 NLK-WIF1-WNT3A 15025 31663 634 53620 7624 CTNNB1-NLK-WIF1 36869 4645 37317 37303 40718 FOSL1-NLK-TCF7L1 10193 14999 53644 2916 50012 CSNK1D-NLK-SENP2 2789 23569 46292 12953 16278 CSNK1A1-NLK-WIF1 11282 8274 56968 38447 50254 FRAT1-NLK-TCF7 46859 4510 41103 2141 38466 CCND1-NLK-WNT2B 9124 21736 38415 27714 2883 Table 2: Rankings of NLK-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf NLK-WNT5A, NLK-PYGO1-WNT2, NLK-WIF1-WNT4, NLK-WIF1-WNT3A and CCND1-NLK-WNT2B. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 9 [21] F. Pez, A. Lopez, M. Kim, J. R. Wands, C. C. de Fromentel, P. Merle, Wnt signaling and hepatocarcinogenesis: molecular targets for the development of innovative anticancer drugs, Journal of hepatology 59 (2013) 1107–1117. [22] T. Ishitani, S. Kishida, J. Hyodo-Miura, N. Ueno, J. Yasuda, M. Waterman, H. Shibuya, R. T. Moon, J. NinomiyaTsuji, K. Matsumoto, The tak1-nlk mitogen-activated protein kinase cascade functions in the wnt-5a/ca2+ pathway to antagonize wnt/β-catenin signaling, Molecular and cellular biology 23 (2003) 131–139. 16