SUMO1/sentrin/SMT3 specific peptidase 2 (SENP2/AXAM2) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

SUMO1/sentrin/SMT3 specific peptidase 2 (SENP2/AXAM2) : 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 SENP2 is cysteine protease that belongs to the family of sentrin-specific protease, which come under the broader group of SUMO-specific isopeptidases and proteases. The ubiquitin-like SUMO (small ubiquitin-related modifier) system is a post-translational protein modification pathway in eukaryotes, where SUMOylation is a highly dynamic process and deconjugation (deSUMOylation) is catalyzed by a family of cysteine proteases, termed SUMO-specific proteases or SUMO isopeptidases. SENP2 processes newly synthesized SUMO1 into the conjugatable form and catalyze the deconjugation of SUMO1-containing species. 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 SENP2 related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for SENP2-X-X combinations, which point to existence of biological synergy of some of these combinations across the different sensitivity methods; and • study the behaviour of some of these combinations related to WNT3A response genes that are ranked by the machine learning search engine (Sinha [2]) in time. Patterns of combinations emerge, some of which have been tested in wet lab, while others require further wet lab analysis. ITime behavioural study of 3-odr SENP2 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 10, 2025 Keywords: Sensitivity analysis, Support vector ranking, Hilbert Schmidt Independence Criterion indices (HSIC) and Sobol indicies, WNT3A 1. Significance Sinha [2] recently demonstrated the use of machine learning based search engine to rank/reveal gene combinations at 2nd order for the time series data by Gujral and MacBeath [1] and showed how it is possible to locate combinations of priority that might be working synergistically, using sensitivity methods and powerful support vector ranking algorithm. However, the problem explodes combinatorially with even a small set of 71 recorded genes in the study by Gujral and MacBeath [1], when one steps to explore 3rd order combinations. With the total number of 71C3(= 57155) combinations, it becomes nearly impossible for any biologist to study the system wide dynamics of any pathway. Also, the amount of time usually needed to search for and test a combination is far more than the search down by the machine learning based search engine. Here, I extend the research work by Sinha [2] to conduct a behavioral study of 3rd order SENP2 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. SUMO1/sentrin/SMT3 specific peptidase 2 (SENP2) Posttranslational modification with small ubiquitin-related modifier (SUMO) proteins is a key regulatory protein modifications in eukaryotic cells where, proteins involved in processes like chromatin organization, transcription, DNA repair, macromolecular assembly, protein homeostasis, trafficking, and signal transduction are subject to reversible sumoylation. Flotho and Melchior [4] summarize basic mechanisms and highlight recent developments in the physiology of sumoylation. Gareau and Lima [5] elucidate an understanding of SUMO regulatory mechanisms which might lead to improved approaches for analysing the function of SUMO and substrate conjugation in distinct cellular pathways. In a summary on SENPs, Nayak and Muller [6] state that the known SUMO-specific isopeptidases and proteases are cysteine proteases that are classified into three distinct families: •the Ulp/SENP (ubiquitin-like protease/sentrin-specific protease) family, •the Desi (deSUMOylating isopeptidase) family and •USPL1 (ubiquitin-specific peptidase-like protein 1). Briefly, Gareau and Lima [5] elucidate the SUMO conjugation cycle in a few steps, which i reiterate for completeness (For graphical understanding please see figure 1 in Gareau and Lima [5]). •SUMO undergoes processing by Ulps and SENPs to its mature form, thus revealing a carboxy-terminal Gly-Gly motif. •SUMO is then adenylated by the SUMO-activating enzyme subunit 1 (SAE1)-ubiquitin-like activating enzyme subunit 2 (UBA2) E1 complex in an ATP◦Mg2+-dependent reaction and transferred to the catalytic Cys of the UBA2 subunit; •Following activation, SUMO is transferred to the catalytic Cys of the E2 conjugating enzyme, ubiquitin-like conjugating enzyme 9 (UBC9). •It can then catalyze conjugation to a substrate in an E3 ligase-independent manner through recognition of SUMO consensus motifs (ΨKXE) that contain a Lys acceptor residue. In addition, SUMO ligases can facilitate SUMO transfer through distinct mechanisms. The authors depict three different mechanism for this from steps 5 to 7 in figure 1 of Gareau and Lima [5]. Substrate specificity imparted by E3-substrate interactions are thought to be particularly important for directing conjugation to nonconsensus Lys residues. •Substrates modified by SUMO can contact SUMO-binding proteins through their SUMO-interacting motifs (SIMs). Finally, •Deconjugation is performed by Ulp and SENP proteases and free SUMO may be recycled for another 3 round of conjugation. AXIN forms a complex with adenomatous polyposis coli (APC) gene product, glycogen synthase kinase-3b (GSK3β), β-catenin, DVL, and protein phosphatase 2A (PP2A) and functions as a scaffold protein in the WNT signaling pathway. In the AXIN complex, GSK3βphosphorylates β-catenin, which is then ubiquitinated and degraded by proteasome. Kadoya et al. [7] isolated a novel protein that binds to AXIN and named it AXAM (for Axin associating molecule). AXAM formed a complex with AXIN in intact cells and bound directly to AXIN, thus inhibiting the complex formation of DVL with AXIN and the activity of DVL to suppress GSK3β-dependent phosphorylation of AXIN. Furthermore, they observed that AXAM induced the degradation of β-catenin in SW480 cells and inhibited WNT-dependent axis duplication in Xenopus embryos. Their results suggested that AXAM regulates the WNT signaling pathway negatively by inhibiting the binding of DVL to AXIN. Nishida et al. [8] cloned and characterized SUMO-1/Smt3-specific isopeptidase, SMT3IP2/AXAM2 (Smt3-specific isopeptidase 2). The sequence data indicated that the amino acid sequence of SMT3IP2 was mostly identical to that of rat AXAM, which binds to AXIN and promotes the degradation of β-catenin. Based on this, the authors designated this isopeptidase SMT3IP2/AXAM2. Further, when human SW480 cells were transfected with wild-type SMT3IP2/AXAM2, β-catenin disappeared. Also, it was observed that when the cells were transfected with the SMT3IP2/AXAM2 C500A mutant, which had neither isopeptidase nor carboxyl-terminal hydrolase activity, or with the 1-352 mutant, which lacked the catalytic domain of the enzyme, again βcatenin disappeared, indicating that the enzyme activities were not necessary for the instability of β-catenin in this transfection assay system and that its competition with DVL for binding to AXIN may be important for the instability of β-catenin as suggested previously for AXAM by Kadoya et al. [7]. AXAM induces the degradation of β-catenin in SW480 cells (human colon cancer cells) and inhibits axis formation in Xenopus embryos. Kadoya et al. [9] show that AXAM has the catalytic activity to remove SUMO-1 from sumoylated proteins and that its mutant without this activity is less able to downregulate β-catenin and to inhibit axis formation of Xenopus embryos. Their results demonstrate that AXAM functions as a desumoylation enzyme to downregulate β-catenin in mammalian cells and suggest that sumoylation is involved in the regulation of the WNT signaling pathway. I present 3rd order combinations of SENP2 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 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 [10]. 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 [10]. 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 5 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]. 6 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 SENP2-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 [11]) and Sobol indicies (with 2002 implementation in Saltelli [12] and martinez implementation in Martinez [13] and Baudin et al. [14]). 6.3. Conserved machine learning rankings for tested SENP2-X-X combinations A total of 2415, 3rd order combinations involving SENP2 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 AXIN1-SENP2-X combinations In the above literature review, it shown that SENP2 binds with AXIN. Looking at the tables above, one finds the following combinations for AXIN1 along with SENP2, to be prominent at 3rd order level - AXIN1-FZD2-SENP2 and AXIN1-MYC-SENP2. 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 DVL-SENP2-X combinations Further, due to the above binding of SENP2 with AXIN, SENP2 inhibits the formation of complex of AXIN with DVL, which reduces the functioning of the WNT pathway. This negative synergy between SENP2 and DVL also gives insight as to which combination of DVL-SENP2 is getting affected at a particular time. Looking at the tables 7 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 FBXW11-LRP6-SENP2 1 34823 45217 17593 40419 DKK1-JUN-SENP2 3 13146 45291 34681 42815 CXXC4-PORCN-SENP2 10 33446 17033 17387 32253 CSNK1D-FGF4-SENP2 12 15434 36642 38886 8419 CSNK2A1-MYC-SENP2 13 32182 51840 11657 9637 FOSL1-FRAT1-SENP2 24 25444 38488 23401 24549 APC-FZD6-SENP2 26 11930 12152 51400 36485 APC-PITX2-SENP2 37 14630 40719 18877 15582 DVL2-JUN-SENP2 40 7571 46728 17699 4151 FZD1-NLK-SENP2 66 7254 6519 12561 16204 DKK1-DVL2-SENP2 73 6472 32886 33074 53536 CSNK1G1-NLK-SENP2 74 35675 3308 48520 19328 FZD7-NKD1-SENP2 78 10179 4761 28020 28474 CCND2-LRP6-SENP2 83 56244 18182 20944 394 CXXC4-FOSL1-SENP2 88 36639 18548 29008 12844 LRP5-NLK-SENP2 99 17426 20510 156 54321 FRZB-JUN-SENP2 109 12704 33983 8160 2937 DKK1-LRP6-SENP2 117 30001 55075 39664 8461 DIXDC1-NKD1-SENP2 139 26878 5252 13422 20937 CTBP2-CTNNB1-SENP2 141 36145 41533 3064 6745 DAAM1-LRP6-SENP2 142 53280 45015 4819 36940 FZD5-CCND2-SENP2 150 29656 19798 20159 54229 FSHB-FZD2-SENP2 155 15792 56338 24860 16086 FZD5-CCND3-SENP2 179 12580 12647 25661 981 FZD7-PORCN-SENP2 204 27924 5434 9587 14745 DKK1-PYGO1-SENP2 253 27760 37224 42160 22797 CSNK1D-PORCN-SENP2 254 26488 43944 21480 22511 FOSL1-PPP2R1A-SENP2 256 39545 1842 16944 18375 FRZB-MYC-SENP2 259 14872 1551 37339 16113 AES-EP300-SENP2 266 39979 55044 31248 12673 SENP2-FBXW4-WNT3A 274 39131 29 44525 46327 DKK1-MYC-SENP2 288 24145 39527 40800 42346 FBXW2-PYGO1-SENP2 295 47321 21813 9500 57018 FRAT1-NLK-SENP2 308 14795 5137 12639 16597 FRZB-GSK3A-SENP2 323 15116 1689 3761 6417 CXXC4-FGF4-SENP2 325 44612 33138 54156 47148 DKK1-FOSL1-SENP2 326 21740 41468 36036 47108 FZD5-PITX2-SENP2 328 35236 22541 1156 14803 DKK1-FOXN1-SENP2 342 12351 29242 3585 34803 FOSL1-PORCN-SENP2 349 31659 11861 10245 21849 FZD5-MYC-SENP2 356 21029 5031 27635 17098 FOSL1-NLK-SENP2 359 18070 3202 3757 21594 DAAM1-PYGO1-SENP2 365 46893 25207 11837 39100 FZD5-PORCN-SENP2 377 32693 14759 8273 55426 FZD1-PORCN-SENP2 382 25494 17903 13765 16485 FBXW11-FOXN1-SENP2 392 5743 6882 5378 5741 DKK1-PORCN-SENP2 400 29700 53693 2734 52517 FRZB-FZD2-SENP2 403 12012 17053 8131 21847 CSNK1G1-PORCN-SENP2 410 36322 35831 12245 17913 CSNK1G1-FZD2-SENP2 430 26396 20526 35632 16355 DKK1-PPP2R1A-SENP2 442 14095 52078 45675 54675 CTNNBIP1-JUN-SENP2 451 45193 55478 33408 6827 FOSL1-JUN-SENP2 458 25557 50663 10786 1378 APC-PORCN-SENP2 466 12387 7261 13497 19215 FRZB-PORCN-SENP2 467 13159 11733 10122 22264 GSK3B-LRP6-SENP2 469 39713 22216 39819 33008 DVL1-MYC-SENP2 471 36864 4815 28745 33686 FZD5-FOXN1-SENP2 473 7569 6670 5785 7868 LRP5-PORCN-SENP2 476 41616 8750 51278 21981 FZD6-PORCN-SENP2 497 45212 45263 687 14394 AES-FOXN1-SENP2 518 22315 8527 7631 2724 DIXDC1-PITX2-SENP2 526 28707 7274 5676 35235 FZD7-PPP2CA-SENP2 540 11483 354 3539 34512 BCL9-FGF4-SENP2 548 29256 46172 46692 39145 FRZB-LRP5-SENP2 559 19130 1798 1543 5708 CTBP2-FOXN1-SENP2 566 19815 6401 2342 17983 FZD5-GSK3A-SENP2 569 25593 683 21843 18713 FSHB-NKD1-SENP2 574 7025 14205 7566 35992 DKK1-NKD1-SENP2 575 5975 43246 35996 27099 FZD5-PYGO1-SENP2 593 19014 1524 25504 36744 SENP2-TLE1-TLE2 610 6333 16429 15833 19287 FBXW11-NKD1-SENP2 618 34583 6281 9193 28276 CSNK1D-FOXN1-SENP2 624 4830 5783 7469 36423 FZD8-PORCN-SENP2 639 19701 11231 9109 12830 FBXW11-GSK3B-SENP2 640 23534 27154 19849 22130 DKK1-FSHB-SENP2 641 24808 11118 11901 46995 DKK1-FRAT1-SENP2 669 29229 40235 2545 51616 SENP2-WNT1-WNT2B 701 40779 2190 9179 41846 FRZB-NKD1-SENP2 705 6025 7511 12942 30682 CSNK1G1-DVL2-SENP2 708 9805 19546 23999 8201 FBXW11-FGF4-SENP2 711 39559 55606 33012 11315 FRZB-LEF1-SENP2 746 18406 20494 19809 3129 NLK-PORCN-SENP2 751 51440 56864 21216 6122 FZD5-FZD2-SENP2 769 23664 3575 3654 30814 FZD1-FZD2-SENP2 791 9528 30021 12952 33087 SENP2-SFRP1-WNT2B 804 39477 39510 38291 12235 FOSL1-FOXN1-SENP2 808 25273 3965 4409 8541 FBXW11-RHOU-SENP2 810 39829 54582 1076 13192 CSNK1G1-LRP5-SENP2 821 46576 17464 17352 30361 CXXC4-JUN-SENP2 843 21048 50347 6595 9660 CSNK1G1-JUN-SENP2 855 23957 55112 11084 3256 FZD1-NKD1-SENP2 865 3117 15529 25963 26289 FRAT1-JUN-SENP2 876 27146 34459 14780 13983 SENP2-WNT1-WNT4 879 37625 2401 4412 29111 DVL1-FOXN1-SENP2 907 37314 6190 2465 34563 FRAT1-PORCN-SENP2 915 19198 9986 14436 18176 DVL1-FBXW11-SENP2 927 27739 8099 22915 52768 APC-FZD2-SENP2 934 24435 31374 10970 32370 FZD5-CTNNBIP1-SENP2 936 41581 21812 4533 34272 SENP2-FBXW4-WNT4 962 28442 9419 12651 42095 AXIN1-FZD2-SENP2 970 21704 36841 4481 4717 FRZB-FSHB-SENP2 1016 13136 7480 5202 23820 FRZB-LRP6-SENP2 1020 16728 2573 7208 6418 DKK1-LEF1-SENP2 1053 32782 23184 36091 24285 CSNK1G1-FSHB-SENP2 1054 47479 13640 1228 8996 KREMEN1-PORCN-SENP2 1055 20253 16697 487 37387 FZD7-GSK3A-SENP2 1057 22214 256 52631 33449 FSHB-GSK3A-SENP2 1073 16288 25162 18111 11005 FBXW11-JUN-SENP2 1078 21114 46139 41233 39344 EP300-GSK3B-SENP2 1093 42030 6696 7981 765 DIXDC1-LRP5-SENP2 1098 18807 1510 3942 4609 DAAM1-GSK3A-SENP2 1101 52332 26964 25607 49696 FZD1-GSK3A-SENP2 1104 10414 2123 23509 7420 DIXDC1-FZD2-SENP2 1148 28328 6949 7791 20834 AXIN1-MYC-SENP2 1162 8878 8434 19760 6540 CTBP1-GSK3A-SENP2 1213 25332 467 15589 11039 FBXW2-PORCN-SENP2 1224 33013 2285 41273 42593 FSHB-LEF1-SENP2 1229 12578 50301 24457 7777 GSK3B-RHOU-SENP2 1230 39467 21376 11806 9365 CSNK2A1-FOXN1-SENP2 1233 22059 16672 4525 3145 FBXW2-JUN-SENP2 1253 32758 51631 42897 55749 CSNK1G1-NKD1-SENP2 1257 16631 15972 26700 19860 BTRC-GSK3A-SENP2 1269 31571 50158 24473 28342 FRZB-PYGO1-SENP2 1288 22336 2406 8695 20479 FBXW11-FBXW2-SENP2 1293 31516 16133 5700 35658 FZD8-GSK3A-SENP2 1313 24932 915 45683 16569 Table 1: Rankings of SENP2-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear above, one finds the following combinations for members of the DVL family along with SENP2, to be prominent at 3rd order level - DVL2-JUN-SENP2, DKK1-DVL2SENP2, DVL1-MYC-SENP2, DVL1-FOXN1-SENP2, DVL1-FBXW11-SENP2 and 8 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 FBXW11-LRP6-SENP2 462 28989 38794 18690 24696 DKK1-JUN-SENP2 2445 33296 14766 10519 28087 CXXC4-PORCN-SENP2 9869 47028 41747 45009 41195 CSNK1D-FGF4-SENP2 2542 27165 19967 35638 32914 CSNK2A1-MYC-SENP2 698 26688 37719 17840 33212 FOSL1-FRAT1-SENP2 15910 20828 47008 39310 20122 APC-FZD6-SENP2 4000 27344 40691 10612 57100 APC-PITX2-SENP2 2251 31790 24604 4114 39754 DVL2-JUN-SENP2 4462 28972 39208 37581 33219 FZD1-NLK-SENP2 4216 33313 50995 20046 16713 DKK1-DVL2-SENP2 12170 26608 1445 16210 24013 CSNK1G1-NLK-SENP2 34480 34469 25805 4202 8014 FZD7-NKD1-SENP2 22248 3166 47262 13293 2567 CCND2-LRP6-SENP2 4694 56422 53343 22864 16505 CXXC4-FOSL1-SENP2 27232 42351 44650 16863 48178 LRP5-NLK-SENP2 28404 31921 48677 23545 26406 FRZB-JUN-SENP2 1481 18469 38799 27435 28090 DKK1-LRP6-SENP2 1861 37831 42104 4554 34077 DIXDC1-NKD1-SENP2 24325 22750 54264 38554 4248 CTBP2-CTNNB1-SENP2 20615 24125 47470 7727 18482 DAAM1-LRP6-SENP2 6978 55181 28837 993 26132 FZD5-CCND2-SENP2 1593 48667 56355 20858 31218 FSHB-FZD2-SENP2 722 17184 1804 8318 40473 FZD5-CCND3-SENP2 682 12899 44614 4156 28575 FZD7-PORCN-SENP2 12209 34605 55753 8086 12262 DKK1-PYGO1-SENP2 403 23098 9845 24707 36625 CSNK1D-PORCN-SENP2 5664 26748 24402 26200 37885 FOSL1-PPP2R1A-SENP2 36531 47500 56688 1297 8711 FRZB-MYC-SENP2 341 12601 46519 38771 50004 AES-EP300-SENP2 36742 43851 9360 56088 25857 SENP2-FBXW4-WNT3A 27065 27541 40533 55578 8502 DKK1-MYC-SENP2 954 23283 49758 23572 34187 FBXW2-PYGO1-SENP2 5592 54522 7624 18559 15058 FRAT1-NLK-SENP2 47712 35472 55874 27952 35046 FRZB-GSK3A-SENP2 1005 18367 54917 45435 43654 CXXC4-FGF4-SENP2 252 42683 39239 31323 30294 DKK1-FOSL1-SENP2 14095 26375 3333 23119 42212 FZD5-PITX2-SENP2 10435 42695 24116 3954 33353 DKK1-FOXN1-SENP2 1097 45908 33686 6660 22662 FOSL1-PORCN-SENP2 314 29835 38646 3075 34319 FZD5-MYC-SENP2 4758 9532 47106 17393 47394 FOSL1-NLK-SENP2 41514 24088 54636 21014 19349 DAAM1-PYGO1-SENP2 7009 46420 6762 21944 29682 FZD5-PORCN-SENP2 13359 46673 16639 12543 32648 FZD1-PORCN-SENP2 5513 34056 9744 10153 31014 FBXW11-FOXN1-SENP2 128 6559 40566 11817 4361 DKK1-PORCN-SENP2 2598 41263 6134 19723 13188 FRZB-FZD2-SENP2 2112 16652 26767 43657 55251 CSNK1G1-PORCN-SENP2 13585 41454 10606 1967 17443 CSNK1G1-FZD2-SENP2 16568 22383 10213 6975 36119 DKK1-PPP2R1A-SENP2 4320 17195 24869 14464 3866 CTNNBIP1-JUN-SENP2 42259 50095 40291 21021 34386 FOSL1-JUN-SENP2 15271 29847 41615 22047 48378 APC-PORCN-SENP2 311 33317 27533 12463 51663 FRZB-PORCN-SENP2 2427 25944 18926 35699 48606 GSK3B-LRP6-SENP2 2447 36212 52160 19143 45638 DVL1-MYC-SENP2 2855 32356 46420 20795 31751 FZD5-FOXN1-SENP2 755 12834 53767 11567 34539 LRP5-PORCN-SENP2 11545 45801 9754 1937 37320 FZD6-PORCN-SENP2 3 53444 8379 12707 32509 AES-FOXN1-SENP2 1218 24082 52757 25404 14040 DIXDC1-PITX2-SENP2 3537 43865 15972 13329 19669 FZD7-PPP2CA-SENP2 32571 2154 49346 21000 26293 BCL9-FGF4-SENP2 7646 28217 10273 19350 40259 FRZB-LRP5-SENP2 555 19606 45855 1859 48730 CTBP2-FOXN1-SENP2 7635 19129 49786 125 42056 FZD5-GSK3A-SENP2 1856 36876 56727 30350 43628 FSHB-NKD1-SENP2 14879 5325 16207 3306 6877 DKK1-NKD1-SENP2 7012 22034 30235 20793 14207 FZD5-PYGO1-SENP2 864 25856 32614 26549 46981 SENP2-TLE1-TLE2 22393 22753 3266 25737 12237 FBXW11-NKD1-SENP2 3968 23882 33729 15929 5877 CSNK1D-FOXN1-SENP2 1289 8520 39455 7070 25852 FZD8-PORCN-SENP2 1042 32328 3606 28410 19273 FBXW11-GSK3B-SENP2 5753 10714 20625 19385 4353 DKK1-FSHB-SENP2 13659 23744 54431 4021 33075 DKK1-FRAT1-SENP2 5714 28221 7591 6962 28179 SENP2-WNT1-WNT2B 2021 43379 30860 2867 24069 FRZB-NKD1-SENP2 3644 10458 50187 29431 36573 CSNK1G1-DVL2-SENP2 10060 33044 6346 24081 29517 FBXW11-FGF4-SENP2 460 23321 17102 23270 7399 FRZB-LEF1-SENP2 306 25220 39312 10442 24101 NLK-PORCN-SENP2 25839 52725 11882 9881 37272 FZD5-FZD2-SENP2 5895 34287 41654 30068 50389 FZD1-FZD2-SENP2 4443 13047 26746 40642 49778 SENP2-SFRP1-WNT2B 12477 36645 18903 52949 54446 FOSL1-FOXN1-SENP2 1644 24800 52856 5786 32696 FBXW11-RHOU-SENP2 2811 29045 28581 338 17622 CSNK1G1-LRP5-SENP2 14135 47074 22615 10563 18356 CXXC4-JUN-SENP2 1851 32478 55139 8858 43014 CSNK1G1-JUN-SENP2 2057 43819 27038 14070 17638 FZD1-NKD1-SENP2 16283 248 42563 17609 26499 FRAT1-JUN-SENP2 8350 32873 42151 5535 36295 SENP2-WNT1-WNT4 595 42309 31627 659 12885 DVL1-FOXN1-SENP2 3061 30960 37499 23295 15142 FRAT1-PORCN-SENP2 1688 40659 28876 5431 52097 DVL1-FBXW11-SENP2 10393 17940 54581 8945 22213 APC-FZD2-SENP2 324 36486 16060 22102 42466 FZD5-CTNNBIP1-SENP2 4249 39970 22055 26513 16307 SENP2-FBXW4-WNT4 7957 13325 39354 38785 4122 AXIN1-FZD2-SENP2 8182 15407 16562 39363 47191 FRZB-FSHB-SENP2 5870 14328 41622 369 53440 FRZB-LRP6-SENP2 1809 20940 39489 3847 40248 DKK1-LEF1-SENP2 1211 36246 13554 12065 5713 CSNK1G1-FSHB-SENP2 41253 35360 30966 2443 33408 KREMEN1-PORCN-SENP2 2897 40815 14540 5841 26554 FZD7-GSK3A-SENP2 290 25036 52263 13397 4756 FSHB-GSK3A-SENP2 6015 32214 13032 15982 30339 FBXW11-JUN-SENP2 2521 15541 36470 25945 625 EP300-GSK3B-SENP2 8327 37174 36829 10925 19701 DIXDC1-LRP5-SENP2 1777 23484 44827 123 12925 DAAM1-GSK3A-SENP2 1185 54603 39296 24751 14243 FZD1-GSK3A-SENP2 1003 14896 54197 10418 35326 DIXDC1-FZD2-SENP2 11918 40028 27691 41589 5926 AXIN1-MYC-SENP2 26539 8188 46118 33138 43486 CTBP1-GSK3A-SENP2 409 42665 56908 22557 34169 FBXW2-PORCN-SENP2 9048 55175 828 25406 16023 FSHB-LEF1-SENP2 16486 20092 5835 4015 10968 GSK3B-RHOU-SENP2 5807 32711 51623 1013 46591 CSNK2A1-FOXN1-SENP2 142 13206 48212 17145 40808 FBXW2-JUN-SENP2 25289 51870 3972 20307 1098 CSNK1G1-NKD1-SENP2 4079 7354 54740 12528 13804 BTRC-GSK3A-SENP2 9345 20665 52714 11947 10821 FRZB-PYGO1-SENP2 334 16496 42795 31671 51686 FBXW11-FBXW2-SENP2 5640 29344 45548 27448 44741 FZD8-GSK3A-SENP2 422 12723 55867 1253 13272 Table 2: Rankings of SENP2-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf CSNK1G1-DVL2-SENP2. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 9