E. coli K-12 sequence data were downloaded from Comprehensive Microbial Resource (CMR) database at http://cmr.jcvi.org. It contains 4289 protein sequences in total [25]. The essential genes of E. coli K-12 were downloaded from the PEC database [7]. The Kato dataset contains 302 essential genes from gene deletion experiments.

A. baylyi ADP1 sequences were collected from the Magnifying Genomes database (http://www.genoscope.cns.fr/agc/mage). Of a total of 3308 genes, 499 are essential genes from de Berardinis et al. [6]

S. cerevisiae S288c sequences were downloaded from Saccharomyces Genome Database at: http://downloads.yeastgenome.org/sequence/genomic_sequence/. It contains 5885 ORFs. The essential gene list was downloaded from Giaever et al. [26]. This dataset contains 1049 essential genes from targeted mutagenesis experiments.

N. crassa OR74A ORFs were downloaded from Neurospora crassa database at Broad Institute at http://www.broadinstitute.org/annotation/genome/neurospora/MultiDownloads.html. Dubious ORFs and pseudogenes were excluded from this list. The essential gene dataset was kindly provided by K. Borkovich at UC Riverside from the systematic genome deletion project in N. crassa. This list contains 7172 experimental verified essential/nonessential genes, and 1251 of them are essential genes.

Gene expression data in these organisms were downloaded from NCBI GEO [27], ArrayExpress [28], and the gene-expression profiles of microarray data from Gasch et al. [29].

Based on our previous research, we considered three main types of features: (A) those intrinsic to a gene’s sequence (e.g., GC content, length); (B) those derived from genomic sequence (e.g., localization signals and codon adaptation measures); and (C) experimental functional genomics data (e.g., gene-expression microarray data) (Table 1). The detailed descriptions of these features and their biological implications can be found in the supplemental materials as well as in Deng et al. [24]. For example, domain enrichment score (DES) reflects the conservation of local domains rather than the entire gene, which is calculated by the ratio of the domain’s occurrence frequencies in essential genes vs. in total genes in a given organism. In another example, phylogenetic score (PHYS) measures the evolutionary conservation of a gene, which is calculated by counting the number of genomes that have orthologous hits. Such conservation has been shown to correlate well with the indispensability of a gene. These diverse types of features suggest that gene essentiality is likely determined not solely by the genomic sequence, but by multiple aspects of biology coinciding.

We evaluated these features based on their predictive power following a procedure described in Deng et al. [24]. To briefly summarize, we performed a logistic regression analysis and ranked all features according to the cover length of log-odds ratio. A longer overall coverage length indicates greater contribution of the corresponding feature to the gene essentiality. Because we were more interested in predicting essential genes rather than non-essential genes, the features with a positive coverage length were our candidate features. We also considered prior biological information to remove feature redundancy.

The training data included the attribute values for each feature and the class assignments. Each gene was assigned a Boolean value regarding its essentiality (1—essential; 0—non-essential). The training data were divided into 10 equal parts. Nine parts were used to train the classifiers and the remaining part was used for testing. The control training set was generated by randomly assigning essential labels to all genes. The same number of random “essential genes” as the number of true essential genes was used in the training and testing frame.

We used a logistic regression classifier to train and test the model. All classifiers were implemented using the Orange software package (http://www.ailab.si/orange/). To train and test our classifier, features were first extracted where available for each ORF and annotated with known essentiality values, thereby creating our “gold standard” data set. Then the “gold standard” dataset was divided into 10 equal parts. Nine parts were used to train the classifiers and the remaining part was used for testing.

Then we applied the model to the target organism, and predicted the probability of essentiality for each gene in that organism. Based on the true gene labels and the predicted probability, we were able to calculate the AUC (Area Under Curve) of the Receiving Operation Curve (ROC) and the Sensitivity (number of correctly predicted essential genes/total essential genes) of the prediction. AUC and Sensitivity were then used to evaluate the performance of the model.

EC is a gram-negative bacterium commonly found in the lower intestine of warm-blooded organisms. It is one of the most well-studied prokaryotic model organisms and has the best-characterized essential genes.

We compared three approaches using our previously developed integrative algorithm (Table 2): (1) the same-organism approach, where we learned traits among the partially known essential genes in EC and predicted the rest of the essential genes; (2) the cross-organism approach, in which we learned traits among the known essential genes in AB, a closely-related model organism, and tried to predict the essential genes in EC; and (3) the combined approach, in which we learned traits among the known essential genes in AB as well as the partially known essential genes in EC and tried to predict the rest of the essential genes in EC. Because in our previous research we have shown that our cross-organism approach outperforms homology mapping [24], we did not compare homology mapping in this study.

In AB, we identified 11 features that are potentially associated with gene essentiality and have relatively weak correlations among themselves [24] (Table 1). We followed the same analysis procedure as in EC. In the same-organism approach, we first used 10 features excluding DES as the input of the classifier to build the “no-DES” model, and then including DES to build the “with-DES” model. The model generated a probability score of gene essentiality for each gene of the entire target organism. Combining this probability score and the true essentiality information of each gene, we were able to evaluate the performance. In Figure 2a, the red and black curves showed the distribution of the AUC scores of the results output from the “no-DES” and “with-DES” models respectively. Both curves increase rapidly before 2% (66/3308) of total genes are known to be essential, achieving more than 95% of the best performance. Compared with “no-DES” results, the results of “with-DES” were significantly improved. Also, the dashed line in Figure 2a shows the AUC of the cross-organism approach using EC essential genes, suggesting that knowing 2% of total genes to be essential is “sufficient” to lead to a prediction better than transfer from EC. Figure 2b and c show the bar charts of the correctly classified essential genes using the “no-DES” and “with-DES” models respectively. For AB, we adopted a similar percentage as the cutoff to predict essential genes as in EC, and the top 400 genes with the largest probability scores were predicted as essential genes. In both Figure 2b and 2c, the performance is nearly stable if the known essential genes take up more than 2% of the total genes in AB. In the combined approach, we combined both the EC essential genes with increasing numbers of known AB essential genes by assigning different weights. The blue curve (Figure 2a) shows the combined approach outperforming the same-organism approach only at the beginning. Compared with Figure 1, the difference between the combined approach and the same-organism approach in AB was less significant than in EC. The green curve in Figure 2a shows the performance of DES feature only. This suggests that the integration of different features is able to make more accurate predictions than using DES alone.

Our results suggested that essential genes are highly predictable by learning the characteristics underlying gene essentiality in prokaryotes. To test whether the same trend can also be observed in eukaryotic species, we chose SC and NC as our test candidate species.

SC is an important eukaryotic model organism in cell biology and is one of the most thoroughly studied eukaryotic microorganisms. There are 1049 essential genes identified by the systematic deletion project [26]. Using the same-organism approach in SC, we identified 14 features potentially associated with gene essentiality (Table 1). Domain enrichment score (DES) was found to be a strong feature in predicting essential genes in eukaryotes as well. This suggests that, much as in prokaryotes, gene essentiality in eukaryotes is likely preserved through the function of protein domains or domain combinations rather than through the conservation of entire genes. First, we used 13 features excluding DES as the input of the classifier. After the 10-fold cross-validation, each gene of the target organism received a probability score of essentiality. Combining this probability score and the true essentiality information of each gene, we were able to evaluate the performance. Figure 3a (red curve) showed the AUC curve of the “no-DES” results. It gradually increases along with the increase of the known essential genes and reaches stable at around 4% point on the x-axis, achieving 95% of the best performance. Besides the AUC curve, we also plotted the bar chart of correctly predicted essential genes (Figure 3b). Since essential genes comprise of about 20% of a eukaryotic genome, we used 1200 as the cutoff, i.e., the 1200 genes with the highest essential scores were predicted as SC essential genes. The performance increased as we increased the size of the training dataset, and the saturation point was at 4%. Figure 3a (green curve) shows that, similar to in prokaryotes, DES is a strong feature to the prediction of gene essentiality and incorporating it with other functional and genomics features is able to achieve an optimal performance.

Next, we added the DES feature into the model. Figure 3a (black curve) and Figure 3c show a similar trend, except the values are significantly higher than those of the “no-DES” results. This further supports the notion that the DES feature has strong power in predicting essential genes in eukaryotic species. Moreover, we note that the saturation occurred at 4% point in both figures. Thus, knowing 4% or more of the total genes is essential to building a reliable prediction.

In the combined approach, we used both NC and the partially known essential genes in SC as the new training set. Would the result be significantly improved again? We followed the same scheme as described above. The results were consistent: As shown in Figure 3a, the performance of the same-organism approach (black curve) dominates the performance of the combined approach (blue curve) from about 1.5% on the x-axis. Although the saturation point of the prediction is different, the dominating points are almost the same as those in EC and AB.

NC is an ascomycete, the red bread mold. Like all fungi, it reproduces by spores. It is used as a eukaryotic model organism because it is easy to grow and has a haploid life cycle which makes genetic analysis easier. There are 1250 essential genes in NC produced by the systematic gene deletion project. We identified 14 features potentially associated with gene essentiality in NC (Table 1). Following the same procedure as above, we analyzed the “no-DES” and “with-DES” dataset of the same-organism approach separately. We assigned the top 1500 genes as the predicted essential genes. Figure 4a shows that when given about 4% of total genes to be essential, the prediction achieves stable AUC with over 95% best performance. Compared with the red curve, the black curve is significantly improved. The blue curve also showed the performance of the combined approach using SC and partial NC known essential genes. The conclusion is similar to that in SC: The same-organism approach in NC (black curve) dominates the combined approach (blue curve) after at least 1.5% of the total genes are known to be essential.

Our results suggest that, in prokaryotes, when the number of known essential genes is greater than 2% of total genes, it will achieve over 95% of the best performance, recovering >68% of total essential genes at the given cutoff. For example, for an understudied organism with 3000 genes, we need to know ~60 essential genes in order to accurately predict the majority of its ~300 essential genes. In contrast, in eukaryotes, achieving the same level of performance requires more than 4% of total genes, reflecting the increased complexity of eukaryotic organisms. The complexity comes from different aspects. One possibility is that eukaryotes have more complex genome structures than prokaryotes, such as the expanded protein domain repertoire. In fact, EC and AB contain 5468 and 4204 unique domains, respectively, while SC and NC contain 6023 and 7031 unique domains, respectively, according to the Interpro database. In addition, higher organisms have larger and more complex cellular structure as well as perform more diversified functions, which also require them to have more essential genes.

We found that the required number of known essential genes was surprisingly small for both prokaryotes and eukaryotes, suggesting that the distribution of genomic features extracted from this small subset already provided a close approximation to the distribution of those extracted from the entire essential gene set. This showed the advantage of predicting essential genes using machine-learning approaches.

We also noticed that as the model reaches saturation, there are still parts of essential genes (i.e., 32% in prokaryotes) that cannot be correctly predicted as essential. We further explored these incorrectly predicted essential genes by plotting the distributions of their associated features. Here we defined the essential genes that were correctly predicted as true positives (TPs) and those that were incorrectly predicted as false negatives (FNs). Figure 5 shows the boxplot of the two parts of genes in AB. The features for which the distributions between the two sets of genes differed most widely are DES and PHYS, followed by CAI, Nc and Aromo, all of which were derived from genomic sequences. This suggests that in order to correctly predict the FNs, relying on features based on genomic sequences is no longer enough. Other strong functional genomics features have to be discovered and incorporated into predictions. This observation also supports the notion that gene essentiality is likely determined not solely by genomic sequence, but by multiple aspects of biology, from sequence to function.

We then performed functional analysis of the FN genes by categorizing them according to the clusters of orthologous groups (COGs) proteins classification. In COGs, genes can be generally classified into four broad functional categories: information storage & processing, cellular processes & signaling, metabolism and poorly characterized. Previous work has shown that essential genes are overrepresented in the category of information storage and processing with basic cellular functions such as RNA processing and modification and DNA replication [32]. Essential genes involved in this category are often well conserved across species. On the other hand, the species-specific essential genes are mainly distributed in cellular processes and metabolic categories, which often reflects a microbe’s unique life style and living environment. Figure S1a and S1b) show the distributions of FN genes across different functional categories in EC and SC respectively. We can see in EC the FN genes are enriched in the metabolic category while in SC these FN genes are enriched in cellular processes and signaling category.

Comparing different sets of features used between the prokaryotes (EC, AB) and eukaryotes (SC, NC) in Table 1, the common features they shared are: Nc, L_aa, PHYS, PA, DES and FLU. These features cover all three categories described in Section 2.2. This supports our conclusion that the computational integration of different genomic and functional features is able to accurately predict essential genes in both prokaryotes and eukaryotes. However, there are some differences of features used between them, such as those sub-cellular localization features. For example, Nucleus, Plasma and PredHel are used only by SC and NC while Inner member is used only by EC and AB. These reflect the differences in cellular structure between prokaryotes and eukaryotes—the eukaryotic cells are much larger and more complex than prokaryotic cells.

Through our analysis, we realize that the evolutionary distance between the understudied organism and the model organism may affect the thresholds observed in our study. Nevertheless, our results suggest that an organism’s own known essential genes usually contain more information about its unique physiology and are a better representative set of its total essential genes.

Logistic regression was chosen in this study mainly because of its simplicity and ease of interpretation of results. Other machine-learning methods could have been used. However, most alternative techniques suffer from their own limitations, e.g., missing value problems or being prohibitively time-consuming, which prevent them from being used in this study. Nevertheless, we expect our conclusions from this investigation are unlikely to change if a different machine-learning technique is used. Since the four species we studied are all microorganisms, the conclusions from this study may not be applicable to more complex systems, such as mouse and human. Finally we believe the results obtained from our study provided important information on accurately predicting essential genes and will greatly facilitate the annotations of microbial genomes.