paired-like homeodomain transcription factor 2 (PITX2) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

paired-like homeodomain transcription factor 2 (PITX2) : 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 104-Madhurisha Heights Phase 1, Risali, Bhilai-490006, India Abstract PITX2 (also known as pituitary homeobox 2), encodes a member of the RIEG/PITX homeobox family (a bicoid class of homeodomain proteins), that acts as a transcription factor and regulates procollagen lysyl hydroxylase gene expression. It is known to play an important role in pituitary, heart, brain, lungs, spleen, twisting of the gut and stomach, as well as the development of the eyes. 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 PITX2 related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for PITX2-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 PITX2 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 February 22, 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 PITX2 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. paired-like homeodomain transcription factor 2 (PITX2) PITX2, encodes a member of the RIEG/PITX homeobox family (a bicoid class of homeodomain proteins (Holland et al. [4])). A homeobox is an approximately 180 base pairs long DNA sequence, that regulates anatomical features in the early stages of embryonic development (Wikipedia contributors [5]). Mutations in a homeobox may change large-scale anatomical features of the full-grown organism. Homeobox genes (Gehring [6] and Gehring [7]) encode homeodomain protein products are transcription factors with important roles in embryonic patterning and cell differentiation, and several have been implicated in human diseases and congenital abnormalities (Boncinelli [8]). ALL1 (human homologue of Drosophila trithorax), is directly involved in human acute leukemias associated with abnormalities at 11q23. Arakawa et al. [9] isolated a gene that is down-regulated in All1 double-knockout mouse embryonic stem (ES) cells and designated it ARP1 (also termed RIEG, PITX2, or OTLX2) belonging to the PRD class homeoboxes and pseudogenes. Logan et al. [10] show that PITX2 encodes a transcription factor expressed through-out the left lateral plate mesoderm and subsequentlyon the left side of asymmetric organs such as the heart and gut during organogenesis in the chick embryo. Misexpression of PITX2 on the right side of the embryo is sufficient to produce reversed heart looping and heart isomerisms, reversed body rotation, and reversed gut situs (Campione et al. [11], Shiratori et al. [12], Zacharias et al. [13]). Finally, different isoforms of the transcription factor: PITX2-A/B/C, each with distinct and non-overlapping functions exist. In this research work, I present 3rd order combinations of PITX2 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 [14]. 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 [14]. 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 PITX2-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 [15]) and Sobol indicies (with 2002 implementation in Saltelli [16] and martinez implementation in Martinez [17] and Baudin et al. [18]). 6.3. Conserved machine learning rankings for tested PITX2-X-X combinations A total of 2415, 3rd order combinations involving PITX2 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-PITX2-X combinations Kioussi et al. [19] report that PITX2 is rapidly induced by the WNT/DVL/β-catenin pathway and is required for effective cell-type-specific proliferation by directly activating specific growth-regulating genes. Regulated exchange of HDAC1/β-catenin converts PITX2 from repressor to activator (analogous to control of TCF/LEF1) which then serves as a competence factor required for the temporally ordered and growth factor-dependent recruitment of a series of specific coactivator complexes that prove necessary for CCND2 gene induction. Since the WNT pathway is strongly involved in ovarian development and cancer, Basu and Roy [20] focused on the possible association between PITX2 and WNT pathway in ovarian carcinoma cells and found that PITX2 interacts and regulates WNT2/5A/9A/6/2B genes of the canonical, noncanonical, or other pathways in the human ovarian adenocarcinoma cell SKOV-3. Chromatin 6 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 APC-PITX2-SFRP4 14 26861 33433 10197 18249 APC-PITX2-SENP2 37 14630 40719 18877 15582 APC-PITX2-TCF7 130 34995 20653 15851 17861 PITX2-PORCN-TLE2 169 22676 35351 44094 14423 PITX2-PORCN-WNT4 177 16891 32175 32123 27627 PITX2-PORCN-SENP2 270 20159 27718 25665 18827 DVL2-JUN-PITX2 293 27343 32163 42607 21387 FZD5-PITX2-SENP2 328 35236 22541 1156 14803 APC-PITX2-PPP2CA 334 14753 2900 19245 30663 APC-PITX2-RHOU 397 38592 32191 27698 15148 PITX2-PORCN-WNT5A 460 36097 17787 53210 23094 PITX2-PORCN-FBXW4 499 12554 20396 26439 17842 DIXDC1-PITX2-SENP2 526 28707 7274 5676 35235 CTNNBIP1-JUN-PITX2 546 6389 45937 54346 11119 CCND1-FGF4-PITX2 554 54983 49474 23953 29838 PITX2-PORCN-TCF7L1 572 42893 22702 25919 13429 DIXDC1-PITX2-SFRP4 614 29602 6543 3868 43507 PITX2-PORCN-WNT2B 630 42884 44910 50269 15186 APC-PITX2-WNT4 634 38339 50192 23301 18227 FRAT1-JUN-PITX2 748 50033 38113 50412 44660 PITX2-PORCN-TLE1 813 43605 21513 22845 15786 DKK1-JUN-PITX2 913 6407 42538 52798 634 AES-AXIN1-PITX2 978 46773 17137 47484 7382 PITX2-PORCN-PPP2R1A 1003 8071 39783 44256 5481 PITX2-PORCN-RHOU 1220 38816 23756 29958 13324 CCND1-JUN-PITX2 1260 51205 42011 18763 52917 FOSL1-JUN-PITX2 1479 1306 37107 54515 12375 FZD6-PITX2-WNT2B 1504 10725 14634 54318 17213 FZD5-PITX2-SFRP4 1559 51198 27058 788 14497 PITX2-PORCN-SFRP4 1607 32189 32121 34063 21972 CCND1-CTBP1-PITX2 1644 56351 33831 12174 34580 FSHB-FZD2-PITX2 1681 25060 56319 33266 14323 PITX2-WNT3-WNT5A 1726 32979 5136 41370 17012 CCND2-LRP6-PITX2 1887 36449 16637 55064 12492 PITX2-PORCN-SFRP1 1905 39236 31192 37387 9110 AES-EP300-PITX2 2125 50901 43504 52709 17083 FZD6-PITX2-SFRP4 2136 44403 22523 5027 25162 PITX2-WNT3-WNT3A 2155 50776 27010 46543 38273 DAAM1-FOXN1-PITX2 2183 45577 23419 17738 1022 CSNK2A1-JUN-PITX2 2295 11006 48321 42767 19026 FBXW11-LRP6-PITX2 2307 48503 41757 51594 35405 CCND1-CTNNBIP1-PITX2 2315 54797 33975 42838 34145 CSNK2A1-FOXN1-PITX2 2356 10265 14777 12628 14201 FOXN1-GSK3A-PITX2 2381 48019 32781 32844 21255 AXIN1-FZD6-PITX2 2480 44926 6159 53367 9917 FRZB-GSK3A-PITX2 2482 10817 2209 668 13402 PITX2-WNT1-WNT5A 2609 5926 14837 51671 5692 BTRC-GSK3A-PITX2 2613 49655 52881 6241 50065 PITX2-SFRP4-WNT2B 2621 47714 20847 52301 32634 DAAM1-JUN-PITX2 2739 53719 47964 55644 657 CXXC4-JUN-PITX2 2757 3424 36286 40345 36376 APC-PITX2-WNT3 2778 27077 34088 34710 13819 PITX2-PORCN-PPP2CA 2847 24874 33030 43172 21878 DIXDC1-PITX2-WNT2B 2863 14619 3889 45440 40568 FBXW11-FOXN1-PITX2 2886 3843 4957 17704 23607 CSNK1D-FGF4-PITX2 3093 11417 24874 53815 30793 LRP5-PITX2-SFRP4 3210 16171 31459 8145 26086 DIXDC1-PITX2-WNT4 3214 52681 19702 7189 37575 FOSL1-GSK3A-PITX2 3246 8961 918 7353 12922 FBXW11-JUN-PITX2 3374 35385 45082 55257 41153 CCND3-PITX2-WNT3A 3484 43666 17937 5868 27350 CSNK2A1-MYC-PITX2 3758 35967 33879 27313 16543 EP300-FZD2-PITX2 3771 12315 30396 16799 22718 CSNK1D-FOXN1-PITX2 3778 6280 4678 21772 36345 FZD1-GSK3A-PITX2 3798 30685 3123 6034 15265 CCND3-PITX2-SFRP4 3846 53365 17972 862 38266 DVL1-EP300-PITX2 3886 37126 11319 53194 36735 DAAM1-GSK3A-PITX2 3913 55523 36819 2364 4273 DKK1-PITX2-SFRP4 3919 36216 54630 36550 651 GSK3B-PITX2-SFRP4 3969 51591 11242 44587 45162 FBXW2-JUN-PITX2 4023 15973 52731 42180 49503 FRZB-FZD2-PITX2 4081 5620 20625 16286 21997 DIXDC1-PITX2-PPP2CA 4123 13781 1911 14325 45522 DAAM1-LRP6-PITX2 4134 55453 49218 56874 3254 FOSL1-FOXN1-PITX2 4149 3704 3591 20411 19698 CTNNB1-FOXN1-PITX2 4154 3460 4095 19749 19696 PITX2-WNT1-WNT2B 4158 13925 1462 19718 12422 CCND3-PITX2-SENP2 4176 37072 17505 1404 25804 FZD5-PITX2-WNT2B 4182 39042 16284 52876 11251 FZD7-GSK3A-PITX2 4302 20752 736 4869 12197 AXIN1-EP300-PITX2 4304 11293 12887 53659 13073 FRAT1-GSK3A-PITX2 4363 56251 2247 18588 44926 CSNK1G1-FZD2-PITX2 4407 7002 19144 19885 20203 FOSL1-FZD2-PITX2 4478 4516 12555 16266 17423 FBXW11-PITX2-SFRP4 4547 50563 47219 11287 28318 CSNK1G1-PITX2-SENP2 4579 38292 32335 49857 17717 PITX2-PYGO1-TLE2 4588 2003 47249 8274 54767 CTBP2-FOXN1-PITX2 4611 37603 5195 14491 24302 DVL1-FOXN1-PITX2 4624 42047 4932 11016 38406 CTBP1-JUN-PITX2 4720 2611 40385 42676 12432 PITX2-WNT1-WNT4 4724 908 3272 33901 10244 DIXDC1-PITX2-RHOU 4739 31170 5147 8935 19768 FZD6-PITX2-TCF7 4754 25933 18851 11368 22426 DKK1-GSK3A-PITX2 4759 23623 33694 50522 6502 FZD6-PITX2-SENP2 4827 47413 31625 7317 23700 APC-PITX2-SLC9A3R1 4832 13233 25730 31544 21292 FBXW11-PITX2-WNT2B 4991 55437 27760 53601 30191 DIXDC1-PITX2-TCF7 5005 35931 12459 6681 32860 CSNK1D-PITX2-SFRP4 5096 37446 11233 10582 41257 FZD5-CCND3-PITX2 5106 9271 1305 14097 20152 FZD6-PITX2-WNT2 5113 30267 46069 12925 22168 AES-FOXN1-PITX2 5216 17207 8200 21874 15128 CSNK1G1-PITX2-RHOU 5258 16813 32518 47070 15599 FZD7-NKD1-PITX2 5310 12439 25127 40994 7486 FGF4-JUN-PITX2 5343 2634 32672 53764 32133 CCND1-NLK-PITX2 5399 39293 9478 4030 37469 FZD6-PITX2-SFRP1 5615 37130 25262 13890 9233 CXXC4-FGF4-PITX2 5669 13032 45784 50894 54142 AXIN1-FOXN1-PITX2 5682 1318 3400 19758 15375 FOSL1-PITX2-SFRP4 5766 29791 9666 5926 21290 FOSL1-NKD1-PITX2 5819 8607 19299 34454 29628 DKK1-PITX2-WNT2B 5967 20722 56765 57114 736 FZD5-PITX2-RHOU 5980 46930 21039 1256 11863 GSK3B-PITX2-SENP2 6007 41103 11874 39352 36153 FZD6-PITX2-TCF7L1 6019 6483 34081 5505 18404 CTBP1-FOXN1-PITX2 6078 7952 6550 21251 24027 FBXW2-GSK3A-PITX2 6113 23145 5408 17937 19874 EP300-GSK3B-PITX2 6131 11194 7972 26156 25577 CTBP1-FGF4-PITX2 6132 3149 40895 31072 24686 FRAT1-FZD2-PITX2 6168 56131 24624 14249 36492 AES-FZD2-PITX2 6222 26972 33042 43053 11722 FBXW11-GSK3A-PITX2 6249 47414 27591 23081 13112 FZD8-JUN-PITX2 6263 42057 38010 54749 2980 CXXC4-FZD2-PITX2 6270 7825 20641 14923 45220 PITX2-SFRP4-TLE2 6342 43420 38012 10662 35267 DIXDC1-FZD2-PITX2 6448 5815 17969 18298 39281 Table 1: Rankings of PITX2-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear immunoprecipitation and promoter-reporter assays further indicated the significant association of PITX2 with WNT2 and WNT5A promoters. Looking at the tables above, 7 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 APC-PITX2-SFRP4 6639 22831 16274 5172 51942 APC-PITX2-SENP2 2251 31790 24604 4114 39754 APC-PITX2-TCF7 5809 43852 29659 2608 54162 PITX2-PORCN-TLE2 13743 33091 10461 36155 54286 PITX2-PORCN-WNT4 9247 2492 36647 13332 52478 PITX2-PORCN-SENP2 9499 29209 4986 29421 35908 DVL2-JUN-PITX2 22623 16521 37051 52719 15020 FZD5-PITX2-SENP2 10435 42695 24116 3954 33353 APC-PITX2-PPP2CA 4042 33446 8698 18579 52910 APC-PITX2-RHOU 4699 39874 24475 1820 49384 PITX2-PORCN-WNT5A 11335 32674 6548 15458 54809 PITX2-PORCN-FBXW4 2782 19946 19676 35972 50951 DIXDC1-PITX2-SENP2 3537 43865 15972 13329 19669 CTNNBIP1-JUN-PITX2 55688 6273 51543 54725 26305 CCND1-FGF4-PITX2 55688 6273 51543 54725 26305 PITX2-PORCN-TCF7L1 13222 48332 9570 21227 51753 DIXDC1-PITX2-SFRP4 9005 33898 35036 1595 29334 PITX2-PORCN-WNT2B 6802 25276 16938 13140 54357 APC-PITX2-WNT4 6441 34135 28508 16023 43494 FRAT1-JUN-PITX2 28349 55075 50998 56838 16856 PITX2-PORCN-TLE1 13872 39019 23792 7146 28106 DKK1-JUN-PITX2 24208 3989 4050 56945 15274 AES-AXIN1-PITX2 37489 47814 10383 53313 22724 PITX2-PORCN-PPP2R1A 11355 50277 26063 28070 55628 PITX2-PORCN-RHOU 11795 30595 6426 8297 54722 CCND1-JUN-PITX2 44312 43519 25962 49672 2955 FOSL1-JUN-PITX2 42099 14135 52254 57017 24935 FZD6-PITX2-WNT2B 8135 7300 14987 7418 3456 FZD5-PITX2-SFRP4 8368 50438 38825 1203 52857 PITX2-PORCN-SFRP4 7652 26224 19994 9630 41059 CCND1-CTBP1-PITX2 7652 26224 19994 9630 41059 FSHB-FZD2-PITX2 11301 38653 1373 55358 36056 PITX2-WNT3-WNT5A 50071 36976 3198 23809 43096 CCND2-LRP6-PITX2 20931 44333 44558 56656 20738 PITX2-PORCN-SFRP1 20244 35446 37738 24843 55456 AES-EP300-PITX2 46927 53837 1549 50756 32506 FZD6-PITX2-SFRP4 7135 52408 16969 864 34132 PITX2-WNT3-WNT3A 36927 41437 49172 9526 14468 DAAM1-FOXN1-PITX2 1685 41262 42245 51064 684 CSNK2A1-JUN-PITX2 25321 4747 44298 56844 22732 FBXW11-LRP6-PITX2 29615 47349 39438 51084 16601 CCND1-CTNNBIP1-PITX2 17845 54257 2633 44741 19765 CSNK2A1-FOXN1-PITX2 1130 13168 44037 50356 32422 FOXN1-GSK3A-PITX2 35488 50787 34525 56639 52918 AXIN1-FZD6-PITX2 33737 44557 47717 57090 46710 FRZB-GSK3A-PITX2 5619 18480 55073 54146 46967 PITX2-WNT1-WNT5A 29674 16693 38632 17220 34621 BTRC-GSK3A-PITX2 2406 44730 43962 54217 10925 PITX2-SFRP4-WNT2B 13474 47608 14111 19231 2624 DAAM1-JUN-PITX2 35874 49308 2846 56449 4164 CXXC4-JUN-PITX2 5093 2871 54929 54382 25342 APC-PITX2-WNT3 18467 40797 31945 31204 47530 PITX2-PORCN-PPP2CA 9603 23189 295 19554 39138 DIXDC1-PITX2-WNT2B 12649 21037 9654 4112 8993 FBXW11-FOXN1-PITX2 661 3042 46901 46989 62 CSNK1D-FGF4-PITX2 21808 22200 7826 55044 47261 LRP5-PITX2-SFRP4 1850 34385 2623 13213 34281 DIXDC1-PITX2-WNT4 11062 47027 42885 4269 14148 FOSL1-GSK3A-PITX2 22118 26574 53921 57069 41599 FBXW11-JUN-PITX2 17945 27019 14279 54975 2329 CCND3-PITX2-WNT3A 14471 39233 2731 800 1147 CSNK2A1-MYC-PITX2 21651 30519 49254 52766 16814 EP300-FZD2-PITX2 21066 1261 6278 52068 50788 CSNK1D-FOXN1-PITX2 11143 1695 49037 55776 7145 FZD1-GSK3A-PITX2 6732 30000 53910 56520 34560 CCND3-PITX2-SFRP4 4452 50957 21986 3532 9719 DVL1-EP300-PITX2 56689 28520 27891 57038 12113 DAAM1-GSK3A-PITX2 1726 56240 42341 56628 12934 DKK1-PITX2-SFRP4 9818 37503 3735 2305 35936 GSK3B-PITX2-SFRP4 5309 55194 34830 18305 53111 FBXW2-JUN-PITX2 42532 23223 17767 54368 980 FRZB-FZD2-PITX2 22096 10208 42171 51487 54482 DIXDC1-PITX2-PPP2CA 5166 50281 13595 5982 18374 DAAM1-LRP6-PITX2 25969 54325 26609 56867 3176 FOSL1-FOXN1-PITX2 10188 3461 55891 51582 2726 CTNNB1-FOXN1-PITX2 7149 4991 55880 53565 3414 PITX2-WNT1-WNT2B 26078 12206 23538 5721 30071 CCND3-PITX2-SENP2 10221 40135 22112 6819 7030 FZD5-PITX2-WNT2B 22980 38933 9787 4035 21144 FZD7-GSK3A-PITX2 3127 14890 47575 57093 5868 AXIN1-EP300-PITX2 56749 23129 25963 57120 24869 FRAT1-GSK3A-PITX2 4495 57021 56892 56898 45139 CSNK1G1-FZD2-PITX2 45412 7430 10137 54602 39686 FOSL1-FZD2-PITX2 12121 784 39252 52428 46106 FBXW11-PITX2-SFRP4 8480 50287 2608 4536 27519 CSNK1G1-PITX2-SENP2 8978 31266 11421 7149 23975 PITX2-PYGO1-TLE2 1782 35079 27236 39307 56772 CTBP2-FOXN1-PITX2 18240 37720 54077 51182 7949 DVL1-FOXN1-PITX2 7131 54107 45985 52139 6298 CTBP1-JUN-PITX2 33380 1220 50964 56252 25801 PITX2-WNT1-WNT4 32926 5300 37141 2973 19943 DIXDC1-PITX2-RHOU 6079 35454 22214 14529 24323 FZD6-PITX2-TCF7 5172 16188 13820 2800 28962 DKK1-GSK3A-PITX2 605 17271 39751 55202 27215 FZD6-PITX2-SENP2 3363 52204 8127 5114 16199 APC-PITX2-SLC9A3R1 6853 5291 25242 18176 16828 FBXW11-PITX2-WNT2B 30130 56623 1327 7485 2572 DIXDC1-PITX2-TCF7 4373 37581 13658 8585 32638 CSNK1D-PITX2-SFRP4 4175 45358 33459 4847 37993 FZD5-CCND3-PITX2 40000 10437 46397 54792 20187 FZD6-PITX2-WNT2 10709 28286 1099 25993 43215 AES-FOXN1-PITX2 3577 24818 43679 53324 2571 CSNK1G1-PITX2-RHOU 11965 12955 21369 13669 45243 FZD7-NKD1-PITX2 25856 8298 48445 57028 4035 FGF4-JUN-PITX2 24971 2275 32263 54277 17002 CCND1-NLK-PITX2 30491 29337 45690 39544 1454 FZD6-PITX2-SFRP1 18690 52116 9763 7836 11500 CXXC4-FGF4-PITX2 3350 14873 39377 55805 47209 AXIN1-FOXN1-PITX2 17522 6988 53149 55878 9496 FOSL1-PITX2-SFRP4 7348 5890 31972 1744 49355 FOSL1-NKD1-PITX2 29467 27288 56470 57104 13679 DKK1-PITX2-WNT2B 17111 13223 40502 378 15000 FZD5-PITX2-RHOU 12500 51905 7871 1962 44656 GSK3B-PITX2-SENP2 915 34496 33084 22723 32507 FZD6-PITX2-TCF7L1 4289 24535 11228 6141 16611 CTBP1-FOXN1-PITX2 8239 9962 54422 50573 10742 FBXW2-GSK3A-PITX2 13991 18085 38156 55688 24970 EP300-GSK3B-PITX2 22813 7384 28301 49131 16578 CTBP1-FGF4-PITX2 24027 10442 12158 56632 50733 FRAT1-FZD2-PITX2 19475 56951 30336 56309 51026 AES-FZD2-PITX2 56089 10520 10321 45652 34757 FBXW11-GSK3A-PITX2 6618 46116 51128 49797 28514 FZD8-JUN-PITX2 40592 40343 33795 57114 7221 CXXC4-FZD2-PITX2 28941 8301 39688 54135 51166 PITX2-SFRP4-TLE2 23954 41848 2647 36476 20017 DIXDC1-FZD2-PITX2 15533 7397 34069 54461 17799 Table 2: Rankings of PITX2-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf one finds the following combinations for member of WNT family along with PITX2, to be prominent at 3rd order level - PITX2-PORCN-WNT4, PITX2-PORCN-WNT5A, APC-PITX2-WNT4, PITX2-WNT3-WNT5A, PITX2-WNT1-WNT5A, PITX2-SFRP48 RANKING @tiUSING SOBOL - 2002 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 APC-PITX2-SFRP4 17003 19660 7752 22464 43680 APC-PITX2-SENP2 16777 21369 5264 21757 43696 APC-PITX2-TCF7 19670 34554 8057 26773 38941 PITX2-PORCN-TLE2 14738 34228 17868 7003 24689 PITX2-PORCN-WNT4 38340 23219 45866 44679 30684 PITX2-PORCN-SENP2 49351 13297 36355 31422 8016 DVL2-JUN-PITX2 23671 1038 12434 27999 54466 FZD5-PITX2-SENP2 521 47250 5679 3657 50275 APC-PITX2-PPP2CA 24251 10201 10127 26604 27627 APC-PITX2-RHOU 39285 21142 46215 32608 9407 PITX2-PORCN-WNT5A 4366 18564 14041 19978 22471 PITX2-PORCN-FBXW4 8808 13705 22864 22147 31748 DIXDC1-PITX2-SENP2 55978 6920 46363 55209 16814 CTNNBIP1-JUN-PITX2 11329 1937 10201 6114 40219 CCND1-FGF4-PITX2 43513 2928 44305 52341 16554 PITX2-PORCN-TCF7L1 7523 29695 12381 16214 18408 DIXDC1-PITX2-SFRP4 46369 10535 43650 52909 13347 PITX2-PORCN-WNT2B 9536 5794 12824 18961 17911 APC-PITX2-WNT4 24477 25329 3199 26367 36930 FRAT1-JUN-PITX2 19630 54721 9834 10848 22067 PITX2-PORCN-TLE1 49615 27631 44758 40897 38885 DKK1-JUN-PITX2 2939 11664 23494 19389 44598 AES-AXIN1-PITX2 47687 38614 55070 30813 9874 PITX2-PORCN-PPP2R1A 10644 13926 20214 8562 45301 PITX2-PORCN-RHOU 7818 43749 20769 25705 49200 CCND1-JUN-PITX2 17592 41812 11511 4995 53682 FOSL1-JUN-PITX2 29544 47341 44123 52018 7644 FZD6-PITX2-WNT2B 42547 47083 32974 29428 5335 FZD5-PITX2-SFRP4 2340 11183 13226 1835 33599 PITX2-PORCN-SFRP4 52035 24948 36616 49778 2115 CCND1-CTBP1-PITX2 47450 37599 38364 47623 15808 FSHB-FZD2-PITX2 21425 53181 12066 7803 49923 PITX2-WNT3-WNT5A 3631 37403 19670 4320 50237 CCND2-LRP6-PITX2 45303 45054 55240 46174 9660 PITX2-PORCN-SFRP1 5118 32289 20516 7388 55055 AES-EP300-PITX2 27429 13782 22774 24073 54041 FZD6-PITX2-SFRP4 2191 34024 23773 8678 52481 PITX2-WNT3-WNT3A 1072 29636 4611 11649 49643 DAAM1-FOXN1-PITX2 23402 15789 15327 5498 42400 CSNK2A1-JUN-PITX2 4226 47140 759 5831 41428 FBXW11-LRP6-PITX2 19674 55920 14183 7236 52984 CCND1-CTNNBIP1-PITX2 23479 13649 20332 26184 43389 CSNK2A1-FOXN1-PITX2 484 10646 14993 25101 56105 FOXN1-GSK3A-PITX2 55917 8017 43971 38630 16813 AXIN1-FZD6-PITX2 45899 20191 43656 43529 4707 FRZB-GSK3A-PITX2 42536 49066 41808 51663 3945 PITX2-WNT1-WNT5A 34 29476 27919 8439 25717 BTRC-GSK3A-PITX2 53128 50908 30242 52659 1281 PITX2-SFRP4-WNT2B 7927 31067 16874 24744 41200 DAAM1-JUN-PITX2 24371 14681 11567 17251 47118 CXXC4-JUN-PITX2 7081 3972 8713 3640 32183 APC-PITX2-WNT3 14234 12446 706 24449 41729 PITX2-PORCN-PPP2CA 48624 10701 36145 29228 15037 DIXDC1-PITX2-WNT2B 3174 55687 15258 13757 29932 FBXW11-FOXN1-PITX2 13141 28980 22463 8005 34303 CSNK1D-FGF4-PITX2 45761 16034 33072 48233 21295 LRP5-PITX2-SFRP4 315 27436 8203 2763 45221 DIXDC1-PITX2-WNT4 44341 8459 33406 35610 21988 FOSL1-GSK3A-PITX2 3336 36071 6692 8964 29002 FBXW11-JUN-PITX2 27953 2910 15908 22 55248 CCND3-PITX2-WNT3A 34394 29164 30661 48295 16862 CSNK2A1-MYC-PITX2 9129 7731 935 12301 36666 EP300-FZD2-PITX2 24012 15242 9973 25729 44122 CSNK1D-FOXN1-PITX2 18384 31000 27911 15993 34137 FZD1-GSK3A-PITX2 49460 16018 43507 46060 9217 CCND3-PITX2-SFRP4 22350 19459 24189 16717 42599 DVL1-EP300-PITX2 548 36053 11918 25848 49131 DAAM1-GSK3A-PITX2 40753 11421 43484 37867 5004 DKK1-PITX2-SFRP4 694 29442 14079 22614 54046 GSK3B-PITX2-SFRP4 14898 11432 9059 22640 47560 FBXW2-JUN-PITX2 12579 4618 17745 364 46971 FRZB-FZD2-PITX2 35229 41345 36872 51138 49950 DIXDC1-PITX2-PPP2CA 53041 37364 46121 33605 10550 DAAM1-LRP6-PITX2 16446 14829 15814 16673 38836 FOSL1-FOXN1-PITX2 54512 5376 32845 52595 9349 CTNNB1-FOXN1-PITX2 29063 19206 49013 56402 27258 PITX2-WNT1-WNT2B 3768 50433 24960 15608 43963 CCND3-PITX2-SENP2 22323 19475 21774 24829 24809 FZD5-PITX2-WNT2B 45840 6879 31831 55937 11210 FZD7-GSK3A-PITX2 8237 8741 24973 13187 10820 AXIN1-EP300-PITX2 1837 53367 4684 5496 23397 FRAT1-GSK3A-PITX2 44421 52054 29767 47337 1646 CSNK1G1-FZD2-PITX2 4443 9218 19882 21920 41937 FOSL1-FZD2-PITX2 18628 35229 27305 27474 41987 FBXW11-PITX2-SFRP4 22007 13276 18287 6972 23461 CSNK1G1-PITX2-SENP2 42929 46890 54375 42726 15165 PITX2-PYGO1-TLE2 19850 10379 18180 6093 40940 CTBP2-FOXN1-PITX2 12690 32085 14231 16779 36765 DVL1-FOXN1-PITX2 13716 11451 12180 2594 46581 CTBP1-JUN-PITX2 24353 53693 13796 3746 36415 PITX2-WNT1-WNT4 55244 8137 33549 51863 7332 DIXDC1-PITX2-RHOU 1183 50113 10813 1973 40351 FZD6-PITX2-TCF7 58 54592 26110 20224 55626 DKK1-GSK3A-PITX2 51992 863 44516 56355 32287 FZD6-PITX2-SENP2 432 817 17937 22896 56866 APC-PITX2-SLC9A3R1 17574 24386 9813 27607 44761 FBXW11-PITX2-WNT2B 29169 24449 32207 29680 32687 DIXDC1-PITX2-TCF7 53422 53152 36175 42927 22338 CSNK1D-PITX2-SFRP4 26609 44292 24260 17256 33381 FZD5-CCND3-PITX2 19393 32161 13355 11683 5330 FZD6-PITX2-WNT2 14637 10126 24195 27724 51796 AES-FOXN1-PITX2 17914 21798 703 10325 20162 CSNK1G1-PITX2-RHOU 14243 10287 2792 14397 41970 FZD7-NKD1-PITX2 1376 4501 11215 16178 40845 FGF4-JUN-PITX2 18457 36152 1440 2969 44768 CCND1-NLK-PITX2 48102 11112 41884 52866 812 FZD6-PITX2-SFRP1 56728 56346 39190 34205 286 CXXC4-FGF4-PITX2 38294 56427 50581 38505 7533 AXIN1-FOXN1-PITX2 4350 36135 20767 6550 49005 FOSL1-PITX2-SFRP4 48140 54056 50405 43960 31198 FOSL1-NKD1-PITX2 9221 29087 12816 22289 29068 DKK1-PITX2-WNT2B 54626 45844 39615 30595 28144 FZD5-PITX2-RHOU 55488 4203 52989 44916 13289 GSK3B-PITX2-SENP2 16336 29784 11616 16048 44166 FZD6-PITX2-TCF7L1 57098 2574 31025 36904 1546 CTBP1-FOXN1-PITX2 8046 12489 6826 22448 30443 FBXW2-GSK3A-PITX2 36714 12730 37356 49810 4808 EP300-GSK3B-PITX2 26038 11762 5959 1368 52250 CTBP1-FGF4-PITX2 41855 4408 56680 38243 15293 FRAT1-FZD2-PITX2 55832 24730 44050 40886 5856 AES-FZD2-PITX2 29806 34809 44098 30337 5206 FBXW11-GSK3A-PITX2 35583 52800 48903 44758 21694 FZD8-JUN-PITX2 14227 28361 22535 6380 50233 CXXC4-FZD2-PITX2 49278 49869 33082 55290 10056 PITX2-SFRP4-TLE2 16042 46434 18733 25251 47254 DIXDC1-FZD2-PITX2 7897 43672 18332 7315 28673 Table 3: Rankings of PITX2-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - SOBOL; Implementation - 2002 WNT2B, CCND3-PITX2-WNT3A, PITX2-WNT1-WNT2B, FZD5-PITX2-WNT2B, PITX2-WNT1-WNT4, FBXW11-PITX2-WNT2B, FZD6-PITX2-WNT2, PITX2-PORCNWNT2B, FZD6-PITX2-WNT2B, PITX2-WNT3-WNT3A, APC-PITX2-WNT3, DIXDC19