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Good experimental designs mitigate experimental error and the impact of factors not under study. Figure 1: ANOVA is used to determine significance using the ratio of variance estimates from sample means and sample values. Figure 2: Blocking improves sensitivity by isolating variation in samples that is independent from treatment effects. Figure 4: Including blocking isolates biological variation from the estimate of within-group variance and improves power.
Reproducible measurement of treatment effects requires studies that can reliably distinguish between systematic treatment effects and noise resulting from biological variation and measurement error. ANOVA calculations are summarized in an ANOVA table, which we provide for Figures 1, 3 and 4 (Supplementary Tables 1,2,3) along with an interactive spreadsheet (Supplementary Table 4). Without blocking, cultures, aliquots and treatments are not matched—a completely randomized design (Fig. To illustrate blocking, we simulate samples to have the same values as in Figure 3a but with half of the variance due to differences in cultures. Having isolated variation owing to cell-culture differences, we increased sensitivity in detecting a treatment effect because our estimate of within-group variance is lower. Martin Krzywinski is a staff scientist at Canada's Michael Smith Genome Sciences Centre. Shankar Subramaniam and Gene Hsiao are in the Department of Bioengineering, the Department of Cellular and Molecular Medicine and the Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California, USA.
Morphometric landmarks used to quantify primaxial shape variance and regionalization in pre-cloacal vertebrae of Mus and Alligator. Extended Data Figure 3: Morphometric landmarks used to quantify primaxial shape variance and regionalization in pre-cloacal vertebrae of Mus and Alligator. Extended Data Figure 1: Skeletal morphology and intracolumnar shape variation in the pre-cloacal vertebral column of limbed lizards and snakes.
Extended Data Figure 4: Best-fit regionalization models for complete pre-cloacal skeletons of Mus, Alligator and select squamates.
Extended Data Figure 5: Comparison of best-fit four-region model with models fitting morphometric regional boundaries to expression boundaries for Hox10 genes. Landmarks document intracolumnar variation in vertebral shape for squamates, Alligator and Mus. Estimation and testing of the effects of multiple treatments, usually including appropriate replication, can be done using analysis of variance (ANOVA). The sums of squares (SS) column shows sums of squared deviations of various quantities from their means. Here, the spikes (red and green) are increasingly difficult to detect as average expression decreases. Brown symbols represent transcripts that would have been exclusively considered differently expressed by the fold-change method. See Extended Data Table 2 and Supplementary Information for description of landmarks and discussion of landmark selection. In each case vertebral shape variables (orange dots) were regressed onto position in the vertebral column (brown lines).
The test statistic, F, is the ratio mean squares MSB and MSW, which are SSB and SSW weighted by d.f. ANOVA is used to assess statistical significance of differences among observed treatment means based on whether their variance is larger than expected because of random variation; if so, systematic treatment effects are inferred. For blocking, we systematically assign treatments to cultures, such as in a randomized complete block design, in which each culture provides a replicate of each treatment (Fig. 4a), and are added to each of the sample values using the complete randomized block design (Fig. In the region of low expression, not only the spikes embedded with background and equally spiked transcripts (gray and yellow), but also the upregulated and downregulated transcripts lay on both sides of the axis. In this study, we collected module templates to infer respective module families, including 58,041 homologous modules in 1,678 species, and PPI families using searches of complete genomic database. P values for paired sample comparison are adjusted for multiple comparison using Tukey's method. We introduce ANOVA with an experiment in which three treatments are compared and show how sensitivity can be increased by isolating biological variability through blocking.Last month, we discussed a one-factor three-level experimental design that limited interference from biological variation by using the same sample to establish both baseline and treatment values1. Correct spike detection, bold green and red circles; false-positive rate, bold yellow squares. We then derived PPI evolution scores and interface evolution scores to describe the module elements, including core and ring components. There we used the t-test, which is not suitable when the number of factors or levels increases, in large part due to its loss of power as a result of multiple-testing correction. Each block is subjected to each of the treatments exactly once, and we can optionally collect technical repeats (repeating data collection from the measurement apparatus or multiple aliquots from the same culture) to minimize the impact of fluctuations in our measuring apparatus; these values would be averaged.
The variance within a sample is thus evenly split between the block effect and the remaining experimental error, which we presumably cannot partition further. Orange shading indicates transcripts found to be overexpressed in adipose tissue of insulin-resistant subjects by VAMPIRE but not captured by the fold-change method (because the change in expression is less than twofold) or t-test; transcripts in this region include subtle but overexpressed immune-related genes. The two-sample t-test is a specific case of ANOVA, but the latter can achieve better power and naturally account for sources of error. The contribution of the block effect to the deviations is shown in Figure 4b, now a substantial component of the variance in each sample, unlike in Figure 3b, where blocking was not accounted for.
The slope of each segment (heavy dark line) represents the shape gradient each region and the residual sum of squares (RSS) represents the lack of fit of the model to the data.
Let us look at how blocking can increase ANOVA sensitivity using the scenario from Figure 1.We will start with three samples (n = 6) (Fig. Mathematically, the blocking variable has the same role in the analysis as an experimental factor.
3a) that measure the effects of treatments A, B and C on aliquots of cells in a completely randomized scheme. The protein assembly can be regarded as a module, which often governs specific processes and is autonomous in relation to other parts of the organism2,3.
However, the number of parameters increases with the number of regions, as does the likelihood of the model; therefore corrected Akaike adjustment (AICc) is required to select the best model. The ANOVA null hypothesis is that all samples are from the same distribution and have equal means. Many works have been proposed to study the biological properties and modularity of the module. Only the posterior boundaries of Hox10 expression are significantly worse fits than the best-fit model.
Under this null, between-group variation of sample means and within-group variation of sample values are predictably related.
When we reject the null, we conclude that not all sample means are the same; additional tests are required to identify which treatment means are different.
These works employed experimental methods1,4, network topology5,6, gene expression-based methods2,7, and evolutionary-based methods8.
Their ratio can be used as a test statistic, F, which will be larger than expected in the presence of treatment effects.

In addition, the modules can be approximately divided into functional module3, variational module3, and evolutionary module9,10.
Although it appears that we are testing equality of variances, we are actually testing whether all the treatment effects are zero.
A functional module is a group of proteins that semi-autonomously assemble together to perform discrete physiological functions. MSW corresponds to variance in the sample after other sources of variation have been accounted for and represents experimental error (σwit2). Because we did not find a significant difference using ANOVA, we do not expect to obtain significant P values from two-sample t-tests applied pairwise to the samples. Moreover, the proteins and protein-protein interactions (PPIs) in a module often change over seconds to assemble and disassemble for performing biological functions, as well as evolve over millions of years as proteins and PPIs are gained and lost11. Indeed, when adjusted for multiple-test correction these Padj values are all greater than 0.05 (Fig.
Investigations of underlying module organization and variance are urgently required for understanding the cellular processes and module evolution.As complete genomes become increasingly available, systems biology approaches based on homologous PPIs and modules across multiple species provide an opportunity to explore organization, evolution, and variance of modules.
For investigating the modularity of the yeast cell machinery, an experimental genome-wide screen approach, based on the isoforms of complexes, was proposed and 491 complexes were identified1. These complexes differentially combined with attachment proteins to execute time–space potential functions in yeast.
In addition, functionally interacting proteins have been shown to be gained or lost together during genome evolution12.
As noise within samples drops, a larger fraction variation is allocated to MSB, and the power of the test improves.
Previously, we inferred the module family, which consists of a group of homologous modules, from complete genomic database (e.g. Assume that it is not possible to derive all required aliquots from a single culture or that it is necessary to use multiple cultures to ensure that the results generalize. Based on the module families and PPI families, we have reconstructed module-module interaction networks (called MoNetFamily15) in vertebrates.
It is likely that aliquots from different cultures will respond differently owing to variation in cell concentration, growth rates, medium composition, among others. However, the understanding of module organization and variance in PPI networks is incomplete.To address these issues, we propose PPI evolution score (PPIES) and interface evolution score (IES) as the basis to study the module organization and variance in PPI networks using module families and PPI families across multiple species.
These so-called nuisance variables confound the real treatment effects: the baseline for each measurement unpredictably varies (Fig. Furthermore, we define protein functional variance (PFV) and module organizational variance (MOV) of PPI networks to measure the functional diversities of proteins and modules, respectively. We can mitigate this by using the same cell culture to create three aliquots, one for each treatment, to propagate these differences equally among measurements (Fig. For a module, the core proteins and PPIs are often conserved and consistently play the essential role for performing biological functions.
Although measurements between cultures still would be shifted, the relative differences between treatments within the same culture remain the same. Compared with ring proteins, core proteins are essential for survival and preferentially constitute hubs of a PPI network. This process is called blocking, and its purpose is to remove as much variability as possible to make differences between treatments more evident. Moreover, core PPIs were co-expressed significantly more than ring PPIs in 7,208 Homo sapiens gene expression sets from Gene Expression Omnibus (GEO)16.
For example, the paired t-test implements blocking by using the same subject or biological sample.
Finally, we applied genome-wide investigations to describe the link from PFV and MOV values to module variance and biological functions in time and space. We believe that our results are useful for understanding the module organization and variance in PPI networks.Results and DiscussionOverviewFigure 1 shows the details of our method for identifying core and ring components of modules, and for elucidating module organization through template-based homologous modules (module families) using the following steps (Fig. Internal PPIs of module templates were then added to templates that lacked PPIs using template-based homologous PPIs, including experimental PPIs from IntAct17, BioGRID18, DIP19, MIPS20, and MINT21, and predicted homologous PPIs14,22 (Fig.
For each PPI of a module, we inferred its PPI family with joint E-values of ?10?40 14 by searching a complete genomic database (Integr8 version 103, containing 6,352,363 protein sequences in 2,274 species23) using previously identified homologous PPIs14,22 (Fig. Subsequently, we utilized MoNetFamily15 to identify homologous modules of module templates according to topological similarities across multiple species (Fig.
Module profiles were then constructed for module families, and protein and PPI components were computed (Fig. Next, we then derived PPIES and IES scores to extrapolate core and ring components of a module. Finally, we constructed PPI networks and genome-wide investigations for organization of a module, including network topology (Fig.
Thus, we proposed PPIES and IES to identify core and ring components of a module by utilizing homologous PPIs and proteins15. To derive homologous modules across multiple species, we collected 1,519 high-quality module templates (?3 proteins in a template), which are manually annotated protein complexes from the MIPS CORUM database4. Based on these module templates and the thresholds of functional and topology similarities15 (Supplementary Fig. S1 and Text S1), we inferred 58,041 homologous modules in 1,678 species from 461,077 sequence-based PPI families and 86,252 structure-based PPI families13,14.
These six divisions include mammals (MAM), vertebrates (VRT), invertebrates (INV), plants (PLN), bacteria (BCT), and archaea (ARC) according to the National Center for Biotechnology Information (NCBI) taxonomy database24.
In a module family, a PPI with high PPIES indicates that its homologous PPIs are highly conserved across species and taxonomic divisions. In addition, IES of the protein i was set to the maximum PPIES of these PPIs, which reflected interactions between the protein i and its partners. For example, the interaction between CDK1 and CCNB1 is conserved across 67 species as observed from the homologous PPIs of the human CDK1–CCNB1 PPI (confirmed by protein kinase assays17 and co-immunoprecipitation experiments19). During the G2 cell cycle phase, the active CDK1–CCNB1 interaction can enhance chromosome condensation and nuclear envelope breakdown to separate the centrosomes26. During the response to DNA damage, PCNA (another core protein) recruits at the replication fork to coordinate DNA replication, and activates DNA repair and damage tolerance pathways.
To assess the connectivity and shared biological functions of two types (core and ring component) of module components and three module types (module template, homologous module, and the respective extended module), we computed connectivity (Ct) and average relative specificity similarity (AvgRSS) scores of Gene Ontology (GO) terms (Supplementary Figs. Among 1,519 module templates, the average Ct value of core components was significantly higher than those of the others, including the ring components (Mann–Whitney U test, P = 7e-6), whole module templates (P = 6e-17), and extended modules (P = 9e-250; Supplementary Fig.
Similarly, the core components of homologous modules have significantly higher average Ct value than those of ring components (P = 1e-40), whole homologous modules (P = 1e-14), and extended modules (; Supplementary Fig. 2A and 2B), and was evaluated based on the characteristic of scale-free networks that can be described as P(k) ~ k?r, in which the probability of a node with k links decreases as the node degree increases on a log–log plot (Fig. The degree exponent ? was 1.60 in this PPI network, which was consistent with the architecture of previously described cellular networks27,28. Figure 2C shows the distribution of node degrees for core proteins, ring proteins, and all proteins in this human PPI network.
Chromosomal passenger complex supermodule, RAD17-RFC-9-1-1 checkpoint module, and CDK1-PCNA-CCNB1-GADD45B module are indicated. The core proteins, such as RFC2, RFC3, RFC4, and RFC5 of RAD17-RFC-9-1-1 checkpoint module, are often hubs (top 25% of the highest degree) of this network.

Core proteins (red) have higher degrees than ring proteins (blue), and constitute the hubs of PPI networks. The IES distribution of these core proteins was consistent with the hub distribution of this PPI network, particularly at the center of the network (Figs. Moreover, 43% of core proteins with degrees of ?10 were hubs, and only 12% of ring proteins were hubs. Interestingly, node degrees of ring proteins in modules were lower than those of all proteins in this network, indicating that core proteins but not ring proteins play major roles in high connectivity of module sub-networks.
Our results suggest that core proteins are preferential constituents of network hubs, as reflected by protein IES values.
This observation is consistent with a previous study showing that highly conserved enzymes in a metabolic network were frequently highly connected at the center of the network and were involved in multiple pathways30. Because homologs of essential proteins are likely to be essential, module proteins were considered essential when they were homologous to those recorded in DEG. 1G).According to the DEG data set, 7,950 proteins from 1,519 module templates were clustered into two groups, including 3,628 mapped essential proteins and 4,322 unannotated proteins without homologous protein in DEG.
Among these mapped essential proteins, IES values of 60% are more than 7 and their IES values are significantly higher than those of unannotated proteins (Mann–Whitney U test, P = 3e-217; Fig. In addition, percentages of mapped essential proteins were correlated with IES (Pearson's r = 0.98) and these increased rapidly with IES ? 7 (Fig. The proteins with IES values of ?7 and <7 were considered core proteins (red) and ring proteins (blue), of a module, respectively. Co-expressions of core protein pairs are significantly higher than those of ring protein pairs.Full size imageBased on these 11,384 essential proteins, we derived 160 essential GO molecular function (MF) terms (Supplementary Table S1, Supplementary Figs. S4 and S5, and Supplementary Text 4) and analyzed functional annotations of core and ring components using hypergeometric distributions (P ? 0.05).
Among these, 462 (38%) were orthologous to essential proteins or were annotated with at least one of the 160 essential GO MF terms. Furthermore, 303 unannotated core proteins (25%) possessed child annotations of the 160 essential GO MF terms; therefore, were considered essential.
Moreover, 76% and 100% of the unannotated core proteins with IES ? 9 or 11, respectively, were annotated with orthologs of essential proteins, were one of 160 essential GO MF terms, or were child annotations of the 160 essential GO MF terms (Table 1). In a module, the number of core components is similar (~50%) to the number of ring components when the module size ?5. We next analyzed the distributions of three kinds of modules: including core-only module, ring-only module, and core-ring module. Interestingly, the percentages of core-only modules were often less than 18% and were much lower than those of ring-only modules (Supplementary Fig.
In the previous studies, functional modules showed limited conservation during evolution, with approximately 40% of 1,161 prokaryotic modules displaying evolutionary cohesion (i.e. The present results suggest that these functional modules contain core and ring components (~50% each), and only core proteins may contribute for the evolutionary cohesion of the module. In addition, the core proteins of a module play the key role for the conservation of functional modules during evolution.Gene co-expression of core and ring componentsDynamic assembly and cooperation of proteins in time and space is essential for biological processes in a cell. In this study, we found that modules can be organized into core and ring components, which represent temporal and spatial conservation of dynamic PPIs and proteins.
Genome-wide gene expression profiles are descriptive of molecular states that are associated with various responses to environmental perturbations and cellular phenotypes33.
For each module among 1,519 templates, we initially selected gene expression sets that contain all proteins in this module, and evaluated co-expressions of intra-module PPIs to construct a correlation matrix (Supplementary Fig. Similarly, when Pearson's r values were ?0.7, the CE of interacting core proteins remained significantly higher than the ratio of interacting ring proteins (P = 3e-14). These results indicate that core PPIs of modules are co-expressed more frequently than ring PPIs, suggesting that core components are often simultaneously active or inactive in time and space.Statistics of protein and module variance in supermodulesProteins often assemble dynamically and cooperate to form the modules that perform biological functions in time and space. Among 1,515 human modules, we found that 1,449 (96%) contain at least one protein that was involved in more than two modules. We iteratively clustered 1,515 human modules into 225 supermodules (including 736 modules) until J(A,B) ? 0.5 for any pair of modules (Figs. We used the functional diversities of a supermodule to understand the characteristics of module organization and variance in PPI networks. Then, we define the functional variance (PFV) of the protein p in a supermodule as , where g is the number of the modules in which protein p involved and G is the total number of modules of this supermodule. Subsequently, the organizational variance (MOV) of the module m in a PPI network is given as , where T is the number of proteins in this module m. The profile of the CPC supermodule with six experimental modules identified by various purification methods.
Module organizational variance (MOV), protein functional variance (PFV), and IES (red) are shown. In the CDK1–PCNA–CCNB1 supermodule, MOV values of four modules were ?0.69 and represented high MES (?6). During early mitosis, CPC is an important mitotic regulatory complex that promotes chromosome alignment by correcting misattachments between chromosomes and microtubules of the mitotic spindle34. The CPC supermodule contained the three core proteins BIRC5, AURKB, and XPO1, and the three ring proteins INCENP, CDCA8, and EVI5. The functions of the CPC can attribute to the action of the enzymatic core, the AURKB34, and the BIRC5 mediates the CPC to target to the centromere and midbody34.
Previous studies indicate that the BIRC5–XPO1 interaction is essential for CPC localization and activity35, implying that XPO1 may play an important role. In human cells, functional CPCs can be targeted, although less efficiently, to centromeres and central spindles in the absence of CDCA8, lack of orthologs in S.
During the late stages of mitosis, EVI5 associates with CPC and plays a role in the completion of cytokinesis.
Therefore, the present results suggest that the functional variance of core proteins are often significantly higher than those of ring proteins.Module variance in different time and spaceHere, we use the CPC supermodule to describe the link from PFV and MOV values to module variance and biological functions in time and space based on 7,208 gene expression data sets (Figs.
To explore the protein and module variance in different cell states, we first utilized CPC supermodule to describe the regulation of cell division (Fig.
From 7,208 gene expression sets, we collected 87 sets, which include all 6 proteins and at least one co-expression (Pearson's r ? 0.5) of interacting protein pairs in CPC supermodule. According to these 87 sets, we derived four modules in CPC supermodule to describe the regulation of cell division in interphase state and mitotic state.
The mitotic state is comprised of prophase, prometaphase, metaphase, anaphase and telophase (not represented here), requiring the assembly and disassembly of specific modules within a supermodule.
For example, for the module 1 (including three proteins AURKB, BIRC5 and CDCA8) in interphase (Fig. The CPC supermodule can represents the dynamical regulation of cell division in interphase state and mitotic state, comprised of prophase, prometaphase, metaphase, anaphase and telophase (not represented here). Based on gene expression sets, the co-expressions of 9?PPIs in the CPC supermodule are measured using Pearson's r values ranging from ?1 (green) to 1 (red).

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