pygopus family PHD finger 1 (PYGO1) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

pygopus family PHD finger 1 (PYGO1) : 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 pygopus family PHD finger 1 (PYGO1), recruitment permits β-catenin to transcriptionally activate WNT target genes. The presence of a PHD domain implicates PYGO proteins in a chromatin-related function. 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 PYGO1 related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for PYGO1-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 PYGO1 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 in WNT3A stimulated cells 1Aspects of unpublished work were presented in a poster session at Cell Symposia: Technology.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 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 PYGO1 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. pygopus family PHD finger 1 (PYGO1) WNT/Wingless signaling controls many fundamental processes during animal development and WNT transduction is mediated by the association of β-catenin with nuclear TCF DNA binding factors. Kramps et al. [4] report the identification of two segment polarity genes in Drosophila, i.e legless (LGS) and PYGO, and show that they are required for WNT signal transduction at the level of nuclear β-catenin. LGS encodes BCL9, and they provide genetic/molecular evidence that these proteins exert their function by physically linking PYGO to β-catenin. The PYGO-BCL9 complex is a chromatin reader, the function of which relies on two ligand-binding surfaces of PYGO’s PHD finger that anchor the histone H3 tail methylated at lysine 4 (H3K4me) with assistance from the BCL9 HD1 domain. Miller et al. [5] report the first use of fragment-based screening by NMR to identify small molecules that block proteinprotein interactions by a PHD finger. Their results suggest that the recruitment of PYGO permits β-catenin to transcriptionally activate WNT target genes. Thompson et al. [6] report the discovery of PYGO, whose mutant phenotypes specifically mimic loss-of-Wingless (Wg) signalling. PYGO is required for dTCFmediated transcription, but not for Wg-induced stabilization of Arm and it is a nuclear protein that is found in a complex with Arm in vivo. Humans possess two PYGO proteins, both of which are required for TCF-mediated transcription in colorectal cancer cells. The presence of a PHD domain implicates PYGO proteins in a chromatin-related function, and the auhtors propose that they mediate chromatin access to TCF or Arm/βcatenin. Homeodomain proteins have been shown to play a major role in the development of various organisms. Schindler et al. [7] isolated a novel Arabidopsis homeodomain protein that had the capability to interact with a DNA motif. HAT3.1 does not contain a leucine zipper motif following the homeodomain and is further characterized by an N-terminal region that shares substantial sequence similarity with the maize homeodomain protein Zmhox1a. Within this conserved region, the presence of eight regularly spaced cysteine/histidine residues (Cys4-His-Cys3motif) was observed that was reminiscent of other metal-binding domains. Being strongly evolutionary conserved, the authors proposed that this region represents a novel protein-motif which is denoted plant homeo-domain-finger (PHD-finger). Further, in vitro DNA binding studies demonstrated that HAT3.1 was capable of interacting with any DNA fragment larger than 100 bp and a deletion of the N-terminal PHD-finger domain completely abolished DNA binding, suggesting that this region might play an important functional role in 3 protein-protein or protein-DNA interaction. HAT3.1 mRNA was primarily detected in root tissue, implying a regulatory function of this protein in root development. The implications of PHD finger in chromatin-mediated transcriptional regulation have been documented in Aasland et al. [8]. In this research work, I present 3rd order combinations of PYGO1 with other genes, that the machine learning based search engine points to, as possible synergistic combinations that might be working in time. 3. Methods Please refer to sections of Sinha [2] for methods, design of study and analysis of data for 2nd order combinations. The same method and design of study is used to generate results for 3rd order combinations presented in this study. 4. Time series data Gujral and MacBeath [1] present a set of 71 WNT-related gene expression values for 6 different times points over a range of 24-hour period using qPCR. The changes represent the fold-change in the expression levels of genes in 200 ng/mL WNT3A-stimulated HEK 293 cells in time relative to their levels in unstimulated, serum-starved cells at 0hour. Gujral and MacBeath [1] state that qPCR data are the means of three biological replicates. Only genes whose mean transcript levels changed by more than two-fold at one or more time points during the 24-hour time course were considered significant. Positive (negative) numbers represent up (down) -regulation. We have already covered the issues related to these data sets in detail in Sinha [9]. 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 [9]. 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 4 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 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 5 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]. 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 PYGO1-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 [10]) and Sobol indicies (with 2002 implementation in Saltelli [11] and martinez implementation in Martinez [12] and Baudin et al. [13]). 6.3. Conserved machine learning rankings for tested PYGO1-X-X combinations A total of 2415, 3rd order combinations involving PYGO1 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 6 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CCND1-PYGO1-WNT2 191 48833 33097 15727 49025 FBXW2-PYGO1-WNT2 214 45234 28842 7216 56378 DKK1-JUN-PYGO1 218 3236 51191 53120 2659 DAAM1-PYGO1-WNT2 228 35434 22217 8095 17961 CCND1-PYGO1-SFRP4 248 49907 20135 22408 46010 DKK1-PYGO1-SENP2 253 27760 37224 42160 22797 FBXW2-PYGO1-SENP2 295 47321 21813 9500 57018 FZD5-JUN-PYGO1 348 1924 32815 54426 36260 DAAM1-PYGO1-SENP2 365 46893 25207 11837 39100 JUN-PYGO1-WNT3A 570 14118 6423 19469 36536 DKK1-PYGO1-WNT2 590 20065 32145 31502 24399 FZD5-PYGO1-SENP2 593 19014 1524 25504 36744 LRP5-PYGO1-WNT2 598 6053 19908 2338 2607 DAAM1-PYGO1-SFRP4 632 42697 21965 12019 5353 PYGO1-WNT2-WNT2B 707 39634 53492 38813 24079 FRZB-PYGO1-WNT2 817 38567 8350 5946 10554 CCND1-PYGO1-TCF7 838 55341 21851 12115 40132 CCND1-PYGO1-WNT3A 859 46424 26699 23831 49470 FBXW2-PYGO1-WNT4 880 37565 28874 6673 56916 FBXW2-PYGO1-SFRP4 895 48164 18463 9004 56766 CTBP1-PYGO1-WNT2 902 24919 8428 7477 7761 CCND1-PYGO1-SLC9A3R1 906 40276 22490 8120 43281 DAAM1-PYGO1-TCF7L1 959 51225 30853 10497 25266 CCND1-PYGO1-RHOU 1040 56164 34165 35225 53648 DKK1-PYGO1-WNT2B 1041 14062 34049 32775 7169 KREMEN1-PYGO1-WNT3A 1064 30070 1340 20277 52737 FBXW2-PYGO1-FBXW4 1225 51095 49445 9156 56717 FBXW2-PYGO1-WNT3A 1243 46844 41378 10348 56667 FRZB-PYGO1-SENP2 1288 22336 2406 8695 20479 JUN-PYGO1-TLE2 1341 24994 40582 4657 37476 CCND3-JUN-PYGO1 1362 50934 48125 55357 25009 PYGO1-WNT2-WNT5A 1374 29615 29500 7763 11360 CTNNBIP1-PYGO1-WNT2 1475 25916 18667 8796 8023 CXXC4-JUN-PYGO1 1496 10929 38139 43065 17470 DKK1-PYGO1-WNT3A 1670 37660 30663 36831 4685 DKK1-PYGO1-TCF7L1 1693 11516 32448 36695 18729 DVL2-PYGO1-WNT2 1756 33028 17795 1917 9628 CTNNBIP1-JUN-PYGO1 1762 8717 41940 46022 26397 FZD8-PYGO1-WNT2 1765 28859 12717 10912 10009 FBXW2-PYGO1-TLE2 1777 51565 50865 5489 56420 FZD5-PYGO1-TLE2 1787 4926 20017 5465 20177 CTBP1-PYGO1-WNT4 1792 40412 9281 9970 26271 FZD6-JUN-PYGO1 1799 8152 37586 49539 6795 JUN-PYGO1-SLC9A3R1 1831 18378 16698 6395 19077 CTBP1-PYGO1-SFRP4 1847 16809 2399 14104 18544 FZD5-PYGO1-FBXW4 1870 26024 50283 20420 38032 FBXW11-PYGO1-WNT2B 1888 54480 51998 19913 52577 DKK1-PYGO1-FBXW4 1953 16029 50510 30614 10640 FBXW11-PYGO1-WNT2 1968 36688 49197 5995 43963 JUN-PYGO1-WNT2B 1971 11759 22992 23296 32538 CSNK1G1-JUN-PYGO1 2002 4879 55264 32395 18429 JUN-PYGO1-RHOU 2122 21105 6824 25993 11386 JUN-PYGO1-TCF7L1 2211 39190 16299 13477 38507 JUN-PYGO1-WNT5A 2273 30941 1607 4887 6388 FZD2-LEF1-PYGO1 2290 40489 23166 26380 24432 FOSL1-PYGO1-WNT2 2296 35937 10116 9410 31529 DKK1-PYGO1-RHOU 2300 4971 25047 37502 11114 CCND1-PYGO1-SENP2 2354 25381 28894 27333 44018 DKK1-PYGO1-TLE2 2419 23834 49694 20745 27128 FBXW11-PYGO1-SENP2 2510 31734 49998 10856 40231 LEF1-PYGO1-WNT2 2594 6119 13281 49 48852 FZD1-PYGO1-SENP2 2614 7568 813 3128 19562 FRZB-PYGO1-SFRP4 2652 36390 1403 9283 23896 BTRC-GSK3A-PYGO1 2771 52085 53096 35408 47985 FZD5-PYGO1-TCF7L1 2870 23621 13839 25788 23143 CCND1-PYGO1-WNT2B 2903 53947 46315 34453 44275 KREMEN1-PYGO1-WNT2B 2904 37451 19332 29917 48436 FBXW11-PYGO1-TLE2 2906 44334 53969 2181 52786 DVL2-PYGO1-WNT3A 2944 11528 11111 13103 36306 EP300-PYGO1-WNT2 2948 43158 15314 8724 20816 CSNK1D-FGF4-PYGO1 2967 23307 41918 28164 3925 FZD5-PYGO1-WNT4 2980 4229 8238 13260 24709 CTBP1-PYGO1-TCF7 3004 9210 11537 8220 11898 CCND1-PYGO1-TLE2 3079 50182 49938 8787 45301 CTBP1-PYGO1-SENP2 3081 8819 2492 14648 22660 FRAT1-JUN-PYGO1 3094 24225 44587 43882 21321 DKK1-PYGO1-SFRP4 3105 19240 32988 43051 11763 DIXDC1-PYGO1-WNT2 3118 7736 11350 8945 27577 LEF1-PYGO1-WNT3 3128 434 1488 29 43589 FBXW11-PYGO1-SFRP4 3151 40355 44072 9884 48388 DIXDC1-PYGO1-TCF7L1 3193 33168 18183 17378 30931 PYGO1-WIF1-WNT4 3238 2703 55318 32252 32949 CCND1-PYGO1-FBXW4 3286 26986 41890 24897 52371 AES-FOXN1-PYGO1 3305 25455 24093 28905 5012 LEF1-PYGO1-WNT3A 3330 4637 9706 492 45999 FZD1-PYGO1-WNT2 3364 25302 3943 1660 5188 FZD1-JUN-PYGO1 3370 32879 29253 28580 37224 FRZB-PYGO1-WNT2B 3417 26749 22590 20939 16614 CCND3-PYGO1-WNT3A 3454 44362 41213 28500 14947 CSNK2A1-PYGO1-WNT2 3524 34440 54530 10724 18467 DVL2-PYGO1-TLE2 3562 38778 46616 3007 4918 CSNK1G1-PYGO1-TLE2 3565 24569 56894 5227 16188 FOSL1-JUN-PYGO1 3590 27459 38794 51790 55928 DVL2-PYGO1-FBXW4 3595 20330 55028 6420 42020 FZD7-PYGO1-WNT3A 3597 13080 6229 10048 9938 LRP5-PYGO1-SFRP4 3644 1525 13977 5563 18801 CTNNBIP1-PYGO1-SENP2 3739 6879 9216 12253 26261 CCND1-PYGO1-TCF7L1 3805 54303 46961 29812 46238 FRZB-PYGO1-TLE2 3809 42613 27606 3105 9575 DVL2-PYGO1-SENP2 3834 9313 17069 10011 29581 GSK3B-PYGO1-TLE2 3889 10232 51499 31294 33743 CSNK1D-JUN-PYGO1 3934 1849 39438 23725 46933 AXIN1-MYC-PYGO1 3954 3444 10994 17667 24234 FBXW11-PYGO1-WNT3A 3985 37584 56193 14716 37160 LEF1-PYGO1-SFRP1 3992 3352 7797 117 11186 FOSL1-PYGO1-SFRP4 4009 35642 2304 16916 49861 FRAT1-PYGO1-WNT3A 4132 14097 12408 18181 22475 FOSL1-PYGO1-WNT2B 4188 9498 24044 24964 53151 NLK-PYGO1-WNT2 4229 27445 40800 13988 7354 AES-JUN-PYGO1 4280 27713 29918 47174 22758 FZD8-PYGO1-WNT2B 4284 33894 27397 24043 46041 LRP6-PYGO1-WIF1 4293 17363 23754 6785 4390 KREMEN1-PYGO1-WNT2 4388 35884 6984 16968 53392 DVL2-PYGO1-TCF7L1 4435 40655 29622 11516 29181 FOSL1-PYGO1-SENP2 4461 29888 2317 13025 53543 DAAM1-PYGO1-TCF7 4470 39048 22767 7968 11799 FZD5-PYGO1-RHOU 4574 8615 5925 32341 7083 PITX2-PYGO1-TLE2 4588 2003 47249 8274 54767 FZD5-PYGO1-SLC9A3R1 4599 10851 8326 6893 16260 DAAM1-PYGO1-TLE1 4607 51419 32265 15738 19668 CCND1-PYGO1-SFRP1 4616 49034 18235 22959 42446 FBXW11-PYGO1-TCF7L1 4731 49531 56943 14286 52062 DAAM1-JUN-PYGO1 4756 47637 25776 47368 4345 CSNK2A1-PYGO1-TCF7 4808 27076 33334 7691 16030 FBXW2-PYGO1-TLE1 4855 13029 28477 2137 56462 GSK3B-PYGO1-WNT2 4907 10086 14344 28902 33359 Table 1: Rankings of PYGO1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear synergy, whether the combination has been tested or unexplored/untested. 7 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CCND1-PYGO1-WNT2 7685 48218 45186 9095 12535 FBXW2-PYGO1-WNT2 6632 47000 10921 10825 10660 DKK1-JUN-PYGO1 35611 92 8244 34065 42310 DAAM1-PYGO1-WNT2 13220 45816 8644 1196 14447 CCND1-PYGO1-SFRP4 7901 42981 32796 28660 4288 DKK1-PYGO1-SENP2 403 23098 9845 24707 36625 FBXW2-PYGO1-SENP2 5592 54522 7624 18559 15058 FZD5-JUN-PYGO1 13399 522 43506 36219 51123 DAAM1-PYGO1-SENP2 7009 46420 6762 21944 29682 JUN-PYGO1-WNT3A 10181 579 35737 33610 43746 DKK1-PYGO1-WNT2 3282 13742 6775 127 50868 FZD5-PYGO1-SENP2 864 25856 32614 26549 46981 LRP5-PYGO1-WNT2 24259 12625 15087 18812 33964 DAAM1-PYGO1-SFRP4 10758 46433 7217 48291 9239 PYGO1-WNT2-WNT2B 42713 30786 13433 45795 1718 FRZB-PYGO1-WNT2 2310 29711 53695 989 52194 CCND1-PYGO1-TCF7 3994 53634 8088 23990 6794 CCND1-PYGO1-WNT3A 2014 38925 42108 33199 4343 FBXW2-PYGO1-WNT4 7669 38818 19627 43015 3643 FBXW2-PYGO1-SFRP4 6016 52622 9354 20433 4893 CTBP1-PYGO1-WNT2 7914 40190 53737 1881 54646 CCND1-PYGO1-SLC9A3R1 8501 30855 32431 9221 12132 DAAM1-PYGO1-TCF7L1 6113 49053 11325 35525 9242 CCND1-PYGO1-RHOU 5175 54648 29737 46772 20403 DKK1-PYGO1-WNT2B 2010 10992 36338 13891 29481 KREMEN1-PYGO1-WNT3A 7864 26771 50128 43544 15239 FBXW2-PYGO1-FBXW4 5992 55287 26603 3782 9116 FBXW2-PYGO1-WNT3A 7391 48320 9248 34651 2524 FRZB-PYGO1-SENP2 334 16496 42795 31671 51686 JUN-PYGO1-TLE2 2091 9953 10078 26860 57045 CCND3-JUN-PYGO1 15052 38950 15637 52389 3265 PYGO1-WNT2-WNT5A 36384 23157 25066 7716 16105 CTNNBIP1-PYGO1-WNT2 20950 23080 54816 1243 54421 CXXC4-JUN-PYGO1 15268 3842 31367 43633 53074 DKK1-PYGO1-WNT3A 1315 30284 30530 24495 19085 DKK1-PYGO1-TCF7L1 2316 814 35496 27049 25451 DVL2-PYGO1-WNT2 6832 31920 27128 7953 48179 CTNNBIP1-JUN-PYGO1 41135 2896 47437 45143 51706 FZD8-PYGO1-WNT2 3462 16415 43751 3201 35160 FBXW2-PYGO1-TLE2 6212 55715 1956 16260 24385 FZD5-PYGO1-TLE2 4104 5653 37820 25448 57153 CTBP1-PYGO1-WNT4 22742 44655 41099 39815 48059 FZD6-JUN-PYGO1 35697 277 641 50698 33247 JUN-PYGO1-SLC9A3R1 3487 15500 27418 13894 51869 CTBP1-PYGO1-SFRP4 22918 27814 51439 38327 43332 FZD5-PYGO1-FBXW4 8568 40214 29428 9395 56877 FBXW11-PYGO1-WNT2B 7490 53715 924 4743 16840 DKK1-PYGO1-FBXW4 4015 24648 4205 73 53593 FBXW11-PYGO1-WNT2 13085 22818 21507 4205 23661 JUN-PYGO1-WNT2B 2703 20164 23828 23294 38517 CSNK1G1-JUN-PYGO1 17775 1546 36260 46060 22759 JUN-PYGO1-RHOU 3507 2626 38630 48273 44356 JUN-PYGO1-TCF7L1 2998 25012 36064 35492 46418 JUN-PYGO1-WNT5A 9776 20912 9445 6655 56641 FZD2-LEF1-PYGO1 19320 30354 33523 35934 37423 FOSL1-PYGO1-WNT2 4646 17601 54904 1115 45855 DKK1-PYGO1-RHOU 594 8755 12396 40458 43195 CCND1-PYGO1-SENP2 2887 16723 33585 4220 12776 DKK1-PYGO1-TLE2 1493 17701 42910 17294 57025 FBXW11-PYGO1-SENP2 882 19979 26917 15962 25523 LEF1-PYGO1-WNT2 4130 36760 36544 4175 29233 FZD1-PYGO1-SENP2 2237 14486 13479 4706 37678 FRZB-PYGO1-SFRP4 2953 27146 15142 30999 39478 BTRC-GSK3A-PYGO1 16077 51303 28870 23885 34429 FZD5-PYGO1-TCF7L1 552 22883 43339 19418 51934 CCND1-PYGO1-WNT2B 4500 49840 12312 25574 14068 KREMEN1-PYGO1-WNT2B 2480 27771 5674 47549 30280 FBXW11-PYGO1-TLE2 3570 44556 20858 19771 39583 DVL2-PYGO1-WNT3A 18087 2223 36690 1889 26351 EP300-PYGO1-WNT2 5709 43420 44821 441 34191 CSNK1D-FGF4-PYGO1 35224 24194 35705 42726 4974 FZD5-PYGO1-WNT4 12619 9688 49504 15069 50337 CTBP1-PYGO1-TCF7 12120 36550 3309 22441 35094 CCND1-PYGO1-TLE2 2708 46475 14041 11551 36187 CTBP1-PYGO1-SENP2 14535 11602 42803 9594 47507 FRAT1-JUN-PYGO1 33906 17235 3856 45519 18398 DKK1-PYGO1-SFRP4 3408 7708 23449 34970 34048 DIXDC1-PYGO1-WNT2 9260 4892 51202 277 17819 LEF1-PYGO1-WNT3 8116 6747 37915 10868 26227 FBXW11-PYGO1-SFRP4 3371 25915 424 42974 31841 DIXDC1-PYGO1-TCF7L1 9179 35935 48383 28960 14143 PYGO1-WIF1-WNT4 30659 11937 27320 45398 3025 CCND1-PYGO1-FBXW4 5824 27098 17674 13615 16815 AES-FOXN1-PYGO1 4657 24703 43459 42184 24604 LEF1-PYGO1-WNT3A 7948 34410 45811 27590 17447 FZD1-PYGO1-WNT2 8801 28775 15560 1399 50819 FZD1-JUN-PYGO1 46076 19069 9867 46865 48594 FRZB-PYGO1-WNT2B 3505 12360 4064 28390 55537 CCND3-PYGO1-WNT3A 782 47470 16204 30209 9636 CSNK2A1-PYGO1-WNT2 6052 32583 28770 2461 39536 DVL2-PYGO1-TLE2 8563 43181 37961 17796 56882 CSNK1G1-PYGO1-TLE2 21495 24434 29013 7562 53728 FOSL1-JUN-PYGO1 39670 8443 35133 55401 48823 DVL2-PYGO1-FBXW4 15883 30156 604 9016 45692 FZD7-PYGO1-WNT3A 2200 3030 44689 22869 39525 LRP5-PYGO1-SFRP4 14664 1251 37823 41590 26535 CTNNBIP1-PYGO1-SENP2 8077 5298 52208 9813 41948 CCND1-PYGO1-TCF7L1 10623 47122 16194 21979 4501 FRZB-PYGO1-TLE2 3510 45630 22284 32164 57136 DVL2-PYGO1-SENP2 3166 806 29432 11396 29074 GSK3B-PYGO1-TLE2 1511 1087 42710 14437 57121 CSNK1D-JUN-PYGO1 46732 424 46278 41608 30058 AXIN1-MYC-PYGO1 33645 8460 51922 49242 34352 FBXW11-PYGO1-WNT3A 5958 23716 24819 17645 5707 LEF1-PYGO1-SFRP1 8248 25313 16956 27035 35434 FOSL1-PYGO1-SFRP4 3428 32371 44049 49180 33552 FRAT1-PYGO1-WNT3A 6165 13829 40997 17174 24514 FOSL1-PYGO1-WNT2B 4892 4674 16682 35879 52932 NLK-PYGO1-WNT2 7759 3583 13307 7257 24124 AES-JUN-PYGO1 25084 9408 7447 50510 20969 FZD8-PYGO1-WNT2B 5074 27177 16095 15562 27187 LRP6-PYGO1-WIF1 40589 27373 31407 1058 42246 KREMEN1-PYGO1-WNT2 2834 38294 45106 1581 41784 DVL2-PYGO1-TCF7L1 4022 45893 41755 25284 37685 FOSL1-PYGO1-SENP2 977 13985 43848 13391 28612 DAAM1-PYGO1-TCF7 1729 42769 4631 5543 14266 FZD5-PYGO1-RHOU 543 3213 11602 49189 47416 PITX2-PYGO1-TLE2 1782 35079 27236 39307 56772 FZD5-PYGO1-SLC9A3R1 13164 6884 38119 28521 55716 DAAM1-PYGO1-TLE1 9367 40988 3088 5163 19658 CCND1-PYGO1-SFRP1 7909 44664 37002 6160 22267 FBXW11-PYGO1-TCF7L1 2771 39588 19054 11993 11919 DAAM1-JUN-PYGO1 35403 45052 14876 50189 5673 CSNK2A1-PYGO1-TCF7 4497 22038 26026 17251 48738 FBXW2-PYGO1-TLE1 11243 2157 3112 11981 5521 GSK3B-PYGO1-WNT2 4395 4042 49269 2154 52107 Table 2: Rankings of PYGO1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf 6.3.1. Examining the behaviour of WNT-PYGO1-X combinations Kramps et al. [4] indicate that TCF and β-catenin function in a tetrapartite complex with LGS/BCL9 and PYGO to transcriptionally activate target genes in response to 8 RANKING @tiUSING SOBOL - 2002 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CCND1-PYGO1-WNT2 23571 36410 15616 2053 54902 FBXW2-PYGO1-WNT2 22809 29745 16419 7178 38040 DKK1-JUN-PYGO1 20453 50366 17707 8188 42484 DAAM1-PYGO1-WNT2 11655 42330 15885 7995 42320 CCND1-PYGO1-SFRP4 6028 42645 2289 1001 55845 DKK1-PYGO1-SENP2 5320 8965 25659 16677 34823 FBXW2-PYGO1-SENP2 19176 47463 19297 20507 39832 FZD5-JUN-PYGO1 22701 20169 18383 5021 52969 DAAM1-PYGO1-SENP2 10224 2416 14099 12136 24858 JUN-PYGO1-WNT3A 1610 17601 24757 13846 37085 DKK1-PYGO1-WNT2 3006 20828 19259 10946 32234 FZD5-PYGO1-SENP2 10582 54199 15471 9662 50406 LRP5-PYGO1-WNT2 6676 12359 19432 21720 43580 DAAM1-PYGO1-SFRP4 12825 5259 14739 27176 39944 PYGO1-WNT2-WNT2B 35098 23545 34784 49087 46216 FRZB-PYGO1-WNT2 12262 22169 15532 4607 50768 CCND1-PYGO1-TCF7 18122 45572 2446 2027 55938 CCND1-PYGO1-WNT3A 39080 19013 56205 51729 13572 FBXW2-PYGO1-WNT4 6048 35274 8914 13383 40180 FBXW2-PYGO1-SFRP4 22052 24720 4613 5903 54788 CTBP1-PYGO1-WNT2 20153 27678 2537 9397 33838 CCND1-PYGO1-SLC9A3R1 5279 1741 18699 16570 29343 DAAM1-PYGO1-TCF7L1 37114 50690 39761 33545 3030 CCND1-PYGO1-RHOU 43775 56261 50329 56095 7953 DKK1-PYGO1-WNT2B 54188 35764 37921 46266 24833 KREMEN1-PYGO1-WNT3A 52932 56977 53771 37472 14726 FBXW2-PYGO1-FBXW4 35105 32258 52561 51292 2367 FBXW2-PYGO1-WNT3A 52031 31884 46340 31823 2792 FRZB-PYGO1-SENP2 11932 6986 25367 12616 52422 JUN-PYGO1-TLE2 3800 11209 18229 255 32111 CCND3-JUN-PYGO1 25910 36673 28134 15173 40843 PYGO1-WNT2-WNT5A 38189 30159 29176 50070 44803 CTNNBIP1-PYGO1-WNT2 11459 19288 18921 4735 9712 CXXC4-JUN-PYGO1 13879 27252 8058 10543 55180 DKK1-PYGO1-WNT3A 49429 22863 28934 47297 24196 DKK1-PYGO1-TCF7L1 53013 53567 39949 56715 29970 DVL2-PYGO1-WNT2 24731 1948 7444 10308 48870 CTNNBIP1-JUN-PYGO1 14511 20205 9590 1997 56057 FZD8-PYGO1-WNT2 1313 6988 26283 14105 56504 FBXW2-PYGO1-TLE2 32326 13530 50413 46764 9323 FZD5-PYGO1-TLE2 43027 104 46448 43876 24737 CTBP1-PYGO1-WNT4 27649 26968 22166 2301 29150 FZD6-JUN-PYGO1 660 283 18899 19152 55094 JUN-PYGO1-SLC9A3R1 39968 7155 33471 32607 20833 CTBP1-PYGO1-SFRP4 18530 26668 2815 1299 30332 FZD5-PYGO1-FBXW4 39183 2104 46072 43193 2921 FBXW11-PYGO1-WNT2B 33541 53563 42544 44866 11547 DKK1-PYGO1-FBXW4 51614 42906 37164 38683 33819 FBXW11-PYGO1-WNT2 23628 3600 14621 12236 45387 JUN-PYGO1-WNT2B 784 29200 21789 1189 45268 CSNK1G1-JUN-PYGO1 39719 47416 54841 47973 10949 JUN-PYGO1-RHOU 3266 37143 23419 11201 38259 JUN-PYGO1-TCF7L1 4196 41759 27014 26374 34930 JUN-PYGO1-WNT5A 2460 21997 22687 2953 49677 FZD2-LEF1-PYGO1 39966 1605 48301 38150 15979 FOSL1-PYGO1-WNT2 47297 50999 30260 50806 4015 DKK1-PYGO1-RHOU 52268 16276 32787 34998 26390 CCND1-PYGO1-SENP2 9363 55936 5775 22711 48701 DKK1-PYGO1-TLE2 53371 13490 36793 44944 18357 FBXW11-PYGO1-SENP2 23322 1344 12785 8511 39644 LEF1-PYGO1-WNT2 17290 10437 14509 19069 34734 FZD1-PYGO1-SENP2 17605 57130 8602 23919 43562 FRZB-PYGO1-SFRP4 19646 20211 10524 5314 31613 BTRC-GSK3A-PYGO1 40306 12238 50108 55258 7556 FZD5-PYGO1-TCF7L1 39929 19214 31569 49425 9668 CCND1-PYGO1-WNT2B 33592 20824 41585 55101 2315 KREMEN1-PYGO1-WNT2B 49601 24278 44028 43212 12272 FBXW11-PYGO1-TLE2 33225 36548 35122 52970 13629 DVL2-PYGO1-WNT3A 35451 32587 46161 49351 14826 EP300-PYGO1-WNT2 31940 56694 45844 45742 12882 CSNK1D-FGF4-PYGO1 41090 20740 34158 34168 20857 FZD5-PYGO1-WNT4 15278 10463 12217 3358 53540 CTBP1-PYGO1-TCF7 19167 24468 5531 3011 33571 CCND1-PYGO1-TLE2 38969 17016 52496 38112 384 CTBP1-PYGO1-SENP2 10240 25052 9151 4681 32852 FRAT1-JUN-PYGO1 17301 5414 8956 6791 9863 DKK1-PYGO1-SFRP4 5555 14281 20084 18507 23471 DIXDC1-PYGO1-WNT2 38631 6548 43841 56224 38207 LEF1-PYGO1-WNT3 16493 40318 11960 27230 25603 FBXW11-PYGO1-SFRP4 19547 42729 11935 6272 45795 DIXDC1-PYGO1-TCF7L1 2188 42426 19263 4130 25766 PYGO1-WIF1-WNT4 35126 29183 31527 51724 48035 CCND1-PYGO1-FBXW4 51130 15106 54885 56151 1320 AES-FOXN1-PYGO1 13627 21324 3166 21211 26154 LEF1-PYGO1-WNT3A 40621 17131 45161 29919 31440 FZD1-PYGO1-WNT2 18743 55194 11811 3018 31667 FZD1-JUN-PYGO1 10842 9463 23552 17495 34735 FRZB-PYGO1-WNT2B 44906 34928 41610 52546 6348 CCND3-PYGO1-WNT3A 51433 27320 30354 36390 39641 CSNK2A1-PYGO1-WNT2 27842 10862 10937 6962 53007 DVL2-PYGO1-TLE2 34256 44308 42625 42719 3422 CSNK1G1-PYGO1-TLE2 17136 9155 11518 17890 32040 FOSL1-JUN-PYGO1 35100 56491 39744 42645 28344 DVL2-PYGO1-FBXW4 29729 33444 33783 33618 40149 FZD7-PYGO1-WNT3A 1165 50482 26897 25768 53340 LRP5-PYGO1-SFRP4 2300 55858 7523 22759 51715 CTNNBIP1-PYGO1-SENP2 21191 36983 19971 3965 11871 CCND1-PYGO1-TCF7L1 39036 11286 54703 55124 1216 FRZB-PYGO1-TLE2 45842 21383 45458 51288 1668 DVL2-PYGO1-SENP2 26270 14793 24368 13556 8825 GSK3B-PYGO1-TLE2 55303 43455 31052 48879 8231 CSNK1D-JUN-PYGO1 24772 39437 27678 10274 47704 AXIN1-MYC-PYGO1 4066 39692 3553 5774 48217 FBXW11-PYGO1-WNT3A 39947 53781 36004 52889 15695 LEF1-PYGO1-SFRP1 53359 2338 48778 30849 55971 FOSL1-PYGO1-SFRP4 39720 40936 40202 47288 2631 FRAT1-PYGO1-WNT3A 37686 56136 39369 37595 23150 FOSL1-PYGO1-WNT2B 12441 11961 5832 1148 30998 NLK-PYGO1-WNT2 7875 21489 20941 18370 48652 AES-JUN-PYGO1 20909 15200 3792 28252 30883 FZD8-PYGO1-WNT2B 55854 50198 30897 43016 651 LRP6-PYGO1-WIF1 44508 17042 34865 29362 9716 KREMEN1-PYGO1-WNT2 7561 33096 13153 14050 44943 DVL2-PYGO1-TCF7L1 30408 40479 30117 35926 43261 FOSL1-PYGO1-SENP2 48594 56124 49849 56650 18878 DAAM1-PYGO1-TCF7 20090 6405 17388 23697 54109 FZD5-PYGO1-RHOU 43941 53488 41361 43989 27808 PITX2-PYGO1-TLE2 19850 10379 18180 6093 40940 FZD5-PYGO1-SLC9A3R1 10744 49408 12251 7758 51542 DAAM1-PYGO1-TLE1 11821 6611 9646 28349 35623 CCND1-PYGO1-SFRP1 47797 1211 51402 34391 8554 FBXW11-PYGO1-TCF7L1 34205 54669 45848 48836 12237 DAAM1-JUN-PYGO1 10734 4256 13652 16493 54555 CSNK2A1-PYGO1-TCF7 15569 3364 11248 16573 53352 FBXW2-PYGO1-TLE1 24866 43447 6766 10408 47911 GSK3B-PYGO1-WNT2 7165 34491 27181 12830 44756 Table 3: Rankings of PYGO1-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - SOBOL; Implementation - 2002 WNT signals. Using in situ hybridization, Schwab et al. [14] examined expression of three WNT7B (Kispert et al. [15]), WNT11 (Majumdar et al. [16]) and WNT9B (Carroll et al. [17]) genes in PYGO mutants. They found that all three genes showed similar expression patterns in PYGO2+/+and PYGO1/PYGO2 double-mutant kid9