beta-transducin repeat containing E3 ubiquitin protein ligase or F-box/WD repeat-containing protein 1A (BTRC/FBXW1A) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

beta-transducin repeat containing E3 ubiquitin protein ligase or F-box/WD repeat-containing protein 1A (BTRC/FBXW1A) : 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 βTrCP (BTRC/FBXW1A) encodes a member of the F-box protein family, characterized by an approximately 40 residue structural motif, the F-box. The F-box proteins form one of the four subunits of ubiquitin protein ligase complex called Skp1Cul1-F-box (SCF) protein, which often, but not always, recognize substrates in a phosphorylation-dependent manner. BTRC associates with phosphorylated β-catenin destruction motifs, probably functioning in multiple transcriptional programs by regulating the WNT pathways. 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 BTRC related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for BTRC-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 ITime behavioural study of 3-odr BTRC 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 18, 2025 further wet lab analysis. 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 BTRC 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 2 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, 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. beta-transducin repeat containing E3 ubiquitin protein ligase (BTRC) Linfoot et al. [4] measured cell-cycle, phase-specific cell kill caused by carmustine (BCNU), in 4 cell lines with different sensitivities to the drug. Enriched subpopulations in various phases of the cell cycle were obtained and assayed for cell survival, after the cells were treated with BCNU for 1 hour. They measured levels of activity of guanine O6-alkyltransferase for each line and and found that only BTRC-19, a clone of the 9L line, had significant levels of alkyltransferase activity and exhibited a relatively flat age-response curve to BCNU. Spevak et al. [5] constructed a Xenopus oocyte cDNA library in a Saccharomyces cerevisiae expression vector and used it to isolate genes that could function in yeast cells to suppress the temperature sensitive (corrected) defect of the CDC15 mutation. Two maternally expressed Xenopus cDNAs which fulfilled these conditions were isolated. One of these clones encoded Xenopus N-ras. They observed that overexpression of Xenopus N-ras in S. cerevisiae did not activate the RAS-cyclic AMP (cAMP) pathway, but resulted in decreased levels of intracellular cAMP in both mutant CDC15 and wild-type cells. Their results suggested that a key step of the cell cycle was dependent upon a phosphorylation event catalyzed by cAMP-dependent protein kinase. Additionally, they observed that the second clone, beta TrCP (BTRC), encoded a protein of 518 amino acids that showed significant homology to the beta subunits of G proteins in its C-terminal half. In this region, BTRC was composed of seven beta-transducin repeats. HIV-1 Vpu interacts with CD4 in the endoplasmic reticulum and triggers CD4 degradation, presumably by proteasomes. Human BTRC identified by interaction with Vpu connected CD4 to this proteolytic machinery, and Margottin et al. [6] via coimmunoprecipitation detected CD4-Vpu-beta TrCP (BTRC) ternary complexes. They observed that BTRC binding to Vpu and its recruitment to membranes required two phosphoserine residues in Vpu essential for CD4 degradation. In BTRC, WD repeats at the C terminus mediated binding to Vpu, and an F-box near the N terminus was involved in 3 interaction with Skp1p (a targeting factor for ubiquitin-mediated proteolysis). Further, an F-box deletion mutant of BTRC had a dominant-negative effect on Vpu-mediated CD4 degradation. Their data suggested that BTRC and Skp1p represented components of a novel ER-associated protein degradation pathway that mediated CD4 proteolysis. Members of the WNT/Wingless (Wg) families of secreted proteins control many aspects of growth and patterning during animal development. Wg signal transduction causes increased stability of Armadillo (Arm/β-catenin), a possible co-factor for the transcriptional regulator LEF1/TCF. Jiang and Struhl [7] described a new gene, slimb (for supernumerary limbs), which negatively regulated the Wg pathway along with the Hedgehog (Hh) pathway. They found that loss of function of slimb resulted in a cellautonomous accumulation of high levels of both Ci and Arm, and the ectopic expression of both Hhand Wgresponsive genes. They observed that the slimb gene encoded a conserved F-box/WD40-repeat protein related to CDC4P (a protein in budding yeast) that targets cell-cycle regulators for degradation by the ubiquitin/proteasome pathway. They further proposed that slimb protein targeted Ci and Arm/β-catenin for processing or degradation by the ubiquitin/proteasome pathway, and that Wg regulate gene expression at least in part by inducing changes in Ci and Arm, which protect them from slimb-mediated proteolysis. Based on the above findings of Jiang and Struhl [7], Marikawa and Elinson [8] examined the role of vertebrate homolog betaTrCp (BTRC) in the WNT/β-catenin signaling and dorsal axis formation in Xenopus embryos. They observed that co-injection of BTRC mRNA diminished Xwnt8 mRNA-induced axis formation and expression of Siamois and Xnr3, thus suggesting that BTRC was a negative regulator of the WNT/β-catenin signaling pathway. An mRNA for a BTRC mutant construct (DeltaF), which lacked the F-box domain, was found to induce an ectopic axis and expression of Siamois and Xnr3. Because this activity of DeltaF was suppressed by co-injection of DeltaF TrCP mRNA, DeltaF was thought to act in a dominant negative fashion. Further, the activity of DeltaF was diminished by C-cadherin, GSK3 and AXIN, but not by a dominant negative dishevelled (DSH/DVL) . Their results pointed that BTRC could act as a negative regulator of dorsal axis formation in Xenopus embryos. While screening a maternal Xenopus expression library for activities that synergize with low levels of injected β-catenin, Lagna et al. [9] isolated a clone encoding the C-terminal end of x-beta TrCP-2, a highly conserved protein belonging to the F-box/WD40 family of ubiquitin-ligase specificity factors. They showed that x-beta TrCP-2 expression reduced dorsal axis formation in Xenopus embryos, while a dominant negative mutant lacking the F-box triggered the opposite effect, thus inducing secondary axes and activation of the expression of WNT responsive genes in ectodermal explants. In light of the existence of BTRC transcripts associated with the vegetal cortex, they proposed that BTRC played an important role in the establishment of the dorsal determinants during cortical rotation in Xenopus. I present 3rd order combinations of BTRC with other genes, that the machine learning based search engine points to, as possible synergistic combinations that might be working in time. 4 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 [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 5 recording of sensitivity index per combination, each combination forms a training example which is alloted a training index and the sensitivity indices of the individual genetic factors form the training example. Thus there are Cn ktraining examples for kth order interaction. Using this training set SVMRank learn Joachims [3] is used to generate a model on default value Cvalue of 20. In the current experiment on toy model Cvalue has not been tunned. The training set helps in the generation of the model as the different gene combinations are numbered in order which are used as rank indices. The model is then used to generate score on the observations in the testing set using the SV MRank classi f y Joachims [3]. Note that due to availability of only one example per combination, after the model has been built, the same training data is used as test data to generates the scores. This procedure is executed for each and every sensitivity analysis method. This is followed by sorting of these scores along with the rank indices (i.e the training indices) already assigned to the gene combinations. The end result is a sorted order of the gene combinations based on the ranking score learned by the SV MRank algorithm. Finally, this entire procedure is computed for sensitivity indices generated for each and every fold change at time point and deviations in fold change at different durations. Observing the changing rank of a particular combination at different times and different time periods will reveal how a combination is behaving. Note that the following is the order in which the files should be executed in R, in order, for obtaining the desired results (Note that the code will not be explained here) - • use source(”mainScript-1-1.R”) with arguments for Dynamic data •source(”SVMRankResults-D.R”), to rank the interactions (again this needs to be done separately for different kinds of SA methods), •use source(”Combine-Time-files.R”), if computing indices separately via previous file, •source(”Sort-n-Plot-D.R”) to sort the interactions. Note that the sorting is chages the interaction ranking in time. Thus •use source(”Interaction-Priority-Intime.R”) to find the prioritized ranking of each and every interaction over the different time points and finally •use source(”Print-RankingAND-Interaction-Rank.R”) to print individual ranking of the required input factor with other interaction factors. 6. Results & Discussion 6.1. Time series data by Gujral and MacBeath [1] NOTE - Ranking was assigned on scores that were sorted in DECREASING values. So, 1 was assigned to highest score and vice versa. Results for the 3rd order interactions are presented here. The results first discuss 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 6 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 BTRC-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 BTRC-X-X combinations A total of 2415, 3rd order combinations involving BTRC 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 FBXW-BTRC-X combinations Suzuki et al. [15] had found that overexpression of an F-box protein βTrCP1 (BTRC) and the structurally related βTrCP2 (FBXW11) augmented ubiquitination of phosphorylated IκBα(pIκBα) induced by tumor necrosis factor-α(TNF-α), but the relationship of the two homologous βTrCP proteins remained unknown. Suzuki et al. [15] revealed that deletion mutants of βTrCP-1/2 lacking the F-box domain suppressed 7 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 BTRC-GSK3A-FBXW4 399 54756 38346 27654 17743 BTRC-GSK3A-WNT4 427 51118 43719 18596 24127 BTRC-GSK3A-T 433 50464 41129 26608 19994 BTRC-GSK3A-NLK 685 15173 52709 30778 8565 APC-BTRC-WNT2 692 20019 7270 10948 40790 BTRC-FOXN1-FZD8 853 10860 9974 20227 10455 APC-BTRC-DAAM1 945 6005 22642 3587 1629 BTRC-GSK3A-SENP2 1269 31571 50158 24473 28342 BTRC-FOXN1-WNT4 1304 7824 14183 18230 50189 BTRC-PPP2CA-WNT4 1638 35087 32587 22025 51750 BTRC-GSK3A-SLC9A3R1 1828 47182 56469 39060 32535 BTRC-GSK3A-WNT2 1829 55217 56594 37274 29011 APC-BTRC-PPP2CA 1858 9257 27876 20401 45249 BTRC-GSK3A-WNT2B 1933 56634 52638 55432 37508 BTRC-GSK3A-WNT3A 1946 45085 56552 39291 36207 APC-BTRC-FRAT1 1993 4234 3760 19668 20988 BTRC-GSK3A-LRP5 2279 50637 43268 46359 31488 BTRC-GSK3A-GSK3B 2331 27348 55816 23870 24273 BTRC-GSK3A-LEF1 2442 51793 56318 34877 43742 APC-BTRC-TCF7 2478 22925 18323 15264 35151 AXIN1-BTRC-DVL2 2500 11477 16610 53250 27050 APC-BTRC-FBXW2 2597 1236 21415 35908 27898 BTRC-GSK3A-PITX2 2613 49655 52881 6241 50065 APC-BTRC-FBXW11 2628 10595 8869 37962 22016 APC-BTRC-FZD5 2646 23572 8780 23130 34875 BTRC-PPP2CA-SFRP4 2649 45450 55216 41081 48220 APC-BTRC-KREMEN1 2657 22730 7427 25126 52825 BTRC-CCND3-WNT4 2710 41552 34711 18962 45323 BTRC-FOXN1-KREMEN1 2723 18292 12669 9692 56435 APC-BTRC-SENP2 2742 2914 7275 11614 33253 BTRC-GSK3A-PYGO1 2771 52085 53096 35408 47985 BTRC-FOXN1-SENP2 2819 7789 14297 7017 45881 BTRC-GSK3A-KREMEN1 3010 54393 56679 45265 52103 BTRC-WNT1-WNT4 3062 33354 28305 33341 21189 APC-BTRC-FZD1 3143 5688 12315 18344 2535 BTRC-RHOU-TCF7 3204 41293 40925 4745 45576 BTRC-RHOU-FBXW4 3368 55758 50831 743 47356 BTRC-GSK3A-SFRP4 3507 52295 54637 26019 28662 APC-BTRC-SFRP4 3513 8753 5458 12692 40484 BTRC-GSK3A-MYC 3555 32516 35803 30274 45481 BTRC-FOXN1-LRP5 3607 18421 14993 15012 46079 BTRC-WNT2-WNT3A 3667 53111 52839 51977 37208 BTRC-FOXN1-FRAT1 3675 26618 6170 28752 42168 BTRC-FOXN1-WNT5A 3687 8784 26520 30828 49695 BTRC-PPP2CA-T 3795 43011 19216 31904 44253 BTRC-FOXN1-SLC9A3R1 3990 7530 9458 10316 38446 AXIN1-BTRC-WNT2 4161 12843 11806 22233 22893 BTRC-NKD1-WIF1 4240 14000 50136 49384 38469 BTRC-GSK3A-TCF7L1 4309 38628 56805 38238 43590 BTRC-PPP2CA-TCF7L1 4339 35835 48253 44827 55748 BTRC-NKD1-WNT2B 4358 53865 52313 44893 36090 BTRC-CCND3-CXXC4 4501 45355 32569 38665 55920 BTRC-GSK3A-TCF7 4603 42589 43515 30573 20648 AES-BTRC-FZD5 4783 25177 12006 24403 11782 BTRC-GSK3A-WNT5A 4818 34238 56433 32265 47742 BTRC-GSK3A-TLE2 4865 53235 52059 36282 26238 BTRC-JUN-TCF7L1 4943 27837 47631 38349 49359 APC-BTRC-CTBP1 4950 9391 8017 9007 18060 BTRC-CCND2-WNT4 4953 52895 11943 23405 44507 BTRC-PPP2CA-TCF7 4981 40531 13651 43079 34410 AES-BTRC-DVL2 5030 12391 15984 50914 7881 APC-BTRC-FZD7 5075 17371 3368 9728 6810 BTRC-FBXW2-WNT3A 5104 43223 55035 20534 48314 BTRC-FGF4-NLK 5183 27874 56631 56082 16933 BTRC-LRP6-FBXW4 5274 56436 32556 47321 9771 BTRC-GSK3A-PPP2R1A 5299 26077 46257 26921 27177 BTRC-GSK3A-RHOU 5363 54749 48852 32167 37017 BTRC-RHOU-SFRP1 5398 50476 50062 18513 5471 APC-BTRC-CSNK1D 5442 10883 12646 22647 6204 BTRC-CCND3-FZD7 5447 42687 17440 28743 32509 BTRC-NKD1-WNT4 5567 46251 34634 38788 50581 APC-BTRC-WNT5A 5579 11328 15422 26429 56417 BTRC-FOXN1-FZD1 5639 18624 18170 16160 42888 BTRC-GSK3A-LRP6 5724 52749 52308 52281 23121 BTRC-JUN-LRP5 5888 37770 52457 34858 25652 APC-BTRC-WNT4 5911 19764 3320 4428 21935 BTRC-JUN-WNT3A 5912 40253 46236 41851 33745 BTRC-FOXN1-TLE2 6027 19449 11379 20626 38897 BTRC-GSK3A-SFRP1 6145 52112 56467 35900 15415 APC-BTRC-SLC9A3R1 6177 4157 5216 19065 21916 AXIN1-BTRC-FOSL1 6468 1244 4919 15349 38579 BTRC-CCND3-WNT2B 6518 55220 31850 31279 47240 BTRC-NKD1-TCF7L1 6683 39081 40177 56129 51053 BTRC-FOXN1-T 6737 27226 10335 37112 39462 BTRC-PPP2CA-SENP2 6802 36289 41584 41333 55323 APC-BTRC-LRP6 6911 28737 4615 26743 4691 AES-BTRC-DKK1 6960 18725 17933 22340 4842 BTRC-CCND3-FOSL1 6965 37686 28713 22894 44780 BTRC-RHOU-SENP2 6988 41062 38132 3821 50210 BTRC-JUN-WNT4 7215 48917 43726 14501 33278 BTRC-NKD1-SENP2 7336 41049 43342 47787 47593 BTRC-NKD1-SFRP1 7350 47032 49057 53468 51 BTRC-CCND3-EP300 7453 26437 27976 19877 47477 BTRC-PPP2CA-RHOU 7476 44384 28579 43147 51079 BTRC-RHOU-WNT4 7503 46563 30678 9407 48820 AES-BTRC-GSK3A 7511 649 23146 16630 18979 BTRC-GSK3A-WIF1 7516 12519 55092 29987 46937 BTRC-CCND3-DKK1 7699 42444 50739 46484 28100 BTRC-CCND3-TLE1 7893 37196 27722 17214 40980 BTRC-WNT1-WNT3A 7906 35272 32813 57093 19625 BTRC-PPP2CA-WNT5A 7995 31259 42194 31725 49589 AES-BTRC-PPP2CA 8064 4470 33612 23597 26264 BTRC-FOXN1-FSHB 8118 14636 21198 33671 46291 AXIN1-BTRC-SENP2 8132 4244 7993 9640 29213 AES-BTRC-RHOU 8185 12590 5280 21149 27171 BTRC-JUN-PYGO1 8263 45096 50540 41901 54741 BTRC-JUN-SENP2 8343 24938 49553 30325 39253 AES-BTRC-JUN 8360 1344 7172 18393 10377 BTRC-CCND3-FZD2 8456 51566 34885 26667 37022 BTRC-PYGO1-WNT3A 8510 43352 44095 22599 55396 BTRC-CCND3-TCF7 8538 37690 31426 32017 39147 APC-BTRC-PYGO1 8570 7302 8530 26749 53032 AES-BTRC-FOSL1 8607 22428 10525 19327 9562 AXIN1-BTRC-FZD5 8616 22820 8767 21827 26979 BTRC-KREMEN1-WNT4 8701 48514 48223 13062 56268 AXIN1-BTRC-CTBP1 8711 1472 9482 8596 26250 BTRC-LRP6-SLC9A3R1 8815 46754 26428 52824 19745 AXIN1-BTRC-CCND3 8836 8488 11500 25054 29424 BTRC-NKD1-PPP2CA 8947 49640 54091 53329 49700 BTRC-JUN-LEF1 8950 36031 39447 23517 51208 BTRC-NKD1-SFRP4 8970 49955 44941 50705 38441 BTRC-NKD1-TLE2 9050 49909 47985 49811 37145 AXIN1-BTRC-PPP2CA 9123 8661 42188 25227 33335 BTRC-FGF4-WNT4 9178 41675 44825 23499 35812 BTRC-JUN-WNT2 9191 44964 44172 23594 37421 AES-BTRC-WIF1 9239 22292 6516 14211 26584 Table 1: Rankings of BTRC-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear ubiquitination and destruction of pIκBαas well as transcriptional activation of NFκB. They observed that the ectopically expressed βTrCP-1/2 formed both homodimer 8 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 BTRC-GSK3A-FBXW4 8681 52442 37486 14095 29234 BTRC-GSK3A-WNT4 12669 46498 44112 7495 6959 BTRC-GSK3A-T 6821 52908 40648 46892 3130 BTRC-GSK3A-NLK 8965 2718 45185 45189 49869 APC-BTRC-WNT2 9163 27280 43155 9369 48381 BTRC-FOXN1-FZD8 2072 28008 41249 39653 29423 APC-BTRC-DAAM1 3743 41091 17783 36176 30576 BTRC-GSK3A-SENP2 9345 20665 52714 11947 10821 BTRC-FOXN1-WNT4 5283 22892 41659 11506 604 BTRC-PPP2CA-WNT4 13782 33555 41012 5416 5243 BTRC-GSK3A-SLC9A3R1 6194 38474 43825 24758 45073 BTRC-GSK3A-WNT2 14070 55767 42437 51240 22931 APC-BTRC-PPP2CA 4261 9237 29395 1410 54704 BTRC-GSK3A-WNT2B 9987 55898 47839 49215 4144 BTRC-GSK3A-WNT3A 12858 35286 25253 43232 19671 APC-BTRC-FRAT1 3582 6272 14221 27977 50407 BTRC-GSK3A-LRP5 11198 46675 45351 47368 14161 BTRC-GSK3A-GSK3B 4319 5498 47667 46132 13660 BTRC-GSK3A-LEF1 12346 48661 30805 40415 35765 APC-BTRC-TCF7 4705 13188 32095 8871 53791 AXIN1-BTRC-DVL2 29410 5833 29596 43603 19764 APC-BTRC-FBXW2 4038 1370 25809 43009 39049 BTRC-GSK3A-PITX2 2406 44730 43962 54217 10925 APC-BTRC-FBXW11 3206 17373 31138 32376 35753 APC-BTRC-FZD5 5256 25681 42284 19958 53619 BTRC-PPP2CA-SFRP4 23701 47316 54163 28713 3631 APC-BTRC-KREMEN1 8265 27604 37492 52851 54717 BTRC-CCND3-WNT4 19497 48624 44461 7332 36428 BTRC-FOXN1-KREMEN1 2135 23342 46688 49929 2379 APC-BTRC-SENP2 2108 12223 33937 28608 53523 BTRC-GSK3A-PYGO1 16077 51303 28870 23885 34429 BTRC-FOXN1-SENP2 1453 25844 25117 25651 4578 BTRC-GSK3A-KREMEN1 5140 53781 54895 53606 19024 BTRC-WNT1-WNT4 32427 25452 32871 49 5853 APC-BTRC-FZD1 2781 7110 14462 30867 34404 BTRC-RHOU-TCF7 35804 52449 25786 16725 22733 BTRC-RHOU-FBXW4 46779 55127 25525 2995 35190 BTRC-GSK3A-SFRP4 1874 50406 40267 35344 14342 APC-BTRC-SFRP4 9796 14815 39313 5822 33503 BTRC-GSK3A-MYC 14888 25284 36568 2248 10669 BTRC-FOXN1-LRP5 3273 30198 36284 23532 241 BTRC-WNT2-WNT3A 31077 52852 5122 22613 1175 BTRC-FOXN1-FRAT1 4169 16478 20795 41841 6870 BTRC-FOXN1-WNT5A 4629 21553 49380 16835 38205 BTRC-PPP2CA-T 42753 54274 45558 42965 26218 BTRC-FOXN1-SLC9A3R1 987 5633 38486 32921 3284 AXIN1-BTRC-WNT2 19940 34779 51998 35294 51645 BTRC-NKD1-WIF1 40459 4738 29145 25508 9960 BTRC-GSK3A-TCF7L1 5048 35224 47809 21415 23988 BTRC-PPP2CA-TCF7L1 12141 39746 46412 24183 1736 BTRC-NKD1-WNT2B 34862 55446 41413 44594 7779 BTRC-CCND3-CXXC4 28171 55841 38665 6723 12780 BTRC-GSK3A-TCF7 2679 48529 45973 20262 37169 AES-BTRC-FZD5 23300 36671 28933 1416 44834 BTRC-GSK3A-WNT5A 1331 34656 55842 14294 39235 BTRC-GSK3A-TLE2 7469 51695 40008 8656 21337 BTRC-JUN-TCF7L1 24959 20714 12947 17672 1488 APC-BTRC-CTBP1 22415 7521 32949 1572 36489 BTRC-CCND2-WNT4 37807 46204 36799 15309 3667 BTRC-PPP2CA-TCF7 21166 51448 42519 19099 5073 AES-BTRC-DVL2 35795 3432 49151 31669 27699 APC-BTRC-FZD7 1697 7624 29404 31973 44902 BTRC-FBXW2-WNT3A 39006 39760 21198 32505 45697 BTRC-FGF4-NLK 3757 10635 33258 31931 37107 BTRC-LRP6-FBXW4 48827 55300 26952 16212 26925 BTRC-GSK3A-PPP2R1A 8962 30689 29658 9241 43973 BTRC-GSK3A-RHOU 7245 54116 45531 48716 24019 BTRC-RHOU-SFRP1 54868 48925 28543 13342 47372 APC-BTRC-CSNK1D 2236 12178 36083 5029 45903 BTRC-CCND3-FZD7 20781 46050 30736 40377 49178 BTRC-NKD1-WNT4 42581 46731 36629 5396 4774 APC-BTRC-WNT5A 7886 8328 47613 21423 25207 BTRC-FOXN1-FZD1 4693 25266 25295 4116 67 BTRC-GSK3A-LRP6 13109 51610 41523 24298 23690 BTRC-JUN-LRP5 47907 24894 17380 45629 3061 APC-BTRC-WNT4 2113 8450 42844 16 50560 BTRC-JUN-WNT3A 37538 33079 9131 18895 7570 BTRC-FOXN1-TLE2 5417 15877 5904 34425 5486 BTRC-GSK3A-SFRP1 1664 48238 36146 6688 23640 APC-BTRC-SLC9A3R1 37704 1044 33896 21821 50112 AXIN1-BTRC-FOSL1 28079 9720 56293 17570 50701 BTRC-CCND3-WNT2B 24254 53442 21428 39052 47106 BTRC-NKD1-TCF7L1 35223 44544 35152 5915 7887 BTRC-FOXN1-T 2442 42400 34919 11494 2235 BTRC-PPP2CA-SENP2 8723 30185 52002 10650 31985 APC-BTRC-LRP6 49993 33786 30995 2710 30279 AES-BTRC-DKK1 29312 29441 54503 3484 32873 BTRC-CCND3-FOSL1 29635 39122 40121 26979 11246 BTRC-RHOU-SENP2 22351 33999 30105 8174 21370 BTRC-JUN-WNT4 35141 42866 20608 11140 4126 BTRC-NKD1-SENP2 37667 27919 25558 3108 6916 BTRC-NKD1-SFRP1 33217 47597 38470 24028 21787 BTRC-CCND3-EP300 16838 27677 31497 24519 27349 BTRC-PPP2CA-RHOU 21096 51135 35466 34465 21156 BTRC-RHOU-WNT4 17430 46737 39943 11925 27423 AES-BTRC-GSK3A 27622 3812 52880 9059 31196 BTRC-GSK3A-WIF1 8879 9323 38999 19148 14457 BTRC-CCND3-DKK1 16607 38588 8857 2264 31589 BTRC-CCND3-TLE1 34230 30664 34418 21643 23378 BTRC-WNT1-WNT3A 35227 22898 11695 12947 7878 BTRC-PPP2CA-WNT5A 32549 27398 48062 6477 24654 AES-BTRC-PPP2CA 30718 1100 13573 25518 52217 BTRC-FOXN1-FSHB 6670 20222 33570 45284 22 AXIN1-BTRC-SENP2 18487 9499 51352 5160 50244 AES-BTRC-RHOU 31407 10383 39972 41558 56068 BTRC-JUN-PYGO1 37910 44163 1594 29208 42451 BTRC-JUN-SENP2 29065 17777 6958 20628 6213 AES-BTRC-JUN 35333 7469 37870 8738 37322 BTRC-CCND3-FZD2 34361 45890 35141 11003 14788 BTRC-PYGO1-WNT3A 30112 36444 28501 12063 23745 BTRC-CCND3-TCF7 23555 47574 37247 26531 11513 APC-BTRC-PYGO1 51355 9058 6097 3990 45511 AES-BTRC-FOSL1 33302 22693 50032 1890 51445 AXIN1-BTRC-FZD5 13481 19478 52911 4874 45918 BTRC-KREMEN1-WNT4 47643 49959 34801 36178 5914 AXIN1-BTRC-CTBP1 33060 3616 54070 3 28263 BTRC-LRP6-SLC9A3R1 44418 44933 17317 32739 29397 AXIN1-BTRC-CCND3 14456 12461 46193 30484 34903 BTRC-NKD1-PPP2CA 29398 53369 45941 27262 4730 BTRC-JUN-LEF1 30590 27148 1645 43584 10953 BTRC-NKD1-SFRP4 43680 50931 6721 32883 11764 BTRC-NKD1-TLE2 39341 53201 13833 15359 18076 AXIN1-BTRC-PPP2CA 18230 23560 32745 6358 50799 BTRC-FGF4-WNT4 3320 45404 24731 7888 11796 BTRC-JUN-WNT2 41795 46313 18106 41395 6164 AES-BTRC-WIF1 31157 16922 12256 24179 30618 Table 2: Rankings of BTRC-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf and heterodimer complexes without displaying the trimer complex. Intriguingly, they further observed that the βTrCP homodimer, but not the heterodimer, was selectively recruited to pIκBαinduced by TNF-α. Their results indicated that not only βTrCP1 9