ras homolog family member U / Wnt-1 responsive Cdc42 homolog (RHOU/WRCH1) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

ras homolog family member U / Wnt-1 responsive Cdc42 homolog (RHOU/WRCH1) : 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 RHOU (orWRCH1) is a small 21 kDa signaling guanine nucleotide-binding protein (G protein), belonging to the class of GTPase (hydrolase enzymes that bind to the nucleotide guanosine triphosphate (GTP) and hydrolyze it to guanosine diphosphate (GDP)), and is a member of the Rho family of GTPases (a subfamily of Rat sarcoma virus or Ras superfamily). 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 RHOU related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for RHOU-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 RHOU/WRCH1 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 13, 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 RHOU related combinations using individual gene expressions measured in time, in WNT3A stimulated HEK 293 cells. 2. Introduction The details of the machine learning based search engine has been recently published in Sinha [2] and deployed to explore the 2nd order combinations of genes in the data set provided by Gujral and MacBeath [1]. Nevertheless, here, I point to the fundamentals of the published work for completeness. 2.1. A combinatorial problem Sensitivity analysis plays a major role in computing the strength of the influence of involved factors in any phenomena under investigation. When applied to expression profiles of various intra/extracellular factors that form an integral part of a signaling pathway, the variance and density based analysis yields a range of sensitivity indices for individual as well as various combinations of factors. These combinations denote the higher order interactions among the involved factors. Computation of higher order interactions is often time consuming but it gives a chance to explore the various combinations that might be of interest in the working mechanism of the pathway. For example, in a range of fourth order combinations among the various factors of the Wnt pathway, it would be easy to assess the influence of the destruction complex formed by APC, AXIN, CSKI and GSK3 interaction. But the effect of these combinations vary over time as measurements of fold changes and deviations in fold changes vary. So it is imperative to know how an interaction or a combination of the involved factors behave in time and Sinha [2] develops a procedure to track the behaviour by exploiting the influences of these involved factors. 2 2.2. A possible solution In this work, after estimating the individual effects of factors for a higher order combination, the individual indices are considered as discriminative features. A combination, then, is a feature set in higher order (≥2 ,i.e multivariate). With an excessively large number of factors involved in the pathway, it is difficult to search for important combinations in a wide search space over different orders. Exploiting the analogy with the issues of prioritizing webpages using ranking algorithms, for a particular order, a full set of combinations of interactions can then be prioritized based on these features using a powerful ranking algorithm via support vectors Joachims [3]. Recording the changing rankings of the combinations over time reveals how higher order interactions behave within the pathway and when an intervention might be necessary to influence the interaction within the pathway. 2.3. ras homolog family member U / Wnt-1 responsive Cdc42 homolog (RHOU/WRCH1) RHOU (orWRCH1) is a small 21 kDa signaling guanine nucleotide-binding protein (G protein), belonging to the class of GTPase (hydrolase enzymes that bind to the nucleotide guanosine triphosphate (GTP) and hydrolyze it to guanosine diphosphate (GDP)), and is a member of the Rho family of GTPases (a subfamily of Rat sarcoma virus or Ras superfamily). The transition of guanine nucleotide binding proteins between the ’on’ (GTP-bound) and ’off’ (GDP-bound) states is a paradigm of molecular switching after a chemical reaction. Stouten et al. [4] try to provide a picture of the process of the mechanism by which the switch signal is transmitted to the downstream recipients in the intracellular signal pathway, though it has been extensively studied by biochemical, biophysical and genetic methods. Based on the similarities of ras-p21 and elongation factor Tu, they proposed a model of the GDP state of ras-p21 that was in agreement with all relevant experimental evidence. Their model provided important clues about: (1) a possible molecular mechanism for signal transmission from the site of GTP hydrolysis to downstream effectors; (2) a major conformational change during signal generation and a key residue involved in this process i.e Tyr-64; and (3) regions in ras-p21 that could be differentially recognized by binding to external partners in a GTP/GDP state dependent fashion, most notably residues D69, Q70, R73, T74, R102, K104, D105 at the end of the α-helices 2 and 3. GTPases of the Rho family play important roles in converting and amplifying external signals into cellular effects. Not only do they control the dynamics of the F-actin cytoskeleton, they have also been implicated in many basic cellular processes that influence cell proliferation, differentiation, motility, adhesion, survival, or secretion. To elucidate the evolutionary history of the Rho family, Boureux et al. [5] analyzed over 20 species covering major eukaryotic clades from unicellular organisms to mammals, and reconstructed the ontogeny and the chronology of emergence of the different subfamilies. Their data established that the 20 mammalian Rho members are structured into 8 subfamilies, among which Rac is the founder of the whole family. Rho, Cdc42, RhoUV, and RhoBTB subfamilies appeared before Coelomates and RhoJQ, Cdc42 iso3 forms, RhoDF, and Rnd emerged in chordates. Their analysis of Rho mRNA expression patterns in mouse tissues showed that subfamilies had tissue-specific and low-level expression that supported their implication only in narrow time windows or in differentiated metabolic functions. The Rho family of GTPases is a subfamily of the Rat sarcoma virus (RAS) superfamily. In the course of routine passage of Moloney’s leukemogenic virus (MLV), Harvey [6] collected plasma from a leukemic rat (Chester Beatty Institute outbred albino strain) which had been inoculated with MLV-containing mouse plasma when newborn. After storage at 70◦C for three months, they diluted the rat plasma 1 in 30 with Hanks’s saline and passed through a ’Selas 02’ filter, tested and found it impervious to Esch. coli. The filtrate was injected into 15 new-born BALB/c mice, for potency test and they reported that only 6 survived to weaning and on the 32nd day, 5 had tumours at or near the injection site, and all had grossly enlarged spleens. This was identified as the beginning of RAS research. Three additional retroviruses were identified, i.e • Kirsten and Mayer [7] passed mouse erythroblastosis virus (MEV) to newborn W/Fu rats. They observed that the rats developed generalized malignant lymphomas after 6-7 months. Two separate serial cell-free passage sedes were initiated. Rat lymphomas induced erythroblastosis in less than 20% of the rats that died within 4 weeks after inoculation. The surviving rats remained apparently healthy for months until they died from lymphomas. Inoculation of newborn C3Hf/Gs mice with the same filtrates caused only lymphomas in 3550% of the mice after 38 months. •Peters et al. [8] identified naturally occurring sarcoma virus of the BALB/cCr mouse; and •Rasheed et al. [9] observed that a Sprague-Dawley (SD-1) rat embryo culture, at low passage level, released an endogenous ecotropic type C virus (SD-RaLV) and after about 20 further passages it underwent spontaneous transformation. The SD-RaLV, released from the transformed cells, did not cause rapid transformation of other rat embryo cells, but, when the transformed cells were repeatedly cocultivated with three different chemically transformed and serially transplanted rat tumor cell lines (sarcoma, carcinoma, and hepatoma), rapidly fibroblast-transforming ”sarcoma” viruses (RaSV) were recovered after each attempt. The productive clones were found to be positive for rat specific p30 antigen and the RaSVs released were serially transmitted to other rat embryo cells. RaSV genome was rescued from the nonproductive clones by superinfection with SDRaLV, wild rat type C virus, and several heterologous type C viruses. Their findings pointed to naturally occurring transformation-specific (src) genes being recovered in vitro in the form of stable ”sarcoma” viruses. Malumbres and Barbacid [10] sumarise the developments related to the first 30 years of research regarding RAS. A survey of RAS mutations in cancer can be found in Prior et al. [11]. Tao et al. [12] reported the isolation and cloning of the WNT-1 responsive Cdc42 homolog (WRCH1) cDNA, whose mRNA level increased in response to WNT-1 signaling in WNT-1 transformed cells, WNT-1 transgene induced mouse mammary tumors, and WNT-1 retrovirus infected cells. To confirm that WRCH1 was regulated by WNT-1 signaling, they infected C57MG cells with either an empty retroviral vector or a WNT-1-expressing retrovirus. WRCH1 mRNA was found to be up-regulated more than fourfold in C57MG/WNT-1 cells versus C57MG/vector cells. Further, overexpression of WRCH1 phenocopied WNT-1 in morphological transformation of mouse mammary epithelial cells. To identify if WRCH1 was a homolog of the Rho family 4 ofGTPases, they cloned full-length mouse and human WRCH1 cDNAs, based on the partial sequence of mouse WRCH1 cDNA isolated from PCR-select cDNA subtraction. They obserevd that the cDNAs of human and mouse WRCH1 encoded proteins of 258 and 261 amino acid residues, respectively, which are 92% identical. Their analysis of the deduced amino acid sequence of WRCH1 identified it as a homolog of the Rho family of GTPases. The human WRCH1 protein shared 57% identity and 70% similarity with Cdc42, and 30%-55% similarity with other members of the Rho family. It was observed that both human and mouse WRCH1 contained GTP and GDP binding domains, the effector domain, and a CAAX lipid modification signal at their C termini, all of which were conserved among most members of the Rho family, as documented in Ridley [13]. Like Cdc42, they found that WRCH1 could activate PAK-1 and JNK-1, and induce filopodium formation and stress fiber dissolution. I present 3rd order combinations of RHOU 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 [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 5 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 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 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]. 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 RHOU-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 RHOU-X-X combinations A total of 2415, 3rd order combinations involving RHOU were obtained from a full set of 71C3= 57155 combinations. Further, from this selected set, using the above criteria 7 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-RHOU-X combinations We know from the above literature that WNT1 up-regulates WRCH1/RHOU. Looking at the tables above, one finds the following combinations for members of WNT family along with RHOU, to be prominent at 3rd order level - LRP6-RHOU-WNT2B, FBXW11-RHOU-WNT2B, RHOU-SLC9A3R1-WNT4, LRP6-RHOU-WNT2, EP300RHOU-WNT2, RHOU-WNT1-WNT4, LRP6-RHOU-WNT5A, RHOU-SFRP1-WNT4 and GSK3B-RHOU-WNT2. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 6.3.2. Examining the behaviour of FZD-RHOU-X combinations It is also known that the WNT signaling pathways are activated by the binding of a WNT-protein ligand to a Frizzled family receptor (FZD), which passes the biological signal to the Dishevelled (DVL) protein inside the cell. Looking at the tables above, one finds the following combinations for members of FZD family along with RHOU, to be prominent at 3rd order level - FZD5-JUN-RHOU, FZD5-CCND2-RHOU, FZD1PORCN-RHOU, FZD2-NKD1-RHOU, APC-FZD6-RHOU, FZD5-GSK3A-RHOU, FZD1NKD1-RHOU, FSHB-FZD2-RHOU, CXXC4-FZD2-RHOU, FZD8-GSK3A-RHOU, FZD1-FZD2-RHOU, FZD8-LRP6-RHOU, FZD7-NKD1-RHOU, CXXC4-FZD7-RHOU, FRZB-FZD2-RHOU, FZD5-NKD1-RHOU, CTNNBIP1-FZD2-RHOU, FZD7-PORCNRHOU, FZD5-LRP6-RHOU, AXIN1-FZD2-RHOU and FZD1-GSK3A-RHOU. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 6.3.3. Examining the behaviour of DVL-RHOU-X combinations Again, it is also known that the WNT signaling pathways are activated by the binding of a WNT-protein ligand to a Frizzled family receptor (FZD), which passes the biological signal to the Dishevelled (DVL) protein inside the cell. Looking at the tables above, one finds the following combinations for members of DVL family along with RHOU, to be prominent at 3rd order level - AXIN1-DVL1-RHOU, DVL1-FBXW11RHOU, DKK1-DVL2-RHOU, DVL2-FGF4-RHOU, DVL1-LRP6-RHOU, CXXC4DVL2-RHOU, DVL1-FOXN1-RHOU, DVL1-RHOU-TCF7 and CTNNBIP1-DVL2RHOU. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 8 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 FBXW11-LRP6-RHOU 11 53077 50648 30258 27900 CCND1-FGF4-RHOU 77 55663 35981 27067 10821 FZD5-JUN-RHOU 105 12942 56571 25707 3718 CTNNBIP1-JUN-RHOU 119 11333 54553 37428 52492 CSNK1D-FGF4-RHOU 137 7470 45846 49163 20155 DAAM1-LRP6-RHOU 160 47568 49021 54157 20385 CCND2-LRP6-RHOU 195 23197 17269 56080 2265 DKK1-JUN-RHOU 210 3670 42736 27568 47765 AXIN1-DVL1-RHOU 314 6052 39138 50246 11753 APC-PITX2-RHOU 397 38592 32191 27698 15148 DKK1-LRP6-RHOU 401 7782 55096 29348 20780 FZD8-LRP6-RHOU 468 41362 6887 53473 47929 CTNNB1-FOXN1-RHOU 475 856 5984 14676 48295 CSNK2A1-MYC-RHOU 501 22087 50879 39343 4386 LRP6-RHOU-WNT2B 521 21284 29060 52854 25865 AES-AXIN1-RHOU 524 50360 32314 44626 11228 CXXC4-FGF4-RHOU 583 24551 34633 53319 56248 FBXW2-RHOU-TCF7 658 32560 43438 3752 18218 FZD5-CCND2-RHOU 694 44791 4209 21405 30546 CXXC4-DVL2-RHOU 703 7173 6556 19343 52966 EP300-GSK3B-RHOU 762 29861 9716 10624 2207 FBXW11-RHOU-SENP2 810 39829 54582 1076 13192 FOSL1-PPP2R1A-RHOU 846 41555 5035 55239 46031 CXXC4-JUN-RHOU 881 1789 43156 41625 53423 FBXW11-RHOU-WNT2B 887 56605 51928 47819 44859 GSK3B-RHOU-TLE2 898 47931 45636 21326 13471 FSHB-NKD1-RHOU 974 40540 14067 9128 35039 CCND1-PYGO1-RHOU 1040 56164 34165 35225 53648 GSK3B-LRP6-RHOU 1052 31885 19160 38602 12879 FRAT1-PORCN-RHOU 1077 31453 10861 21530 17749 FZD1-PORCN-RHOU 1095 21176 12741 16941 18130 EP300-RHOU-WNT2 1132 42400 48712 18390 28303 GSK3B-RHOU-TCF7 1149 7136 32592 11483 26116 BCL9-FGF4-RHOU 1153 22570 51717 42895 26298 CTBP1-FGF4-RHOU 1171 15515 48677 31280 24137 RHOU-WNT1-WNT4 1198 602 1780 21941 43967 CTBP2-GSK3B-RHOU 1205 55707 18585 4716 40362 PITX2-PORCN-RHOU 1220 38816 23756 29958 13324 GSK3B-RHOU-SENP2 1230 39467 21376 11806 9365 CXXC4-FOXN1-RHOU 1258 949 4951 19719 52102 BCL9-PORCN-RHOU 1284 46597 6968 29490 21809 CSNK1A1-LRP6-RHOU 1294 10065 15184 54599 10820 CSNK1G1-PORCN-RHOU 1299 27191 33972 15284 20376 FZD7-NKD1-RHOU 1307 26801 3329 51286 46329 FZD2-NKD1-RHOU 1310 19610 4807 33843 1134 AXIN1-EP300-RHOU 1312 1646 32903 47413 5408 FOSL1-PORCN-RHOU 1333 44749 10281 23020 23848 CTNNBIP1-FGF4-RHOU 1375 44903 56902 26308 45676 DVL1-FBXW11-RHOU 1388 30499 7484 11321 46544 DVL1-FOXN1-RHOU 1438 38257 4549 11910 29038 APC-FZD6-RHOU 1482 46230 8189 40700 5636 AXIN1-FOXN1-RHOU 1511 738 4253 15602 21213 FBXW11-RHOU-SFRP4 1516 48741 46254 2195 24642 DKK1-FGF4-RHOU 1553 5607 24412 21107 41674 KREMEN1-RHOU-TCF7 1573 55772 27141 223 46704 CSNK1G1-FOXN1-RHOU 1587 4796 8477 31603 16974 BCL9-JUN-RHOU 1653 6622 56085 44704 6331 FOSL1-FOXN1-RHOU 1660 21880 3384 19296 29104 DKK1-RHOU-SENP2 1744 25698 53164 542 50407 CXXC4-FZD7-RHOU 1774 20795 27044 52150 54907 DIXDC1-NKD1-RHOU 1798 6195 3765 22405 3157 FBXW11-GSK3B-RHOU 1864 39036 24146 19812 16311 DKK1-DVL2-RHOU 1867 1810 33595 42349 53523 FRZB-GSK3B-RHOU 1880 22893 26634 12199 52276 CSNK1G1-JUN-RHOU 1898 1165 55257 34817 23988 FRZB-FZD2-RHOU 1944 892 20805 28505 49730 DAAM1-FOXN1-RHOU 1998 39331 29857 17353 20914 DVL1-RHOU-TCF7 2030 52920 36405 7523 7698 LRP5-PORCN-RHOU 2053 8242 9590 48746 20172 FZD5-NKD1-RHOU 2086 9792 3471 18764 2521 FZD5-GSK3A-RHOU 2110 29982 2718 17049 4051 JUN-PYGO1-RHOU 2122 21105 6824 25993 11386 FZD1-NKD1-RHOU 2176 20088 11316 49737 2429 RHOU-TCF7-TLE2 2188 38946 13808 2888 33725 FSHB-FZD2-RHOU 2193 41442 55751 28895 48790 FRZB-GSK3A-RHOU 2205 2231 3514 26794 25129 CTBP1-GSK3A-RHOU 2252 6219 1718 35013 4228 CXXC4-GSK3A-RHOU 2262 20534 4082 47103 49826 DKK1-PYGO1-RHOU 2300 4971 25047 37502 11114 DKK1-FOXN1-RHOU 2310 27439 38761 12307 33517 CXXC4-FZD2-RHOU 2317 6671 22273 26084 55079 CSNK1G1-NKD1-RHOU 2328 3565 14141 34128 1880 FZD8-GSK3A-RHOU 2345 48981 3671 53392 35952 LRP6-RHOU-WNT5A 2371 52871 42173 56381 27277 DKK1-GSK3A-RHOU 2372 2731 45043 25134 42183 CTNNBIP1-FZD2-RHOU 2379 32067 25451 19277 52045 DVL2-FGF4-RHOU 2435 40706 45840 38213 42586 FZD7-PORCN-RHOU 2438 54301 6262 19661 38352 RHOU-SLC9A3R1-WNT4 2468 14726 19963 23342 24539 DAAM1-GSK3A-RHOU 2493 51743 28750 45637 28520 FRZB-LRP6-RHOU 2562 9229 2215 54525 26580 CTNNBIP1-DVL2-RHOU 2585 40458 19092 23270 50147 FBXW11-FOXN1-RHOU 2589 20834 7791 16907 24143 RHOU-SFRP1-WNT4 2662 39129 39941 42257 16102 DVL1-LRP6-RHOU 2680 50479 18313 55087 36829 FSHB-GSK3A-RHOU 2698 43462 34330 18933 10698 FZD1-FZD2-RHOU 2705 42439 38341 30031 28378 DKK1-PORCN-RHOU 2715 27097 49203 3892 51823 CCND3-PORCN-RHOU 2736 51197 20602 16051 28331 GSK3B-RHOU-WNT2 2741 33291 48297 6678 23276 FRZB-PORCN-RHOU 2754 2260 14728 21581 34283 FBXW2-RHOU-SENP2 2810 46432 53903 6485 38309 CTNNBIP1-LEF1-RHOU 2851 53935 15418 28550 56338 CSNK1D-FOXN1-RHOU 2891 4517 7734 29359 18640 CTNNBIP1-FRAT1-RHOU 2910 38029 54971 19935 51723 CTBP2-LRP6-RHOU 3030 56710 12170 56649 31539 FBXW11-FGF4-RHOU 3056 50852 55649 31582 13375 FZD5-LRP6-RHOU 3179 36603 10552 23856 22468 CSNK1G1-GSK3B-RHOU 3190 3405 4726 1433 8406 CTNNBIP1-NKD1-RHOU 3194 27112 11412 35287 15481 BTRC-RHOU-TCF7 3204 41293 40925 4745 45576 AXIN1-FZD2-RHOU 3216 31244 38793 27939 11583 CSNK1G1-DIXDC1-RHOU 3247 13611 55894 17887 29476 CSNK1G1-GSK3A-RHOU 3261 12094 4223 43874 25027 DAAM1-JUN-RHOU 3292 50276 41716 52344 40041 FBXW2-RHOU-SFRP4 3317 44736 54923 11444 31855 CTNNBIP1-NLK-RHOU 3322 501 7291 43407 48933 DIXDC1-JUN-RHOU 3325 2215 36161 42538 1991 BTRC-RHOU-FBXW4 3368 55758 50831 743 47356 CTNNBIP1-PORCN-RHOU 3494 46942 8439 8140 23879 FRZB-NKD1-RHOU 3499 2171 5014 35449 27330 FZD1-GSK3A-RHOU 3616 49363 7865 50000 3642 LRP6-RHOU-WNT2 3651 45818 48676 55006 6351 APC-GSK3A-RHOU 3658 24361 6768 42843 11981 DAAM1-FGF4-RHOU 3669 42155 55076 53871 14927 DIXDC1-GSK3A-RHOU 3688 25193 1738 30131 17732 Table 1: Rankings of RHOU-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear 9