Exploring the Robustness of Causal Structures in Omics Data: A Sweet Cherry Proteogenomic Perspective

Abstract

Causal discovery is a highly promising tool with a broad perspective in the field of biology. In this study, a causal structure robustness assessment algorithm is proposed and employed on the causal structures obtained, based on transcriptomic, proteomic, and the combined datasets, emerging from a quantitative proteogenomic atlas of 15 sweet cherry (Prunus avium L.) cv. ‘Tragana Edessis’ tissues. The algorithm assesses the impact of intervening in the datasets of the causal structures, using various criteria. The results showed that specific tissues exhibited an intense impact on the causal structures that were considered. In addition, the proteogenomic case demonstrated that biologically related tissues that referred to the same organ induced a similar impact on the causal structures considered, as was biologically expected. However, this result was subtler in both the transcriptomic and the proteomic cases. Furthermore, the causal structures based on a single omic analysis were found to be impacted to a larger extent, compared to the proteogenomic case, probably due to the distinctive biological features related to the proteome or the transcriptome. This study showcases the significance and perspective of assessing the causal structure robustness based on omic databases, in conjunction with causal discovery, and reveals advantages when employing a multiomics (proteogenomic) analysis compared to a single-omic (transcriptomic, proteomic) analysis.

1. Introduction

The elucidation of gene and protein expression, along with their interplays, stands as a cornerstone in biological sciences [1]. Transcriptome profiling on a large scale has gained traction as a primary technique to scrutinize the variety within biological specimens. Such analyses have traditionally been organ-specific or encompass entire entities, like plants, but there is a growing emphasis on detailed transcriptome profiles of distinct tissues or cells due to their potential to unravel gene functionality [2].

The field of proteogenomics emerged as an innovative approach, expanding the scope of genomic analysis through the integration of transcriptomic and proteomic data [3]. This methodological fusion seeks to concurrently examine alterations at the genetic level—such as mutations, polymorphisms, and insertions/deletions—with those at the protein level [4]. Proteogenomic databases are pivotal in correlating gene expression with protein production, thereby enhancing the comprehension of gene models [3,5,6]. Beyond its established utility in augmenting genome annotation and protein identification in non-model plant species [7], proteogenomics holds considerable promise in biotechnological endeavors, particularly plant breeding. For instance, proteogenomics facilitates a detailed elucidation of biosynthetic pathways, aiming to augment agronomic traits, a concept recently applied to pear breeding through gene co-expression module analysis [8]. Furthermore, proteogenomic analyses contribute to the exploration of alternative splicing events and post-translational modifications in plant species [9]. An application of proteogenomic analysis has also been noted in examining the role of carbamoyltransferase genes during the ripening of fleshy fruits [10]. Nonetheless, the development of bioinformatic tools to adeptly manage and interpret this wealth of proteogenomic data for actionable insights remains in its nascent stages [6].

Causal models are used to investigate the structure of causal relationships between different variables. Causal discovery justifies the causal nature of a relationship between two variables based on its persistence [11]. An advantage of causal model development, compared to traditional statistical association, is the existence of direction in the causal relationships between variables, which characterizes the cause and the effect variable in each relation [11]. This is of particular importance in several scientific fields, including biology, and contrasts with the typically used correlation indices, which are mostly bidirectional. Thus, causal discovery demonstrates a wide potential in the field of biology. Obtaining the causal structure may validate expectations and/or uncover new knowledge, facilitating scientific interpretations. Causal discovery has been used in the literature within different contexts (see, e.g., [12,13,14,15,16,17]). Particularly, in the field of genetics, causal methods or their underlying ideas have been applied, among else, to detect causal relationships among phenotypes [18,19] to infer gene regulatory networks [20,21,22,23,24,25], and to infer causal associations between gene expression and disease [26]. A more detailed discussion on causal discovery in biology can be found in Glymour et al. [27].

Causal structure investigation and Directed Acyclic Graphs (DAGs), in particular, have been employed by our group in several studies that involved multiomics data. Employing causal structure learning in olive leaves and roots at a proteogenomic level, unveiled key interaction networks involved in salt priming in olive trees [28]. A causal model-based multiomics pipeline was introduced in Boutsika, et al. [29] to determine the molecular portrait of the PGI potatoes of the Naxos Island. Genome-wide DNA methylation, RNA sequencing and quantitative proteomics were exploited, revealing key environment-derived molecular factors, putative epimarkers and key microbes, relevant to authenticating Naxos potato [29]. In addition, causal discovery was employed in sweet cherry multiomics data, leading to understanding the cause–effect relationships that are important in the fruit softening and ripening process in sweet cherry (Prunus avium L.) [30]. The analysis in Ganopoulou et al. [30] was based on a plant tissue proteogenomic atlas that contains a combination of sweet cherry (Prunus avium L.) tree transcriptomic and proteomic datasets (represented by 29,247 genes and 7584 proteins, respectively), involving 15 sweet cherry tissue samples [31]. The sweet cherry, a perennial fruit tree belonging to the Rosaceae family, holds a prominent economic position globally [32,33,34]. Its non-climacteric ripening pattern distinguishes it from other Prunus species like peach and apricot, adding to the significance of its study [35].

A question arising when determining the causal structure is related to the robustness of the causal structure itself. Towards this direction, a causal structure robustness assessment approach has been recently introduced, aiming to assess the robustness of the causal relationships of genetic risk factors that affect the Syntax Score, an index that evaluates the complexity of coronary artery disease [36]. This approach investigated the impact on the obtained causal structures, both local and global, under different levels of interventions, reflected in the increasing number of patients (observations) that were randomly excluded from the datasets considered.

The aim herein was to propose a new causal structure robustness assessment algorithm, specifically designed for single-omic or multiomics data involving plant tissue samples, and employ sweet cherry as an example to apply it and assess the robustness of the related obtained causal structures. In contrast to Ganopoulou et al. [30], where causal discovery referred to the gene/protein consensus modules (clusters) that were obtained by employing weighted gene co-expression network analysis (WGCNA) [37], herein, it referred directly to the gene/proteins. The transcriptomic and proteomic data were separately considered at first, and the results were compared with the case when they were jointly used in a multiomics analysis. The proposed approach assesses the robustness of the obtained causal structures by evaluating the impact of intervening in the datasets of these causal structures using diverse criteria. The differences compared to the approach proposed in Ganopoulou et al. [36] are that, herein, each of the observations (plant tissues) involved is removed, one at a time, from the datasets (compared to the random exclusion of an increasing number of observations/patients in [36]), and the causal structure is re-determined and compared not only to the initial causal structure but, in addition, to the remaining re-determined causal structures. The reason for separately treating each tissue is that plant tissue samples are, in general, straightforwardly related to specific biological functions. Assessing the robustness of causal structures that are obtained, either in a single-omic or in a multiomics context, on top of validating causal discovery and related inferred knowledge and conclusions, may provide valuable insight regarding specific tissues and their impact when determining causal relationships.

2. Materials and Methods

2.1. Directed Acyclic Graphs (DAGs)

Bayesian networks constitute a distinct category of graphical models used for illustrating and explicating the causal relationships among random variables. These networks are constructed as DAGs that were initially proposed by Pearl [38]. DAGs employ nodes (or vertices) and directed edges (or arcs) as fundamental components to visualize the causal structure. Each node typically corresponds to a random variable. The graphical representation enables the visualization of statistical dependencies existing among various variables. Within the framework of DAGs, paths (or chains) are delineated as sequences of interconnected edges. If a directed edge connects variable $X$ to $Y$, $X$ is identified as the parent (or cause) of $Y$, while $Y$ is considered the child (or effect) of $X$. DAGs exhibit an acyclic structure, namely no paths of edges originating from a node and terminating at the same node exist.

A completed partially-directed acyclic graph (CPDAG) represents the Markov equivalence class of a DAG [39]. All DAGs that belong to a specific equivalence class describe the same conditional independence relationships since they are structured with the same skeleton (adjacencies) and the same v-structures. Assume $D$ is a DAG. The skeleton of $D$ is the undirected graph that is formed by removing the directions of all the edges in the DAG. A v-structure in $D$ is an ordered triplet of nodes ($x, y, z$), such that $D$ contains the directions of $x\to y$ and y←z; additionally, the nodes $x, z$ are not connected with an edge in $D$. Some edges may exhibit an undetermined direction (so-called bidirected/undirected edges). This means that they have the opposite direction from one DAG in the equivalence class to another DAG in the same equivalence class.

2.2. Data Description

Sweet cherry cv. ‘Tragana Edessis’ tissue samples (15 in total) were collected (represented by 29,247 genes and 7584 proteins) related to the most important organs. In particular, the tissues covered the annual sweet cherry shoot (“1st Year shoot”), early growth leaves (“Young leaves”), fully developed leaves (“Leaves”), dormant flower (“Flower buds”), dormant vegetative buds (“Dormancy buds”, early in spring, ecodormancy stage), flowers at both white tip stage (“1st Bloom”) and full flowering phase (“Flower”). Sweet cherry fruit (exo-mesocarp) were sampled during four developmental stages, corresponding to the fruit set (8 days after full bloom [DAFB]; “Fruit 1st stage”), the beginning of fruit coloring from green to yellow (20 DAFB; “Fruit 2nd stage”), the coloring from yellow to red (34 DAFB; “Fruit 3rd stage”), and to the fruit ripe for harvest (44 DAFB; “Fruit 4th stage”). The corresponding stems were collected at the same developmental stages (“Stem 1st stage”, “Stem 2nd stage”, “Stem 3rd stage” and “Stem 4th stage”). More details can be found in Xanthopoulou et al. [31]. The transcript expression and protein abundances are available in the SweetBiOmics database (www.GrCherrydb.com, accessed on 1 September 2023).

2.3. Robustness Assessment Algorithm

The causal structure robustness assessment algorithm was tailored for single-omic or multiomics data involving plant tissue samples. It is focused on assessing the robustness of the related obtained causal structures by evaluating the impact of intervening in the datasets based on which these causal structures were determined. It entails the following steps:

i.

Determine/estimate the initial causal structure (CPDAG) based on the related omic database (assume that it entails $n$ plant tissues), using a selected causal structure learning algorithm.

ii.

Each of the plant tissues (observations) involved is removed, one at a time, from the database and the causal structure is re-determined, resulting in $n$ new causal structures (CPDAGs), each corresponding to a particular plant tissue excluded.

iii.

Each of the CPDAGs is compared to all CPDAGs ($n+1$, both the initial and the re-determined CPDAGs), each of which is assumed to be the reference causal structure in each comparison.

iv.

The comparison is performed based on various metrics. In particular:

a.

The structural Hamming distance (SHD) between two CPDAGs [40]. This distance accounts for the number of operators required to make two CPDAGs match, or more specifically, to add or delete an undirected edge, and add, remove, or reverse the orientation of an edge. The SHD is computed for all pairs of CPDAGs.

b.

The percentage of common bidirected edges. The percentage of bidirected edges in each reference CPDAG that remained bidirected in each CPDAG.

c.

The percentage of common directed edges. The percentage of directed edges in each reference CPDAG that remained directed with the same direction in each CPDAG.

d.

The percentage of directed to bidirected edges. The percentage of directed edges in each reference CPDAG that turned into bidirected in each CPDAG.

e.

The percentage of directed edges that changed direction. The percentage of directed edges in each reference CPDAG that changed direction in each CPDAG.

v.

Hierarchical clustering is performed based on the above metrics and/or combinations of the metrics and is used to cluster the $n+1$ CPDAGs based on their comparison to all CPDAGs (when considered as the reference causal structures). In particular, the $n+1$ vectors, which correspond to the values of a selected metric when each of the $n+1$ CPDAGs is compared to all CPDAGs (reference causal structures), are used to hierarchically cluster the CPDAGs.

Reasoning

The reasoning within Steps (ii) and (iii) is that, since plant tissue samples are, in general, related to specific biological functions, by removing the data related to a specific plant tissue from the database and re-determining the causal structure, valuable insight may emerge pertained to this tissue. For example, based on the differences between the re-determined causal structure compared to the initial causal structure, conclusions can be drawn regarding the impact of a specific tissue on the estimated initial causal relationships. In addition, CPDAGs corresponding to the exclusion of biologically similar tissues (e.g., covering the same organ) may be expected to be similar. If not, it may be of interest to understand the differences in the corresponding causal structures. Moreover, two re-determined CPDAGs may exhibit many differences compared to the initial CPDAG, and at the same time be very similar to each other, or exhibit many differences as well when being compared to each other. The selection of criteria in step (iv) aimed to efficiently describe the CPDAGs comparison, based both on an overall assessment (SHD) and specific characteristics of the CPDAGs, such as similarities in bidirected/directed edges and changes that have occurred from one CPDAG to another. The reasoning within Step (v) is to evaluate the obtained CPDAG clusters and draw specific conclusions. An interesting aspect is to investigate whether CPDAGs corresponding to the exclusion of biologically similar tissues are clustered together.

2.4. Sweet Cherry Proteogenomic Atlas–Causal Structure Robustness Assessment

The analysis was based on the protein abundances and the transcript FPKMs in the Sweet Cherry Proteogenomic Atlas [31]. Initially, the pre-processing of the data was performed as described in Xanthopoulou et al. [31]. Additionally, only gene/protein pairs with valid values for all tissues at both proteomic and transcriptomic levels were selected (n = 7244). Of these, only the gene/protein pairs with values greater than 1 in at least 5 tissues (one out of three) at both protein and transcriptomic levels were further assessed, resulting in 6332 cases. Both the proteomic and the transcriptomic data were standardized per protein/gene ID across all 15 tissues.

Then, the causal structure robustness assessment algorithm, described in Section 2.3, was separately performed in three cases, (a) single-omic: only the transcriptomic data were considered (n = 6332, 15 tissues), (b) single-omic: only the proteomic data were considered (n = 6332, 15 tissues), and (c) multiomics: both the transcriptomic and the proteomic data were considered (n = 6332, 30 tissues).

At step (i) of the algorithm, the causal relationships among (a) the 6332 genes, (b) the 6332 proteins, and (c) the 6332 gene/protein pairs were initially determined based on all 15 tissues with the constrained-based PC algorithm [41,42], which is a common algorithm used to learn the structure of a causal Bayesian network, named after its inventors, Peter Spirtes and Clark Glymour. The CPDAG that was obtained was represented by “All15T” (in all three cases (a), (b) and (c)). It was typically assumed that causal sufficiency holds [11]. This condition implies that for each pair of measured variables, all their common direct causes are measured as well. That is to say, there are no hidden, unmeasured confounders for any pair of variables. The PC algorithm was applied using the R package “MXM” [43]. The skeleton of the causal network was developed with the function “pc.con”, which performs a faster implementation of the PC algorithm compared to the “pc.skel” function (in the same R package), but is limited to continuous data only as was the case in this study. The method argument was opted to be “pearson”, and the significance level “alpha” was set to 0.01, both being the default values in this function.

Then (step (ii)), each of the available 15 tissues was removed from each dataset, one at a time, and the causal structure was re-determined resulting in 15 newly determined CPDAGs in each case, based on 14, 14 and 28 tissues considered, respectively, ((a), (b) and (c)), since in the case of the proteogenomic analysis each tissue was removed from both datasets. These 15 re-determined CPDAGs were represented by “T$\mathrm{i}$”, where i = 1, 2, …, 15, corresponded to the ith tissue that was removed from the analysis. Namely, “T$\mathrm{i}$” stands for the CPDAG that was based on all 15 tissues except for the ith tissue. For example, if the 5th tissue was removed from a dataset, then the re-determined CPDAG was represented by “T5”. The order of the 15 tissues was “1st Bloom”, “1st Year shoot”, “Fruit 1st stage”, “Fruit 2nd stage”, “Fruit 3rd stage”, “Fruit 4th stage”, “Stem 1st stage”, “Stem 2nd stage”, “Stem 3rd stage”, “Stem 4th stage”, “Dormancy buds”, “Flower”, “Flower buds”, “Leaves”, and “Young leaves”. Thus, the corresponding CPDAGs when each of these 15 tissues was removed from each dataset were “T1”, “T2”, “T3”, …, “T14” and “T15”. The names of the CPDAGs were the same in all three analyses, i.e., “T3” represented the CPDAG not including the third tissue in the case of the transcriptomic, the proteomic analysis, and the proteogenomic analysis.

Next, each of the 16 CPDAGs (“All15T”, “T1”, “T2”, …, “T15”) was compared to all 16 CPDAGs in each case (step (iii)). In step (iv), the metrics employed were, the SHD, the percentage of the directed edges in each of the 16 causal structures (when considered as reference) that remained directed with the same direction in each of the 16 CPDAGs, and the percentage of the directed edges in each of the 16 reference CPDAGs that either remained directed with the same direction, or were transformed into a bidirected edge in each of the 16 CPDAGs. The above metrics were employed in hierarchical clustering in step (v). The hierarchical clustering was performed and visualized with the “pheatmap” function in R using the Euclidean as clustering distance and the complete clustering method. The absolute numbers of all the metrics in step (iv) of the algorithm ((iv) a–e, Section 2.3) were computed as well.

All the analyses were performed with the R programming language, Version 4.2.1.

3. Results

In the transcriptomic case, the results of the comparison based on the SHD and the percentage of the directed edges in each of the reference causal structures that remained directed with the same direction in each of the remaining causal structures are displayed in Figure 1. It is shown in Figure 1A that in the case that the 11th tissue (“Dormancy buds”) was removed from the transcriptomic database, the impact was the highest of all cases, since the CPDAG T11 exhibited the highest SHD compared to ALL15T (2256) among all CPDAGs, and, in addition, T11 exhibited the highest SHD to each of the reference CPDAGs, compared to all other CPDAGs. The smallest SHD compared to ALL15T was observed in the case of CPDAG T5 (882). Other than that, it was observed that CPDAGs corresponding to the removal of tissues with similar biological functions, such as tissues 3–6 (“Fruit 1st stage”, “Fruit 2nd stage”, “Fruit 3rd stage”, and “Fruit 4th stage”) were not clustered together in the heatmap. Similarly, the CPDAGs T7–T10 (“Stem 1st stage”, “Stem 2nd stage”, “ Stem 3rd stage”, and “ Stem 4th stage”), the CPDAGs T1–T13 (“Dormancy buds”, “Flower”, “Flower buds”), and T14–T15 (“Leaves”, “Young leaves”) were not clustered together as well (Figure 1A).

In the case of the assessment of the percentage of directed edges in each of the reference causal structures that remained directed with the same direction in each of the remaining 15 CPDAGs (Figure 1B), it was similarly observed that CPDAGs corresponding to the removal of tissues with similar biological function did not cluster together with the exception of CPDAGs T4–T6. In addition, CPDAG T3 (corresponding to the exclusion of “Fruit 1st stage”) was the one that exhibited the lowest percentage in almost all cases (except when compared to T4). The highest percentage (similarity in terms of directed edges) compared to ALL15T was observed in the case of CPDAG T8 (58.82).

Finally, when assessing the percentage of directed edges in each of the reference CPDAGs that either remained directed with the same direction or turned into bidirected, in each of the remaining causal structures (Figure A1), it was observed that the CPDAGs corresponding to excluded tissues with similar biological function did not, in general, cluster together with the exception of CPDAGs T4–T6, as was the case also in Figure 1B, and T8–T9. No CPDAG exhibited very low or very high percentages compared to the remaining CPDAGs. Still, T3 was the one that exhibited the lowest percentage compared to the CPDAG All15T (23.53%), while the highest percentage, respectively, was observed again in the case of T8 (70.59%).

The numerical details regarding the metrics that were considered, in particular, the SHD between each pair of CPDAGs, the number of bidirected edges in each reference CPDAG that remained bidirected in each of the remaining causal structures, and the number of directed edges in each reference CPDAG that remained directed with the same direction, or turned into bidirected, or changed direction in each of the remaining causal structures are displayed in

Table A1. Transcriptomic analysis. The comparison of each of the 16 CPDAGs (rows) to all 16 reference CPDAGs (columns) is numerically displayed. The comparison is based on the structural Hamming distance (SHD) between each pair of CPDAGs, the number of bidirected edges in each reference CPDAG (columns) that remained bidirected (BiD) in each of the remaining CPDAGs (rows), the number of directed edges in each reference CPDAG (columns) that remained directed with the same direction (Dir) in each of the remaining CPDAGs (rows), the number of directed edges in each reference CPDAG (columns) that turned into bidirected (DtoB) in each of the remaining CPDAGs (rows), and the number of directed edges in each reference CPDAG (columns) that changed direction (DCh) in each of the remaining CPDAGs (rows).

CPDAGs	Metrics	All15T	T1	T2	T3	T4	T5	T6	T7	T8	T9	T10	T11	T12	T13	T14	T15
All15T	SHD	0	1822	1818	1741	1268	882	1191	1334	1064	900	1644	2256	1540	1478	1772	1932
	BiD	1125	669	677	690	803	907	804	780	841	890	700	553	732	761	661	625
	Dir	34	8	10	4	10	10	14	8	20	18	10	6	10	18	10	12
	DtoB	0	10	7	7	8	4	10	8	7	6	12	9	15	6	10	6
	DCh	0	0	0	1	0	0	1	0	0	0	0	0	0	0	0	0
T1	SHD	1822	0	2502	2604	2268	2074	2255	2312	2166	2074	2501	2900	2352	2352	2540	2570
	BiD	669	1117	506	470	552	608	541	536	565	595	487	390	531	540	470	464
	Dir	8	34	6	2	2	4	2	4	10	10	8	4	6	8	6	6
	DtoB	9	0	2	5	8	3	5	3	7	5	4	8	5	10	9	6
	DCh	0	0	0	0	0	0	1	0	0	0	1	0	0	0	0	0
T2	SHD	1818	2502	0	2590	2238	2042	2259	2242	2118	2022	2458	2882	2436	2340	2550	2592
	BiD	677	506	1131	482	567	623	546	561	584	615	502	402	515	551	474	465
	Dir	10	6	30	2	2	4	9	6	6	10	6	6	10	8	6	6
	DtoB	8	9	0	7	7	4	4	4	10	5	10	4	7	7	6	6
	DCh	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
T3	SHD	1741	2604	2590	0	2186	2042	2154	2191	2126	2022	2507	2810	2420	2334	2576	2582
	BiD	690	470	482	1113	571	614	564	563	573	607	483	410	511	546	458	457
	Dir	4	2	2	22	4	2	2	2	4	4	2	2	4	4	2	4
	DtoB	4	9	2	0	4	2	4	6	9	6	6	8	6	6	6	6
	DCh	1	0	0	0	0	0	0	1	0	0	1	0	0	0	0	0
T4	SHD	1268	2268	2238	2186	0	1438	1730	1852	1696	1606	2102	2600	2106	2070	2250	2368
	BiD	803	552	567	571	1110	760	664	646	676	707	579	459	586	607	534	510
	Dir	10	2	2	4	28	8	12	6	12	10	4	2	6	6	6	6
	DtoB	8	10	8	5	0	4	8	2	9	8	12	10	10	10	12	6
	DCh	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
T5	SHD	882	2074	2042	2042	1438	0	1457	1660	1490	1316	1898	2504	1832	1856	2068	2190
	BiD	907	608	623	614	760	1127	740	700	737	787	638	490	662	668	589	562
	Dir	10	4	4	2	8	18	8	4	10	8	6	2	8	4	6	4
	DtoB	9	10	7	7	9	0	10	8	8	7	11	9	10	10	6	5
	DCh	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
T6	SHD	1191	2255	2259	2154	1730	1457	0	1834	1659	1481	2051	2622	2005	2031	2273	2429
	BiD	804	541	546	564	664	740	1078	634	669	721	576	439	593	600	513	480
	Dir	14	2	9	2	12	8	30	8	10	12	4	6	10	8	6	4
	DtoB	7	10	4	6	4	2	0	4	8	6	9	6	11	9	8	5
	DCh	1	1	1	0	0	1	0	0	1	1	1	0	1	1	1	1
T7	SHD	1334	2312	2242	2191	1852	1660	1834	0	1768	1642	2132	2652	2139	2090	2194	2398
	BiD	780	536	561	563	646	700	634	1102	653	693	569	443	570	599	545	497
	Dir	8	4	6	2	6	4	8	18	8	10	6	6	8	6	8	6
	DtoB	10	10	4	5	9	5	7	0	10	6	5	4	11	6	6	5
	DCh	0	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0
T8	SHD	1064	2166	2118	2126	1696	1490	1659	1768	0	1318	1890	2482	1942	1928	2014	2242
	BiD	841	565	584	573	676	737	669	653	1088	766	621	480	613	631	582	530
	Dir	20	10	6	4	12	10	10	8	30	16	10	4	10	14	12	12
	DtoB	4	7	6	5	6	2	10	6	0	5	6	6	11	7	8	3
	DCh	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
T9	SHD	900	2074	2022	2022	1606	1316	1481	1642	1318	0	1830	2412	1822	1804	2016	2182
	BiD	890	595	615	607	707	787	721	693	766	1102	643	503	652	669	589	551
	Dir	18	10	10	4	10	8	12	10	16	28	8	6	10	14	10	10
	DtoB	4	8	6	5	5	5	8	4	7	0	10	7	9	7	7	6
	DCh	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
T10	SHD	1644	2501	2458	2507	2102	1898	2051	2132	1890	1830	0	2714	2335	2368	2356	2622
	BiD	700	487	502	483	579	638	576	569	621	643	1091	425	520	525	502	436
	Dir	10	8	6	2	4	6	4	6	10	8	36	4	8	8	8	8
	DtoB	7	6	6	5	8	3	11	5	9	6	0	6	7	7	9	6
	DCh	0	1	0	1	0	0	1	0	0	0	0	0	1	0	0	0
T11	SHD	2256	2900	2882	2810	2600	2504	2622	2652	2482	2412	2714	0	2782	2684	2750	2827
	BiD	553	390	402	410	459	490	439	443	480	503	425	1102	414	452	407	391
	Dir	6	4	6	2	2	2	6	6	4	6	4	24	6	4	4	4
	DtoB	7	6	5	3	8	7	6	3	6	5	6	0	7	5	8	3
	DCh	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
T12	SHD	1540	2352	2436	2420	2106	1832	2005	2139	1942	1822	2335	2782	0	2230	2336	2490
	BiD	732	531	515	511	586	662	593	570	613	652	520	414	1104	566	512	477
	Dir	10	6	10	4	6	8	10	8	10	10	8	6	36	6	10	6
	DtoB	5	7	3	4	5	0	5	4	7	4	8	4	0	7	8	5
	DCh	0	0	0	0	0	0	1	1	0	0	1	0	0	0	0	0
T13	SHD	1478	2352	2340	2334	2070	1856	2031	2090	1928	1804	2368	2684	2230	0	2416	2338
	BiD	761	540	551	546	607	668	600	599	631	669	525	452	566	1130	506	529
	Dir	18	8	8	4	6	4	8	6	14	14	8	4	6	36	10	12
	DtoB	5	8	7	3	7	6	8	4	4	3	8	7	10	0	6	3
	DCh	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
T14	SHD	1772	2540	2550	2576	2250	2068	2273	2194	2014	2016	2356	2750	2336	2416	0	2424
	BiD	661	470	474	458	534	589	513	545	582	589	502	407	512	506	1080	481
	Dir	10	6	6	2	6	6	6	8	12	10	8	4	10	10	28	10
	DtoB	8	3	5	6	7	6	10	4	6	7	4	7	6	6	0	2
	DCh	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
T15	SHD	1932	2570	2592	2582	2368	2190	2429	2398	2242	2182	2622	2827	2490	2338	2424	0
	BiD	625	464	465	457	510	562	480	497	530	551	436	391	477	529	481	1083
	Dir	12	6	6	4	6	4	4	6	12	10	8	4	6	12	10	26
	DtoB	4	5	4	5	4	4	5	3	3	3	8	7	8	2	4	0
	DCh	0	0	0	0	0	0	1	0	0	0	0	1	0	0	0	0

. It was observed that the number of directed edges in each reference CPDAG that changed direction was in almost all cases zero, with a few exceptions of ones. Particularly, in comparison to the CPDAG All15T, only in the case of CPDAGs T3 and T6 one change in direction was observed, while in all other cases, the direction changes were zero.

In Figure 2A, it is shown that in the proteomic case, when the first tissue (“1st Bloom”) was removed from the database, the impact was the highest of all cases since CPDAG T1 exhibited by far the highest SHD compared to ALL15T (2672) among all CPDAGs. T1 exhibited the highest SHD to each of the CPDAGs considered as reference causal structures, compared to all other CPDAGs as well. The smallest SHD compared to ALL15T was observed in the case of CPDAG T9 (1312). On the other hand, the CPDAGs corresponding to the exclusion of tissues 3–5, related to fruit stages, were clustered together in the heatmap (Figure 2A). Similarly, the CPDAGs T7–T10, corresponding to the four stem stages, were also clustered together. Moreover, CPDAGs T1–T13 (corresponding to the tissues “Dormancy buds”, “Flower”, “Flower buds”), and T14–T15 (“Leaves”, “Young leaves”) were clustered very close to each other, respectively, as well (Figure 2A).

This was not the case, however, when the percentage of directed edges in each of the reference causal structures that remained directed with the same direction in each of the remaining causal structures was assessed (Figure 2B). In this case, it was observed that CPDAGs corresponding to the exclusion of tissues with similar biological functions did not cluster together. In addition, there was no CPDAG that demonstrated systematically high or low values of percentages of common directed edges to each of the reference CPDAGs, compared to all other CPDAGs. Still, the lowest percentage of commonly directed edges to the All15T CPDAG was observed in the case of T1 with 5.88% (Figure 2B), while the highest percentage was in the case of CPDAG T3 and T14 (35.29).

When the percentage of directed edges in each of the reference causal structures that either remained directed with the same direction or turned into bidirected in each of the remaining causal structures was assessed (Figure A2), the results were very similar to in the previous case (Figure 2B). More specifically, the CPDAGs corresponding to excluded tissues with similar biological functions did not cluster together and the lowest percentage of directed edges in the CPDAG All15T that either were retained or turned into bidirected was observed in the case of T1 with 29.41% (Figure A2). The highest percentage involved CPDAG T9 (61.76%) followed by CPDAG T3 (58.82%).

Numerical details regarding the metrics considered are displayed in

Table A2. Proteomic analysis. The comparison of each of the 16 CPDAGs (rows) to all 16 reference CPDAGs (columns) is numerically displayed. The comparison is based on the structural Hamming distance (SHD) between each pair of CPDAGs, the number of bidirected edges in each reference CPDAG (columns) that remained bidirected (BiD) in each of the remaining CPDAGs (rows), the number of directed edges in each reference CPDAG (columns) that remained directed with the same direction (Dir) in each of the remaining CPDAGs (rows), the number of directed edges in each reference CPDAG (columns) that turned into bidirected (DtoB) in each of the remaining CPDAGs (rows), and the number of directed edges in each reference CPDAG (columns) that changed direction (DCh) in each of the remaining CPDAGs (rows).

CPDAGs	Metrics	All15T	T1	T2	T3	T4	T5	T6	T7	T8	T9	T10	T11	T12	T13	T14	T15
All15T	SHD	0	2672	1557	1546	1484	1450	1794	1390	1345	1312	1314	1656	1616	1832	1914	1938
	BiD	1049	399	669	645	680	679	599	679	707	717	712	632	646	585	572	563
	Dir	34	2	8	12	8	8	9	10	8	10	10	10	5	9	12	6
	DtoB	0	12	11	15	11	19	16	13	20	15	11	12	11	23	10	10
	DCh	0	0	1	0	0	0	0	0	1	0	0	0	0	0	0	0
T1	SHD	2672	0	3034	2938	2982	2950	3095	2882	2902	2928	2864	2982	2944	3050	3088	3046
	BiD	399	1066	317	318	323	324	291	326	340	336	342	319	331	300	298	303
	Dir	2	48	0	6	4	4	0	2	4	0	6	2	4	4	4	4
	DtoB	8	0	9	8	4	6	11	7	8	7	5	7	6	13	5	3
	DCh	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
T2	SHD	1557	3034	0	2186	2236	2202	2366	2090	2118	2090	2042	2353	2259	2339	2432	2514
	BiD	669	317	1062	498	500	502	466	514	524	535	537	467	495	471	453	427
	Dir	8	0	32	4	2	4	5	4	4	4	4	2	2	3	2	2
	DtoB	8	8	0	7	10	10	10	9	14	9	10	9	10	14	8	8
	DCh	1	0	0	0	0	0	0	0	0	0	0	1	1	1	0	0
T3	SHD	1546	2938	2186	0	2186	2100	2370	2042	2094	2048	2006	2280	2240	2408	2511	2496
	BiD	645	318	498	1007	489	502	441	502	505	520	524	463	474	429	409	408
	Dir	12	6	4	50	10	12	3	10	12	12	10	2	9	7	10	8
	DtoB	8	3	10	0	5	9	13	6	11	8	5	9	6	15	6	3
	DCh	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
T4	SHD	1484	2982	2236	2186	0	2077	2363	2090	2056	2100	2022	2244	2214	2404	2456	2446
	BiD	680	323	500	489	1040	524	459	506	530	525	535	488	499	444	440	437
	Dir	8	4	2	10	42	8	2	8	6	6	10	2	3	4	4	2
	DtoB	6	6	9	7	0	10	10	8	15	6	6	9	7	17	7	5
	DCh	0	0	0	0	0	1	1	0	0	0	0	0	0	0	0	0
T5	SHD	1450	2950	2202	2100	2077	0	2244	2062	2040	2050	2056	2228	2222	2402	2434	2428
	BiD	679	324	502	502	524	1027	479	504	526	531	521	481	488	437	436	434
	Dir	8	4	4	12	8	44	4	8	10	6	6	2	5	5	8	4
	DtoB	5	6	8	6	5	0	13	9	12	4	4	11	8	17	6	5
	DCh	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
T6	SHD	1794	3095	2366	2370	2363	2244	0	2328	2312	2300	2314	2458	2450	2557	2622	2616
	BiD	599	291	466	441	459	479	1033	443	466	473	459	427	437	406	393	393
	Dir	9	0	5	3	2	4	52	8	1	1	2	4	0	0	3	3
	DtoB	5	8	7	8	8	11	0	7	12	7	7	12	8	16	8	4
	DCh	0	1	0	0	1	0	0	0	0	0	0	0	0	1	0	0
T7	SHD	1390	2882	2090	2042	2090	2062	2328	0	1941	1826	1856	2187	2112	2312	2330	2338
	BiD	679	326	514	502	506	504	443	1001	538	569	555	478	501	448	447	443
	Dir	10	2	4	10	8	8	8	36	4	6	6	4	1	3	4	2
	DtoB	9	7	11	10	7	12	13	0	14	10	6	11	9	15	9	8
	DCh	0	0	0	0	0	0	0	0	1	0	0	1	0	0	0	0
T8	SHD	1345	2902	2118	2094	2056	2040	2312	1941	0	1860	1872	2194	2139	2261	2273	2396
	BiD	707	340	524	505	530	526	466	538	1033	578	566	495	510	476	481	443
	Dir	8	4	4	12	6	10	1	4	46	8	6	2	7	8	6	8
	DtoB	7	3	9	8	8	11	14	10	0	8	8	9	10	14	5	5
	DCh	1	0	0	0	0	0	0	1	0	0	0	0	1	1	1	0
T9	SHD	1312	2928	2090	2048	2100	2050	2300	1826	1860	0	1902	2160	2170	2260	2312	2329
	BiD	717	336	535	520	525	531	473	569	578	1039	564	505	509	480	474	463
	Dir	10	0	4	12	6	6	1	6	8	42	4	3	4	5	6	6
	DtoB	11	7	10	8	9	12	15	12	14	0	7	14	4	14	8	6
	DCh	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
T10	SHD	1314	2864	2042	2006	2022	2056	2314	1856	1872	1902	0	2150	2084	2267	2322	2316
	BiD	712	342	537	524	535	521	459	555	566	564	1024	500	521	469	463	460
	Dir	10	6	4	10	10	6	2	6	6	4	36	2	5	6	4	4
	DtoB	6	5	11	8	6	11	17	11	16	12	0	12	5	13	8	7
	DCh	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
T11	SHD	1656	2982	2353	2280	2244	2228	2458	2187	2194	2160	2150	0	2260	2388	2508	2392
	BiD	632	319	467	463	488	481	427	478	495	505	500	1032	484	447	423	448
	Dir	10	2	2	2	2	2	4	4	2	3	2	46	3	6	2	6
	DtoB	7	7	11	10	7	15	15	9	13	8	8	0	7	13	9	5
	DCh	0	0	1	0	0	0	0	1	0	0	0	0	0	0	0	0
T12	SHD	1616	2944	2259	2240	2214	2222	2450	2112	2139	2170	2084	2260	0	2400	2478	2466
	BiD	646	331	495	474	499	488	437	501	510	509	521	484	1043	444	433	432
	Dir	5	4	2	9	3	5	0	1	7	4	5	3	38	5	6	6
	DtoB	12	8	8	11	8	11	14	13	11	11	10	9	0	18	10	7
	DCh	0	0	1	0	0	0	0	0	1	0	0	0	0	0	0	0
T13	SHD	1832	3050	2339	2408	2404	2402	2557	2312	2261	2260	2267	2388	2400	0	2580	2550
	BiD	585	300	471	429	444	437	406	448	476	480	469	447	444	1027	404	405
	Dir	9	4	3	7	4	5	0	3	8	5	6	6	5	60	5	7
	DtoB	5	5	6	5	7	9	9	6	8	8	8	5	8	0	5	2
	DCh	0	0	1	0	0	0	1	0	1	0	1	0	0	0	0	0
T14	SHD	1914	3088	2432	2511	2456	2434	2622	2330	2273	2312	2322	2508	2478	2580	0	2567
	BiD	572	298	453	409	440	436	393	447	481	474	463	423	433	404	1044	408
	Dir	12	4	2	10	4	8	3	4	6	6	4	2	6	5	40	6
	DtoB	7	5	10	6	6	10	15	11	10	6	7	8	5	13	0	6
	DCh	0	0	0	1	0	0	0	0	1	0	0	0	0	0	0	1
T15	SHD	1938	3046	2514	2496	2446	2428	2616	2338	2396	2329	2316	2392	2466	2550	2567	0
	BiD	563	303	427	408	437	434	393	443	443	463	460	448	432	405	408	1036
	Dir	6	4	2	8	2	4	3	2	8	6	4	6	6	7	6	32
	DtoB	7	6	9	9	9	10	10	6	11	9	5	4	4	15	4	0
	DCh	0	0	0	0	0	0	0	0	0	1	0	0	0	0	1	0

. Similarly, as in the case of the transcriptomic analysis, it was observed that the number of directed edges in each reference CPDAG that changed direction was in almost all cases zero. Compared to the CPDAG All15T, only in the case of CPDAGs T2 and T8, there was observed one change in direction, while in all other cases, the direction changes were zero.

In the proteogenomic case, it is shown in Figure 3A that when the 1st tissue (“1st Bloom”) was removed from the combined database, the impact was the highest of all cases and CPDAG T1 exhibited by far the highest SHD among all CPDAGs, compared to ALL15T (3270). T1 exhibited the highest SHD to each of the CPDAGs when treated as a reference, compared to all other CPDAGs as well. The smallest SHD compared to the CPDAG ALL15T was observed in the case of CPDAG T9 (1654). These results are similar to the respective results in the proteomic analysis. Moreover, the CPDAGs corresponding to the exclusion of tissues 3–4, which are related to the fruiting stage, were clustered together in the heatmap (Figure 3A). Similarly, the CPDAGs T7–T10 that correspond to the four stem stages were also clustered close to each other. In addition, CPDAGs T11–T12 (corresponding to the tissues “Dormancy buds” and “Flower”), and T14–T15 (“Leaves”, “Young leaves”) were clustered together, respectively, as well (Figure 3A).

These results were observed as well when assessing the percentage of directed edges in each of the reference causal structures that retained their direction in each of the remaining causal structures (Figure 3B). In this case, the results were even more emphatical, since the CPDAGs T4–T6 (correspond to fruit stages), the CPDAGs T7–T10 (four stem stages), the CPDAGs T11–T13 (buds and flowers) and the CPDAGs T14–T15 (leaves) were also clustered together, respectively. (Figure 3B). On top of that, similarly to the assessment of SHD (Figure 3A), the CPDAG that exhibited the least similarity to all other reference CPDAGs was T1. Particularly, when compared to All15T, it exhibited a percentage of 25.19%, which was by far lower than any other CPDAG (the highest percentage was 52.89% and was observed in the cases of both T7 and T9).

Next, the percentage of directed edges in each of the reference causal structures that either remained directed with the same direction or turned into bidirected, in each of the remaining causal structures was assessed (Figure A3). The results were very similar to the previous case (Figure 3B) and the case when the SHD was assessed (Figure 3A). On top of the fact that CPDAGs corresponding to the exclusion of biologically similar tissues were clustered together, CPDAG T1 again exhibited the least similarity to all other reference CPDAGs. The lowest by far percentage of directed edges in the CPDAG All15T that either were retained or turned into bidirected was 46.74% (T1), while the highest was 70.80% followed by 70.62% (again involving T9 and T7, respectively).

Numerical details regarding the metrics considered are displayed in

Table A3. Proteogenomic analysis. The comparison of each of the 16 CPDAGs (rows) to all 16 reference CPDAGs (columns) is numerically displayed. The comparison is based on the structural Hamming distance (SHD) between each pair of CPDAGs, the number of bidirected edges in each reference CPDAG (columns) that remained bidirected (BiD) in each of the remaining CPDAGs (rows), the number of directed edges in each reference CPDAG (columns) that remained directed with the same direction (Dir) in each of the remaining CPDAGs (rows), the number of directed edges in each reference CPDAG (columns) that turned into bidirected (DtoB) in each of the remaining CPDAGs (rows), and the number of directed edges in each reference CPDAG (columns) that changed direction (DCh) in each of the remaining CPDAGs (rows).

CPDAGs	Metrics	All15T	T1	T2	T3	T4	T5	T6	T7	T8	T9	T10	T11	T12	T13	T14	T15
All15T	SHD	0	3270	1879	1994	2110	1897	2288	1698	1711	1654	1807	2245	2185	2413	2344	2379
	BiD	1444	784	1047	1029	1002	1037	967	1064	1084	1111	1049	960	988	940	957	954
	Dir	1072	270	524	512	462	493	437	567	542	567	531	448	461	445	423	400
	DtoB	0	216	151	145	166	182	192	161	139	118	157	193	152	166	160	178
	DCh	0	86	61	55	68	52	69	65	59	57	54	63	69	73	78	77
T1	SHD	3270	0	3660	3679	3713	3730	3875	3563	3549	3570	3609	3786	3733	3910	3903	3824
	BiD	784	1509	718	723	712	720	683	725	736	753	722	700	718	672	666	688
	Dir	270	948	221	201	206	203	194	235	203	208	193	199	186	207	188	197
	DtoB	231	0	212	197	199	191	207	210	209	192	203	202	196	192	198	208
	DCh	86	0	58	78	63	65	62	68	65	69	84	64	69	72	69	56
T2	SHD	1879	3660	0	2654	2762	2574	2971	2479	2436	2439	2499	2878	2842	3008	3002	3008
	BiD	1047	718	1488	908	893	927	845	929	953	960	929	858	876	831	827	843
	Dir	524	221	950	365	342	351	302	368	356	353	383	315	326	297	292	287
	DtoB	204	218	0	177	180	206	207	211	184	192	187	214	185	206	205	191
	DCh	61	58	0	59	60	51	72	80	74	64	56	72	58	72	60	74
T3	SHD	1994	3679	2654	0	2685	2741	2948	2605	2576	2567	2650	2915	2842	3097	3019	3026
	BiD	1029	723	908	1468	912	887	867	896	924	937	892	848	873	814	829	834
	Dir	512	201	365	941	336	328	313	364	340	370	360	335	338	295	305	275
	DtoB	179	199	187	0	170	193	180	199	177	161	192	187	172	201	183	205
	DCh	55	78	59	0	62	51	56	65	65	61	56	56	53	66	68	63
T4	SHD	2110	3713	2762	2685	0	2677	3034	2606	2643	2619	2623	2960	2956	3124	3073	3107
	BiD	1002	712	893	912	1483	891	837	912	913	931	913	846	850	819	823	826
	Dir	462	206	342	336	928	346	315	361	344	342	354	307	303	278	280	281
	DtoB	206	213	191	182	0	201	188	193	184	172	185	203	193	210	201	197
	DCh	68	63	60	62	0	60	63	77	59	66	52	64	66	72	63	61
T5	SHD	1897	3730	2574	2741	2677	0	2811	2535	2512	2533	2590	2849	2873	2995	2994	3092
	BiD	1037	720	927	887	891	1492	867	906	926	937	903	854	862	838	832	818
	Dir	493	203	351	328	346	935	324	360	339	339	343	326	315	295	280	265
	DtoB	216	211	199	207	209	0	232	230	214	196	220	213	198	211	207	216
	DCh	52	65	51	51	60	0	55	63	53	55	48	54	54	62	63	57
T6	SHD	2288	3875	2971	2948	3034	2811	0	2778	2848	2790	2854	3098	3113	3328	3200	3253
	BiD	967	683	845	867	837	867	1477	867	863	904	852	813	822	775	801	800
	Dir	437	194	302	313	315	324	963	357	336	345	329	306	277	263	265	258
	DtoB	197	206	201	168	180	195	0	197	183	151	190	200	184	197	187	193
	DCh	69	62	72	56	63	55	0	72	61	72	64	57	66	69	69	56
T7	SHD	1698	3563	2479	2605	2606	2535	2778	0	2262	2167	2358	2670	2669	2883	2804	2783
	BiD	1064	725	929	896	912	906	867	1454	977	1004	939	879	898	842	861	871
	Dir	567	235	368	364	361	360	357	987	409	451	410	364	356	347	345	326
	DtoB	190	220	194	196	175	206	193	0	168	150	178	205	168	197	181	195
	DCh	65	68	80	65	77	63	72	0	59	57	60	69	70	66	59	68
T8	SHD	1711	3549	2436	2576	2643	2512	2848	2262	0	2231	2307	2704	2725	2875	2837	2807
	BiD	1084	736	953	924	913	926	863	977	1475	1007	968	889	892	851	868	878
	Dir	542	203	356	340	344	339	336	409	934	404	397	340	315	317	296	319
	DtoB	188	234	204	195	184	214	201	198	0	161	174	201	188	213	202	196
	DCh	59	65	74	65	59	53	61	59	0	58	54	62	79	71	63	59
T9	SHD	1654	3570	2439	2567	2619	2533	2790	2167	2231	0	2280	2663	2663	2873	2780	2802
	BiD	1111	753	960	937	931	937	904	1004	1007	1520	985	907	920	865	893	889
	Dir	567	208	353	370	342	339	345	451	404	909	415	347	327	311	342	310
	DtoB	192	232	221	194	203	231	198	201	193	0	193	222	200	228	191	219
	DCh	57	69	64	61	66	55	72	57	58	0	50	66	58	64	61	55
T10	SHD	1807	3609	2499	2650	2623	2590	2854	2358	2307	2280	0	2774	2776	2904	2854	2897
	BiD	1049	722	929	892	913	903	852	939	968	985	1460	861	868	844	848	856
	Dir	531	193	383	360	354	343	329	410	397	415	941	359	329	315	317	297
	DtoB	194	227	188	180	175	202	207	203	185	162	0	197	195	205	197	196
	DCh	54	84	56	56	52	48	64	60	54	50	0	59	57	65	55	56
T11	SHD	2245	3786	2878	2915	2960	2849	3098	2670	2704	2663	2774	0	3021	3143	3101	3058
	BiD	960	700	858	848	846	854	813	879	889	907	861	1473	826	805	817	828
	Dir	448	199	315	335	307	326	306	364	340	347	359	964	303	289	275	282
	DtoB	220	212	198	190	188	216	204	206	195	182	191	0	201	207	195	199
	DCh	63	64	72	56	64	54	57	69	62	66	59	0	59	59	65	62
T12	SHD	2185	3733	2842	2842	2956	2873	3113	2669	2725	2663	2776	3021	0	3196	3138	3072
	BiD	988	718	876	873	850	862	822	898	892	920	868	826	1487	806	812	836
	Dir	461	186	326	338	303	315	277	356	315	327	329	303	920	300	265	262
	DtoB	211	211	197	182	187	206	211	205	200	194	201	206	0	186	196	200
	DCh	69	69	58	53	66	54	66	70	79	58	57	59	0	56	52	78
T13	SHD	2413	3910	3008	3097	3124	2995	3328	2883	2875	2873	2904	3143	3196	0	3299	3207
	BiD	940	672	831	814	819	838	775	842	851	865	844	805	806	1470	771	805
	Dir	445	207	297	295	278	295	263	347	317	311	315	289	300	962	259	274
	DtoB	197	200	209	184	174	200	201	196	188	188	189	199	174	0	194	186
	DCh	73	72	72	66	72	62	69	66	71	64	65	59	56	0	67	61
T14	SHD	2344	3903	3002	3019	3073	2994	3200	2804	2837	2780	2854	3101	3138	3299	0	3169
	BiD	957	666	827	829	823	832	801	861	868	893	848	817	812	771	1473	799
	Dir	423	188	292	305	280	280	265	345	296	342	317	275	265	259	918	266
	DtoB	204	211	213	181	184	212	202	200	190	167	198	200	199	205	0	207
	DCh	78	69	60	68	63	63	69	59	63	61	55	65	52	67	0	69
T15	SHD	2379	3824	3008	3026	3107	3092	3253	2783	2807	2802	2897	3058	3072	3207	3169	0
	BiD	954	688	843	834	826	818	800	871	878	889	856	828	836	805	799	1503
	Dir	400	197	287	275	281	265	258	326	319	310	297	282	262	274	266	910
	DtoB	224	220	216	204	191	226	211	217	196	197	207	216	196	205	200	0
	DCh	77	56	74	63	61	57	56	68	59	55	56	62	78	61	69	0

. In this case, it was observed that the number of directed edges in each reference CPDAG that changed direction received large numbers in almost all cases. When considering the CPDAG All15T as a reference, CPDAG T1 exhibited the highest number of direction changes (86), which additionally was the highest number of direction changes overall (Table A3).

4. Discussion

This study proposes a causal structure robustness assessment algorithm for single-omic or multiomics data involving plant tissues and demonstrates its application on a sweet cherry proteogenomic atlas. The robustness assessment of the causal structures based on the transcriptomic, proteomic, and combined proteogenomic datasets underscored that different tissues were revealed, in each case, to exhibit the highest impact when excluded from the corresponding databases. Notably, by excluding the tissues “Dormancy buds” and “Fruit 1st stage”, the causal structure based on the transcriptomic data was pronouncedly more influenced compared to the exclusion of the remaining tissues (based on the SHD, Figure 1A and the percentage of directed edges retained, Figure 1B, respectively). This could be attributed to the fact that while the transcriptional regulation in dormant buds is limited, during the transition from endodormancy to ecodormancy an explosion of transcription activity has been observed that clearly divided the ecodormancy from other dormancy stages in sweet cherries [44,45,46]. Similarly, the early stage of fruit development is characterized by elevated transcriptional activity due to continuous cell division that progressively decreases in the following stages [47,48]. Hence, the endorsement of transcriptional activity was observed.

On the other hand, in the case of both the proteomic and the proteogenomic analysis, it was shown that when the first tissue (“1st Bloom”) was excluded from the data, the impact inflicted on the causal structure was the highest compared to all other tissues (Figure 2A and Figure 3A,B). The high impact of the exclusion of the “1st Bloom” tissue was even more evident in the case of the proteogenomic analysis. This may be attributed to the fact that “1st Bloom” is related to protein abundance that clearly separates it from the remaining tissues. This was observed as well and discussed in a previous publication of our group [31], and also noticed in Arabidopsis thaliana where exclusive proteins were found in abundance at pollen, callus, seed and flower of the plant [49].

Moreover, it was expected that the CPDAGs corresponding to the exclusion of biologically similar tissues would be clustered together or close to each other. In particular, the CPDAGs corresponding to the tissues 3–5 related to the fruiting stage, the CPDAGs T7–T10, corresponding to the four stem stages, the CPDAGs T1–T13 corresponding to the tissues “Dormancy buds”, “Flower” and “Flower buds”, and the CPDAGs T14–T15 corresponding to the tissues “Leaves” and “Young leaves”. This expectation was based on the fact that the only thing that theoretically changes is the developmental stage and not the histological one. When assessing the clustering of the CPDAGs, based on their SHD to all other CPDAGs, and the percentage of common directed edges (or directed and directed that turned into bidirected) with all other CPDAGs, it was found that in the transcriptomic case, this expectation was not satisfied (Figure 1 and Figure A1). Indeed, in a transcriptomic analysis of quality changes during sweet cherry fruit development, the transcriptome of the organs has been found to exhibit strong differentiation depending on the developmental stage [50,51].

This expectation was satisfied, however, in the case of both the proteomic and the proteogenomic analysis, at least when considering the SHD as the metric to assess the causal structure differences (Figure 2A and Figure 3A). In the case that the hierarchical clustering was based on the percentage of the directed edges in each of the reference causal structures that remained directed with the same direction in each of the remaining CPDAGs, and on the percentage of the directed edges in each of the reference causal structures that either remained directed with the same direction, or turned into bidirected in each of the CPDAGs, it was found that this expectation was fulfilled only in the case of the proteogenomic analysis (Figure 3A,B). This is probably because the combined analysis of proteome and transcriptome managed to separate tissues belonging to other organs, by reducing the noise from analyzing the proteome or transcriptome alone.

The fact that the expectation of CPDAGs corresponding to the removal of tissues with similar biological function to be clustered together was satisfied, the best in the case of the proteogenomic analysis additionally implies that collecting and analyzing fewer tissue samples from an organ, when this is relevant or necessary, may be facilitated in case a combined proteogenomic analysis is considered. Namely, in the case of a proteogenomic analysis, opting to use fewer representative tissues of a specific organ is expected to result in a milder impact on the corresponding causal structure, compared to the case of the single omic analysis of the proteome or the transcriptome.

By an overall comparison of the percentages of the directed edges in each of the reference causal structures that remained directed with the same direction in each of the remaining 15 CPDAGs (Figure 1B, Figure 2B and Figure 3B), it can be clearly observed that they are much higher in the case of the proteogenomic analysis compared to the other two cases. Since the SHD as a metric cannot be employed to technically compare the results, because it is largely influenced by the complexity of the CPDAGs considered, which in the case of the proteogenomic analysis is much more pronounced (see Table A1, Table A2 and Table A3 in Appendix A for more details), the above result is indicative of obtaining more robust causal structures in the case of jointly employing the proteome and transcriptome databases. These results reinforce the importance of a multi-omics approach to capture the full breadth of biological processes [52,53,54].

Lastly, the biological implications of analyzing and assessing the robustness of the obtained causal structures concern the reliability of the biological interpretations that may emerge from these causal structures. Namely, a robustness analysis may further support the biological conclusions emerging from causal discovery and at the same time highlight hidden aspects in the data.

5. Conclusions

By employing the proposed algorithm to assess omic sweet cherry causal structures, it is showcased that specific tissues exhibited a strong impact when removed from the analysis. In the proteogenomic case, a similar impact was induced on the causal structures when biologically related tissues were excluded. This result was less pronounced in the proteomic analysis and especially in the transcriptomic analysis. This may be attributed to the distinctive biological features related to proteome and transcriptome. Moreover, causal structures based on single omic analyses were impacted to a larger extent, compared to proteogenomic analysis. Thus, this study reveals the importance of assessing the causal structure robustness, along with causal discovery, within the framework of omics data, and showcases the added advantages and perspective. Furthermore, while not questioning the importance of separately performing a transcriptomic or proteomic analysis, it provides valuable insight into the benefits of employing a proteogenomic analysis, further supporting the usage of multiomics analysis in research.