protein phosphatase 2A structural/scaffold subunit A, alpha isoform (PPP2R1A) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

protein phosphatase 2A structural/scaffold subunit A, alpha isoform (PPP2R1A) : 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 PPP2R1A forms a component of the PP2A holoenzyme complex. PPP2R1A is the predominant PP2A scaffold A-subunit that is required for functional PP2A complex formation and PPP2R1A depletion results in comprehensive PP2A complex inhibition. Gujral and MacBeath [1] provides a quantitative, and dynamic study of WNT3Amediated 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 PPP2R1A related 3rd order combinations in a forest of 71C3combinations using four different sensitivity methods; •show the conserved rankings for PPP2R1A-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 PPP2R1A 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 in WNT3A stimulated cells 1Aspects of unpublished work were presented in a poster session at Cell Symposia: Technology.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 12, 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 PPP2R1A related combinations using individual gene expressions measured in time, in WNT3A stimulated HEK 293 cells. 2. Introduction The details of the machine learning based search engine has been recently published in Sinha [2] and deployed to explore the 2nd order combinations of genes in the data set provided by Gujral and MacBeath [1]. Nevertheless, here, I point to the fundamentals of the published work for completeness. 2.1. A combinatorial problem Sensitivity analysis plays a major role in computing the strength of the influence of involved factors in any phenomena under investigation. When applied to expression profiles of various intra/extracellular factors that form an integral part of a signaling pathway, the variance and density based analysis yields a range of sensitivity indices for individual as well as various combinations of factors. These combinations denote the higher order interactions among the involved factors. Computation of higher order interactions is often time consuming but it gives a chance to explore the various combinations that might be of interest in the working mechanism of the pathway. For example, in a range of fourth order combinations among the various factors of the Wnt pathway, it would be easy to assess the influence of the destruction complex formed by APC, AXIN, CSKI and GSK3 interaction. But the effect of these combinations vary over time as measurements of fold changes and deviations in fold changes vary. So it is imperative to know how an interaction or a combination of the involved factors behave in time and Sinha [2] develops a procedure to track the behaviour by exploiting the influences of these involved factors. 2.2. A possible solution In this work, after estimating the individual effects of factors for a higher order combination, the individual indices are considered as discriminative features. A combination, 2 then, is a feature set in higher order (≥2 ,i.e multivariate). With an excessively large number of factors involved in the pathway, it is difficult to search for important combinations in a wide search space over different orders. Exploiting the analogy with the issues of prioritizing webpages using ranking algorithms, for a particular order, a full set of combinations of interactions can then be prioritized based on these features using a powerful ranking algorithm via support vectors Joachims [3]. Recording the changing rankings of the combinations over time reveals how higher order interactions behave within the pathway and when an intervention might be necessary to influence the interaction within the pathway. 2.3. protein phosphatase 2A structural/scaffold subunit A, alpha isoform (PPP2R1A) Protein phosphorylation is a reversible protein posttranslational modification (PTM). Phosphorylation involves the transfer of phosphate groups from ATP to the enzyme, the energy for which comes from hydrolysing ATP into ADP or AMP. Protein kinases (PKs) are the effectors of phosphorylation and catalyse the transfer of a γ-phosphate from ATP to specific amino acids on proteins. Proteins are phosphorylated predominantly on Ser, Thr and Tyr residues. In contrast, protein phosphatases (PPs) are the primary effectors of dephosphorylation and can be grouped into three main classes based on sequence, structure and catalytic function. Dephosphorylation releases phosphates into solution as free ions, because attaching them back to ATP would require energy input. PP2A holoenzyme complex comprises a scaffolding (A), regulatory (B), and catalytic (C) subunit, with protein phosphatase 2A, catalytic subunit, alpha isoform (PPP2CA) being the principal catalytic subunit. There are two isoforms of the catalytic (PPP2CA aka Cαand PPP2CB aka Cβ), two isoforms of the scaffold A subunit (PPP2R1A aka Aαand PPP2R1B aka Aβ) and at least 17 different B subunit proteins that are members of predominantly of three families identified as B family (aka B55; gene symbol PPP2R2), B’ family (aka B56; gene symbol PPP2R5) and B” family (aka PR72/130; gene symbol PPP2R3); and Ruvolo [4] tabulate a few of them and provide references for them. Shi [5] studied the mechanism through structure of the serine/threonine phosphatases. The enzyme protein serine/threonine phosphatase acts upon phosphorylated serine/threonine residues as follows (from Wikipedia contributors [6]) : [protein]−serine/threonine−phosphate+H2O= [protein]−serine/threonine+phosphate (1) In their review, Seshacharyulu et al. [7] focus on the structural complexity of serine/threonine phosphatase PP2A and summarize its expression pattern in cancer while discussing about the PP2A interacting and regulatory proteins and substrates. Finally, they also review the mouse models developed to understand the biological role of PP2A subunits in an in vivo model system. Further, Reynhout and Janssens [8] summarize current knowledge on physiologic functions of PP2A in germ cell maturation, tumor suppression, metabolic regulation, embryonic development, and homeostasis of adult brain, liver, heart, immune system, lung, kidney, intestine, skin, eye and bone, all of which were retrieved from in vivo studies using PP2A transgenic, knockout or knockin 3 mice. Hemmings et al. [9] purified Protein phosphatase 2A (polycation-stimulated protein phosphatase L), from porcine kidney and skeletal muscle. Via reverse-phase HPLC, they separated the 36-kDa catalytic and the 65-kDa putative regulatory (hereafter termed PR65) subunits of protein phosphatase 2A2. Molecular cloning showed that two distinct mRNAs (termed α(PP2A-Aalpha)and β(PP2A-Abeta)) encoded the PR65 subunit. The cDNA encoding the α-isotype spanned 2.2 kilobases (kb) and contained an open reading frame of 1767 bases predicting a protein of 65 kDa, while the cDNAs encoding the β-isotype contained an open reading frame of size similar to that of α-form but lacked an initiator ATG. Further, Zhou et al. [10] generated Aβ-specific antibodies and determined the cell cycle expression, subcellular distribution, and metabolic stability of Aβin comparison with Aβ. I present 3rd order combinations of PPP2R1A 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 [11]. 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 [11]. 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 4 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. 5 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 PPP2R1A-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 [12]) and Sobol indicies (with 2002 implementation in Saltelli [13] and martinez implementation in Martinez [14] and Baudin et al. [15]). 6.3. Conserved machine learning rankings for tested PPP2R1A-XX combinations A total of 2415, 3rd order combinations involving PPP2R1A were obtained from a full set of 71C3= 57155 combinations. Further, from this selected set, using the above cri6 teria 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 PPP2CA-PPP2R1A-X combinations Goudreault et al. [16] indicate that the PP2A catalytic (PP2A-C) subunit binds directly to the PP2A-A scaffolding subunit (two 85% identical proteins, PP2A-Aαand PP2AAβ, are present in human cells), to form the PP2A dimeric core. This core serves as a platform for the association of a regulatory or B subunit to generate a trimeric complex important for substrate recruitment and subcellular targeting. The core enzyme of PP2A comprises a 65 kDa scaffolding subunit and a 36 kDa catalytic subunit. Xing et al. [17] report the crystal structures of the PP2A core enzyme bound to two of its inhibitors. They observe that the catalytic subunit recognizes one end of the elongated scaffolding subunit by interacting with the conserved ridges of HEAT repeats 11-15. Formation of the core enzyme forced the scaffolding subunit to undergo pronounced structural rearrangement. The scaffolding subunit exhibited considerable conformational flexibility, which is proposed to play an essential role in PP2A function. These structures, together with biochemical analyses, revealed significant insights into PP2A function and serve as a framework for deciphering the diverse roles of PP2A in cellular physiology. Further, inactivation of both the αand βisoforms of the PP2A scaffolding subunit has been linked to cancer. They cite various references where mutations in the scaffolding subunit result in compromised binding to the regulatory or catalytic subunit of PP2A or a total absence or substantial reduction of the scaffolding subunit, which are closely associated with a variety of primary human tumors. PPP2R1A is the predominant PP2A scaffold A-subunit that is required for functional PP2A complex formation. Kauko et al. [18] observed that unlike depletion of the catalytic PP2A subunit PPP2CA, siRNA of PPP2R1A did not cause cell lethality and, on the other hand, did not affect the PPP2CA expression. However, and as expected, PPP2R1A depletion resulted in destabilization of PPP2R5A (B56) and PPP2R2A (B55) B-subunits. Their results confirmed that PPP2R1A depletion results in comprehensive PP2A complex inhibition. One finds the following combinations for PPP2CA along with PPP2R1A, to be prominent at 3rd order level - LEF1-PPP2CA-PPP2R1A, FZD7-PPP2CA-PPP2R1A, PPP2CA-PPP2R1A-FBXW4, NKD1-PPP2CA-PPP2R1A, PPP2CA-PPP2R1A-SENP2, PPP2CA-PPP2R1A-TLE2, PPP2CA-PPP2R1A-WNT5A, PPP2CA-PPP2R1A-WNT3A, KREMEN1-PPP2CA-PPP2R1A, FZD5-PPP2CA-PPP2R1A, DVL1-PPP2CA-PPP2R1A, GSK3A-PPP2CA-PPP2R1A, AES-PPP2CA-PPP2R1A, AXIN1-PPP2CA-PPP2R1A, EP300-PPP2CA-PPP2R1A, CCND2-PPP2CA-PPP2R1A, PPP2CA-PPP2R1A-WNT2B, FOXN1-PPP2CA-PPP2R1A, FZD1-PPP2CA-PPP2R1A, PPP2CA-PPP2R1A-TCF7, DAAM1PPP2CA-PPP2R1A, CXXC4-PPP2CA-PPP2R1A, FBXW11-PPP2CA-PPP2R1A, APCPPP2CA-PPP2R1A, DVL2-PPP2CA-PPP2R1A, FZD6-PPP2CA-PPP2R1A, FBXW27 RANKING @tiUSING HSIC - LINEAR 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CSNK1D-FGF4-PPP2R1A 72 17401 22364 53716 30729 FSHB-NKD1-PPP2R1A 134 11978 48147 4744 11658 FOXN1-KREMEN1-PPP2R1A 187 38390 45372 22596 7296 FSHB-FZD2-PPP2R1A 216 20883 30530 35125 19903 CTNNBIP1-JUN-PPP2R1A 222 17930 41664 52992 44848 CCND1-FGF4-PPP2R1A 231 42431 52577 39266 5985 CXXC4-FOSL1-PPP2R1A 255 24314 35136 31526 39110 FOSL1-PPP2R1A-SENP2 256 39545 1842 16944 18375 DKK1-JUN-PPP2R1A 267 12255 56230 48454 54215 FRZB-GSK3A-PPP2R1A 353 14275 17584 12248 25992 CSNK2A1-CTBP1-PPP2R1A 386 22561 33967 27086 25647 DAAM1-FGF4-PPP2R1A 419 31801 52927 54325 31945 CXXC4-PORCN-PPP2R1A 424 27798 37533 50501 37618 DKK1-PPP2R1A-SENP2 442 14095 52078 45675 54675 AES-FOXN1-PPP2R1A 486 23646 9985 11397 37399 DVL2-JUN-PPP2R1A 555 45651 45029 17035 30388 AES-AXIN1-PPP2R1A 562 47451 24435 49898 51110 LEF1-NKD1-PPP2R1A 793 3084 55944 23057 25903 FZD8-PORCN-PPP2R1A 807 27524 31540 26322 40650 FOSL1-PPP2R1A-RHOU 846 41555 5035 55239 46031 FBXW11-LRP6-PPP2R1A 920 16519 19037 17797 45281 CSNK1G1-FOXN1-PPP2R1A 960 4562 8931 10045 26824 CTNNB1-FOXN1-PPP2R1A 966 1729 7371 11775 25639 CSNK1D-PPP2R1A-WNT5A 992 931 1207 30631 56811 PITX2-PORCN-PPP2R1A 1003 8071 39783 44256 5481 FBXW11-FGF4-PPP2R1A 1030 29187 47593 48874 21413 CXXC4-FGF4-PPP2R1A 1044 30931 36251 44472 52608 CSNK1D-PPP2R1A-TCF7L1 1128 12625 3602 38061 56712 LEF1-PORCN-PPP2R1A 1139 34004 43790 26178 5620 CCND1-CTBP1-PPP2R1A 1192 36857 14658 39423 20532 DKK1-FGF4-PPP2R1A 1228 16772 51023 37645 49558 FZD1-PORCN-PPP2R1A 1234 19388 36871 41947 10191 DVL1-FOXN1-PPP2R1A 1316 40931 10069 3721 36477 PPP2R1A-WNT1-WNT4 1345 13482 18287 10132 56367 DVL2-FGF4-PPP2R1A 1363 45199 42753 22929 46333 CSNK1D-PPP2R1A-TCF7 1430 4169 153 38743 7414 CSNK2A1-MYC-PPP2R1A 1454 17389 25178 16938 14057 FBXW11-FOXN1-PPP2R1A 1485 2012 6552 10843 25217 CTBP1-FGF4-PPP2R1A 1692 30523 34482 40227 19588 FBXW2-FGF4-PPP2R1A 1759 32973 44562 51245 8907 CSNK2A1-FOXN1-PPP2R1A 1773 10252 16688 5889 9126 CXXC4-JUN-PPP2R1A 1782 11540 37923 13434 43762 PPP2R1A-WNT3-WNT3A 1817 55448 5096 45267 43648 CSNK2A1-FGF4-PPP2R1A 1819 25704 42101 34434 17125 FRZB-PORCN-PPP2R1A 1881 14863 41848 44601 12655 AXIN1-FOXN1-PPP2R1A 1913 4756 8847 11042 32343 FOSL1-PPP2R1A-SFRP4 1952 52448 1955 16120 30096 CSNK1G1-JUN-PPP2R1A 1986 10228 52696 13904 47706 LEF1-MYC-PPP2R1A 1990 40461 15570 31458 22391 FBXW11-JUN-PPP2R1A 2029 7720 56156 47859 37754 FZD2-PORCN-PPP2R1A 2085 13234 40114 30182 21029 CCND3-PORCN-PPP2R1A 2099 25783 29032 23766 18843 CSNK1A1-FGF4-PPP2R1A 2100 34624 20608 35480 22746 DKK1-GSK3A-PPP2R1A 2104 13726 28756 56201 53104 DIXDC1-NKD1-PPP2R1A 2140 5484 54992 25998 568 FZD6-PORCN-PPP2R1A 2181 22169 35065 11807 6867 FZD1-JUN-PPP2R1A 2184 21063 36959 28810 6175 BCL9-FGF4-PPP2R1A 2209 19748 39118 49100 20100 FZD5-PPP2R1A-WNT5A 2239 9275 9172 22179 32268 FSHB-GSK3A-PPP2R1A 2267 11196 31968 18565 24240 PPP2R1A-WNT3-WNT4 2411 43365 6520 45456 48427 FRAT1-JUN-PPP2R1A 2465 21726 41887 23096 41465 FBXW11-FZD2-PPP2R1A 2469 12611 33445 15277 21128 DAAM1-GSK3A-PPP2R1A 2495 39121 35124 30013 51000 CSNK1G1-FGF4-PPP2R1A 2535 19539 51865 57137 46652 PPP2R1A-TLE1-TLE2 2603 23452 51446 28086 54181 FZD8-JUN-PPP2R1A 2633 37008 34949 19872 55616 APC-FZD6-PPP2R1A 2668 19187 290 54948 5882 FOSL1-JUN-PPP2R1A 2696 46872 41797 35276 27908 CSNK1G1-PORCN-PPP2R1A 2697 18740 49826 20704 24737 CCND2-LRP6-PPP2R1A 2763 48463 13066 23230 6578 DKK1-FOXN1-PPP2R1A 2783 23484 22053 10586 44403 CSNK2A1-GSK3A-PPP2R1A 2846 28306 32715 6544 36708 CSNK1D-PORCN-PPP2R1A 2896 17111 34991 43683 19157 PPP2R1A-TLE1-WNT4 2902 4217 52852 23987 31073 CTNNBIP1-FGF4-PPP2R1A 2959 22853 37005 28725 35681 PPP2R1A-WNT1-WNT3A 2989 13277 15619 27990 53390 BCL9-PORCN-PPP2R1A 3009 23888 28332 49136 12024 FGF4-PPP2R1A-SFRP4 3037 8718 1707 14759 34549 EP300-FOXN1-PPP2R1A 3054 31254 9485 1045 4738 FZD1-NLK-PPP2R1A 3063 6647 16715 10003 26509 DAAM1-FOXN1-PPP2R1A 3097 26397 35409 10550 45683 PPP2R1A-SFRP1-TCF7 3233 44109 34973 47932 35401 DVL1-FGF4-PPP2R1A 3242 41242 45411 17324 23922 FZD7-PORCN-PPP2R1A 3293 54918 29516 41742 23131 FZD5-FGF4-PPP2R1A 3315 19006 41149 46199 17261 FOSL1-PORCN-PPP2R1A 3418 54803 40086 41005 20335 FBXW11-GSK3A-PPP2R1A 3471 17513 23616 47087 26387 AXIN1-FZD2-PPP2R1A 3530 36160 24224 14226 14076 DVL1-GSK3A-PPP2R1A 3570 44275 16001 23234 34855 EP300-PORCN-PPP2R1A 3588 55435 38638 36180 44771 FBXW11-PORCN-PPP2R1A 3600 13551 28934 48860 10946 PPP2R1A-SFRP1-FBXW4 3602 34385 50714 10310 44807 FZD5-NKD1-PPP2R1A 3621 21515 54524 36048 1557 CTNNB1-PORCN-PPP2R1A 3628 8334 43683 23768 39432 FRAT1-PORCN-PPP2R1A 3641 17091 37502 41949 11356 DAAM1-PORCN-PPP2R1A 3682 30772 17215 29018 29847 CCND1-JUN-PPP2R1A 3683 12869 49497 55359 13160 LRP5-NLK-PPP2R1A 3749 6866 25722 95 55900 CSNK1G1-NLK-PPP2R1A 3754 21618 10600 22928 48421 CCND3-PPP2R1A-SENP2 3947 20724 4140 11034 41552 DKK1-PORCN-PPP2R1A 4028 22121 57008 12032 54395 EP300-FGF4-PPP2R1A 4059 54172 38740 54434 30530 GSK3B-LRP6-PPP2R1A 4082 43470 10296 43375 25140 EP300-JUN-PPP2R1A 4089 45635 48485 28347 10942 FZD5-PORCN-PPP2R1A 4090 33288 41287 38390 34991 FRAT1-NLK-PPP2R1A 4096 7150 14882 4380 42041 CTBP1-PPP2R1A-TCF7 4108 3719 931 22058 13655 CSNK2A1-NKD1-PPP2R1A 4118 2001 56920 13318 8736 CTNNBIP1-NLK-PPP2R1A 4168 17696 21970 43414 47292 DKK1-PPP2R1A-TLE2 4213 1676 48827 40467 57091 CTNNBIP1-FRAT1-PPP2R1A 4272 14548 33170 16600 48598 CTBP1-GSK3A-PPP2R1A 4275 19056 10307 24065 37785 GSK3B-JUN-PPP2R1A 4299 50524 49319 35755 3146 PPP2R1A-TLE1-WIF1 4307 33741 44977 32847 32390 DIXDC1-FOXN1-PPP2R1A 4318 4042 7718 10315 5136 PPP2R1A-SFRP1-WNT3A 4336 49933 48304 18593 24856 FZD7-JUN-PPP2R1A 4369 47090 33547 30519 53889 BCL9-JUN-PPP2R1A 4379 12860 38522 50713 4351 CSNK1A1-PORCN-PPP2R1A 4422 33823 41491 28773 10648 CXXC4-PPP2R1A-RHOU 4427 19193 3464 42655 56387 FOSL1-PPP2R1A-TCF7 4468 34122 1739 41424 25089 FZD8-GSK3A-PPP2R1A 4484 40441 18881 46804 54756 PPP2R1A-RHOU-SLC9A3R1 4485 42742 45200 38226 53842 DKK1-PPP2R1A-WNT5A 4534 3478 36759 50853 55700 FZD1-NKD1-PPP2R1A 4562 26290 43026 35994 1774 Table 1: Rankings of PPP2R1A-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - linear PPP2CA-PPP2R1A, CSNK2A1-PPP2CA-PPP2R1A, CTNNB1-PPP2CA-PPP2R1A, FOSL1PPP2CA-PPP2R1A, LRP5-PPP2CA-PPP2R1A, FZD8-PPP2CA-PPP2R1A, MYC-PPP2CAPPP2R1A, CSNK1D-PPP2CA-PPP2R1A, PPP2CA-PPP2R1A-PYGO1, PORCN-PPP2CAPPP2R1A, FRAT1-PPP2CA-PPP2R1A, JUN-PPP2CA-PPP2R1A, CTBP1-PPP2CA8 RANKING @tiUSING HSIC - RBF 3rd order comb. t1t3t6t12 t24 3rd order comb. t1t3t6t12 t24 CSNK1D-FGF4-PPP2R1A 3004 29048 12442 15684 23801 FSHB-NKD1-PPP2R1A 25236 3206 25555 29398 54336 FOXN1-KREMEN1-PPP2R1A 21547 15130 581 7154 55001 FSHB-FZD2-PPP2R1A 10535 30086 26859 11239 24594 CTNNBIP1-JUN-PPP2R1A 42662 30325 24952 5762 37211 CCND1-FGF4-PPP2R1A 9841 27457 12592 18053 2791 CXXC4-FOSL1-PPP2R1A 52227 34156 6226 46113 43359 FOSL1-PPP2R1A-SENP2 36531 47500 56688 1297 8711 DKK1-JUN-PPP2R1A 19726 15606 1085 29841 36603 FRZB-GSK3A-PPP2R1A 1658 24598 48047 40183 47791 CSNK2A1-CTBP1-PPP2R1A 51425 30212 13474 42814 33263 DAAM1-FGF4-PPP2R1A 1363 39705 27194 16188 12922 CXXC4-PORCN-PPP2R1A 20998 30567 5511 22186 56640 DKK1-PPP2R1A-SENP2 4320 17195 24869 14464 3866 AES-FOXN1-PPP2R1A 723 21691 22365 18788 29319 DVL2-JUN-PPP2R1A 7790 48428 6855 9490 40633 AES-AXIN1-PPP2R1A 37649 36390 27090 29535 33374 LEF1-NKD1-PPP2R1A 24944 9286 39491 44583 37109 FZD8-PORCN-PPP2R1A 3136 21194 9602 10973 55135 FOSL1-PPP2R1A-RHOU 19254 49825 54278 50968 41085 FBXW11-LRP6-PPP2R1A 2990 7171 41891 45594 39934 CSNK1G1-FOXN1-PPP2R1A 3415 1125 22606 474 39586 CTNNB1-FOXN1-PPP2R1A 6266 597 36708 568 27942 CSNK1D-PPP2R1A-WNT5A 27528 4279 14277 4265 42405 PITX2-PORCN-PPP2R1A 11355 50277 26063 28070 55628 FBXW11-FGF4-PPP2R1A 2311 3713 32222 41780 18993 CXXC4-FGF4-PPP2R1A 1192 9614 5570 26405 23051 CSNK1D-PPP2R1A-TCF7L1 34388 5648 48876 25681 52823 LEF1-PORCN-PPP2R1A 9650 37275 29706 14200 48587 CCND1-CTBP1-PPP2R1A 42960 11026 30626 24182 7494 DKK1-FGF4-PPP2R1A 1885 5747 727 4631 30783 FZD1-PORCN-PPP2R1A 24806 24942 1636 2232 55350 DVL1-FOXN1-PPP2R1A 7337 28739 5315 11310 23091 PPP2R1A-WNT1-WNT4 13056 3776 48355 444 25289 DVL2-FGF4-PPP2R1A 3678 46957 3278 19048 26196 CSNK1D-PPP2R1A-TCF7 34317 14103 3740 45791 33515 CSNK2A1-MYC-PPP2R1A 8973 18254 44398 29894 43896 FBXW11-FOXN1-PPP2R1A 848 15861 49514 22629 20720 CTBP1-FGF4-PPP2R1A 2812 38280 137 44051 39921 FBXW2-FGF4-PPP2R1A 849 18830 22979 9327 14927 CSNK2A1-FOXN1-PPP2R1A 647 14324 25472 4074 30161 CXXC4-JUN-PPP2R1A 8147 19410 4343 32567 48732 PPP2R1A-WNT3-WNT3A 9441 54192 34392 53766 7535 CSNK2A1-FGF4-PPP2R1A 166 29600 18823 44833 19787 FRZB-PORCN-PPP2R1A 13914 23845 13959 7815 56301 AXIN1-FOXN1-PPP2R1A 12949 15322 34068 9033 35734 FOSL1-PPP2R1A-SFRP4 50064 57024 56666 31648 53883 CSNK1G1-JUN-PPP2R1A 2410 8342 5954 20586 31871 LEF1-MYC-PPP2R1A 5271 38043 45068 15629 15850 FBXW11-JUN-PPP2R1A 15642 5206 44646 46199 19057 FZD2-PORCN-PPP2R1A 335 12575 8770 1810 55522 CCND3-PORCN-PPP2R1A 23176 16220 12632 6835 44417 CSNK1A1-FGF4-PPP2R1A 4863 12539 3164 12998 34074 DKK1-GSK3A-PPP2R1A 37 15243 34284 9621 35620 DIXDC1-NKD1-PPP2R1A 41282 2633 37452 52221 22216 FZD6-PORCN-PPP2R1A 23 17577 25321 670 56053 FZD1-JUN-PPP2R1A 32015 23065 8067 12950 35467 BCL9-FGF4-PPP2R1A 10398 5395 4459 43209 26087 FZD5-PPP2R1A-WNT5A 17060 9682 37942 54060 54700 FSHB-GSK3A-PPP2R1A 2994 22740 47062 16574 48029 PPP2R1A-WNT3-WNT4 6466 47384 44643 26384 8285 FRAT1-JUN-PPP2R1A 14775 16627 12246 41797 26468 FBXW11-FZD2-PPP2R1A 8700 4798 40674 36207 15746 DAAM1-GSK3A-PPP2R1A 6522 35629 52023 19728 17125 CSNK1G1-FGF4-PPP2R1A 8938 29139 2598 16353 38899 PPP2R1A-TLE1-TLE2 44598 3120 16931 19408 1179 FZD8-JUN-PPP2R1A 7769 37927 11864 24690 38173 APC-FZD6-PPP2R1A 26156 38611 29925 13305 29320 FOSL1-JUN-PPP2R1A 20816 55928 16147 47523 47242 CSNK1G1-PORCN-PPP2R1A 16024 19421 9392 5370 55173 CCND2-LRP6-PPP2R1A 7525 49696 47315 30017 29589 DKK1-FOXN1-PPP2R1A 1768 15517 15329 5073 18412 CSNK2A1-GSK3A-PPP2R1A 6662 21693 51937 52594 38018 CSNK1D-PORCN-PPP2R1A 16940 28022 22571 2476 54099 PPP2R1A-TLE1-WNT4 34919 1417 25861 8678 8293 CTNNBIP1-FGF4-PPP2R1A 2426 9206 12675 669 32498 PPP2R1A-WNT1-WNT3A 2644 9345 37570 29489 17577 BCL9-PORCN-PPP2R1A 28259 20478 5854 26873 52990 FGF4-PPP2R1A-SFRP4 8036 9755 54750 29227 49177 EP300-FOXN1-PPP2R1A 1354 35385 45759 2306 27930 FZD1-NLK-PPP2R1A 20834 8886 52092 12766 24248 DAAM1-FOXN1-PPP2R1A 1334 13230 49009 5916 8662 PPP2R1A-SFRP1-TCF7 8562 33991 8051 54700 29578 DVL1-FGF4-PPP2R1A 5991 18327 77 43200 54479 FZD7-PORCN-PPP2R1A 39388 55931 21995 3462 52550 FZD5-FGF4-PPP2R1A 1273 30877 9798 36227 30025 FOSL1-PORCN-PPP2R1A 1690 56373 15424 4340 55845 FBXW11-GSK3A-PPP2R1A 2166 8382 55946 44477 32821 AXIN1-FZD2-PPP2R1A 26985 37883 10434 10353 20291 DVL1-GSK3A-PPP2R1A 15051 28660 39098 46332 48932 EP300-PORCN-PPP2R1A 9705 56176 25373 738 50930 FBXW11-PORCN-PPP2R1A 5633 5510 29166 19086 52513 PPP2R1A-SFRP1-FBXW4 43447 35660 2162 20015 15609 FZD5-NKD1-PPP2R1A 23335 9105 47323 31744 56453 CTNNB1-PORCN-PPP2R1A 12296 20951 22147 236 56429 FRAT1-PORCN-PPP2R1A 14510 12147 3493 8420 55974 DAAM1-PORCN-PPP2R1A 43717 12829 27614 274 42068 CCND1-JUN-PPP2R1A 28970 7761 24201 8661 5096 LRP5-NLK-PPP2R1A 22739 10079 12169 17484 38120 CSNK1G1-NLK-PPP2R1A 35195 9424 21823 20710 43474 CCND3-PPP2R1A-SENP2 10144 14970 33230 89 13210 DKK1-PORCN-PPP2R1A 15567 20860 1442 5709 55732 EP300-FGF4-PPP2R1A 434 56284 13608 15792 27194 GSK3B-LRP6-PPP2R1A 6362 47681 43483 14542 49585 EP300-JUN-PPP2R1A 5997 52619 15125 40032 31600 FZD5-PORCN-PPP2R1A 23669 41306 11440 2543 56519 FRAT1-NLK-PPP2R1A 47257 5675 39028 27369 25057 CTBP1-PPP2R1A-TCF7 13922 7113 7010 44002 53010 CSNK2A1-NKD1-PPP2R1A 19188 9240 34119 49629 44582 CTNNBIP1-NLK-PPP2R1A 27842 23336 43647 19091 40032 DKK1-PPP2R1A-TLE2 18876 4979 33058 36302 34591 CTNNBIP1-FRAT1-PPP2R1A 19452 31715 19287 3657 50902 CTBP1-GSK3A-PPP2R1A 193 46150 47414 42441 47384 GSK3B-JUN-PPP2R1A 4762 52417 19413 19919 45463 PPP2R1A-TLE1-WIF1 18734 28938 477 39566 970 DIXDC1-FOXN1-PPP2R1A 3585 17552 18249 8440 13079 PPP2R1A-SFRP1-WNT3A 10638 51919 14638 49471 17076 FZD7-JUN-PPP2R1A 15754 47453 8319 37051 11201 BCL9-JUN-PPP2R1A 38825 31345 7280 45954 33797 CSNK1A1-PORCN-PPP2R1A 32307 17216 8460 87 56661 CXXC4-PPP2R1A-RHOU 24725 6975 48923 38600 48066 FOSL1-PPP2R1A-TCF7 32156 40396 19240 52936 29464 FZD8-GSK3A-PPP2R1A 442 39080 49490 18545 37574 PPP2R1A-RHOU-SLC9A3R1 50539 48128 21287 4442 19281 DKK1-PPP2R1A-WNT5A 17268 5548 34963 48461 43857 FZD1-NKD1-PPP2R1A 38340 8464 17462 30009 50089 Table 2: Rankings of PPP2R1A-X-X. A list of approximately first 125 combinations with rankings below 10,000 out of 57,155. SA - HSIC; Kernel - rbf PPP2R1A, CTNNBIP1-PPP2CA-PPP2R1A, FGF4-PPP2CA-PPP2R1A, CSNK1A1PPP2CA-PPP2R1A, CCND1-PPP2CA-PPP2R1A, PPP2CA-PPP2R1A-T, and NLKPPP2CA-PPP2R1A. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations (Table not shown, but data available in supplementary files). 9 manner. Further, the nuclear phosphoprotein c-JUN is a major component of the AP1 transcription factor, whose activity is augmented by many oncogenes. An important mechanism to stimulate AP1 function is N-terminal phosphorylation of c-JUN at the serine residues 63 and 73 by the c-JUN N-terminal kinases (JNKs). To determine the function of c-JUN N-terminal phosphorylation (JNP) during oncogenic transformation in vitro and in vivo, Behrens et al. [32] used mice and cells harboring a mutant allele of c-JUN, which has the JNK phosphoacceptor serines changed to alanines (JUN-AA). JUN-AA immortalized fibroblasts expressing v-RAS and v-FOS showed reduced tumorigenicity in nude mice, but the efficiency of v-SRC transformation was unaffected by the lack of JNP. To assess the significance of JNP in tumour development in vivo, two transgenic mouse tumour models were employed. Skin tumour development caused by constitutive activation of the RAS pathway by K5-SOS-F expression and c-FOS-induced osteosarcoma formation were impaired in mice lacking JNP. Thus there is a connection between c-JUN and FOSL1, that might be existing. Finally, figure 4 in Clark and Ohlmeyer [33] shows c-JUN which combines with c-FOS and protein dephosphorylation is initiated by PP2A. Looking at the tables above, one finds the following combinations for FOSL1 along with PPP2R1A, to be prominent at 3rd order level - CXXC4-FOSL1-PPP2R1A, FOSL1-PPP2R1A-SFRP4, FOSL1-JUN-PPP2R1A, FOSL1-PORCN-PPP2R1A, FOSL1PPP2R1A-SENP2, FOSL1-PPP2R1A-RHOU and FOSL1-PPP2R1A-TCF7. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 6.4.10. Examining the behaviour of FOX-PPP2CA-X combinations CONNECTION OF FOX-PPP2CA - PP2A is a tumour suppressor whose strong inhibition underlies the phosphorylation-dependent, anti-apoptotic mechanisms in chronic lymphocytic leukemia (CLL). Inactivation of PP2A is due to the cooperative action of the phosphorylation of Y307 of its catalytic subunit by the aberrant cytosolic pool of the SRC family kinase LYN and the interaction with its protein inhibitor SET, which is overexpressed in CLL. Pagano et al. [34] developed a library of compounds, the most potent being the one named CC11, which restores PP2A activity by disrupting the PP2A/SET complex, thereby triggering the mitochondrial pathway of apoptosis. They observe that this process involves the recruitment of the proapoptotic BH3-only proteins BAD and BIM to mitochondria, the former upon direct dephosphorylation and the latter being newly expressed upon dephosphorylation and activation of its transcription factor FOXO3A. Their findings highlighted that PP2A antagonized the prosurvival pathways controlled by AKT, which phosphorylates and thereby suppresses a variety of pro-apoptotic factors and tumour suppressors including BAD and FOXO3A. Looking at the tables above, one finds the following combinations for members of FOX family along with PPP2R1A, to be prominent at 3rd order level - FOXN1KREMEN1-PPP2R1A, AES-FOXN1-PPP2R1A, CTNNB1-FOXN1-PPP2R1A, DVL1FOXN1-PPP2R1A, CSNK2A1-FOXN1-PPP2R1A, CSNK1G1-FOXN1-PPP2R1A, FBXW11FOXN1-PPP2R1A, AXIN1-FOXN1-PPP2R1A, DKK1-FOXN1-PPP2R1A, EP300-FOXN1PPP2R1A, DAAM1-FOXN1-PPP2R1A and DIXDC1-FOXN1-PPP2R1A. All these 16 combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 6.4.11. Examining the behaviour of EP300-PPP2R1A-X combinations CONNECTION OF EP300-PPP2CA - Transcriptional coactivator p300 (or EP300) is required for embryonic development and cell proliferation. Valproic acid, a histone deacetylase inhibitor, is widely used in the therapy of epilepsy and bipolar disorder. Chen et al. [35] report that valproic acid stimulates proteasome-dependent p300 degradation through augmentation of gene expression of the B56γregulatory subunits of protein phosphatase 2A. The B56γ3 regulatory and catalytic subunits of protein phosphatase 2A interact with p300. Overexpression of the B56γ3 subunit led to proteasomemediated p300 degradation and repressed p300-dependent transcriptional activation, which required the B56γ3 interaction domain of p300. Conversely, silencing of the B56γsubunit expression by RNA interference increased the stability and transcriptional activity of p300. Via quantitative phospho-proteomic analysis, Brewer et al. [23] identified EP300 to be substrate of PPP2CA. Looking at the tables above, one finds the following combinations for EP300 along with PPP2R1A, to be prominent at 3rd order level - EP300-PORCN-PPP2R1A, EP300FGF4-PPP2R1A, EP300-JUN-PPP2R1A and EP300-FOXN1-PPP2R1A. All these combinations indicate the existence of a possible synergy when they take a higher rank in the list of combinations. 7. Conclusion This manuscript studies the time behaviour of 3rd order combinations of PPP2R1A in WNT3A stimulated HEK 293 cells. Based on the extablished 2nd order combinations of the PPP2R1A, 3rd order combinations emerge using the machine learning based search engine. These 3rd order combinations might be of interest for further wet lab investigations. Competing interests No competing interest is declared. Author contributions statement SS conceived and designed the experiments; wrote the code; performed the experiments; analyzed the data; wrote the manuscript. 17 Availability of code Code for time series data available at CERN based Zenodo on https://zenodo.org/ records/14637456. Acknowledgments Special thanks to Mrs. Rita Sinha and late Mr. Prabhat Sinha for supporting the author financially, without which this work could not have been made possible. 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