NKD inhibitor of WNT signaling pathway 1 / naked cuticle homolog 1 (NKD1) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

NKD inhibitor of WNT signaling pathway 1 / naked cuticle homolog 1 (NKD1) : 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 Address : 104-Madhurisha Heights Phase 1, Risali, Bhilai-490006, India Corresponding author email : [email protected] Abstract NKD1 is a member of naked cuticle (NKD) family that inhibits the WNT signaling pathway, by binding to Dishevelled (DVL) family of proteins. 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 NKD1 related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for NKD1-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 NKD1 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 in WNT3A stimulated cells 1Aspects of unpublished work were presented in a poster session at Cell Symposia: Technology.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 2, 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 NKD1 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. NKD inhibitor of WNT signaling pathway 1 / naked cuticle homolog 1 (NKD1) Naked cuticle (NKD) is a conserved family of intracellular proteins encoded in most animal genomes, the original mutants of which were discovered by 1995 Nobel laureates Christiane Nusslein-Volhard and Eric F. Wieschaus and colleagues in their genetic screens for pattern-formation mutants in Drosophila melanogaster Jurgens et al. [4]. During animal development, cells have to respond appropriately to localized secreted signals and WNT signals have been found to be crucial in development and neoplasia. Zeng et al. [5] show that NKD, a Drosophila segment-polarity gene, encodes an inducible antagonist for the WNT signal Wingless (WG). In fly embryos and imaginal discs nkd transcription is induced by WG while, overproduction of NKD in Drosophila and misexpression of NKD in the vertebrate Xenopus laevis, result in phenotypes resembling those of loss of WG/Wnt function. Using ectopic expression, Rousset et al. [6] found that NKD affected, in a cell-autonomous manner, a transduction step between the WNT signaling components Drosophila Dishevelled (DSH) and Zeste-white 3 kinase (ZW3). Their results showed that NKD acted directly through DSH to limit WG activity and determined how efficiently WNT signals stabilized Armadillo (Arm)/βcatenin and activated downstream genes. In the fruit fly Drosophila, embryos defective in signaling mediated by the WNT protein Wingless (WG) exhibit severe segmentation defects. The Drosophila segment polarity gene NKD encodes an EF hand protein that regulates early WG activity by acting as an inducible antagonist. NKD antagonizes WG via a direct interaction with the Wnt signaling component Drosophila Dishevelled (DSH). Wharton Jr et al. [7] describe two mouse and human proteins, NKD-1/2, related to fly NKD. They observe that the most conserved region among the fly and vertebrate proteins, the EFX domain, includes the putative EF hand and flanking sequences where EFX corresponds to a minimal domain required for fly or vertebrate NKD to interact with the basic/PDZ domains of fly DSH or vertebrate DVL proteins in the yeast two-hybrid assay. Katoh [8] cloned and characterized human NKD-1/2. Both were predicted to encode 470and 451amino-acid polypeptide, respectively. NKD-1/2, showed 43.8% total amino-acid identity, were more homologous in the NH1, NH2, NH3, and NH4 domains. The conserved sequence blocks, from N-terminal to C-terminal, are as follows: •a N-terminal membrane anchoring motif, which in mammals is subject to myristoylation; Li et al. [9] demonstrate that a member of the NKD famil is myristoylated. Both NKD1 and 3 NKD2 contain the consensus sequence for N-myristoyl transferase (Met-Gly-X-X-XSer/Thr), along with adjacent basic residues and a polyhistidine tract at their C termini. Their study identified an unexpected function of NKD2 that is not shared by NKD1, that is, myristoylation-dependent escorting of TGFαto the basolateral surface of polarized epithelial cells. Mammalian NKD homologs have N-terminal consensus sequences that direct the post-translational addition of a lipophilic myristoyl moiety, but fly and mosquito NKD, while sharing N-terminal sequence homology, lack a myristoylation consensus sequence. Chan et al. [10] provide evidence that fly NKD acts cell-autonomously in the embryo, with its N-terminus able to confer unique functional properties and membrane association that cannot be mimicked in vivo by heterologous myristoylation consensus sequences. •a single, extended EF hand motif (called ”EFX” or ”NH2”) that binds DSH/DVL proteins; in Wharton Jr et al. [7] as mentioned earlier and Yan et al. [11] identified an interacting protein, mNKD, that is 30% identical to Drosophila NKD and both mNKD and Drosophila NKD contain a single EF-hand (common helix-loop-helix calcium-binding motif) calcium-binding motif which has the most similarity to the EF-hand found in the Recoverin family of calcium-binding proteins. The domain of mNKD that interacts with mDVL in the yeast two-hybrid experiments is located between amino acids 107 and 230 and includes the EF-hand. •a thirty amino acid motif in the fly NKD protein mediates nuclear translocation; Nkd can bind and inhibit the WNT signal transducer Dishevelled (DSH), but the mechanism by which NKD limits Wnt signaling in the fly embryo is not understood. Waldrop et al. [12] show that NKD mutants exhibit elevated levels of the beta-catenin homolog Armadillo but no alteration in DSH abundance or distribution. While DSH-binding regions of NKD contribute to its activity, they identified a conserved 30-amino-acid motif, separable from DSH-binding regions, that is essential for NKD function and nuclear localization. Replacement of the 30-amino-acid motif with a conventional nuclear localization sequence rescued a small fraction of NKD mutant animals to adulthood. And, Guo et al. [13] show that one function of the vertebrate NKD 30-amino-acid motif is to oppose NKD1-EFX/DVL interactions, which is itself apparently opposed by further C-terminal sequence that is deleted in their MSI-CRC tumors. •a C-terminal Histidine-rich sequence of unknown function. Wnt signaling controls a wide range of developmental processes and its aberrant regulation can lead to disease. To better understand the regulation of this pathway, Van Raay et al. [14] identified zebrafish homologues of NKD, i.e NKD-1/2, which have previously been shown to inhibit canonical WNT/β-catenin signaling. They observed that zebrafish NKD1 expression increased substantially after the mid-blastula transition in a pattern mirroring that of activated canonical WNT/β-catenin signaling, being expressed in both the ventrolateral blastoderm margin and also in the axial mesendoderm. In contrast, zebrafish NKD2 was maternally and ubiquitously expressed. Overexpression of NKD-1/2A suppressed canonical WNT/β-catenin signaling at multiple stages of early zebrafish development and also exacerbated the cyclopia and axial mesendoderm convergence and extension (C&E) defect in the non-canonical WNT/PCP mutant silberblick (SLB/WNT11). Further, the establishment of the left-right (LR) axis in zebrafish embryos relies on signals from the dorsal forerunner cells (DFC) and the Kupffer’s vesicle (KV). Schneider et al. [15] analyzed the expression patterns of three zebrafish NKD homologs and found enriched expression of NKD1 in DFCs and KV. 4 They found DVL degraded upon NKD1 overexpression in zebrafish. Their findings showed that NKD1 acted as a β-catenin antagonist in the DFCs necessary for LR patterning. I present 3rd order combinations of NKD1 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. 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 [16]. 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 [16]. 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 5 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 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 sensi6 tivities 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]. 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 NKD1-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 [17]) and Sobol indicies (with 2002 implementation in Saltelli [18] and martinez implementation in Martinez [19] and Baudin et al. [20]). 6.3. Conserved machine learning rankings for tested NKD1-X-X combinations A total of 2415, 3rd order combinations involving NKD1 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. 7 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 FZD7-NKD1-SENP2 78 10179 4761 28020 28474 FSHB-NKD1-PPP2R1A 134 11978 48147 4744 11658 DIXDC1-NKD1-SENP2 139 26878 5252 13422 20937 FZD7-NKD1-WNT2B 140 22580 30435 30959 23507 DIXDC1-NKD1-TLE2 211 181 25309 23711 748 DIXDC1-NKD1-TCF7L1 239 17174 2661 14197 5839 FZD7-NKD1-PPP2CA 369 8802 35791 35537 25608 FZD7-NKD1-SFRP4 384 21227 4937 21897 25651 FSHB-NKD1-TLE2 425 30274 24343 8644 12849 DIXDC1-NKD1-PPP2CA 440 13162 40123 35144 6197 FZD5-NKD1-WNT2B 450 18227 31166 30382 5811 FSHB-NKD1-SENP2 574 7025 14205 7566 35992 DKK1-NKD1-SENP2 575 5975 43246 35996 27099 FBXW11-NKD1-SENP2 618 34583 6281 9193 28276 FZD7-NKD1-TCF7L1 657 23179 2067 50336 28795 FSHB-NKD1-WNT2B 699 45757 26960 8191 17214 FRZB-NKD1-SENP2 705 6025 7511 12942 30682 FZD7-NKD1-FBXW4 729 9858 18476 41281 18997 FZD5-NKD1-TLE2 785 4126 18422 33090 3434 FZD2-NKD1-WNT2 792 33006 2260 28026 532 LEF1-NKD1-PPP2R1A 793 3084 55944 23057 25903 FRZB-NKD1-WNT2B 861 8764 29474 26264 14733 FZD1-NKD1-SENP2 865 3117 15529 25963 26289 FOSL1-NKD1-SFRP4 875 160 5276 11851 11033 DIXDC1-NKD1-WNT2 883 442 1751 18827 1642 DKK1-NKD1-WNT2B 912 10412 49963 52787 8425 CSNK1G1-NKD1-PPP2CA 926 17356 35232 35369 12912 FSHB-NKD1-RHOU 974 40540 14067 9128 35039 FSHB-NKD1-SFRP1 1011 27987 21471 7065 1983 FBXW11-NKD1-WNT2B 1027 51970 24642 25865 43366 CCND3-NKD1-WNT2B 1067 19542 49729 33902 7166 FZD7-NKD1-WNT2 1099 15793 1721 33173 28181 FZD7-NKD1-TLE1 1127 6936 12734 50934 40716 FZD5-NKD1-SFRP4 1137 15039 9065 28525 21751 FSHB-NKD1-WNT5A 1146 8921 29165 19619 2206 CSNK1G1-NKD1-TCF7L1 1194 9892 6186 28656 13545 FZD1-NKD1-SFRP4 1200 13902 31686 31642 11656 CSNK1G1-NKD1-SENP2 1257 16631 15972 26700 19860 FZD1-NKD1-WNT2B 1274 10870 41498 34943 5517 FRZB-NKD1-SFRP4 1296 647 21775 12472 26405 FZD7-NKD1-RHOU 1307 26801 3329 51286 46329 FZD2-NKD1-RHOU 1310 19610 4807 33843 1134 FSHB-NKD1-TCF7L1 1387 37613 10650 8338 29279 KREMEN1-NKD1-WNT2B 1400 34496 34759 43275 20181 LRP5-NKD1-SENP2 1447 1797 8631 4376 40581 KREMEN1-NKD1-SENP2 1463 18745 6060 20808 42111 CSNK1G1-NKD1-SFRP4 1474 513 13103 24557 6931 LRP5-NKD1-SFRP4 1486 21467 6314 10196 31377 FZD2-NKD1-TLE2 1505 29421 21252 27865 2130 FZD1-NKD1-TLE2 1523 3791 21524 33601 4582 FSHB-NKD1-TCF7 1528 46050 40792 9733 32939 DIXDC1-NKD1-WNT4 1536 13509 3143 4994 28564 FBXW2-NKD1-WNT2B 1547 22973 29232 13160 53054 FZD7-NKD1-TCF7 1550 5115 43100 44210 33757 FZD7-NKD1-WNT3A 1664 5491 2056 28279 37124 LRP5-NKD1-WNT2B 1686 21363 28403 16564 24813 KREMEN1-NKD1-TCF7L1 1699 28241 2070 41242 30439 DIXDC1-NKD1-RHOU 1798 6195 3765 22405 3157 LRP5-NKD1-TCF7L1 1804 29713 4980 13354 42899 DIXDC1-NKD1-WNT5A 1830 5103 33835 49403 2232 FOSL1-NKD1-PPP2CA 1845 14335 40783 24581 23211 FZD5-NKD1-TCF7L1 1914 20430 1935 26746 22679 FRZB-NKD1-PPP2CA 1923 12714 42040 19751 23511 APC-NKD1-TLE2 1939 24 20649 13050 16733 CCND3-NKD1-WNT3A 1995 32953 30709 40159 23393 NKD1-WIF1-WNT3A 2028 3129 43733 48011 30914 FZD8-NKD1-WNT2B 2038 34027 33288 19731 46263 FZD5-NKD1-FBXW4 2042 6515 20216 24601 16637 CTBP1-NKD1-SFRP4 2057 1716 14512 24063 41784 FZD7-NKD1-SLC9A3R1 2065 23275 9662 24185 39745 FZD5-NKD1-RHOU 2086 9792 3471 18764 2521 DIXDC1-NKD1-PPP2R1A 2140 5484 54992 25998 568 DKK1-NKD1-PPP2CA 2158 21388 52610 49493 9273 FZD1-NKD1-RHOU 2176 20088 11316 49737 2429 CXXC4-NKD1-WNT2B 2217 9878 36698 23848 1631 FRZB-NKD1-TLE2 2272 121 33128 21637 12907 CSNK1G1-NKD1-RHOU 2328 3565 14141 34128 1880 FOSL1-NKD1-SENP2 2466 6869 5781 10026 30259 FZD2-NKD1-SENP2 2523 36940 7846 15207 17515 FSHB-NKD1-WNT2 2558 23961 6398 3570 16109 KREMEN1-NKD1-TLE2 2619 18016 16139 44657 37610 FZD5-NKD1-WNT4 2642 3099 2732 32040 47167 KREMEN1-NKD1-WNT3A 2675 23678 2816 47552 40285 DIXDC1-NKD1-TCF7 2704 16324 46726 24262 6288 FZD5-NKD1-TCF7 2753 4697 38384 26960 22996 FBXW2-NKD1-PPP2CA 2839 23721 34814 16169 56279 CTBP1-NKD1-TCF7L1 2845 7922 3120 35646 35460 CTBP2-FZD7-NKD1 2976 52126 40799 40259 46777 GSK3B-NKD1-TLE2 2977 22800 23954 42499 38689 FBXW2-NKD1-SENP2 2988 37184 10657 11033 56876 NKD1-WIF1-WNT4 2997 2461 45561 55000 34857 FZD5-NKD1-WNT5A 3021 6206 35575 52940 2092 CXXC4-NKD1-SENP2 3069 14633 9774 13334 17352 CCND3-NKD1-SFRP4 3074 31551 41849 39607 12267 DVL1-NKD1-WNT2B 3089 2831 24130 36326 51502 KREMEN1-NKD1-FBXW4 3108 22301 16832 29059 23025 CSNK2A1-NKD1-WNT2B 3148 4519 40339 22219 23905 CXXC4-NKD1-TLE2 3160 26 22413 13930 94 NKD1-PPP2CA-SFRP4 3169 46409 13326 29656 43339 CTNNBIP1-NKD1-RHOU 3194 27112 11412 35287 15481 CCND3-NKD1-PPP2CA 3285 34449 42225 49257 26308 NKD1-WNT2B-WNT4 3336 43254 28275 6099 51615 CCND1-NKD1-PPP2CA 3363 11274 37598 54652 44854 FZD7-NKD1-WNT5A 3371 2073 37837 34079 40424 FZD2-NKD1-WIF1 3430 39091 22109 26358 3 FZD2-NKD1-WNT2B 3444 30135 33767 29289 1990 NKD1-WNT2B-WNT3A 3477 51633 33941 7298 45111 FRZB-NKD1-RHOU 3499 2171 5014 35449 27330 CSNK1G1-NKD1-WNT2 3527 1109 9218 26094 482 FZD5-NKD1-PPP2R1A 3621 21515 54524 36048 1557 CCND3-NKD1-WNT2 3637 32192 36071 49096 2809 FSHB-NKD1-FBXW4 3657 26327 16817 8776 23172 FZD8-NKD1-PPP2CA 3681 49836 33279 27543 15965 FZD7-NKD1-WNT4 3704 14766 3963 41558 50663 FBXW11-NKD1-TCF7L1 3783 32677 2358 19136 41733 LEF1-NKD1-WNT3 3813 14659 40690 18495 25196 FBXW2-NKD1-WNT4 3822 22628 8291 3237 57029 KREMEN1-NKD1-WNT4 3871 11426 4535 41285 47213 DIXDC1-NKD1-WIF1 3909 12873 22358 12920 23739 DAAM1-NKD1-WNT2B 3944 45573 30236 23673 33353 CXXC4-NKD1-RHOU 3957 5011 6876 36465 23781 LEF1-NKD1-SFRP1 3999 1638 28264 15491 1219 GSK3B-NKD1-TCF7L1 4012 30306 1476 36252 37466 CSNK2A1-NKD1-PPP2CA 4025 15782 45180 27270 33423 FBXW2-NKD1-TLE2 4091 22177 18065 12184 55575 CSNK2A1-NKD1-PPP2R1A 4118 2001 56920 13318 8736 Table 1: Rankings of NKD1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear 8 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 FZD7-NKD1-SENP2 22248 3166 47262 13293 2567 FSHB-NKD1-PPP2R1A 25236 3206 25555 29398 54336 DIXDC1-NKD1-SENP2 24325 22750 54264 38554 4248 FZD7-NKD1-WNT2B 47917 26281 13366 54412 1630 DIXDC1-NKD1-TLE2 22103 8452 55942 25492 11873 DIXDC1-NKD1-TCF7L1 32308 45794 57018 24322 3679 FZD7-NKD1-PPP2CA 15127 35957 31673 37533 1778 FZD7-NKD1-SFRP4 22923 15141 38823 43517 2354 FSHB-NKD1-TLE2 17403 24824 7167 5397 44661 DIXDC1-NKD1-PPP2CA 9807 43231 37477 30170 1078 FZD5-NKD1-WNT2B 18497 19475 22567 24649 24247 FSHB-NKD1-SENP2 14879 5325 16207 3306 6877 DKK1-NKD1-SENP2 7012 22034 30235 20793 14207 FBXW11-NKD1-SENP2 3968 23882 33729 15929 5877 FZD7-NKD1-TCF7L1 40741 32897 48058 29669 1354 FSHB-NKD1-WNT2B 24792 50507 25909 42911 36692 FRZB-NKD1-SENP2 3644 10458 50187 29431 36573 FZD7-NKD1-FBXW4 39942 9295 41002 45990 5647 FZD5-NKD1-TLE2 3831 2363 53067 35683 47894 FZD2-NKD1-WNT2 54548 26947 57006 32814 25385 LEF1-NKD1-PPP2R1A 24944 9286 39491 44583 37109 FRZB-NKD1-WNT2B 26947 18964 19602 32120 37731 FZD1-NKD1-SENP2 16283 248 42563 17609 26499 FOSL1-NKD1-SFRP4 38557 1693 50390 24818 21820 DIXDC1-NKD1-WNT2 30452 9192 55932 6605 10010 DKK1-NKD1-WNT2B 33321 46336 43515 12948 3783 CSNK1G1-NKD1-PPP2CA 8799 37693 42013 33688 15900 FSHB-NKD1-RHOU 13620 39126 15440 38560 46234 FSHB-NKD1-SFRP1 28217 31095 6105 12696 47885 FBXW11-NKD1-WNT2B 42436 56089 5208 5851 6025 CCND3-NKD1-WNT2B 31750 9905 43256 46510 4045 FZD7-NKD1-WNT2 38995 9386 56253 3799 2844 FZD7-NKD1-TLE1 27415 7679 53298 43858 894 FZD5-NKD1-SFRP4 15328 9399 47362 16033 40262 FSHB-NKD1-WNT5A 45339 3228 1592 43013 28219 CSNK1G1-NKD1-TCF7L1 6006 22577 49200 31622 30401 FZD1-NKD1-SFRP4 43048 8656 45237 21687 17892 CSNK1G1-NKD1-SENP2 4079 7354 54740 12528 13804 FZD1-NKD1-WNT2B 35381 16131 32653 43586 18237 FRZB-NKD1-SFRP4 30663 4537 52953 18729 25710 FZD7-NKD1-RHOU 29725 14170 51670 56277 8735 FZD2-NKD1-RHOU 50910 12898 54711 9572 46912 FSHB-NKD1-TCF7L1 29187 51071 22006 21070 31900 KREMEN1-NKD1-WNT2B 10715 45017 15095 25349 17172 LRP5-NKD1-SENP2 14990 3717 34426 11779 16566 KREMEN1-NKD1-SENP2 730 3287 51067 20876 22424 CSNK1G1-NKD1-SFRP4 10332 8994 35937 45547 19919 LRP5-NKD1-SFRP4 26254 21185 21350 26108 17079 FZD2-NKD1-TLE2 24712 20087 50718 44876 38227 FZD1-NKD1-TLE2 24945 3728 49365 3491 46221 FSHB-NKD1-TCF7 16167 43862 3127 18402 9845 DIXDC1-NKD1-WNT4 28297 20930 51455 19765 821 FBXW2-NKD1-WNT2B 33781 33859 11109 13486 210 FZD7-NKD1-TCF7 37444 15437 35879 47781 305 FZD7-NKD1-WNT3A 16651 467 45031 55399 13378 LRP5-NKD1-WNT2B 32145 41013 38068 34089 24010 KREMEN1-NKD1-TCF7L1 6544 33167 55781 7544 9258 DIXDC1-NKD1-RHOU 22817 19488 48855 52946 7640 LRP5-NKD1-TCF7L1 17394 31853 35078 16573 14922 DIXDC1-NKD1-WNT5A 50477 15744 20410 52735 35648 FOSL1-NKD1-PPP2CA 21934 29546 42661 35675 17456 FZD5-NKD1-TCF7L1 18061 23794 54846 25790 41167 FRZB-NKD1-PPP2CA 1942 36043 22753 20309 35265 APC-NKD1-TLE2 23869 4453 50209 22108 50421 CCND3-NKD1-WNT3A 19177 14820 26493 56175 64 NKD1-WIF1-WNT3A 48793 3970 17300 56778 21427 FZD8-NKD1-WNT2B 49791 35392 25199 27885 3968 FZD5-NKD1-FBXW4 9460 12253 43946 48270 55667 CTBP1-NKD1-SFRP4 34262 7238 53046 16240 32125 FZD7-NKD1-SLC9A3R1 40405 7627 50823 42113 3058 FZD5-NKD1-RHOU 17419 5033 39813 31860 48308 DIXDC1-NKD1-PPP2R1A 41282 2633 37452 52221 22216 DKK1-NKD1-PPP2CA 845 43108 38644 15851 21492 FZD1-NKD1-RHOU 9230 9523 50610 53836 44264 CXXC4-NKD1-WNT2B 33112 30020 8852 27851 43373 FRZB-NKD1-TLE2 14829 3484 49881 39277 47223 CSNK1G1-NKD1-RHOU 7968 13163 45029 45281 48042 FOSL1-NKD1-SENP2 15372 3697 55084 25337 9352 FZD2-NKD1-SENP2 25897 35442 55987 51047 12409 FSHB-NKD1-WNT2 18619 15105 23935 22810 37921 KREMEN1-NKD1-TLE2 2919 14915 47965 33551 33612 FZD5-NKD1-WNT4 12678 521 57060 25537 26670 KREMEN1-NKD1-WNT3A 9700 7837 52991 45907 10853 DIXDC1-NKD1-TCF7 22420 28291 44348 38473 4381 FZD5-NKD1-TCF7 16271 1612 53778 20615 31084 FBXW2-NKD1-PPP2CA 15124 44885 17926 12733 2217 CTBP1-NKD1-TCF7L1 22297 13060 56917 8766 27600 CTBP2-FZD7-NKD1 31868 50353 6812 34202 44114 GSK3B-NKD1-TLE2 7424 17188 52854 26876 49828 FBXW2-NKD1-SENP2 11695 33380 11958 18807 1265 NKD1-WIF1-WNT4 20047 23652 20170 17000 48569 FZD5-NKD1-WNT5A 33749 1909 44565 56409 39882 CXXC4-NKD1-SENP2 23566 21575 56539 18663 8724 CCND3-NKD1-SFRP4 21810 15481 41109 37803 2086 DVL1-NKD1-WNT2B 38080 13959 43055 47296 2221 KREMEN1-NKD1-FBXW4 16975 10848 31634 30290 26950 CSNK2A1-NKD1-WNT2B 17855 5115 19163 36411 21386 CXXC4-NKD1-TLE2 14475 5894 51388 28114 51127 NKD1-PPP2CA-SFRP4 40324 48641 51898 9183 19710 CTNNBIP1-NKD1-RHOU 49378 32634 47683 47402 32347 CCND3-NKD1-PPP2CA 19772 35706 47585 36014 3731 NKD1-WNT2B-WNT4 31109 52225 48686 5473 15716 CCND1-NKD1-PPP2CA 31094 31919 45839 10804 5523 FZD7-NKD1-WNT5A 53120 6594 44749 54824 2305 FZD2-NKD1-WIF1 45250 38648 56326 24018 7601 FZD2-NKD1-WNT2B 53572 28271 33551 10732 5520 NKD1-WNT2B-WNT3A 50905 55634 51652 46273 6139 FRZB-NKD1-RHOU 9972 3765 49769 37400 50607 CSNK1G1-NKD1-WNT2 6387 6428 51082 8449 39348 FZD5-NKD1-PPP2R1A 23335 9105 47323 31744 56453 CCND3-NKD1-WNT2 36776 17718 45542 2330 4094 FSHB-NKD1-FBXW4 37869 19703 30672 38958 40988 FZD8-NKD1-PPP2CA 31727 55399 17443 4434 10950 FZD7-NKD1-WNT4 19019 5699 47235 25398 489 FBXW11-NKD1-TCF7L1 8257 42198 35700 9053 14548 LEF1-NKD1-WNT3 33634 12910 24295 24445 28299 FBXW2-NKD1-WNT4 15630 22910 34768 11469 618 KREMEN1-NKD1-WNT4 1146 12492 44039 43786 11253 DIXDC1-NKD1-WIF1 44180 9421 57087 48747 10766 DAAM1-NKD1-WNT2B 21385 46690 24575 48240 1108 CXXC4-NKD1-RHOU 49373 16254 50519 35698 48470 LEF1-NKD1-SFRP1 33942 6111 31628 47136 38942 GSK3B-NKD1-TCF7L1 43296 37741 56267 44754 33094 CSNK2A1-NKD1-PPP2CA 6422 22743 30647 42195 19402 FBXW2-NKD1-TLE2 16737 27286 16157 17903 3635 CSNK2A1-NKD1-PPP2R1A 19188 9240 34119 49629 44582 Table 2: Rankings of NKD1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf 6.3.1. Examining the behaviour of DIXDC1-NKD1-X combinations Dishevelled (DVL-1/2/3) are DIX-domain proteins implicated in the WNT signaling pathway. NKD1 is a member of naked cuticle (NKD) family that inhibits the 9