WNT inhibitory factor 1 (WIF1) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

WNT inhibitory factor 1 (WIF1) : 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 WNT inhibitory factor 1 (WIF1), a secreted protein that binds to WNT proteins and inhibits their activities. 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 WIF1 related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for WIF1-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 WIF1 comb. in WNT3A stimulated cells Email address: [email protected] (shriprakash sinha) 1Aspects of unpublished work were presented in a poster session at Cell Symposia: Technology. Biology. Data Science, 9-11 October 2016, Berkeley, California, USA. Preprint submitted to Preprint March 1, 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 WIF1 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. WNT inhibitory factor 1 (WIF1) Hsieh et al. [4] describe that WIF1 binds to WNT proteins and inhibits their activities. Using Xenopus embryos they show that WIF1 overexpression affects somitogenesis (the generation of trunk mesoderm segments), in agreement with its normal expression in paraxial mesoderm and further, in vitro, WIF1 binds to Drosophila Wingless and Xenopus WNT8 produced by Drosophila S2 cells. Their results indicate that WNT proteins interact with structurally diverse extracellular inhibitors to fine-tune the spatial and temporal patterns of WNT activity. Reguart et al. [5] report the identification of the 5’ promoter region ( 1.5 kb) of the human WIF1 gene, functional analysis of whic shows that a whole fragment displays high basal promoter activity in different cell lines, while the truncated forms do not, indicating that integrity of the WIF1 promoter region may be important for WIF1 activity. Liepinsh et al. [6] and Malinauskas et al. [7], study the crystal structure of WIF1 and the molecular mechanims of WNT inhibition via WIF1. Malinauskas et al. [7] report that WIF1 is present across vertebrate families and consists of an N-terminal secretion signal sequence, the WIF domain (WD, 143 amino acid residues), five EGF-like domains (3133 residues each) and a hydrophilic C terminus. The WIF domain of WIF1 is sufficient to inhibit Wnt signalling7, but the function of the five EGF-like domains (EGFs IV) has remained obscure. They used a series of WIF1 constructs in a WNT response assay, to investigate the roles of the domains of WIF1 in inhibition of WNT3A. WNT3A signaling was inhibited in a dose-dependent manner (33500 nM) by WIF1∆C. WIF1WD and WIF1W D−EGF−Iwere also inhibitory, consistent with Hsieh et al. [4] report that the WIF domain in isolation can inhibit WNT signaling, but both these constructs were notably less effective than the molecules that contained the WIF domain and EGFs IV. In this research work, I present 3rd order combinations of WIF1 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. 3 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 [8]. 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 [8]. 5. Design of experiment 5.1. Pipeline for time series data For the case of time series data, interactions among the contributing factors are studied by comparing triplets of fold-changes at single time points. The prodecure begins with the generation of distribution around measurements at single time points with added noise is done to estimate the indices. A distribution is generated for the fold changes at single time points. Then for every gene, there is a vector of values representing fold changes as well as deviations in fold changes for different time points and durations between time points, respectively. Next a listing of all Cn kcombinations for knumber of genes from a total of ngenes is generated. kis ≥2 and ≤(n−1). Each of the combination of order krepresents a unique set of interaction between the involved genetic factors. After this, the datasets are combined in a specifed format which go as input as per the requirement of a particular sensitivity analysis method. Thus for each pth combination in Cn kcombinations, the dataset is prepared in the required format from the distributions for two separate cases which have been discussed above. (See .R code in mainScript-1-1.R). After the data has been transformed, vectorized programming is employed for density based sensitivity analysis and looping is employed for variance based sensitivity analysis to compute the required sensitivity indices for each of the pcombinations. This procedure is done for different kinds of sensitivity analysis methods. After the above sensitivity indices have been stored for each of the pth combination, the next step in the design of experiment is conducted. Since there is only one recording of sensitivity index per combination, each combination forms a training example which is alloted a training index and the sensitivity indices of the individual genetic factors form the training example. Thus there are Cn ktraining examples for kth order interaction. Using this training set SVMRank learn Joachims [3] is used to generate a model on default value Cvalue of 20. In the current experiment on toy model Cvalue has not been tunned. The training set helps in the generation of the model as the different gene combinations are numbered in order which are used as rank indices. The 4 model is then used to generate score on the observations in the testing set using the SV MRank classi f y Joachims [3]. Note that due to availability of only one example per combination, after the model has been built, the same training data is used as test data to generates the scores. This procedure is executed for each and every sensitivity analysis method. This is followed by sorting of these scores along with the rank indices (i.e the training indices) already assigned to the gene combinations. The end result is a sorted order of the gene combinations based on the ranking score learned by the SV MRank algorithm. Finally, this entire procedure is computed for sensitivity indices generated for each and every fold change at time point and deviations in fold change at different durations. Observing the changing rank of a particular combination at different times and different time periods will reveal how a combination is behaving. Note that the following is the order in which the files should be executed in R, in order, for obtaining the desired results (Note that the code will not be explained here) - • use source(”mainScript-1-1.R”) with arguments for Dynamic data •source(”SVMRankResults-D.R”), to rank the interactions (again this needs to be done separately for different kinds of SA methods), •use source(”Combine-Time-files.R”), if computing indices separately via previous file, •source(”Sort-n-Plot-D.R”) to sort the interactions. Note that the sorting is chages the interaction ranking in time. Thus •use source(”Interaction-Priority-Intime.R”) to find the prioritized ranking of each and every interaction over the different time points and finally •use source(”Print-RankingAND-Interaction-Rank.R”) to print individual ranking of the required input factor with other interaction factors. 6. Results & Discussion 6.1. Time series data by Gujral and MacBeath [1] NOTE - Ranking was assigned on scores that were sorted in DECREASING values. So, 1 was assigned to highest score and vice versa. Results for the 3rd order interactions are presented here. The results first discuss the behaviour of interactions across the snapshots of time using the computed sensitivities on fold change measurements per time snapshot. The analysis was done using 4 different sensitivity indices. Out of the 71C3combinations, I consider/present only those combinations that show a ranking within first 10,000 out of 57,155. This choice is liberal and biologists/oncologists can have a more stricter choice as per need. Two observations are made, •the ranking of a particular combination is conserved (i.e within the 10,000 range) in a particular time point or in the early phase or late phase of WNT3A stimulation, across the majority of the four sensitivity methods, which is a strict criteria of assessment or •the ranking of a particular combination is conserved across time points/phase (i.e they are within the 10,000 range) and the majority of the four sensitivity methods, which is relaxed criteria of assessment. Applying this filter helps reveal important combinations of interest that might be working synergistically at a higher order level in the cell. Regarding technical points of implementation, the rankings were generated without scaling/normalizing the time series data provided by Gujral and MacBeath [1]. 5 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 WIF1-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 [9]) and Sobol indicies (with 2002 implementation in Saltelli [10] and martinez implementation in Martinez [11] and Baudin et al. [12]). 6.3. Conserved machine learning rankings for tested WIF1-X-X combinations A total of 2415, 3rd order combinations involving WIF1 were obtained from a full set of 71C3= 57155 combinations. Further, from this selected set, using the above criteria for conserved rankings, I report/tabulate the meaningful combinations that might be working synergistically. Tables 2, 3 and 4 show the rankings for the same combinations as in table 1, but using rbf kernel for HSIC, 2002 implementation for SOBOL and martinez implementation for SOBOL, respectively. As one tallies the rankings of across these tables for a particular combination, one finds that the role of the combination of interest is conserved. This conservation points to the existence of the biological synergy, whether the combination has been tested or unexplored/untested. 6.3.1. Examining the behaviour of WNT-WIF1-X combinations Gudjonsson et al. [13] subjected 58 paired biopsies from lesional and uninvolved psoriatic skin and 64 biopsies from normal skin to global gene expression profiling. They found WNT5A transcripts upregulated fivefold in lesional skin, accompanied by increased WNT5A protein levels. In contrast, expression of WIF1 mRNA was downregulated ¿10-fold in lesional skin, along with decreased WIF1 immunostaining. These results suggested a shift away from canonical Wnt signaling toward noncanonical pathways driven by interactions between WNT5A and its cognate receptors in psoriasis, accompanied by impaired homeostatic inhibition of Wnt signaling by WIF1 and dickkopf. In early osteochondrosis (OC) cartilage canal chondrocytes compared to controls, Kinsley et al. [14] found significantly decreased WNT11 and increased β-catenin, WNT5B, DKK1, LRP6, WIF1, AXIN1, and SC-PEP gene expression. 6 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CTNNBIP1-WIF1-WNT2B 5 716 18217 51222 29536 TLE1-WIF1-WNT2B 65 13326 20278 36821 11947 CCND1-WIF1-WNT2B 86 32096 35653 38353 29538 CTNNBIP1-WIF1-WNT5A 128 2117 50325 55816 30661 TLE1-WIF1-WNT2 152 12574 27880 35684 24762 TLE2-WIF1-WNT2B 162 206 11704 50552 55877 CTNNBIP1-WIF1-WNT4 380 415 11991 33905 19908 NLK-WIF1-WNT2 431 13840 49796 35119 6813 CCND1-WIF1-WNT4 439 23377 41096 38262 34292 TLE1-WIF1-WNT3A 449 13164 8253 51282 7381 CTNNBIP1-WIF1-WNT3A 603 57 12000 57039 19928 FOSL1-WIF1-WNT2B 727 2770 23114 37617 17980 DVL2-JUN-WIF1 788 37918 18319 11932 34672 NLK-WIF1-WNT2B 877 15574 29869 50706 14922 FBXW11-WIF1-WNT2B 980 2151 19852 53626 35239 CTNNBIP1-WIF1-WNT3 1062 2046 28129 43847 22398 TLE1-WIF1-WNT4 1157 30379 12684 11265 1014 TLE1-WIF1-WNT5A 1188 23457 43932 51409 21021 FZD1-WIF1-WNT2B 1329 23 38111 30027 18511 CCND1-WIF1-WNT2 1543 11595 53523 46295 23076 TLE2-WIF1-WNT3A 1645 195 4085 52703 19685 CXXC4-WIF1-WNT3A 1745 353 12465 51440 34488 DKK1-JUN-WIF1 1820 23431 35933 34937 52606 FBXW11-JUN-WIF1 1901 11991 20361 28288 29058 TCF7L1-WIF1-WNT3A 2015 7414 38348 38153 24687 NKD1-WIF1-WNT3A 2028 3129 43733 48011 30914 CCND1-WIF1-WNT3A 2203 19821 39265 34450 38713 CCND1-WIF1-WNT5A 2206 17920 56231 50097 15244 TCF7L1-WIF1-WNT4 2218 10007 38673 37345 36797 SLC9A3R1-TLE1-WIF1 2489 8000 13237 31531 3962 CSNK1G1-WIF1-WNT2B 2561 1995 24404 34807 53934 CSNK1G1-WIF1-WNT4 2582 628 24563 33380 53761 CTNNB1-FRAT1-WIF1 2625 18691 37238 24416 4230 KREMEN1-WIF1-WNT3A 2762 721 11586 56871 31145 CXXC4-WIF1-WNT2 2794 318 38171 33660 55940 CXXC4-WIF1-WNT2B 2798 244 27556 44507 52219 BCL9-FGF4-WIF1 2803 15565 47332 49359 43280 FBXW2-WIF1-WNT4 2836 2416 50951 26493 30178 CTBP2-JUN-WIF1 2868 17637 22151 3690 5044 GSK3B-JUN-WIF1 2874 57004 14204 24719 995 LRP6-TCF7L1-WIF1 2890 24748 56683 45634 14436 NKD1-WIF1-WNT4 2997 2461 45561 55000 34857 AES-FOXN1-WIF1 3020 27902 1754 12067 18564 DAAM1-WIF1-WNT2B 3043 759 50931 27606 47145 FRAT1-WIF1-WNT4 3157 3802 25184 32202 1523 CSNK1D-FGF4-WIF1 3202 18099 34798 40988 22019 EP300-JUN-WIF1 3213 26743 1259 1082 53260 PYGO1-WIF1-WNT4 3238 2703 55318 32252 32949 FZD8-WIF1-WNT2B 3269 243 27377 19078 48272 FZD7-WIF1-WNT3A 3300 22512 13048 31811 10684 LRP5-WIF1-WNT2 3309 8027 54170 21981 39712 FRAT1-WIF1-WNT3A 3328 15377 26382 55074 7682 FBXW4-WIF1-WNT2B 3407 2879 36747 43254 40889 FZD1-WIF1-WNT4 3425 32 39696 18088 22320 FZD2-NKD1-WIF1 3430 39091 22109 26358 3 FZD1-WIF1-WNT2 3541 469 55529 20037 32149 FRZB-WIF1-WNT2B 3820 12763 27144 38688 14118 DIXDC1-NKD1-WIF1 3909 12873 22358 12920 23739 FBXW2-JUN-WIF1 3982 6153 53985 45810 46608 TCF7L1-WIF1-WNT5A 4007 25712 49240 53231 50932 FZD5-CTNNBIP1-WIF1 4022 52675 7175 11477 29088 FZD5-WIF1-WNT5A 4070 24066 49908 53334 34000 SFRP4-WIF1-WNT3A 4077 1667 15047 43673 14284 LEF1-WIF1-WNT3 4224 9702 36696 52931 22759 BTRC-NKD1-WIF1 4240 14000 50136 49384 38469 LRP6-PYGO1-WIF1 4293 17363 23754 6785 4390 PPP2R1A-TLE1-WIF1 4307 33741 44977 32847 32390 TCF7L1-WIF1-WNT2 4345 20158 51362 40340 48389 NLK-WIF1-WNT4 4406 21046 38575 49983 13952 KREMEN1-NKD1-WIF1 4459 12175 15117 38622 27477 AES-JUN-WIF1 4472 28415 49294 40746 21208 FRZB-WIF1-WNT4 4481 3483 22127 37869 5037 KREMEN1-WIF1-WNT4 4505 6 32895 41843 42797 CSNK1G1-WIF1-WNT3A 4524 651 24433 41940 24409 DKK1-WIF1-WNT4 4532 13090 48760 30623 55584 FRAT1-WIF1-WNT2 4559 16950 52343 25199 28909 FSHB-NKD1-WIF1 4621 8153 24750 5910 428 CCND3-JUN-WIF1 4630 5154 35719 23637 33462 CSNK1G1-JUN-WIF1 4634 18256 33517 5537 47380 FBXW11-FGF4-WIF1 4650 8304 41904 29881 15466 NLK-WIF1-WNT3A 4697 36349 45660 34357 1641 CCND3-NKD1-WIF1 4703 15466 48536 38259 5001 CTNNB1-NLK-WIF1 4707 9899 6192 11981 1923 JUN-WIF1-WNT5A 4730 23210 50885 51206 36664 FOSL1-TLE1-WIF1 4735 9994 4780 43075 2516 CSNK1A1-NLK-WIF1 4795 14710 6213 20851 31609 FZD8-JUN-WIF1 4797 14662 20872 250 14885 FZD7-NKD1-WIF1 4840 43438 23817 39330 17629 AXIN1-FZD2-WIF1 4880 56931 43233 17761 6844 GSK3B-NLK-WIF1 4909 52847 4703 44869 2761 PYGO1-WIF1-WNT5A 4948 8911 30428 21376 24898 SENP2-WIF1-WNT2 4997 18610 47165 55988 55683 PPP2R1A-WIF1-WNT4 5019 37728 49097 41364 45936 CSNK1G1-NLK-WIF1 5054 9876 3023 50217 40547 FBXW11-TLE1-WIF1 5151 21116 13884 43214 2581 CXXC4-NLK-WIF1 5268 10350 6512 1160 15363 SENP2-WIF1-WNT4 5283 14344 21051 43416 45904 BCL9-NLK-WIF1 5369 11251 10475 3676 22747 FBXW11-PYGO1-WIF1 5380 8837 55777 3899 37175 FOSL1-WIF1-WNT2 5404 15643 45844 47156 39486 CTNNB1-T-WIF1 5406 20960 19739 11635 21009 CXXC4-WIF1-WNT4 5410 19 16924 45160 54529 TCF7L1-WIF1-WNT3 5469 28902 52401 25619 27868 DVL1-JUN-WIF1 5674 37144 16904 4823 37727 FRZB-WIF1-WNT2 5709 5485 51972 46418 31405 DKK1-FGF4-WIF1 5714 42039 36616 21416 49824 FZD6-PORCN-WIF1 5717 34355 48055 274 39658 DKK1-WIF1-WNT2 5738 10295 54604 36927 57021 PPP2CA-WIF1-WNT4 5751 1807 53735 25829 47191 DAAM1-JUN-WIF1 5830 12099 53131 3838 44361 FBXW11-FOXN1-WIF1 5840 10050 554 10106 13305 EP300-FGF4-WIF1 5848 31277 41493 38422 55833 PPP2R1A-WIF1-WNT3A 5919 34346 48174 40443 24235 EP300-TLE1-WIF1 5972 16128 8443 34895 42825 LRP6-NKD1-WIF1 5998 19435 35302 21912 36590 DVL2-WIF1-WNT4 6024 27351 28400 29068 46173 FBXW2-PYGO1-WIF1 6116 9988 36252 7568 54910 PPP2R1A-WIF1-WNT2B 6135 34753 36857 36017 55555 CSNK1D-JUN-WIF1 6149 20727 36070 15822 2807 CXXC4-FRAT1-WIF1 6172 16667 52879 168 44602 SFRP1-WIF1-WNT2 6253 42208 44024 23110 51839 FOSL1-WIF1-WNT5A 6286 2387 48506 51990 25900 DAAM1-PYGO1-WIF1 6296 13073 20827 9619 26318 AXIN1-FOXN1-WIF1 6413 26633 589 11640 3200 LRP5-TLE1-WIF1 6476 8699 27950 38670 3372 FSHB-WIF1-WNT4 6540 764 36551 30104 9874 Table 1: Rankings of WIF1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear Looking at the tables above, one finds the following combinations for WNT3A along with WIF1, to be prominent at 3rd order level - CTNNBIP1-WIF1-WNT3A, 7 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CTNNBIP1-WIF1-WNT2B 38092 3733 8392 37231 50461 TLE1-WIF1-WNT2B 39953 13690 3178 37473 11178 CCND1-WIF1-WNT2B 36761 20542 11221 38644 7317 CTNNBIP1-WIF1-WNT5A 23143 5998 4289 37385 52573 TLE1-WIF1-WNT2 43453 5975 28430 42450 32889 TLE2-WIF1-WNT2B 39741 6829 13257 43555 31091 CTNNBIP1-WIF1-WNT4 28408 15354 16297 16001 53872 NLK-WIF1-WNT2 40307 10226 11647 34273 29809 CCND1-WIF1-WNT4 29821 25068 12712 33994 6600 TLE1-WIF1-WNT3A 50523 24823 48636 56307 10235 CTNNBIP1-WIF1-WNT3A 28101 8157 26911 47091 41515 FOSL1-WIF1-WNT2B 41773 13018 2276 54404 49689 DVL2-JUN-WIF1 6060 40504 15256 30934 48673 NLK-WIF1-WNT2B 20533 18090 8143 25594 25892 FBXW11-WIF1-WNT2B 38776 30910 903 8803 21329 CTNNBIP1-WIF1-WNT3 44721 9765 12738 26593 56684 TLE1-WIF1-WNT4 40180 37225 30537 13365 9063 TLE1-WIF1-WNT5A 40747 33211 3589 52410 46132 FZD1-WIF1-WNT2B 46438 3992 11382 45997 45602 CCND1-WIF1-WNT2 37082 11406 11541 14342 16511 TLE2-WIF1-WNT3A 40072 5491 24360 49488 34844 CXXC4-WIF1-WNT3A 11746 12153 2343 56809 35373 DKK1-JUN-WIF1 14470 30176 11543 7858 42039 FBXW11-JUN-WIF1 13667 34474 37922 11980 35650 TCF7L1-WIF1-WNT3A 2909 25918 43790 53902 35000 NKD1-WIF1-WNT3A 48793 3970 17300 56778 21427 CCND1-WIF1-WNT3A 22745 5551 30083 51087 4790 CCND1-WIF1-WNT5A 37414 8236 3639 32526 9840 TCF7L1-WIF1-WNT4 13995 23515 42960 42008 36503 SLC9A3R1-TLE1-WIF1 31186 3969 23029 44406 46868 CSNK1G1-WIF1-WNT2B 38910 5666 25272 47015 36127 CSNK1G1-WIF1-WNT4 16896 27273 7830 48279 26589 CTNNB1-FRAT1-WIF1 47615 22068 25131 13309 23212 KREMEN1-WIF1-WNT3A 38760 4243 33739 39807 7207 CXXC4-WIF1-WNT2 51580 27076 41572 21992 55327 CXXC4-WIF1-WNT2B 39278 29517 3444 42367 49205 BCL9-FGF4-WIF1 11263 34919 2796 10943 15683 FBXW2-WIF1-WNT4 20440 27918 8101 14377 2991 CTBP2-JUN-WIF1 8251 10577 39311 24911 56633 GSK3B-JUN-WIF1 8724 56927 50822 35202 56101 LRP6-TCF7L1-WIF1 48592 41414 27227 22690 3657 NKD1-WIF1-WNT4 20047 23652 20170 17000 48569 AES-FOXN1-WIF1 1100 27353 38089 31438 12357 DAAM1-WIF1-WNT2B 45979 2760 20066 47459 10609 FRAT1-WIF1-WNT4 11715 10008 40620 23391 16427 CSNK1D-FGF4-WIF1 2570 27850 35517 16644 26870 EP300-JUN-WIF1 11523 21819 31185 9903 31253 PYGO1-WIF1-WNT4 30659 11937 27320 45398 3025 FZD8-WIF1-WNT2B 15532 7478 16375 18773 20549 FZD7-WIF1-WNT3A 3521 32340 43606 53450 22727 LRP5-WIF1-WNT2 27791 17603 14834 26995 40760 FRAT1-WIF1-WNT3A 9771 4923 24250 54851 24596 FBXW4-WIF1-WNT2B 27391 4792 20325 52634 39190 FZD1-WIF1-WNT4 42556 11976 32015 44929 41241 FZD2-NKD1-WIF1 45250 38648 56326 24018 7601 FZD1-WIF1-WNT2 38666 2790 24054 10334 47807 FRZB-WIF1-WNT2B 12032 17926 1240 36454 45817 DIXDC1-NKD1-WIF1 44180 9421 57087 48747 10766 FBXW2-JUN-WIF1 46353 25273 18325 14967 6352 TCF7L1-WIF1-WNT5A 19561 51039 4589 44974 51657 FZD5-CTNNBIP1-WIF1 14151 52702 31378 42083 18375 FZD5-WIF1-WNT5A 8783 34105 21011 56941 51881 SFRP4-WIF1-WNT3A 43798 5901 48178 45486 27167 LEF1-WIF1-WNT3 36462 29053 27342 16772 47153 BTRC-NKD1-WIF1 40459 4738 29145 25508 9960 LRP6-PYGO1-WIF1 40589 27373 31407 1058 42246 PPP2R1A-TLE1-WIF1 18734 28938 477 39566 970 TCF7L1-WIF1-WNT2 18637 24345 47332 21762 47245 NLK-WIF1-WNT4 27894 29051 3153 6969 779 KREMEN1-NKD1-WIF1 11200 6413 56333 14493 14792 AES-JUN-WIF1 10120 24212 19751 10267 44412 FRZB-WIF1-WNT4 7084 20245 38285 19795 37188 KREMEN1-WIF1-WNT4 15263 25410 14854 30920 27336 CSNK1G1-WIF1-WNT3A 39224 8471 4045 39840 22187 DKK1-WIF1-WNT4 31737 32517 6740 28018 30494 FRAT1-WIF1-WNT2 9313 6116 22848 25187 25230 FSHB-NKD1-WIF1 24095 15522 18330 7234 28767 CCND3-JUN-WIF1 13838 6148 31656 30680 20733 CSNK1G1-JUN-WIF1 4351 22508 8866 26497 52893 FBXW11-FGF4-WIF1 5724 14852 19141 15691 14573 NLK-WIF1-WNT3A 15025 31663 634 53620 7624 CCND3-NKD1-WIF1 36891 17882 28735 49874 2688 CTNNB1-NLK-WIF1 36869 4645 37317 37303 40718 JUN-WIF1-WNT5A 17879 25683 7574 50125 47128 FOSL1-TLE1-WIF1 31047 3632 40704 50017 52759 CSNK1A1-NLK-WIF1 11282 8274 56968 38447 50254 FZD8-JUN-WIF1 21742 21278 37642 8182 16093 FZD7-NKD1-WIF1 50953 34059 55345 47706 386 AXIN1-FZD2-WIF1 7321 57022 1548 25380 17152 GSK3B-NLK-WIF1 54258 51883 54492 6800 41476 PYGO1-WIF1-WNT5A 42194 2788 21830 11541 35248 SENP2-WIF1-WNT2 32421 15895 24851 26629 35264 PPP2R1A-WIF1-WNT4 26629 52985 27249 6249 3150 CSNK1G1-NLK-WIF1 47859 22704 35817 25257 48817 FBXW11-TLE1-WIF1 14107 27186 19295 24017 3290 CXXC4-NLK-WIF1 37250 20017 55603 45686 50949 SENP2-WIF1-WNT4 21321 27321 19436 29566 8098 BCL9-NLK-WIF1 42377 8645 50877 47640 35234 FBXW11-PYGO1-WIF1 2569 13645 24651 1922 27374 FOSL1-WIF1-WNT2 45340 16844 53312 9456 53004 CTNNB1-T-WIF1 7778 26191 45773 17171 20512 CXXC4-WIF1-WNT4 42891 41168 17267 19696 42795 TCF7L1-WIF1-WNT3 34046 41878 23724 48456 52552 DVL1-JUN-WIF1 26119 22108 34781 31590 19241 FRZB-WIF1-WNT2 36167 6734 39162 17055 44934 DKK1-FGF4-WIF1 3492 49887 7655 5221 44988 FZD6-PORCN-WIF1 480 48176 21990 7324 56972 DKK1-WIF1-WNT2 16362 15213 7425 4997 43739 PPP2CA-WIF1-WNT4 17433 21585 17502 30799 13227 DAAM1-JUN-WIF1 26905 6840 9993 8788 19186 FBXW11-FOXN1-WIF1 419 2385 47172 11148 12509 EP300-FGF4-WIF1 1112 29993 9169 25908 27395 PPP2R1A-WIF1-WNT3A 17742 45653 30117 54996 1436 EP300-TLE1-WIF1 44472 4388 23964 55747 29783 LRP6-NKD1-WIF1 30969 16249 36176 44255 21690 DVL2-WIF1-WNT4 52812 33588 6800 19576 11848 FBXW2-PYGO1-WIF1 7912 12588 25947 9153 9982 PPP2R1A-WIF1-WNT2B 32326 45372 32478 24409 8115 CSNK1D-JUN-WIF1 31036 23659 55667 9066 28938 CXXC4-FRAT1-WIF1 6873 35270 49661 19416 37560 SFRP1-WIF1-WNT2 9718 49056 22258 22488 18176 FOSL1-WIF1-WNT5A 32757 9493 2822 49605 45745 DAAM1-PYGO1-WIF1 3980 697 11295 592 10924 AXIN1-FOXN1-WIF1 2440 40095 51373 27135 13422 LRP5-TLE1-WIF1 34546 9992 6916 37075 13965 FSHB-WIF1-WNT4 55011 29325 3556 5035 26747 Table 2: Rankings of WIF1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf TLE2-WIF1-WNT3A, TCF7L1-WIF1-WNT3A, CCND1-WIF1-WNT3A, SFRP4-WIF1WNT3A, NLK-WIF1-WNT3A, PPP2R1A-WIF1-WNT3A, TLE1-WIF1-WNT3A, CXXC4WIF1-WNT3A, NKD1-WIF1-WNT3A, KREMEN1-WIF1-WNT3A, FZD7-WIF1-WNT3A, 8 RANKING @tiUSING SOBOL - 2002 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CTNNBIP1-WIF1-WNT2B 32269 9564 44982 43273 5808 TLE1-WIF1-WNT2B 42718 23842 52893 55585 8492 CCND1-WIF1-WNT2B 53452 50296 53198 44416 331 CTNNBIP1-WIF1-WNT5A 37517 8726 47830 33901 17853 TLE1-WIF1-WNT2 14466 33261 4260 1575 48694 TLE2-WIF1-WNT2B 35013 18233 37906 28769 3346 CTNNBIP1-WIF1-WNT4 19686 48738 9309 23329 39168 NLK-WIF1-WNT2 8017 43046 20756 8948 54881 CCND1-WIF1-WNT4 4841 13848 2511 11475 50379 TLE1-WIF1-WNT3A 50693 6752 56468 57096 11947 CTNNBIP1-WIF1-WNT3A 41974 54167 46904 51223 14244 FOSL1-WIF1-WNT2B 25173 2114 24567 1335 44580 DVL2-JUN-WIF1 15451 4813 8548 10559 52944 NLK-WIF1-WNT2B 49149 14168 36378 48222 2298 FBXW11-WIF1-WNT2B 29590 51803 34137 33592 22138 CTNNBIP1-WIF1-WNT3 15189 2978 10191 5960 42924 TLE1-WIF1-WNT4 24611 48165 2574 1753 54527 TLE1-WIF1-WNT5A 32505 9057 54581 55409 2636 FZD1-WIF1-WNT2B 41197 35896 29093 49255 31536 CCND1-WIF1-WNT2 3711 6976 3951 12662 56830 TLE2-WIF1-WNT3A 33475 13433 36234 29978 9382 CXXC4-WIF1-WNT3A 54553 44801 48557 52030 1570 DKK1-JUN-WIF1 6674 53375 11978 4656 40657 FBXW11-JUN-WIF1 28563 6852 14244 2120 54094 TCF7L1-WIF1-WNT3A 50706 10131 45130 48883 856 NKD1-WIF1-WNT3A 37352 21808 33337 55217 6162 CCND1-WIF1-WNT3A 30286 43921 47521 55757 2241 CCND1-WIF1-WNT5A 52311 43612 54645 45673 6949 TCF7L1-WIF1-WNT4 11430 37104 6438 4338 54134 SLC9A3R1-TLE1-WIF1 49432 25242 42714 39347 50342 CSNK1G1-WIF1-WNT2B 13733 56852 4680 24169 53252 CSNK1G1-WIF1-WNT4 53996 12035 47320 37468 7141 CTNNB1-FRAT1-WIF1 20069 13878 9022 3674 41411 KREMEN1-WIF1-WNT3A 36608 31863 33558 56397 51574 CXXC4-WIF1-WNT2 15365 18609 6335 8974 52925 CXXC4-WIF1-WNT2B 41811 38799 50795 48219 4194 BCL9-FGF4-WIF1 6521 47584 531 5681 51087 FBXW2-WIF1-WNT4 1570 2869 13912 18127 41471 CTBP2-JUN-WIF1 26632 28197 10200 26952 24504 GSK3B-JUN-WIF1 2820 53362 17047 20670 42347 LRP6-TCF7L1-WIF1 46690 44500 38326 52913 1244 NKD1-WIF1-WNT4 27161 54046 639 3320 54064 AES-FOXN1-WIF1 14926 30887 11020 27362 56513 DAAM1-WIF1-WNT2B 51968 9011 43968 43585 1804 FRAT1-WIF1-WNT4 23572 3207 18683 9445 56168 CSNK1D-FGF4-WIF1 34683 24427 28639 39649 25219 EP300-JUN-WIF1 42039 52746 44541 44510 6591 PYGO1-WIF1-WNT4 35126 29183 31527 51724 48035 FZD8-WIF1-WNT2B 56387 21556 34997 44557 31717 FZD7-WIF1-WNT3A 462 1898 24495 17586 7553 LRP5-WIF1-WNT2 26293 46706 8593 21321 39427 FRAT1-WIF1-WNT3A 38203 56268 35949 38506 8834 FBXW4-WIF1-WNT2B 40094 8029 54106 49256 2718 FZD1-WIF1-WNT4 4277 11332 28577 4077 43256 FZD2-NKD1-WIF1 48304 2115 44826 40847 8209 FZD1-WIF1-WNT2 16007 21304 28054 7826 25984 FRZB-WIF1-WNT2B 40472 54680 38479 42695 53648 DIXDC1-NKD1-WIF1 2783 6193 1919 15666 44738 FBXW2-JUN-WIF1 13125 27968 19762 1412 50668 TCF7L1-WIF1-WNT5A 45712 19992 50710 52827 3045 FZD5-CTNNBIP1-WIF1 3612 9589 10637 15392 7584 FZD5-WIF1-WNT5A 46018 34226 43880 48456 34278 SFRP4-WIF1-WNT3A 11286 51732 2804 2874 51088 LEF1-WIF1-WNT3 6586 23760 7555 20182 48604 BTRC-NKD1-WIF1 48449 54705 56221 55648 12202 LRP6-PYGO1-WIF1 44508 17042 34865 29362 9716 PPP2R1A-TLE1-WIF1 45090 23493 53498 33748 24410 TCF7L1-WIF1-WNT2 10773 36458 5086 1330 38184 NLK-WIF1-WNT4 8622 27260 19165 3572 56997 KREMEN1-NKD1-WIF1 41242 46530 54613 56937 13792 AES-JUN-WIF1 15247 17980 7285 26738 54994 FRZB-WIF1-WNT4 19577 3033 23872 23782 7044 KREMEN1-WIF1-WNT4 9057 21375 20526 13352 5900 CSNK1G1-WIF1-WNT3A 3166 45406 9828 19653 50304 DKK1-WIF1-WNT4 11135 42111 15998 24015 43039 FRAT1-WIF1-WNT2 15701 80 23990 2644 43140 FSHB-NKD1-WIF1 8501 17679 24446 9809 47619 CCND3-JUN-WIF1 24199 9395 27874 18876 36923 CSNK1G1-JUN-WIF1 50325 56104 52234 45553 1152 FBXW11-FGF4-WIF1 35293 36422 33789 54132 26098 NLK-WIF1-WNT3A 38872 26733 39808 47467 11370 CCND3-NKD1-WIF1 36042 23837 33038 45243 36980 CTNNB1-NLK-WIF1 27962 27173 4445 7873 33696 JUN-WIF1-WNT5A 11573 40788 5006 2485 37662 FOSL1-TLE1-WIF1 23465 12761 28282 7112 46249 CSNK1A1-NLK-WIF1 32459 19376 28696 36711 12615 FZD8-JUN-WIF1 9234 4498 18346 7363 52993 FZD7-NKD1-WIF1 20117 52838 9275 5598 51615 AXIN1-FZD2-WIF1 52063 20768 50568 49372 8948 GSK3B-NLK-WIF1 48655 42899 46413 40079 20496 PYGO1-WIF1-WNT5A 9422 32695 26276 12872 6210 SENP2-WIF1-WNT2 21618 32250 3233 7633 26426 PPP2R1A-WIF1-WNT4 25703 38532 8212 14678 55797 CSNK1G1-NLK-WIF1 11567 4092 1250 25403 55481 FBXW11-TLE1-WIF1 30644 52535 45101 43945 12232 CXXC4-NLK-WIF1 47523 52787 49697 39912 8695 SENP2-WIF1-WNT4 26805 33663 4825 21788 43902 BCL9-NLK-WIF1 8901 32070 18405 1896 47629 FBXW11-PYGO1-WIF1 25061 37723 9816 10733 38354 FOSL1-WIF1-WNT2 31773 4678 36771 49261 17929 CTNNB1-T-WIF1 21499 29614 11202 15378 31898 CXXC4-WIF1-WNT4 9049 33567 635 7452 53825 TCF7L1-WIF1-WNT3 6465 46841 11999 8295 56290 DVL1-JUN-WIF1 133 39629 17853 21639 41516 FRZB-WIF1-WNT2 16627 2487 18655 14490 3420 DKK1-FGF4-WIF1 46668 45941 37440 39369 52245 FZD6-PORCN-WIF1 158 1040 22006 19159 51608 DKK1-WIF1-WNT2 15360 23242 18889 22471 39072 PPP2CA-WIF1-WNT4 15333 32299 8636 19834 50303 DAAM1-JUN-WIF1 17770 14297 8451 520 24284 FBXW11-FOXN1-WIF1 22524 9008 6699 14880 46642 EP300-FGF4-WIF1 21091 2394 11152 17151 51131 PPP2R1A-WIF1-WNT3A 46290 12066 50238 34915 12432 EP300-TLE1-WIF1 24274 39167 8540 1490 50475 LRP6-NKD1-WIF1 2949 22887 2144 9835 53060 DVL2-WIF1-WNT4 21201 2424 24042 11008 43966 FBXW2-PYGO1-WIF1 23813 40455 7171 7535 53909 PPP2R1A-WIF1-WNT2B 40634 31244 45244 35349 8785 CSNK1D-JUN-WIF1 15080 11320 26129 19806 34275 CXXC4-FRAT1-WIF1 48970 56362 46322 38709 39988 SFRP1-WIF1-WNT2 15158 45628 2995 27504 34635 FOSL1-WIF1-WNT5A 22573 9683 23381 1031 51508 DAAM1-PYGO1-WIF1 14907 56052 14575 20848 37739 AXIN1-FOXN1-WIF1 5961 53853 25598 20239 32508 LRP5-TLE1-WIF1 36205 52063 56337 55035 4521 FSHB-WIF1-WNT4 31734 34663 50353 51787 17129 Table 3: Rankings of WIF1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - SOBOL; Implementation - 2002 FRAT1-WIF1-WNT3A and CSNK1G1-WIF1-WNT3A. Looking at the tables above, one finds the following combinations for other members of WNT family, along with WIF1, to be prominent at 3rd order level - CTNNBIP1-WIF1-WNT2B, CCND1-WIF19