KIAA1735/Dixin DIX domain containing 1 (DIXDC1) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

KIAA1735/Dixin DIX domain containing 1 (DIXDC1) : 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 DIXDC1, when active, is known to stop cancer metastasis due to extreme stickiness, both in vitro and in vivo and it turns out to be inhibited in cancer and mestastasis. 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 DIXDC1 related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for DIXDC1-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 DIXDC1 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 in WNT3A stimulated cells 1Aspects of unpublished work were presented in a poster session at Cell Symposia: Technology.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 5, 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 DIXDC1 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. KIAA1735/Dixin DIX domain containing 1 (DIXDC1) Dishevelled DVL-1/2/3 are DIX-domain proteins implicated in the WNT signaling pathway. Katoh and Katoh [4] searched found an uncharacterized human KIAA1735 gene encoding a novel DIX-domain protein, using bioinformatics. They identified mouse ortholog of human KIAA1735 gene, and the nucleotide sequence of mouse KIAA1735 cDNA was determined in silico by assembling nucleotide sequences of ESTs BY753211, BQ931084, CA750490, BQ960056 and a 5’-truncated partial cDNA AK082960. Myosine-tail homologous (MTH) domain and C-terminal DIX domain were conserved between human KIAA1735 and mouse KIAA1735 proteins. A tyrosine phosphorylation site (Tyr 242) within the MTH domain was conserved between human KIAA1735 and mouse KIAA1735 proteins. KIAA1735 gene (consisting of 16 exons), was about 45 kb in size and on human chromosome 11q23.1, was located between D11S1391 and D11S1347 loci, the region deleted in sporadic breast cancer. This was the first report on comprehensive characterization of the KIAA1735 gene. To become mobile, cancer cells usually override cellular machinery that keeps cells rooted within their respective locations. Deviously, cancer can switch on and off molecular anchors protruding from the cell membrane (called focal adhesion complexes), preparing the cell for migration. This allows cancer cells to begin the processes to traverse the body through the bloodstream and take up residence in new organs. Cancers missing polarization-related protein LKB1 or serine/threonine kinase 11 (PeutzJeghers syndrome) (LKB1/STK11) are often aggressive, rapidly spreading through the body. However, it was not known, how LKB1 and focal adhesions were connected. In an medical press release by the Salk Institute on July 17, 2014 in https:// medicalxpress.com/news/2014-07-gene-deadly-cancer.html#nRlv, the Salk Institute team found the connection and a new target for therapy: DIXDC1. They discovered that DIXDC1 received instructions from LKB1 to go to focal adhesions and change their size and number. When DIXDC1 was active, focal adhesions grew large and sticky, anchoring cells to their spot, while when DIXDC1 was inactive, focal adhesions became small and numerous, resulting in hundreds of small hands that pull the cell forward in response to extracellular cues. That increased tendency to be mobile, aids in the escape from, for example, the lungs and allows tumor cells to survive travel through the bloodstream and dock at organs throughout the body. It turned out that DIXDC1 was inhibited in cancer and metastasis. I present 3rd order combinations of DIXDC1 with other genes, that the machine learning based search engine points to, as possible synergistic combinations that might 3 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 [5]. 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 [5]. 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. 4 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 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 5 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 DIXDC1-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 [6]) and Sobol indicies (with 2002 implementation in Saltelli [7] and martinez implementation in Martinez [8] and Baudin et al. [9]). 6.3. Conserved machine learning rankings for tested DIXDC1-X-X combinations A total of 2415, 3rd order combinations involving DIXDC1 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 GSK3-DIXDC1-X combinations Martin et al. [10] propose that rare missense single-nucleotide variants (SNVs) in DIXDC1 contribute to psychiatric pathogenesis by reducing spine and glutamatergic synapse density downstream of GSK3 in the WNT/β-catenin pathway. Looking at the 6 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 APC-DIXDC1-WNT2B 89 27000 33475 27891 27710 DIXDC1-NKD1-SENP2 139 26878 5252 13422 20937 DIXDC1-NKD1-TLE2 211 181 25309 23711 748 DIXDC1-NKD1-TCF7L1 239 17174 2661 14197 5839 DIXDC1-FOXN1-FBXW4 330 3748 17556 12016 30746 DIXDC1-NKD1-PPP2CA 440 13162 40123 35144 6197 CCND1-CTBP1-DIXDC1 516 56574 53031 16545 48176 DIXDC1-PITX2-SENP2 526 28707 7274 5676 35235 DIXDC1-FOXN1-TLE2 581 740 1891 12323 28293 DIXDC1-FOXN1-FZD8 584 8409 1800 17070 5733 DIXDC1-PITX2-SFRP4 614 29602 6543 3868 43507 DIXDC1-PORCN-WNT4 690 39847 12582 10499 56262 DIXDC1-FSHB-LEF1 777 45272 10940 6689 22555 DIXDC1-NKD1-WNT2 883 442 1751 18827 1642 DIXDC1-FOXN1-KREMEN1 939 687 5376 7847 13303 DIXDC1-FZD2-LEF1 942 12211 3020 42787 29981 DIXDC1-LRP5-SENP2 1098 18807 1510 3942 4609 DIXDC1-FZD2-TCF7L1 1100 22783 49446 23638 20089 DIXDC1-FGF4-FBXW4 1142 8123 30879 12840 50692 DIXDC1-FZD2-SENP2 1148 28328 6949 7791 20834 DIXDC1-WNT3-WNT4 1279 51438 14477 19803 17251 DIXDC1-JUN-FBXW4 1340 27624 17009 49472 50306 DIXDC1-JUN-TCF7L1 1397 18158 39442 41838 15514 DIXDC1-FOXN1-FRZB 1442 1877 4968 4749 2791 DIXDC1-FZD2-FZD8 1466 11545 29932 40243 14229 DIXDC1-FZD2-FZD7 1473 21462 19307 23718 22870 APC-DIXDC1-FRZB 1488 36338 55199 25861 797 DIXDC1-FOXN1-SENP2 1491 2077 4322 6058 1110 DIXDC1-PORCN-SENP2 1529 21963 6981 10680 50015 DIXDC1-FGF4-FRAT1 1533 9050 41138 51810 43824 DIXDC1-NKD1-WNT4 1536 13509 3143 4994 28564 DIXDC1-FZD2-WNT4 1576 35367 3250 12254 41951 DIXDC1-GSK3B-SLC9A3R1 1609 31242 3865 16239 26807 DIXDC1-GSK3A-SENP2 1621 28519 557 27468 36407 DIXDC1-FZD2-KREMEN1 1727 6226 28247 11263 35521 DIXDC1-NKD1-RHOU 1798 6195 3765 22405 3157 DIXDC1-NKD1-WNT5A 1830 5103 33835 49403 2232 DIXDC1-FGF4-FOSL1 1834 22981 29680 27665 50757 DIXDC1-FGF4-TLE2 1838 19948 33519 25723 52981 DIXDC1-FGF4-FZD8 1912 23178 24551 54089 31538 APC-DIXDC1-SFRP4 1940 34105 56875 25938 15956 APC-DIXDC1-DKK1 1973 39613 14672 51391 14145 DIXDC1-JUN-KREMEN1 2010 2457 38608 53030 25504 DIXDC1-FZD2-TLE2 2059 1052 41611 34129 44387 DIXDC1-FOXN1-WNT4 2069 18260 5558 10405 1210 FZD5-DIXDC1-FRZB 2081 26083 51583 4776 41242 DIXDC1-LRP5-WNT4 2098 56736 1699 4505 8233 DIXDC1-NLK-WNT4 2128 13920 3978 2846 15403 DIXDC1-WNT1-WNT4 2134 8527 1926 11050 9192 DIXDC1-JUN-SENP2 2137 30487 37871 53712 15183 DIXDC1-NKD1-PPP2R1A 2140 5484 54992 25998 568 DIXDC1-FGF4-FZD1 2148 34299 35191 38859 49381 DIXDC1-FZD2-FBXW4 2156 27392 32655 28804 43752 DIXDC1-GSK3A-WNT4 2177 45494 1826 20781 48238 DIXDC1-JUN-SLC9A3R1 2235 15861 11040 56361 22586 DIXDC1-JUN-TLE2 2288 253 494 55465 49628 DIXDC1-FOXN1-WNT2 2324 510 6244 12086 918 DIXDC1-PORCN-FBXW4 2360 25666 16237 7265 54640 DIXDC1-TLE1-TLE2 2398 24851 22502 52222 23488 DIXDC1-JUN-WNT2 2424 1633 23267 35271 23259 DIXDC1-FZD2-LRP5 2550 15903 14969 51496 19500 CSNK1G1-DIXDC1-WNT2B 2602 9079 34225 44850 51306 FZD5-DIXDC1-SENP2 2634 37000 48018 1887 44271 DIXDC1-FGF4-SENP2 2635 18261 53316 27142 35362 APC-DIXDC1-TCF7L1 2672 33791 54110 6164 16187 DIXDC1-GSK3A-SLC9A3R1 2673 40171 11882 42208 52840 DIXDC1-NKD1-TCF7 2704 16324 46726 24262 6288 DIXDC1-SFRP1-WNT4 2827 56975 50212 3166 44324 DIXDC1-PITX2-WNT2B 2863 14619 3889 45440 40568 DIXDC1-FOXN1-SLC9A3R1 2905 17149 580 6704 6648 CSNK1G1-DIXDC1-SENP2 2907 45126 54761 32938 29362 DIXDC1-GSK3A-SFRP4 3011 7186 9197 19775 49994 DIXDC1-FGF4-TCF7L1 3076 32005 36386 8205 35936 DIXDC1-FZD2-WNT2B 3115 8791 13513 44897 31757 DIXDC1-PYGO1-WNT2 3118 7736 11350 8945 27577 DIXDC1-FZD2-SFRP4 3134 5020 36408 6731 42615 DIXDC1-FSHB-FZD1 3136 45375 11211 11425 29794 DIXDC1-PORCN-TLE2 3192 8903 21007 23935 55707 DIXDC1-PYGO1-TCF7L1 3193 33168 18183 17378 30931 DIXDC1-PITX2-WNT4 3214 52681 19702 7189 37575 FZD5-DIXDC1-WNT2B 3222 37056 32234 42255 42076 DIXDC1-FOXN1-PPP2CA 3235 4976 13715 8671 2172 CSNK1G1-DIXDC1-RHOU 3247 13611 55894 17887 29476 DIXDC1-FSHB-T 3255 34040 47003 6560 49035 DIXDC1-PORCN-WNT2B 3266 11238 38406 37800 51881 DIXDC1-DVL2-FRAT1 3310 15749 16154 12064 34806 DIXDC1-JUN-RHOU 3325 2215 36161 42538 1991 DIXDC1-FOXN1-LEF1 3327 3173 8059 15927 10884 DIXDC1-GSK3A-KREMEN1 3347 13841 2607 50326 30275 DIXDC1-SFRP1-FBXW4 3348 22994 35667 16096 50638 DIXDC1-FGF4-TCF7 3385 34777 40983 22775 42381 APC-DIXDC1-FBXW2 3395 2911 34269 1471 6570 DIXDC1-EP300-FBXW11 3401 6056 10476 24069 55750 DIXDC1-FGF4-WNT5A 3402 30477 40511 46509 49117 DIXDC1-SFRP1-TCF7 3404 44931 42751 37910 31320 DIXDC1-NLK-FBXW4 3436 6471 26909 5680 17650 CSNK1G1-DIXDC1-DKK1 3474 22358 26349 38523 54006 DIXDC1-GSK3A-WNT2 3514 7982 20770 47082 45891 FZD5-CCND3-DIXDC1 3536 349 4283 26959 12747 DIXDC1-JUN-WNT3A 3551 836 21850 41587 6942 DIXDC1-FZD2-PPP2CA 3662 17928 10686 40372 29250 DIXDC1-GSK3A-RHOU 3688 25193 1738 30131 17732 DIXDC1-FZD6-FZD8 3726 30855 3487 51102 3333 DIXDC1-FOXN1-SFRP4 3785 1242 4939 11642 2468 DIXDC1-FOXN1-FZD1 3799 13273 8362 12714 28800 DIXDC1-FOXN1-FZD7 3818 4807 3291 13093 46632 DIXDC1-FGF4-SLC9A3R1 3858 41464 33881 21954 50193 DIXDC1-FOXN1-WNT5A 3863 7743 18318 21775 11741 DIXDC1-PORCN-WNT5A 3885 26867 8379 47688 52084 DIXDC1-NKD1-WIF1 3909 12873 22358 12920 23739 DIXDC1-FGF4-WNT4 4006 46441 40742 22331 52314 DIXDC1-PORCN-RHOU 4036 27252 7449 17205 39479 DIXDC1-GSK3A-TCF7L1 4067 26243 14041 22033 41642 DIXDC1-FOXN1-WNT2B 4120 780 1909 4603 6598 DIXDC1-PITX2-PPP2CA 4123 13781 1911 14325 45522 DIXDC1-FZD2-TCF7 4146 31420 19458 30214 27951 DIXDC1-PORCN-SLC9A3R1 4147 35870 12879 23397 50086 DIXDC1-FOXN1-LRP6 4184 4399 11080 16729 11346 DIXDC1-DVL2-FOSL1 4189 23516 3806 16734 50139 DIXDC1-FZD2-WNT2 4199 3075 55905 23835 33613 DIXDC1-FGF4-LRP5 4209 32587 26371 42858 41494 DIXDC1-FOXN1-PPP2R1A 4318 4042 7718 10315 5136 CSNK1G1-DIXDC1-FRZB 4374 20252 52588 28893 38695 APC-DIXDC1-FOSL1 4389 42880 52076 6079 13090 DIXDC1-JUN-TLE1 4454 18781 16283 26133 14897 DIXDC1-GSK3A-TLE2 4469 19803 48789 49172 55138 Table 1: Rankings of DIXDC1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear tables above, one finds the following combinations for members of GSK family along with DIXDC1, to be prominent at 3rd order level - DIXDC1-GSK3B-SLC9A3R1, DIXDC1-GSK3A-KREMEN1, DIXDC1-GSK3A-TCF7L1, DIXDC1-GSK3A-SENP2, DIXDC1-GSK3A-WNT4, DIXDC1-GSK3A-SLC9A3R1, DIXDC1-GSK3A-SFRP4, 7 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 APC-DIXDC1-WNT2B 33671 16882 4145 48106 51792 DIXDC1-NKD1-SENP2 24325 22750 54264 38554 4248 DIXDC1-NKD1-TLE2 22103 8452 55942 25492 11873 DIXDC1-NKD1-TCF7L1 32308 45794 57018 24322 3679 DIXDC1-FOXN1-FBXW4 3530 9085 27138 3878 80 DIXDC1-NKD1-PPP2CA 9807 43231 37477 30170 1078 CCND1-CTBP1-DIXDC1 43082 54629 13851 25493 5299 DIXDC1-PITX2-SENP2 3537 43865 15972 13329 19669 DIXDC1-FOXN1-TLE2 1845 16001 48828 19868 1211 DIXDC1-FOXN1-FZD8 2700 34651 54623 33036 17361 DIXDC1-PITX2-SFRP4 9005 33898 35036 1595 29334 DIXDC1-PORCN-WNT4 25202 25146 26100 53862 33842 DIXDC1-FSHB-LEF1 56469 45507 52727 16153 8570 DIXDC1-NKD1-WNT2 30452 9192 55932 6605 10010 DIXDC1-FOXN1-KREMEN1 3184 5794 52693 37317 689 DIXDC1-FZD2-LEF1 35664 4924 22855 3469 6648 DIXDC1-LRP5-SENP2 1777 23484 44827 123 12925 DIXDC1-FZD2-TCF7L1 22093 37245 28474 19140 2863 DIXDC1-FGF4-FBXW4 863 8394 9981 4999 2166 DIXDC1-FZD2-SENP2 11918 40028 27691 41589 5926 DIXDC1-WNT3-WNT4 23687 55063 42305 53552 6689 DIXDC1-JUN-FBXW4 53699 39669 27414 16988 3729 DIXDC1-JUN-TCF7L1 36423 32144 31736 45585 462 DIXDC1-FOXN1-FRZB 2525 19420 51785 5266 224 DIXDC1-FZD2-FZD8 12238 10132 30096 29586 5638 DIXDC1-FZD2-FZD7 20526 11029 56170 887 16741 APC-DIXDC1-FRZB 10225 33713 18843 30318 48974 DIXDC1-FOXN1-SENP2 1565 39282 50555 4197 2183 DIXDC1-PORCN-SENP2 16346 39480 19973 18502 14705 DIXDC1-FGF4-FRAT1 2503 5561 19946 26820 16773 DIXDC1-NKD1-WNT4 28297 20930 51455 19765 821 DIXDC1-FZD2-WNT4 16200 33727 42194 2888 3723 DIXDC1-GSK3B-SLC9A3R1 40658 33882 42168 6416 5904 DIXDC1-GSK3A-SENP2 407 29880 52868 49762 5769 DIXDC1-FZD2-KREMEN1 14683 17223 32337 21120 1723 DIXDC1-NKD1-RHOU 22817 19488 48855 52946 7640 DIXDC1-NKD1-WNT5A 50477 15744 20410 52735 35648 DIXDC1-FGF4-FOSL1 2494 21424 29421 5565 13873 DIXDC1-FGF4-TLE2 483 5164 27361 31117 107 DIXDC1-FGF4-FZD8 298 43502 31467 49346 4208 APC-DIXDC1-SFRP4 35041 36541 11687 4001 53042 APC-DIXDC1-DKK1 15397 35669 351 47431 19313 DIXDC1-JUN-KREMEN1 28857 3 41815 56574 3054 DIXDC1-FZD2-TLE2 27650 769 44018 38166 114 DIXDC1-FOXN1-WNT4 3943 26131 55172 7688 2054 FZD5-DIXDC1-FRZB 7782 18262 19011 49028 55000 DIXDC1-LRP5-WNT4 7502 57090 41500 5927 3494 DIXDC1-NLK-WNT4 5010 8900 42377 1999 3181 DIXDC1-WNT1-WNT4 8940 3055 44478 355 3113 DIXDC1-JUN-SENP2 14743 34149 32447 35142 1484 DIXDC1-NKD1-PPP2R1A 41282 2633 37452 52221 22216 DIXDC1-FGF4-FZD1 747 28163 2771 16612 5332 DIXDC1-FZD2-FBXW4 10826 17817 13933 14350 2675 DIXDC1-GSK3A-WNT4 1408 54188 56943 11999 14706 DIXDC1-JUN-SLC9A3R1 52675 33774 46150 40855 4391 DIXDC1-JUN-TLE2 20372 1335 37154 33910 5318 DIXDC1-FOXN1-WNT2 4715 14636 41748 5 92 DIXDC1-PORCN-FBXW4 17443 35486 7874 10595 38652 DIXDC1-TLE1-TLE2 47116 48849 22114 26437 1356 DIXDC1-JUN-WNT2 54748 2832 42019 31686 7633 DIXDC1-FZD2-LRP5 38335 7398 15968 15952 6915 CSNK1G1-DIXDC1-WNT2B 56105 5718 34204 36658 46240 FZD5-DIXDC1-SENP2 7671 36100 18300 18941 42529 DIXDC1-FGF4-SENP2 160 19260 11857 32192 2906 APC-DIXDC1-TCF7L1 12380 40622 3158 36294 44580 DIXDC1-GSK3A-SLC9A3R1 2313 39361 52671 23807 16817 DIXDC1-NKD1-TCF7 22420 28291 44348 38473 4381 DIXDC1-SFRP1-WNT4 33874 55995 36243 38745 9587 DIXDC1-PITX2-WNT2B 12649 21037 9654 4112 8993 DIXDC1-FOXN1-SLC9A3R1 5496 29137 51814 26182 1076 CSNK1G1-DIXDC1-SENP2 37857 43110 9454 11888 27966 DIXDC1-GSK3A-SFRP4 1515 4288 53430 32178 8501 DIXDC1-FGF4-TCF7L1 651 50224 24155 46787 4158 DIXDC1-FZD2-WNT2B 29750 42429 10691 1083 508 DIXDC1-PYGO1-WNT2 9260 4892 51202 277 17819 DIXDC1-FZD2-SFRP4 12606 2707 46976 3589 4712 DIXDC1-FSHB-FZD1 3527 44586 55840 4528 2895 DIXDC1-PORCN-TLE2 19616 669 29894 3284 37516 DIXDC1-PYGO1-TCF7L1 9179 35935 48383 28960 14143 DIXDC1-PITX2-WNT4 11062 47027 42885 4269 14148 FZD5-DIXDC1-WNT2B 23182 22191 7617 31293 49776 DIXDC1-FOXN1-PPP2CA 1796 26077 33448 2622 1308 CSNK1G1-DIXDC1-RHOU 49459 11518 16506 41618 49774 DIXDC1-FSHB-T 36455 36262 54691 1183 12572 DIXDC1-PORCN-WNT2B 20111 15273 9550 18377 30375 DIXDC1-DVL2-FRAT1 34751 15623 55443 44289 5640 DIXDC1-JUN-RHOU 18846 1396 22896 56027 5582 DIXDC1-FOXN1-LEF1 4484 22384 44563 30946 6976 DIXDC1-GSK3A-KREMEN1 962 5165 52201 49330 13895 DIXDC1-SFRP1-FBXW4 45118 28237 10152 6125 20898 DIXDC1-FGF4-TCF7 212 40331 3449 35829 42516 APC-DIXDC1-FBXW2 10263 2964 14162 56148 46075 DIXDC1-EP300-FBXW11 24668 2475 1975 54678 8438 DIXDC1-FGF4-WNT5A 4107 43702 11521 38540 15389 DIXDC1-SFRP1-TCF7 8030 45487 21797 52378 10376 DIXDC1-NLK-FBXW4 25837 3880 29684 25017 18802 CSNK1G1-DIXDC1-DKK1 26769 29764 1454 44361 36145 DIXDC1-GSK3A-WNT2 6700 15468 53440 14555 7349 FZD5-CCND3-DIXDC1 11879 28312 52076 14071 46337 DIXDC1-JUN-WNT3A 26524 53 54094 51456 1811 DIXDC1-FZD2-PPP2CA 8902 30326 5894 8118 11004 DIXDC1-GSK3A-RHOU 1189 22635 55336 44689 20684 DIXDC1-FZD6-FZD8 49470 13675 53674 51243 47473 DIXDC1-FOXN1-SFRP4 3331 12759 51727 22386 2313 DIXDC1-FOXN1-FZD1 1993 16416 32872 56 73 DIXDC1-FOXN1-FZD7 4124 10434 48541 5064 21094 DIXDC1-FGF4-SLC9A3R1 5138 30311 47799 27456 9771 DIXDC1-FOXN1-WNT5A 5575 34443 41139 40268 26945 DIXDC1-PORCN-WNT5A 17412 29192 9192 10144 42283 DIXDC1-NKD1-WIF1 44180 9421 57087 48747 10766 DIXDC1-FGF4-WNT4 313 50493 39435 43390 15890 DIXDC1-PORCN-RHOU 12463 7504 10181 47443 33854 DIXDC1-GSK3A-TCF7L1 1618 40131 51849 34033 22311 DIXDC1-FOXN1-WNT2B 4897 28389 42117 706 3398 DIXDC1-PITX2-PPP2CA 5166 50281 13595 5982 18374 DIXDC1-FZD2-TCF7 10913 27332 15382 32534 9573 DIXDC1-PORCN-SLC9A3R1 29598 31337 32266 1590 25940 DIXDC1-FOXN1-LRP6 11784 23013 33845 22671 7286 DIXDC1-DVL2-FOSL1 43944 24373 54411 4440 3516 DIXDC1-FZD2-WNT2 20495 10746 26583 29184 3097 DIXDC1-FGF4-LRP5 2094 38170 10348 51983 7277 DIXDC1-FOXN1-PPP2R1A 3585 17552 18249 8440 13079 CSNK1G1-DIXDC1-FRZB 40009 20796 7792 3587 52750 APC-DIXDC1-FOSL1 29898 50944 4006 7452 38509 DIXDC1-JUN-TLE1 38829 51316 25565 40475 1022 DIXDC1-GSK3A-TLE2 619 4353 47970 38190 7644 Table 2: Rankings of DIXDC1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf DIXDC1-GSK3A-WNT2, DIXDC1-GSK3A-RHOU and DIXDC1-GSK3A-TLE2. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 8 RANKING @tiUSING SOBOL - 2002 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 APC-DIXDC1-WNT2B 32686 46138 57032 49706 8604 DIXDC1-NKD1-SENP2 12200 40063 24628 25782 18022 DIXDC1-NKD1-TLE2 43632 33173 40815 48692 18613 DIXDC1-NKD1-TCF7L1 55683 3768 38514 52231 4444 DIXDC1-FOXN1-FBXW4 3908 42858 13043 142 51587 DIXDC1-NKD1-PPP2CA 13275 33550 23785 28183 10803 CCND1-CTBP1-DIXDC1 51559 45701 51922 55396 12393 DIXDC1-PITX2-SENP2 55978 6920 46363 55209 16814 DIXDC1-FOXN1-TLE2 862 48313 19636 847 30685 DIXDC1-FOXN1-FZD8 1805 11167 25446 13189 38746 DIXDC1-PITX2-SFRP4 46369 10535 43650 52909 13347 DIXDC1-PORCN-WNT4 52700 17940 45762 56841 2056 DIXDC1-FSHB-LEF1 48274 9621 43078 41675 11440 DIXDC1-NKD1-WNT2 2739 39551 16389 12555 40067 DIXDC1-FOXN1-KREMEN1 21482 50446 17603 1664 40258 DIXDC1-FZD2-LEF1 1088 23042 12774 26014 35884 DIXDC1-LRP5-SENP2 4268 28488 25270 8378 13292 DIXDC1-FZD2-TCF7L1 56033 13065 46115 48353 32433 DIXDC1-FGF4-FBXW4 55336 3744 38325 50113 22659 DIXDC1-FZD2-SENP2 6691 25178 18767 17941 39342 DIXDC1-WNT3-WNT4 46662 7426 56710 34574 35761 DIXDC1-JUN-FBXW4 23517 23502 15073 18409 44877 DIXDC1-JUN-TCF7L1 9143 45568 15142 2009 35636 DIXDC1-FOXN1-FRZB 7469 45639 21161 7194 29894 DIXDC1-FZD2-FZD8 56260 17140 40677 41871 25346 DIXDC1-FZD2-FZD7 897 39906 16491 15323 31948 APC-DIXDC1-FRZB 31034 40280 35412 35124 5166 DIXDC1-FOXN1-SENP2 49092 3697 41057 55136 27309 DIXDC1-PORCN-SENP2 34245 4241 41483 50058 10738 DIXDC1-FGF4-FRAT1 2172 8556 22888 20956 35669 DIXDC1-NKD1-WNT4 4313 56293 22786 21278 56181 DIXDC1-FZD2-WNT4 230 13998 10061 1865 31112 DIXDC1-GSK3B-SLC9A3R1 234 54581 21361 4437 35419 DIXDC1-GSK3A-SENP2 4187 45495 18577 15069 48321 DIXDC1-FZD2-KREMEN1 37975 14894 44042 43100 25518 DIXDC1-NKD1-RHOU 51754 30025 31933 35781 48497 DIXDC1-NKD1-WNT5A 52842 853 34383 35927 975 DIXDC1-FGF4-FOSL1 3396 43706 23582 7101 52388 DIXDC1-FGF4-TLE2 54285 6424 40061 52770 29144 DIXDC1-FGF4-FZD8 40380 33429 31354 35470 16312 APC-DIXDC1-SFRP4 15501 36469 4573 12207 49027 APC-DIXDC1-DKK1 28809 54348 55519 53961 4157 DIXDC1-JUN-KREMEN1 460 53163 11120 19183 46244 DIXDC1-FZD2-TLE2 44992 16577 34379 33577 22179 DIXDC1-FOXN1-WNT4 56220 46188 42283 53911 12529 FZD5-DIXDC1-FRZB 51905 1632 56983 53968 5137 DIXDC1-LRP5-WNT4 22389 29687 26166 18602 8466 DIXDC1-NLK-WNT4 16250 51618 16235 15399 35237 DIXDC1-WNT1-WNT4 45923 10872 37922 33117 17030 DIXDC1-JUN-SENP2 38065 7371 44233 41749 19679 DIXDC1-NKD1-PPP2R1A 43958 23448 33394 28989 46225 DIXDC1-FGF4-FZD1 44874 43035 30939 38627 8168 DIXDC1-FZD2-FBXW4 56232 25918 42123 46272 12936 DIXDC1-GSK3A-WNT4 1153 10495 17804 9290 36662 DIXDC1-JUN-SLC9A3R1 33623 33561 42103 38759 12207 DIXDC1-JUN-TLE2 7892 39524 19988 13521 40054 DIXDC1-FOXN1-WNT2 43535 35529 42565 47624 18417 DIXDC1-PORCN-FBXW4 1721 49990 10280 3777 54067 DIXDC1-TLE1-TLE2 45671 17341 43136 37364 19250 DIXDC1-JUN-WNT2 56245 48642 40270 44652 20598 DIXDC1-FZD2-LRP5 56074 33993 44384 31111 21236 CSNK1G1-DIXDC1-WNT2B 12114 7749 26029 14404 44639 FZD5-DIXDC1-SENP2 12548 45142 1799 1150 54604 DIXDC1-FGF4-SENP2 454 43789 15313 3448 36983 APC-DIXDC1-TCF7L1 38058 40213 34148 43547 5611 DIXDC1-GSK3A-SLC9A3R1 9860 10843 21802 13865 42962 DIXDC1-NKD1-TCF7 1474 53318 18628 4936 52772 DIXDC1-SFRP1-WNT4 182 13057 19225 8756 34550 DIXDC1-PITX2-WNT2B 3174 55687 15258 13757 29932 DIXDC1-FOXN1-SLC9A3R1 53240 14302 44216 57016 5570 CSNK1G1-DIXDC1-SENP2 41101 55342 49465 39012 8801 DIXDC1-GSK3A-SFRP4 945 4750 12057 2266 34917 DIXDC1-FGF4-TCF7L1 50862 18674 31836 42480 10593 DIXDC1-FZD2-WNT2B 56478 39042 43251 43795 29912 DIXDC1-PYGO1-WNT2 38631 6548 43841 56224 38207 DIXDC1-FZD2-SFRP4 921 31332 15052 10925 44257 DIXDC1-FSHB-FZD1 26998 49234 15449 5156 42294 DIXDC1-PORCN-TLE2 8703 44992 26681 8337 53434 DIXDC1-PYGO1-TCF7L1 2188 42426 19263 4130 25766 DIXDC1-PITX2-WNT4 44341 8459 33406 35610 21988 FZD5-DIXDC1-WNT2B 54948 13222 54779 55520 8127 DIXDC1-FOXN1-PPP2CA 55813 13913 43667 51754 13189 CSNK1G1-DIXDC1-RHOU 16058 1799 7780 18030 48278 DIXDC1-FSHB-T 13832 55402 22848 25333 31832 DIXDC1-PORCN-WNT2B 3373 21084 13572 18388 49569 DIXDC1-DVL2-FRAT1 1757 23783 11410 15776 43723 DIXDC1-JUN-RHOU 19039 49606 12978 15409 37376 DIXDC1-FOXN1-LEF1 35678 6740 39623 55489 17084 DIXDC1-GSK3A-KREMEN1 56097 50759 42458 41643 27236 DIXDC1-SFRP1-FBXW4 55949 41407 41264 47501 25268 DIXDC1-FGF4-TCF7 6315 38617 25338 14741 46743 APC-DIXDC1-FBXW2 14383 8045 12142 11236 52411 DIXDC1-EP300-FBXW11 16478 41314 19565 26955 35640 DIXDC1-FGF4-WNT5A 54426 18498 38052 43829 24212 DIXDC1-SFRP1-TCF7 890 1914 16315 5621 27382 DIXDC1-NLK-FBXW4 54866 7550 40448 43753 13270 CSNK1G1-DIXDC1-DKK1 5009 2538 5529 18100 16388 DIXDC1-GSK3A-WNT2 597 7535 13277 13073 47490 FZD5-CCND3-DIXDC1 3555 36661 15848 15568 15517 DIXDC1-JUN-WNT3A 642 31777 12679 15634 45593 DIXDC1-FZD2-PPP2CA 5808 37464 22448 10828 35992 DIXDC1-GSK3A-RHOU 54644 35360 40518 47979 9311 DIXDC1-FZD6-FZD8 56956 15247 44176 49716 7398 DIXDC1-FOXN1-SFRP4 53999 36905 42015 41308 11320 DIXDC1-FOXN1-FZD1 1478 52928 13983 8965 23821 DIXDC1-FOXN1-FZD7 50549 11423 33617 36938 24059 DIXDC1-FGF4-SLC9A3R1 803 49054 15124 7558 23915 DIXDC1-FOXN1-WNT5A 7919 48369 15784 27764 27632 DIXDC1-PORCN-WNT5A 952 7968 6431 9090 46718 DIXDC1-NKD1-WIF1 2783 6193 1919 15666 44738 DIXDC1-FGF4-WNT4 2727 38766 19126 13360 32955 DIXDC1-PORCN-RHOU 22917 52952 15739 7094 46487 DIXDC1-GSK3A-TCF7L1 55304 4458 37900 47670 20477 DIXDC1-FOXN1-WNT2B 12833 46485 21688 21438 30822 DIXDC1-PITX2-PPP2CA 53041 37364 46121 33605 10550 DIXDC1-FZD2-TCF7 1127 43943 11040 8787 25066 DIXDC1-PORCN-SLC9A3R1 55438 7194 46909 53393 3075 DIXDC1-FOXN1-LRP6 55653 44861 40676 56911 28411 DIXDC1-DVL2-FOSL1 13850 26222 9929 15760 22430 DIXDC1-FZD2-WNT2 674 18194 13987 13381 27396 DIXDC1-FGF4-LRP5 50687 4628 32622 28888 25725 DIXDC1-FOXN1-PPP2R1A 6911 39828 26802 5793 42038 CSNK1G1-DIXDC1-FRZB 9906 50249 14891 20119 39408 APC-DIXDC1-FOSL1 20176 3680 12346 13612 45427 DIXDC1-JUN-TLE1 47964 11280 42049 55138 21421 DIXDC1-GSK3A-TLE2 44093 27389 37086 47589 18303 Table 3: Rankings of DIXDC1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - SOBOL; Implementation - 2002 6.3.2. Examining the behaviour of CCND-DIXDC1-X combinations DIXDC1 is the human homolog of Coiled-coil0-DIX1 (CCD1), a recently identified DIX domain containing protein in zebrafish. It is a positive regulator in the WNT signaling pathway functioning downstream of WNT and upstream of AXIN. Wang et al. 9