CXXC-type zinc finger protein 4 (CXXC4) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

CXXC-type zinc finger protein 4 (CXXC4) : 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 CXXC4 (or Dishevelled DVL-binding protein - inhibition of the DVL and AXIN complex (IDAX)) encodes a CXXC-type zinc finger domain-containing protein that antagonizes the canonical WNT signaling pathway. This domain contains eight conserved cysteine residues that bind to two zinc ions. The encoded protein negatively regulates WNT signaling through interaction with the postsynaptic density protein (PSD95) / Drosophila disc large tumor suppressor (DlgA) / zonula occludens-1 protein (ZO-1) or (PDZ) protein domain of DVL, that is required for the stabilization of the transcriptional co-activator β-catenin. 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 CXXC4 related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for CXXC4-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. ITime behavioural study of 3-odr CXXC4 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 8, 2025 Keywords: Sensitivity analysis, Support vector ranking, Hilbert Schmidt Independence Criterion indices (HSIC) and Sobol indicies, WNT3A 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 CXXC4 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 2.2. 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, 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. CXXC-type zinc finger protein 4 (CXXC4) CXXC4 is belongs to the class of Zinc fingers. A zinc finger is a small protein structural motif which contain multiple finger-like protrusions that make contacts with their target molecule and are characterized by the coordination of one or more zinc ions (Zn2+) which stabilizes the fold. Some of these domains bind zinc, but many do not; instead binding other metals such as iron, or no metal at all. This domain contains eight conserved cysteine residues that bind to two zinc ions. The CXXC domain is found in a variety of chromatin-associated proteins and binds to non-methylated CpG dinucleotides. The domain is characterised by two CGXCXXC repeats. In attempting to clarify the roles of DVL in the WNT signaling pathway, Hino et al. [4] identified a novel protein which binds to the PDZ domain of DVL and named it IDAX (for inhibition of the Dvl and Axin complex or CXXC4). IDAX and AXIN competed with each other for the binding to DVL and immunocytochemical analyses showed that the former was localized to the same place as DVL in cells and that expression of the later inhibited the colocalization of DVL and IDAX. Further, WNTinduced accumulation of β-catenin and activation of T-cell factor in mammalian cells were suppressed by expression of Idax. Since DVL is a positive regulator in the WNT signaling pathway and that the PDZ domain is important for this activity, their results suggested that IDAX acted as a negative regulator of the WNT signaling pathway by directly binding to the PDZ domain of Dvl. Kojima et al. [5] identified a CXXC4 homozygous deletion at 4q24 in an aggressive renal cell carcinoma (RCC) using single-nucleotide polymorphism (SNP) arrays. They found significantly lower CXXC4 mRNA levels in tumor samples in patients with metastases compared with those without. Further, knockdown of CXXC4 induced the nuclear translocation of β-catenin and altered expression of a set of genes involved in cell proliferation, invasion and survival. I present 3rd order combinations of CXXC4 with other genes, that the machine learning based search engine points to, as possible synergistic combinations that might be working in time. 3 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 [6]. 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 [6]. 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 4 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 SV MRank 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 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 5 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 CXXC4-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 [7]) and Sobol indicies (with 2002 implementation in Saltelli [8] and martinez implementation in Martinez [9] and Baudin et al. [10]). 6.3. Conserved machine learning rankings for tested CXXC4-X-X combinations A total of 2415, 3rd order combinations involving CXXC4 were obtained from a full set of 71C3= 57155 combinations. Further, from this selected set, using the above criteria for conserved rankings, I report/tabulate the meaningful combinations that might be working synergistically. Tables 2, 3 and 4 show the rankings for the same combinations as in table 1, but using rbf kernel for HSIC, 2002 implementation for SOBOL and martinez implementation for SOBOL, respectively. As one tallies the rankings of across these tables for a particular combination, one finds that the role of the combination of interest is conserved. This conservation points to the existence of the biological synergy, whether the combination has been tested or unexplored/untested. 6.3.1. Examining the behaviour of DVL-CXXC4-X combinations It is known from above literature that CXXC4 binds with DVL to antagonize the WNT signaling pathway. Looking at the tables above, one finds the following combinations for members of DVL family along with CXXC4, to be prominent at 3rd order level - CXXC4-DVL2-FRZB, CXXC4-DVL2-SFRP4, CXXC4-DVL2-LRP5, CXXC4-DVL2RHOU, CXXC4-DVL2-WNT2B, CXXC4-DVL2-FZD1 and CXXC4-DVL2-WNT3A. 6 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CXXC4-PORCN-SENP2 10 33446 17033 17387 32253 CXXC4-PORCN-WNT4 49 6186 19448 20672 51388 CXXC4-PORCN-WNT2B 60 17097 46765 26682 32940 CXXC4-FRAT1-FRZB 64 19925 35266 282 20625 CXXC4-PORCN-SFRP4 80 28448 27819 28835 44315 CXXC4-FOSL1-SENP2 88 36639 18548 29008 12844 CXXC4-FZD7-PPP2CA 90 9819 23105 12397 36836 CXXC4-FZD7-SFRP4 136 18277 38915 34583 33873 CXXC4-PORCN-TCF7 147 56042 37081 25343 32394 CXXC4-PORCN-FBXW4 168 26465 19028 12201 29004 CXXC4-FRAT1-TLE2 212 18126 46011 57 25507 CXXC4-FOSL1-PPP2R1A 255 24314 35136 31526 39110 CXXC4-FRAT1-FZD1 296 10717 21805 2575 15715 CXXC4-FRAT1-FBXW4 304 26037 23203 450 10918 CXXC4-FGF4-SENP2 325 44612 33138 54156 47148 CXXC4-PORCN-PPP2R1A 424 27798 37533 50501 37618 CXXC4-FGF4-FRZB 461 19762 30000 22761 54575 CXXC4-FZD7-WNT2B 472 12278 44001 31202 33433 CXXC4-DVL2-FRZB 479 9516 3524 8282 38815 CXXC4-PORCN-PPP2CA 481 22027 38709 38555 36190 CXXC4-NLK-WNT4 491 167 4767 2069 15953 CXXC4-FRAT1-TCF7L1 519 13366 30568 2083 18784 CXXC4-PORCN-WNT5A 535 15961 16253 55679 46631 CXXC4-FGF4-RHOU 583 24551 34633 53319 56248 CXXC4-NLK-FBXW4 591 19400 24702 2318 5774 CXXC4-DVL2-RHOU 703 7173 6556 19343 52966 CXXC4-FOSL1-FRAT1 731 20058 29538 14504 27891 CXXC4-JUN-TLE2 764 1040 837 11709 30876 CXXC4-FGF4-LRP5 826 10603 47963 24020 51425 CXXC4-FRAT1-FZD8 827 10881 39520 3401 24688 CXXC4-JUN-SENP2 843 21048 50347 6595 9660 CXXC4-FGF4-TLE2 870 21534 50726 38272 53250 CXXC4-JUN-RHOU 881 1789 43156 41625 53423 CXXC4-FGF4-WNT3A 905 28520 52397 52668 30693 CXXC4-FGF4-WNT5A 957 4552 41511 51712 55041 CXXC4-JUN-LRP5 971 1353 33173 6860 26690 CXXC4-FGF4-PPP2R1A 1044 30931 36251 44472 52608 CXXC4-FOXN1-SLC9A3R1 1089 2458 1605 6818 34700 CXXC4-FGF4-TCF7 1091 38819 31734 49434 48726 CSNK1G1-CXXC4-FOSL1 1094 46700 26853 25310 54546 CXXC4-JUN-FBXW4 1138 13192 17971 6537 17461 CXXC4-FOXN1-RHOU 1258 949 4951 19719 52102 CSNK1D-CXXC4-FZD1 1263 2919 24873 24770 29960 CXXC4-JUN-SFRP4 1308 4014 25558 7639 24982 CXXC4-DVL2-SFRP4 1347 5287 2872 6219 37139 CXXC4-DVL2-WNT2B 1361 15018 7269 31481 39016 CXXC4-FGF4-FOSL1 1368 22243 14796 45725 54959 CXXC4-JUN-TCF7 1379 21025 34076 34379 37036 CXXC4-FRAT1-WNT3A 1421 24998 29856 17406 1342 CXXC4-NLK-TLE2 1467 3249 13379 2815 22591 CXXC4-JUN-PYGO1 1496 10929 38139 43065 17470 CXXC4-FOXN1-FRZB 1502 99 9554 17642 46105 CXXC4-NLK-SFRP1 1520 3860 3645 1038 15312 CXXC4-JUN-TCF7L1 1561 16594 47993 27451 26786 CXXC4-FZD2-LEF1 1642 3090 9287 23149 51524 CXXC4-GSK3A-WNT2 1689 13832 6873 29230 43303 CXXC4-WIF1-WNT3A 1745 353 12465 51440 34488 CXXC4-FGF4-WNT4 1747 5857 34419 49599 54246 CXXC4-FGF4-FZD1 1751 11265 20257 55084 52255 CXXC4-FOXN1-SENP2 1771 9020 6263 7094 11868 CXXC4-FZD7-RHOU 1774 20795 27044 52150 54907 CXXC4-JUN-PPP2R1A 1782 11540 37923 13434 43762 CXXC4-FOSL1-WNT5A 1800 15338 42242 52718 32578 CXXC4-FRAT1-LRP5 1810 3252 48463 383 12590 CXXC4-JUN-SLC9A3R1 1862 8225 23228 21414 44419 CXXC4-FGF4-KREMEN1 1948 42829 14565 52294 56300 CXXC4-FZD2-SFRP4 1951 1938 36455 2988 50465 CXXC4-DVL2-FZD1 2007 11971 18762 3053 35259 CXXC4-FZD1-SENP2 2050 40723 10326 38271 17504 CXXC4-FGF4-SFRP4 2200 21598 27619 50838 52265 CXXC4-NLK-WNT2B 2202 5290 1484 56489 12898 CXXC4-NKD1-WNT2B 2217 9878 36698 23848 1631 CXXC4-GSK3A-RHOU 2262 20534 4082 47103 49826 CXXC4-PORCN-WNT3 2291 2240 24537 6255 30135 CXXC4-FZD2-RHOU 2317 6671 22273 26084 55079 CXXC4-FGF4-GSK3B 2336 2158 53607 41323 48886 CXXC4-FOXN1-FZD8 2405 10212 3200 15737 15007 CXXC4-FOXN1-SFRP4 2487 1405 7515 14548 25337 CSNK1G1-CXXC4-DKK1 2488 45829 37872 27388 55403 CSNK1G1-CXXC4-FRAT1 2496 24384 49297 7946 49881 CXXC4-FZD7-SENP2 2507 35237 27610 27855 26307 CXXC4-SFRP1-WNT2B 2551 24274 44184 31848 27946 BCL9-CXXC4-FZD7 2587 37095 21041 33971 29584 CXXC4-GSK3A-SFRP4 2604 10596 14291 21482 35934 CXXC4-FZD2-PPP2CA 2607 29974 9988 18663 50107 CXXC4-JUN-WNT4 2688 13375 46722 2824 3108 CXXC4-DVL2-LRP5 2699 16595 48005 8211 27106 CXXC4-WNT1-WNT3A 2734 34306 282 36977 4488 CSNK1D-CXXC4-FRAT1 2744 18327 34701 8594 2661 CXXC4-JUN-PITX2 2757 3424 36286 40345 36376 CXXC4-FGF4-NLK 2780 22054 41988 28791 40205 CXXC4-WIF1-WNT2 2794 318 38171 33660 55940 CXXC4-FOXN1-WNT3A 2796 53 5860 22254 12575 CXXC4-GSK3A-LRP5 2801 2556 3529 23047 42324 CXXC4-FGF4-FRAT1 2842 9594 30978 23790 51147 CXXC4-FZD7-KREMEN1 2872 42910 42232 51357 48270 CXXC4-FRAT1-WNT2 2894 23698 18152 32 32646 CXXC4-FZD2-SENP2 2916 26793 21261 5858 39928 CXXC4-FZD2-LRP5 2946 717 14065 26069 44141 CXXC4-FZD1-LRP5 2998 7300 42894 19351 29464 CXXC4-FZD2-GSK3B 3060 14042 29298 42224 44272 CXXC4-NKD1-SENP2 3069 14633 9774 13334 17352 CXXC4-FOXN1-WNT5A 3109 8816 13105 18798 36097 CXXC4-NKD1-TLE2 3160 26 22413 13930 94 CXXC4-FOXN1-FBXW4 3181 4297 20629 11517 21464 CXXC4-DVL2-WNT3A 3186 7341 5733 24584 2313 CSNK1A1-CTBP2-CXXC4 3187 741 15084 41906 44957 CXXC4-GSK3A-SENP2 3196 30564 1921 32171 26223 CXXC4-FOXN1-PPP2CA 3277 19301 19575 24116 33763 CXXC4-FGF4-PPP2CA 3340 9402 29074 35299 53290 CXXC4-JUN-TLE1 3367 30489 24344 6356 85 CXXC4-GSK3A-SLC9A3R1 3506 9586 9125 48353 50314 CXXC4-FOXN1-WNT2 3532 201 7409 18120 37271 CXXC4-FRAT1-KREMEN1 3542 41044 29584 5685 51990 CXXC4-FZD1-FZD7 3585 25420 10832 32645 23514 CXXC4-FGF4-WNT3 3619 587 35000 56680 49419 CXXC4-FOXN1-LRP5 3643 1872 9789 44781 31650 CXXC4-JUN-PPP2CA 3661 32213 26859 462 30021 CXXC4-FGF4-LRP6 3678 11467 49324 42483 34171 CXXC4-FZD7-TCF7 3714 44164 27210 52158 40111 CXXC4-FOXN1-FZD6 3727 251 19904 12481 33219 CXXC4-FZD2-WNT2B 3800 9215 15294 40680 45553 CXXC4-FGF4-FZD8 3802 3981 51255 45882 40409 CXXC4-NLK-TCF7L1 3843 4771 10375 1945 20127 CXXC4-FZD1-WNT4 3921 4043 24475 36885 25822 CXXC4-NLK-WNT5A 3932 2627 16679 25816 15722 Table 1: Rankings of CXXC4-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 7 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CXXC4-PORCN-SENP2 9869 47028 41747 45009 41195 CXXC4-PORCN-WNT4 12492 2278 24920 46755 55842 CXXC4-PORCN-WNT2B 11272 21120 2288 41634 56160 CXXC4-FRAT1-FRZB 4615 7359 56816 34657 49785 CXXC4-PORCN-SFRP4 9369 30775 45417 32220 54090 CXXC4-FOSL1-SENP2 27232 42351 44650 16863 48178 CXXC4-FZD7-PPP2CA 7569 8146 8359 8809 29695 CXXC4-FZD7-SFRP4 20307 23535 39439 24195 53332 CXXC4-PORCN-TCF7 8174 50291 19771 4132 42869 CXXC4-PORCN-FBXW4 19853 43651 1014 10933 51164 CXXC4-FRAT1-TLE2 38894 11877 48833 6512 54567 CXXC4-FOSL1-PPP2R1A 52227 34156 6226 46113 43359 CXXC4-FRAT1-FZD1 7404 4364 36104 35047 22551 CXXC4-FRAT1-FBXW4 14668 46919 1016 36914 42585 CXXC4-FGF4-SENP2 252 42683 39239 31323 30294 CXXC4-PORCN-PPP2R1A 20998 30567 5511 22186 56640 CXXC4-FGF4-FRZB 275 29756 38685 40122 49864 CXXC4-FZD7-WNT2B 3497 13030 1072 53710 54739 CXXC4-DVL2-FRZB 4886 7544 48054 28005 23326 CXXC4-PORCN-PPP2CA 9663 20715 7491 12348 51537 CXXC4-NLK-WNT4 22955 3089 37410 121 47163 CXXC4-FRAT1-TCF7L1 14983 16373 55100 8101 42887 CXXC4-PORCN-WNT5A 24704 5412 10695 26556 50085 CXXC4-FGF4-RHOU 2335 25378 25285 54463 41595 CXXC4-NLK-FBXW4 36361 6924 5576 32715 39457 CXXC4-DVL2-RHOU 24302 4880 47885 35622 25708 CXXC4-FOSL1-FRAT1 46607 15174 26086 25252 40912 CXXC4-JUN-TLE2 2337 10507 41107 15818 46481 CXXC4-FGF4-LRP5 1846 12123 15671 39128 29876 CXXC4-FRAT1-FZD8 6745 11128 54253 54080 39603 CXXC4-JUN-SENP2 1851 32478 55139 8858 43014 CXXC4-FGF4-TLE2 591 38121 27919 26190 19771 CXXC4-JUN-RHOU 7270 2533 37155 46380 45935 CXXC4-FGF4-WNT3A 376 11041 597 49220 57138 CXXC4-FGF4-WNT5A 6438 9457 13415 42775 42269 CXXC4-JUN-LRP5 15539 1611 30933 39991 28813 CXXC4-FGF4-PPP2R1A 1192 9614 5570 26405 23051 CXXC4-FOXN1-SLC9A3R1 5835 4242 55138 22461 50612 CXXC4-FGF4-TCF7 1232 32544 24487 22245 56783 CSNK1G1-CXXC4-FOSL1 18872 46435 17556 11771 54033 CXXC4-JUN-FBXW4 14457 30498 1036 36322 33651 CXXC4-FOXN1-RHOU 4808 4398 51558 29746 40158 CSNK1D-CXXC4-FZD1 7144 1734 27303 7250 11481 CXXC4-JUN-SFRP4 8489 12877 51306 12233 26552 CXXC4-DVL2-SFRP4 16351 4938 49667 29954 34883 CXXC4-DVL2-WNT2B 14916 7821 10829 36605 32745 CXXC4-FGF4-FOSL1 553 41867 29836 8057 53097 CXXC4-JUN-TCF7 2896 16477 22826 15141 21339 CXXC4-FRAT1-WNT3A 5682 22392 33504 50525 42228 CXXC4-NLK-TLE2 21331 11904 46279 1885 30976 CXXC4-JUN-PYGO1 15268 3842 31367 43633 53074 CXXC4-FOXN1-FRZB 2132 6567 49876 23824 32081 CXXC4-NLK-SFRP1 49331 4153 49861 27131 33193 CXXC4-JUN-TCF7L1 5069 16399 50288 29076 25853 CXXC4-FZD2-LEF1 38950 1181 32681 4532 22634 CXXC4-GSK3A-WNT2 1230 15380 52831 13794 54110 CXXC4-WIF1-WNT3A 11746 12153 2343 56809 35373 CXXC4-FGF4-WNT4 299 4403 10799 6662 56255 CXXC4-FGF4-FZD1 412 10632 11544 31326 47937 CXXC4-FOXN1-SENP2 515 15255 52769 4140 43381 CXXC4-FZD7-RHOU 8290 22007 17701 54867 39963 CXXC4-JUN-PPP2R1A 8147 19410 4343 32567 48732 CXXC4-FOSL1-WNT5A 53822 4385 5771 55698 30961 CXXC4-FRAT1-LRP5 23317 429 29024 48013 32482 CXXC4-JUN-SLC9A3R1 13688 4927 33829 15408 20050 CXXC4-FGF4-KREMEN1 1514 40573 41207 46205 49688 CXXC4-FZD2-SFRP4 16662 2511 31631 1790 20964 CXXC4-DVL2-FZD1 6039 15880 42432 32927 19633 CXXC4-FZD1-SENP2 34090 36346 54606 22792 22438 CXXC4-FGF4-SFRP4 1800 28754 47520 10479 30525 CXXC4-NLK-WNT2B 28869 300 28004 21112 54426 CXXC4-NKD1-WNT2B 33112 30020 8852 27851 43373 CXXC4-GSK3A-RHOU 258 9516 53313 35938 49928 CXXC4-PORCN-WNT3 37775 8521 7319 54045 46168 CXXC4-FZD2-RHOU 10828 29932 33193 7959 25644 CXXC4-FGF4-GSK3B 2513 1585 2338 49143 54753 CXXC4-FOXN1-FZD8 2538 22024 56449 30002 56254 CXXC4-FOXN1-SFRP4 2063 2782 54618 3345 15870 CSNK1G1-CXXC4-DKK1 18870 49739 2762 48160 29218 CSNK1G1-CXXC4-FRAT1 10676 6045 28407 52045 39223 CXXC4-FZD7-SENP2 1262 39914 29126 38452 45236 CXXC4-SFRP1-WNT2B 9023 37294 3518 45010 56925 BCL9-CXXC4-FZD7 9941 29991 34446 25812 41178 CXXC4-GSK3A-SFRP4 170 13696 53514 4388 43098 CXXC4-FZD2-PPP2CA 11564 33338 12458 3001 54858 CXXC4-JUN-WNT4 4946 4363 31447 4600 32510 CXXC4-DVL2-LRP5 11745 7304 42550 26847 15371 CXXC4-WNT1-WNT3A 1236 41816 5972 30693 33822 CSNK1D-CXXC4-FRAT1 14134 8276 23947 22453 12908 CXXC4-JUN-PITX2 5093 2871 54929 54382 25342 CXXC4-FGF4-NLK 1507 4569 5986 44776 54536 CXXC4-WIF1-WNT2 51580 27076 41572 21992 55327 CXXC4-FOXN1-WNT3A 2235 1906 54317 41438 43489 CXXC4-GSK3A-LRP5 385 9378 49161 34343 36785 CXXC4-FGF4-FRAT1 4283 5655 31886 10011 47555 CXXC4-FZD7-KREMEN1 3201 51583 32100 52166 52493 CXXC4-FRAT1-WNT2 31513 32492 56401 22069 45177 CXXC4-FZD2-SENP2 11373 32779 36118 41772 48711 CXXC4-FZD2-LRP5 17864 7669 25949 15071 31594 CXXC4-FZD1-LRP5 50587 2520 47210 49401 49419 CXXC4-FZD2-GSK3B 11449 20532 5769 43469 53376 CXXC4-NKD1-SENP2 23566 21575 56539 18663 8724 CXXC4-FOXN1-WNT5A 6575 17827 51655 52301 55304 CXXC4-NKD1-TLE2 14475 5894 51388 28114 51127 CXXC4-FOXN1-FBXW4 3459 16395 8588 13912 10169 CXXC4-DVL2-WNT3A 5548 8944 24906 33696 42805 CSNK1A1-CTBP2-CXXC4 6148 356 31122 45700 47540 CXXC4-GSK3A-SENP2 74 32451 54211 24002 33327 CXXC4-FOXN1-PPP2CA 1922 14941 49768 109 32177 CXXC4-FGF4-PPP2CA 896 24972 12137 33837 43059 CXXC4-JUN-TLE1 12052 20822 44884 32576 24749 CXXC4-GSK3A-SLC9A3R1 467 8014 47156 13152 55436 CXXC4-FOXN1-WNT2 4136 8477 52268 544 46007 CXXC4-FRAT1-KREMEN1 9306 45373 50696 51816 46911 CXXC4-FZD1-FZD7 49954 12547 56459 23869 41132 CXXC4-FGF4-WNT3 3561 311 5182 29806 42876 CXXC4-FOXN1-LRP5 960 9617 46621 12430 9349 CXXC4-JUN-PPP2CA 2697 40480 12704 20114 45550 CXXC4-FGF4-LRP6 2697 40480 12704 20114 45550 CXXC4-FZD7-TCF7 7210 39983 16805 19991 41633 CXXC4-FOXN1-FZD6 4475 608 35118 18286 44561 CXXC4-FZD2-WNT2B 20369 10806 14946 7965 25615 CXXC4-FGF4-FZD8 292 11900 36098 42761 36334 CXXC4-NLK-TCF7L1 38206 4994 56442 3145 46853 CXXC4-FZD1-WNT4 34012 9183 32309 19082 29352 CXXC4-NLK-WNT5A 46697 2350 52931 39870 42513 Table 2: Rankings of CXXC4-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf 6.3.2. Examining the behaviour of GSK3-CXXC4-X combinations In gastric cancer, Lu et al. [11] show that CXXC4 interacts with DVL1 directly and the mutation of critical residues in the DVL-interacting domain abrogated its interac8 RANKING @tiUSING SOBOL - 2002 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CXXC4-PORCN-SENP2 4981 10546 9375 17394 34482 CXXC4-PORCN-WNT4 9600 4879 1294 6463 37839 CXXC4-PORCN-WNT2B 39582 44080 51571 43634 12796 CXXC4-FRAT1-FRZB 13855 16693 7772 24610 15521 CXXC4-PORCN-SFRP4 3428 54623 4989 9629 43028 CXXC4-FOSL1-SENP2 9857 21302 3091 25681 49127 CXXC4-FZD7-PPP2CA 6148 28592 25213 26202 44025 CXXC4-FZD7-SFRP4 8226 37912 21420 24728 27141 CXXC4-PORCN-TCF7 2527 11671 4576 9976 25876 CXXC4-PORCN-FBXW4 53747 2497 52161 47571 14085 CXXC4-FRAT1-TLE2 8172 787 10839 18520 17014 CXXC4-FOSL1-PPP2R1A 33024 20784 45045 33319 8066 CXXC4-FRAT1-FZD1 9682 502 6322 25277 1837 CXXC4-FRAT1-FBXW4 25898 41741 14499 23277 897 CXXC4-FGF4-SENP2 56902 51611 35174 38140 4316 CXXC4-PORCN-PPP2R1A 44156 3317 53822 38916 15985 CXXC4-FGF4-FRZB 655 16082 9480 20416 46553 CXXC4-FZD7-WNT2B 49726 31087 32815 31314 18255 CXXC4-DVL2-FRZB 6421 47272 15558 23096 47407 CXXC4-PORCN-PPP2CA 13026 53831 3318 18245 41235 CXXC4-NLK-WNT4 53246 51233 55370 49749 15337 CXXC4-FRAT1-TCF7L1 18548 15555 6549 27894 2409 CXXC4-PORCN-WNT5A 47497 52019 55859 50726 19154 CXXC4-FGF4-RHOU 252 5480 21939 19031 52845 CXXC4-NLK-FBXW4 5974 6674 24560 10110 44194 CXXC4-DVL2-RHOU 13662 45063 23761 15178 35600 CXXC4-FOSL1-FRAT1 13778 2749 16108 6403 43145 CXXC4-JUN-TLE2 47401 2576 46879 53365 10616 CXXC4-FGF4-LRP5 19668 6338 18685 9517 51966 CXXC4-FRAT1-FZD8 19654 576 4332 16136 19365 CXXC4-JUN-SENP2 8825 8401 12932 7871 27023 CXXC4-FGF4-TLE2 2464 6054 13953 11679 56111 CXXC4-JUN-RHOU 43332 26892 49071 46614 1986 CXXC4-FGF4-WNT3A 7493 411 15315 24389 48926 CXXC4-FGF4-WNT5A 4008 46378 14592 16580 56090 CXXC4-JUN-LRP5 33040 7608 43755 38567 13643 CXXC4-FGF4-PPP2R1A 6382 430 21801 13251 51268 CXXC4-FOXN1-SLC9A3R1 3959 7438 19286 25956 7951 CXXC4-FGF4-TCF7 45370 46737 48467 45014 23299 CSNK1G1-CXXC4-FOSL1 25168 1437 11571 16056 25721 CXXC4-JUN-FBXW4 49484 2831 37278 49282 3845 CXXC4-FOXN1-RHOU 49343 54575 54627 33981 50794 CSNK1D-CXXC4-FZD1 15838 20986 27843 15827 35450 CXXC4-JUN-SFRP4 7686 54368 19771 7870 53296 CXXC4-DVL2-SFRP4 40484 4674 42806 42655 30934 CXXC4-DVL2-WNT2B 6744 50339 17055 22295 46522 CXXC4-FGF4-FOSL1 52810 50470 34544 37927 3516 CXXC4-JUN-TCF7 1115 20606 6634 9559 44618 CXXC4-FRAT1-WNT3A 7869 2751 20454 26029 9961 CXXC4-NLK-TLE2 9628 4363 7425 17260 48958 CXXC4-JUN-PYGO1 13879 27252 8058 10543 55180 CXXC4-FOXN1-FRZB 47727 56222 50026 44836 51771 CXXC4-NLK-SFRP1 17728 56469 8386 24896 33148 CXXC4-JUN-TCF7L1 56040 37157 50497 47616 12624 CXXC4-FZD2-LEF1 43791 16576 35344 56737 19650 CXXC4-GSK3A-WNT2 55861 49041 34404 46788 7541 CXXC4-WIF1-WNT3A 54553 44801 48557 52030 1570 CXXC4-FGF4-WNT4 49638 56741 41820 32756 8361 CXXC4-FGF4-FZD1 10610 51496 17191 13677 52657 CXXC4-FOXN1-SENP2 20619 376 16314 23024 6715 CXXC4-FZD7-RHOU 42809 25100 32087 29550 5695 CXXC4-JUN-PPP2R1A 44274 1712 51774 45829 14514 CXXC4-FOSL1-WNT5A 45823 54747 52368 41434 48001 CXXC4-FRAT1-LRP5 14447 55550 4187 25428 10791 CXXC4-JUN-SLC9A3R1 3663 5023 4043 7111 47297 CXXC4-FGF4-KREMEN1 9212 1819 7168 7601 47095 CXXC4-FZD2-SFRP4 50903 14206 47616 54449 8766 CXXC4-DVL2-FZD1 8469 13264 13510 23889 17063 CXXC4-FZD1-SENP2 12809 49359 6206 3069 42315 CXXC4-FGF4-SFRP4 44465 38386 38344 41294 134 CXXC4-NLK-WNT2B 17363 10111 1772 5324 38194 CXXC4-NKD1-WNT2B 15436 10525 10086 1323 45129 CXXC4-GSK3A-RHOU 14260 7037 2619 8274 28887 CXXC4-PORCN-WNT3 13 8251 9046 18094 39176 CXXC4-FZD2-RHOU 6780 8109 9925 14270 49006 CXXC4-FGF4-GSK3B 9304 6529 4812 8493 41990 CXXC4-FOXN1-FZD8 55264 46656 51687 38480 50201 CXXC4-FOXN1-SFRP4 13446 237 16807 20244 1750 CSNK1G1-CXXC4-DKK1 29722 16090 47827 56588 1654 CSNK1G1-CXXC4-FRAT1 27618 3778 3433 676 48257 CXXC4-FZD7-SENP2 4691 36054 25571 25112 38500 CXXC4-SFRP1-WNT2B 5270 10347 14597 16518 33006 BCL9-CXXC4-FZD7 12890 55435 14964 14600 32799 CXXC4-GSK3A-SFRP4 42048 44931 50649 47022 11196 CXXC4-FZD2-PPP2CA 48257 39680 46070 54823 47811 CXXC4-JUN-WNT4 11461 1911 4636 18755 45271 CXXC4-DVL2-LRP5 12022 50320 14484 24733 24341 CXXC4-WNT1-WNT3A 46602 51045 38468 51607 4562 CSNK1D-CXXC4-FRAT1 34042 35885 29812 41264 26139 CXXC4-JUN-PITX2 7081 3972 8713 3640 32183 CXXC4-FGF4-NLK 18745 698 6566 18659 49649 CXXC4-WIF1-WNT2 15365 18609 6335 8974 52925 CXXC4-FOXN1-WNT3A 51263 50390 30984 42574 46666 CXXC4-GSK3A-LRP5 2369 28526 3451 15002 30988 CXXC4-FGF4-FRAT1 50820 53673 45701 44615 8451 CXXC4-FZD7-KREMEN1 38479 27988 31220 33378 4766 CXXC4-FRAT1-WNT2 41126 2126 46459 30168 34144 CXXC4-FZD2-SENP2 50382 48962 47212 42891 8509 CXXC4-FZD2-LRP5 10970 45825 5695 222 27035 CXXC4-FZD1-LRP5 51552 42608 31364 30529 12998 CXXC4-FZD2-GSK3B 7116 23758 13803 1131 52308 CXXC4-NKD1-SENP2 53247 30638 52373 44913 3619 CXXC4-FOXN1-WNT5A 45779 49880 48086 39298 56659 CXXC4-NKD1-TLE2 667 11124 4405 10259 37949 CXXC4-FOXN1-FBXW4 43717 56917 40334 36937 55377 CXXC4-DVL2-WNT3A 17336 51748 14847 23229 36228 CSNK1A1-CTBP2-CXXC4 32731 6104 30912 45061 27995 CXXC4-GSK3A-SENP2 42993 50176 54509 48854 28496 CXXC4-FOXN1-PPP2CA 3477 1511 1989 21870 13869 CXXC4-FGF4-PPP2CA 45268 56658 41145 41538 2318 CXXC4-JUN-TLE1 9806 54580 10229 3795 46539 CXXC4-GSK3A-SLC9A3R1 55602 51900 49035 38962 23048 CXXC4-FOXN1-WNT2 20914 24314 16648 24201 21980 CXXC4-FRAT1-KREMEN1 17526 25193 23946 23550 12450 CXXC4-FZD1-FZD7 11040 53941 8320 18995 41701 CXXC4-FGF4-WNT3 37990 37288 42279 35654 7889 CXXC4-FOXN1-LRP5 42375 52933 50994 41421 52542 CXXC4-JUN-PPP2CA 12942 55409 5351 11313 42743 CXXC4-FGF4-LRP6 37441 50826 38434 47652 5185 CXXC4-FZD7-TCF7 7168 23159 23535 24415 44261 CXXC4-FOXN1-FZD6 50432 53386 52863 37651 44074 CXXC4-FZD2-WNT2B 9145 29828 19209 12741 40862 CXXC4-FGF4-FZD8 2927 5577 12374 5513 30264 CXXC4-NLK-TCF7L1 20204 45005 6311 11503 39338 CXXC4-FZD1-WNT4 18374 14688 10406 5900 46576 CXXC4-NLK-WNT5A 12448 41748 17765 12599 37639 Table 3: Rankings of CXXC4-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - SOBOL; Implementation - 2002 tion with DVL1. Importantly, the association of DVL1 with AXIN1 and GSK3βwas disrupted upon the expression of wild-type but not the mutated CXXC4 that failed to interact with DVL1. Further, the wild-type but not the mutated CXXC4 reduced the amount of β-catenin and inhibited the phosphorylation of GSK3β, while knockdown 9