Sources of known autism-associated genes.

Several databases contained information about a number of autism-associated genes. Each resource, however, gathered data from sources with different levels of evidence, ranging from recurrent mutations in patients with autism to nebulous links gleaned from text-mining thousands of PubMed abstracts. In an effort to be comprehensive in putting together our initial picture of autism genetics, we collected genes linked to autism from all these sources (up to December 2013) and classified them into four evidence levels, each associated with an evidence-weight that was commensurate with the quality of the evidence (Supplementary Table 1). For example, genes from categories 1 and 2 in SFARI51 found by statistically significant rare variant associations or nominally significant (but replicated) common variant associations, as well as genes from OMIM52 (a total of 19 genes) were designated as evidence-level 1 (E1) and given a weight of 1.00. Thirty-one candidate genes with two lines of literature evidence annotated to category 3 in SFARI were designated as evidence level 2 (E2) and given a weight of 0.50. Databases HUGE53 and GAD54 together record 413 genes identified based on genetic association studies, which were designated as evidence level 3 (E3). 131 genes inferred purely based on text-mining PubMed abstracts from the Gene2MeSH (http://gene2mesh.ncibi.org) and DGA55 databases, as well as those assigned with minimal-evidence (to category 4) in SFARI were designated as evidence level 4 (E4). Genes in levels 3 and 4 were given a weight of 0.25. Each gene was uniquely assigned to the highest evidence level. In total, we curated 594 autism-associated genes with evidence weights ranging from 0.25 to 1.

Human brain-specific functional interaction network.

The brain-specific functional network was built by integrating thousands of large-scale genomic data using a regularized Bayesian approach21 (Supplementary Fig. 13). We first trained a naive Bayesian classifier specifically for the brain using curated brain-specific knowledge, reflecting what we currently know based on high-quality low-throughput experiments exploring which genes are specifically expressed in the brain and participate in the same biological processes/pathways. The Bayesian model that underlies our integration includes a class node indicating the presence or absence of a functional relationship between a pair of genes that is conditioned on hundreds of other nodes, one for each data set. The contribution of each data set is estimated in the model based on how relevant and accurate it is in reflecting how cellular pathways function in the brain. Since the assumption of conditional independence required for the naive Bayes classifier is violated for the large-scale genomics data sets, we incorporated regularization by calculating the mutual information between data sets and down-weighting similar data sets accordingly. Finally, the naive Bayes functional-relationship posterior probability for each gene pair is calculated proportionally to the product of the weighted likelihoods. We used this model, now trained on brain-specific knowledge, to make genome-wide predictions by estimating the probability of brain-specific functional interactions between all pairs of genes (25,825 genes represented in at least one data set). The predicted posterior probabilities were scaled based on the assumption that the prior probability of a functional relationship is 0.01. The final network of functional relationships reflects how likely each pair of genes in the genome is to participate in the same pathway in the brain.

We have shown that multiple genes associated with a particular disease often tend to have similar patterns of connectivity in a relevant tissue-specific functional network21. We use this notion (further described below) to discover autism-associated genes in the context of the brain-specific gene network.

Learning and cross-validation of the network-based classifier.

We used a machine learning approach to predict autism-association genes. Our approach had two steps: (i) Building a statistical model that captured the connectivity patterns of known autism-associated genes in the brain-specific network, and (ii) using this model to subsequently predict whether each of the other 'unknown/unlabeled' genes in the network looks like an autism-associated gene based on its connectivity in the network. We trained an evidence-weighted linear support vector machine (SVM) classifier using the gold standard of known autism-associated genes (along with their weights) as positives and 1,189 genes associated with non-mental-health diseases (from OMIM, with weights equal to 1) as negatives. The brain-specific interaction probabilities of each gene to all the genes in the brain network were used as features. Given the network features (x i ) and a positive/negative label (y i ) for all the m training genes, the linear SVM solves the following optimization problem56:

where l i is a penalty parameter specific to each gene that influences how costly it is to misclassify that gene. By setting l i equal to the evidence-weight of the labeled gene (where negatives have l i of 1), we ensured that our model rarely misclassifies high-confidence genes while giving certain latitude in correctly classifying low-confidence genes.

To evaluate this approach, we employed a stringent five-fold cross-validation scheme: in each fold, we trained a model on 4/5 of the labeled (positive and negative) genes and evaluated the model on only high-confidence (E1) positives (and all negatives) in the remaining 1/5 of the labeled genes. The model with weights equal to 1.00, 0.50, 0.25 and 0.25 for E1, E2, E3, and E4 genes had an AUC of 0.80. Taking model variance into account by repeating the five-fold cross-validation 50 times, we demonstrated that this model performs significantly better than one trained only using high-confidence genes (weights 1, 0, 0, 0; AUC = 0.73; P < 2.2 × 10−16, two-sided Wilcoxon rank-sum test; weights 1, 1, 0, 0; AUC = 0.76; P < 2.4 × 10−15) and significantly better than one trained with real E1–E2 supplemented with random genes simultaneously matched with E3–E4 for gene length, brain expression and neuronal gene ontology (AUC = 0.74, P < 2.2 × 10−16). Therefore, we used the evidence-weighted model to make further predictions.

Genome-wide prediction using evidence-weighted network classifier.

We coupled whole-genome prediction with five-fold cross-validation. A prediction for each labeled gene (positive/negative) was recorded only from the fold that did not include the gene for training, which ensured that the model relies only on the gene's network-based similarity to other genes instead of its own prior evidence. A prediction for an unlabeled gene is recorded as the average of predictions from the five folds. Each prediction corresponds to the distance of the gene from the hyperplane that separates positive genes from negative genes, and these distances are used to rank all the genes in the genome. For interpretability, the distances are also converted to probabilities using isotonic regression (see below). This produces a genome-wide ranking of 25,825 genes based on their predicted level of association with autism.

Evaluation of autism-associated gene ranking on independent de novo mutations.

De novo mutations from exome-sequencing study. The Simons Simplex Collection57 (SSC) contains more than 2,500 families, each of which has a single child with ASD (a proband). Most of these families have at least one unaffected sibling. A recent study used whole exome sequencing of the SSC to identify de novo LGD mutations in children with autism and their unaffected siblings7. 350 and 174 genes were targets of LGD mutations in probands and unaffected siblings, respectively. Among the 350 LGD genes in probands, 27 were observed in more than one proband (recurrent LGD), indicating that these are very likely to be true autism-associated genes. We used these sets of genes—proband recurrent LGD (27), proband LGD (350) and sibling LGD (174)—to benchmark our genome-wide autism-associated gene ranking. When testing each LGD set, we used 462 genes containing synonymous mutations in unaffected siblings (sibling SYN) as a control. Further, to account for potential biases in exome sequencing coverage, when defining a genomic background, we removed the 8,054 genes in which no rare variants from reference were reliably detected anywhere within genic boundaries.

Preliminary de novo mutation data on 682 SSC families were published in three separate reports in 2012 (refs. 3, 4, 6). Since it was likely that some of these data were represented in our training set of autism-associated genes, we created an 'unpublished' evaluation data set from SSC which was released after our prediction. This data set was created from the new SSC families in the 2014 study7 (i.e., 1,835 families after removing the previously published 682 from the total of 2,517 families), which underwent whole exome sequencing to identify de novo LGD mutations in children with autism and their unaffected siblings. We used this unpublished set of mutations to re-test the significance of our findings derived based on the entire SSC cohort (Supplementary Fig. 4).

We also obtained the 107 likely ASD-associated genes from a study independent of the SSC8 and used this set to evaluate our predictions.

Decile enrichment test. After removing SSC genes without rare variants from the autism-associated gene prediction rankings, the remaining genome-wide gene ranking was divided into deciles. For a given set of LGD genes, we used the binomial test to assess whether a larger fraction of the LGD genes occurred in the first decile when compared to the expected fraction based on the occurrence of sibling SYN genes. Reassuringly, sibling SYN genes were roughly apportioned 10% to each decile, indicating that it is a good control set.

Rank-based enrichment test. To demonstrate robustness of our evaluation to specific rank cutoffs (as our decile enrichment test assesses genes above a 10% rank cutoff), we also formulated a rank-based test. This test takes the entire genome-wide ranking and assesses the set of LGD genes for a skewed distribution toward the top of the ranking relative to the control set. First, based on the genome-wide autism-association ranking, we calculated an exponential score s i for each gene i based on its autism-associated rank rank(i) as follows:

Here N is the total number of genes equal to 25,825, and b was set to 100. The score s i ranges between 1 for the top-ranked gene dropping exponentially to 0 for the lowest ranked gene. The rank-based test then proceeds in three steps: (i) calculate the observed difference (d obs ) between the mean rank-based score of the test LGD gene set (for example, proband LGD) and the control gene set (sibling SYN); (ii) shuffle the gene labels in the test and control gene sets 100,000 times and, each time, record the difference between mean(test) and mean(control) (d permut ); (iii) calculate a P-value for d obs equal to the fraction of permuted differences d permut that were equal to or greater than d obs ; and calculate an effect size for d obs as a z-score:

where μ and σ are the mean and s.d. of the distribution of d permut values.

Evaluation controlling for gene length. Genes linked to ASD are known to be longer in size than genomic background23. To test if our genome-wide ranking is driven by prioritizing long genes, we repeated our LGD evaluation while controlling for gene length. We sorted all genes by their length, divided the genes into bins of 500 genes (of very similar lengths), randomized ASD ranks of genes within each bin, and calculated the top-decile enrichment of LGD-target genes. A P-value is calculated by repeating this procedure 10,000 times and calculating the fraction of times the permuted top-decile enrichment P-value is less than or equal to the observed P-value.

Evaluation controlling for bias in brain-/neural-functional annotations. To demonstrate that brain and/or neural genes are not biasing our results, we evaluated our predictions on whether they could prioritize proband LGD genes within a non-neural-annotated gene set. We created this set by including proband LGD genes that are neither annotated to neural or brain-related functions in Gene Ontology nor part of our training gold standard. Fisher's exact test was then used to calculate significance.

Evolutionary constraint of ASD-associated genes. Evolutionary constraint estimates of genes were obtained from two different studies58,59, one providing a quantitative (RVIS) score for each gene, and the other providing a single set of 1,003 constrained genes. The Wilcoxon rank-sum test was used to assess the difference between the RVIS scores for genes in our top-decile compared to the rest of the ranking, and Fisher's exact test was used to calculate the enrichment of the constrained gene set in our top decile. We also evaluated both sets using a rank-based permutation test that does not involve any rank cutoffs. For the RVIS score, a test statistic equal to the Spearman correlation coefficient between genes ranked by our method and by RVIS scores was calculated; a P-value for this statistic was estimated by permuting the ASD candidate gene ranking one million (1,000,000) times and calculating the fraction of times the permuted correlation was less than or equal to the observed one. For the constrained genes, a test statistic equal to the mean rank-based scores (s i ) of genes in the set was calculated; a P-value for this statistic was then estimated by permuting ASD gene ranks one million times and calculating the fraction of times the permuted statistic was greater than or equal to the observed one.

Developmental expression of autism-associated genes in the brain.

Defining spatiotemporal expression signatures. The spatiotemporal developmental gene-expression data for the human brain was obtained from Brainspan29. Raw data from this study were downloaded from NCBI GEO60 accession code GSE25219. CEL files were background corrected, normalized, and summarized using RMA61 based on a custom CDF62, and expression levels for each gene were averaged across replicates. Further analysis was restricted to 13 stages from early fetal (10–13 weeks postconception) to late adulthood (≥60 years) that contained expression data for all 16 brain regions. We first established a gene-expression signature for each of the 208 spatiotemporal windows (combination of 16 regions and 13 stages) specific to that window with respect to other stages as well as other regions. For example, a signature for the striatum (region) at the late midfetal stage was calculated in three steps.

(i) For each gene i, two modified z-scores were calculated by comparing , the gene's expression in that region (striatum) and stage (late-midfetal), to the distribution of its expression values across all regions at late-midfetal stage (to get ) and across all stages of striatum (to get ).

where and , respectively, are the median expression levels of gene i across all regions at late-midfetal stage and all stages of striatum; and are the corresponding median absolute deviations (MAD). Since median and MAD are stable measures of central tendency and variance of a distribution without being influenced by outliers, scaling using these measures aids in identifying expression values that are particularly high.

(ii) These two z-scores were then combined into a meta z-score that tends to be high when the expression of the gene deviates substantially from its nominal expression along both the spatial and temporal axes.

(iii) Finally, the set of genes with were used as the gene-expression signature (of late midfetal striatum, in this example).

We employed this procedure to compute a signature for all 208 combinations of regions and stages.

Rank-based enrichment test of spatiotemporal signatures. This test was very similar to the rank-based test detailed above. For each signature, a test statistic equal to the mean exponential rank-based autism-association scores (s i , described above) of genes in that signature was calculated. Mean scores based on random signatures of the same size sampled from the union of all genes in all signatures were then used to set up an empirical distribution. A P-value for the signature was ultimately calculated as the fraction of permuted mean scores that were equal to or greater than the observed mean score for the real signature. We carried out this test for all 208 region-stage combinations and corrected for multiple tests using the Benjamini–Hochberg correction63 to get Q-values.

Clustering the autism-associated brain network.

In order to identify autism-associated functional modules in the brain, we created a subset of the brain-specific functional network containing the top 2,500 autism-associated genes from our genome-wide ranking and all the edges between them. Then, we used an approach based on shared k-nearest-neighbors (SKNN) and the Louvain community-finding algorithm64 to cluster the network into distinct modules of tightly connected genes. The SKNN-based strategy has the advantages of alleviating the effect of high-degree genes and accentuating local network structure by connecting genes that are likely to be functionally clustered together. Given a graph G with V nodes (genes) and E edges, with each edge between genes i and j associated with a weight p ij , this technique proceeds as follows: (i) calculate a new weight for the edge between each pair of nodes i and j that is equal to the number of k nearest neighbors (based on the original weights p ij ) shared by i and j; (ii) choose the top 5% of the edges based on the new edge weights, and apply a graph clustering algorithm. This approach has two key desirable characteristics: (i) choosing the highest k values instead of all edges deemphasizes high-degree 'hub' nodes and brings equal attention to highly specific edges between low-degree nodes; and (ii) emphasizing local network-structure by connecting nodes that share a number of local neighbors automatically links genes that are highly likely to be part of the same cluster. We used a k of 50 to obtain the shared-nearest-neighbor autism-associated brain network and used the Louvain algorithm to cluster this network into distinct modules. We confirmed that the node membership and cluster sizes are robust by testing a range of values for k from 10 to 100. To stabilize clustering across different runs of the Louvain algorithm, we ran the algorithm 100 times and calculated cluster comembership scores for each pair of genes that was equal to the fraction of times (out of 100) the pair was assigned to the same cluster. These comembership scores were used to layout the network in Figure 4 (using Cytoscape65), which represents all clusters that contained at least 10 genes, defined by a comembership score ≥ 0.9. We confirmed the statistical significance of this score using a permutation test, randomizing the k-nearest neighbors of each node in the network of top ASD-associated genes and redoing the clustering procedure (Supplementary Fig. 10).

One-sided Fisher's exact tests were used to find GO biological processes66 enriched in each cluster. Benjamini–Hochberg corrections were used to correct for multiple tests, and GO terms with Q ≤ 0.1 were deemed significant. The entire table of enriched GO terms is provided in Supplementary Table 6.

Prioritizing genes in autism-associated CNVs.

We selected the eight most statistically significant and frequent autism-associated CNVs50 and obtained the genes in the intervals from UCSC67. An expert independently annotated genes in each interval with genetic or functional evidence for association with autism from existing literature. Genetic evidence refers to direct genetic evidence implicating a gene in autism or a related disorder (for example, schizophrenia or epilepsy). Functional evidence refers to the annotation of a gene to a function, process or pathway involved in autism, but without direct genetic evidence.

Identification of CNV-specific intermediate genes. The goal here was to identify key genes and the related cellular functions that may be deregulated by each CNV by tracing a biomolecular path from the CNV to the molecular phenotype of autism. We first marked the most autism-associated genes in each CNV as those within the top 10% of our genome-wide autism-associated gene ranking. Then, we defined the 19 E1 (high-confidence) genes as the core genes representing the molecular phenotype of autism. Taking advantage of the underlying brain-specific network, for each CNV, we calculated the betweenness centrality (BC) of each network gene as the fraction of shortest paths from the top-ranked CNV genes to the core autism-associated genes that also pass through that gene. The brain network was prefiltered to contain only around top 1% of its edges, and path length was calculated as the reciprocal of the functional linkage score. Genes with high BC are molecular mediators between the CNV and autism. We identified genes with high BCs that were also specific to a given CNV (with T total genes and t top-ranked genes) by keeping the core autism-associated genes constant and repeating the BC calculation for random set of t genes from random genomic intervals with T genes. Finally, a permutation-based P-value was computed for each network gene as the fraction of times that gene's BC with random intervals was equal to or greater than the gene's BC with the real CNV (n = 100,000). Upon Benjamini–Hochberg correction for testing the BC of thousands of genes, those with Q ≤ 0.1 were identified as mediator genes specific to the given CNV.

Text mining for autism-associated processes. We queried all available PubMed abstracts from 2000 to May 2015 for (autism OR ASD OR autistic), and retrieved these autism-associated abstracts. GO biological processes terms were mapped to each abstract using simple text search, and a given term was considered associated with autism if it was found in at least two abstracts.

Functional impact of multiple CNVs. The next goal was to use the CNV-specific mediator genes to determine cellular functions that are likely deregulated by multiple CNVs. For this, we used Fisher's exact test to find sets of genes annotated to autism-associated GO biological processes that overlapped significantly with the CNV-specific mediator gene set. Processes and pathways that were significantly associated (Q ≤ 0.05) with two or more CNVs and annotated to at least two mediator genes were analyzed further and were summarized to general terms based on gene overlap, term description and their relationships in the ontology.

Identification of MAZ targets. Computationally predicted targets were generated by using FIMO68 to map the binding site of MAZ (obtained from HOCOMOCO69) to the 1,000-bp upstream regions of all the genes in the genome. 2,446 genes with matches of at Q ≤ 0.01 were selected as potential targets of MAZ. Enrichment analysis for MAZ targets against the autism-associated gene predictions was applied using one-sided Fisher's exact test against the top 2,500 ranked gene predictions (top decile).

ASD webserver.

The web interface is implemented using the D3 library70 for visualization, which enables use on any modern web browser without plugin installation.

Probability estimates for predicted autism-related genes. We estimated prior probabilities for several biological pathways and gene sets known to be enriched for autism-associated genes by calculating the fraction of genes with de novo LGD mutations occurring in quad family probands over all de novo LGDs. These pathways and sets include CHD8 targets, chromatin remodeling genes, FMRP targets, MAPK pathway genes, post-synaptic density genes, TOP1 targets and Wnt–β-catenin pathway genes.

To improve interpretability for our autism-associated gene predictions, we calibrated the SVM scores using isotonic regression. Isotonic regression, or monotonic regression, minimizes the same condition as a least-squares regression while imposing a monotonicity constraint (i.e., if gene A has a higher rank in original predictions than gene B, isotonic regression enforces that the fitted probability estimate for gene A will also be higher than that of gene B), and it has been previously shown to have more power when sufficient data is available71. The response variable (probability of a gene being autism-related) was estimated based on the gene's enrichment among the SSC proband LGDs. To prevent overfitting in our probability estimation, we used ten-fold cross validation to find the 'knots' for the regression results of each held-out fold. We fit an isotonic regression curve through all knots, with Hermite spline interpolation between knots, and provide the resulting estimated probabilities on the web interface.

Permutation-based P-values and Q-values for our genome-wide predictions. In order to improve the interpretability of our genome-wide ranking, we calculated a permutation-based P-value and a corresponding Q-value for each gene (Supplementary Table 3), and provide these in our ASD web-server. We permuted labels of gold standards and retrained the model 1,000 times. P-values were calculated as the probability of the gene being predicted to be as extreme as it is (considering both 'highly ASD-associated' and 'highly non-ASD associated', n = 1,000), and were corrected to Q-values by the Benjamini–Hochberg method63.

Webserver updates. We will keep the ASD gene predictions on our web server updated for the community. As the set of annotated ASD candidate genes increases, we will retrain our model with the most up-to-date ASD candidate gene collection. As of this writing (July 2016) we have retrained our model with the entire collection of known ASD genes up to October 2015 (with the same gene evidence weighting criteria), and those predictions are available at http://asd.princeton.edu/v2.

Code availability.

Software to perform disease-gene prediction using the brain-specific network with user-defined gold standards is available at http://asd.princeton.edu. Additional software used to build the brain-specific network is available at http://libsleipnir.bitbucket.org.

Data availability.

All data supporting the findings of this study are available within the article, its supplementary information files, and at http://asd.princeton.edu. Additional information about data sets used to build the brain-specific network is available at http://giant.princeton.edu.

A Supplementary Methods Checklist is available.