Introduction

Tumorigenesis in each patient is driven by mutations in the patient’s genome. Hence, a central goal of cancer genomics is to identify all driving mutations in each patient. This task is particularly challenging because each driving mutation is present in only a small fraction of patients. As the number of driver mutations in each patient has been estimated to be >5 (Armitage and Doll 1954; Bozic et al. 2010; Hanahan and Weinberg 2011; Belikov 2017; Anandakrishnan et al. 2019), the total number of driver mutations summed over all patients must be quite high.

This study, together with the companion paper (supplement File S2), are based on one simple premise: In the massively repeated evolution of cancers, any advantageous cancer-driving mutation should recur frequently, say i times in n patients. The converse that non-recurrent mutations are not advantageous is part of the same premise. We focus on point mutations, referred to as Cancer Driving Nucleotides (CDNs), and formulate the maximum of i (denoted i*) in n patients if mutations are not advantageous. For example, in the TCGA database with n generally in the range of 500∼1000, i* = 3. Hence, any point mutation with i ≥ 3 is a CDN. At present, a CDN would have a prevalence of 0.3% among cancer patients. If the sample size approaches 10⁶, a CDN only needs to be prevalent at 5×10⁻⁵, the theoretical limit (supplement File S2).

Although there are many other driver mutations (e.g., fusion genes, chromosomal aberrations, epigenetic changes, etc.), CDNs should be sufficiently numerous and quantifiable to lead to innovations in functional tests and treatment strategies. Given the current sample sizes of various databases (Cerami et al. 2012; Weinstein et al. 2013; Tate et al. 2019; de Bruijn et al. 2023), each cancer type has yielded 50∼150 CDNs while the CDNs to be discovered should be at least 10 times more numerous. The number of CDNs currently observed in each patient is 0∼2 for most cancer types. This low-level of discovery has limited functional studies and hampered treatment strategies.

While we are proposing the scale-up of sample size to discover most CDNs, we now characterize CDNs that have been discovered. The main issues are the distributions of CDNs among genes, across cancer types and, most important, among patients. In this context, cancer driver genes (CDGs) would be a generic term. We shall use “canonical CDGs” (or conventional CDGs) for the driver genes in the union set of three commonly used lists (Bailey et al. 2018; Sondka et al. 2018; Martínez-Jiménez et al. 2020). In parallel, CDN-harboring genes, referred to “CDN genes”, constitute a new and expanded class of CDGs.

The first issue is that CDNs are not evenly distributed among genes. The canonical cancer drivers such as TP53, KRAS and EGFR tend to have many CDNs. However, the majority of CDNs, especially those yet-to-be-identified ones, may be rather evenly distributed with each gene harboring only 1∼2 CDNs. Hence, the number of genes with tumorigenic potential may be far larger than realized so far. The second issue is the distribution of CDNs and CDGs among cancer types. It is generally understood that the canonical CDGs are not widely shared among cancer types. However, much (but not all) of the presumed cancer-type specificity may be due to low statistical resolution at the genic level.

The third issue concerns the distribution of CDNs among patients. Clearly, the CDN load of a patient is crucial in diagnosis and treatment. However, the conventional diagnosis at the gene level may have two potential problems. One is that many CDNs do not fall in canonical CDGs as signals from one or two CDNs get diluted. Second, a canonical CDG, when mutated, may be mutated at a non-CDN site. In those patients, the said CDG does not drive tumorigenesis. We shall clarify the relationships between CDN mutations and genes that may or may not harbor them.

The characterizations of discovered CDNs are informative and offer a road map for expanding the CDN list. A complete CDN list for each cancer type will be most useful in functional test, diagnosis and treatment. We should note that, given the sharing of CDNs across cancer types, CDN lists in a subset of cancer types may be of general use across other cancer types.

Results

In molecular evolution, a gene under positive selection is recognized by its elevated evolutionary rate (Fig. 1A and 1C). There have been numerous methods for determining the extent of rate elevation (Li et al. 1985; Nei and Gojobori 1986; Yang and Swanson 2002; Lawrence et al. 2013; Martincorena et al. 2017; Sherman et al. 2022) and cancer evolution studies have adopted many of them. However, no model has been developed to take advantage of the massively repeated evolution of cancers (Fig. 1B), which happens in tens of millions of people at any time.

Figure 1:

In the whole-gene analysis, Fig. 1C-E are identical, each with A : S = 10 : 1 where A and S denote nonsynonymous and synonymous mutations, respectively. However, the presence of a 4-hit site in Fig. 1E is far less likely to be neutral than Fig. 1C and 1D. Although ratio in Fig. 1F, A : S = 4 : 1, is statistically indistinguishable from the neutral ratio of about 2.5 : 1, Fig. 1F in fact has much more power to reject the neutral ratio than Fig. 1C and 1D. After all, the probability that multiple hits are at the same site in a big genome is obviously very small.

1. The analyses of CDNs across the whole genome

For the entire coding regions in the cancer genome data, we define A_i (or S_i) as the number of nonsynonymous (or synonymous) sites that harbor a mutation with i recurrences. Table 1 presents the distribution of A_i and S_i across the 12 cancer types with n > 300 (Weinstein et al. 2013).

Table 1

For neutral mutations, we define i* as the threshold above which the expected numbers of A_i would be <1, i.e. E[A_i≥i∗] < 1, The corollary is that all A_i≥i∗ sites are advantageous CDNs. (Since S_i is ∼ A_i/2.3, the same i* would apply to S_i as well: E[S_i≥i∗] < 1) As i* is a function of the number of patients (n), it is shown mathematically in the companion study (supplement File S2) that i* = 3 for n < 1000. Interestingly, while the E[A_i≥3] is < 1, the expected E[A_i≥4] is ≪ 1, in the order of 0.001. Hence, i* = 4 may be considered unnecessarily stringent.

We should note that this study is constrained by n < 1000 in the TCGA databases. (Databases with larger n’s are also used where the actual n’s are often uncertain.) At i* = 3, we could detect only a fraction (<10%; see below) of CDNs. Many more tumorigenic mutations may be found in the i = 1 or 2 classes although not every one of them is a CDN. Since these two classes of mutations are far more numerous, they should account for the bulk of CDNs to be discovered. Indeed, Table 1 shows 76 A_i≥3 CDN mutations per cancer type but 681 A₂ and 56,648 A₁ mutations in the lower recurrence groups. If n reaches 10^5∼6, most of the undiscovered CDNs in the A₁ and A₂ classes should be identified (see supplement File S2).

In Table 2, we estimate the proportion of the A₁ and A₂ mutations that are possible CDNs. The relationships of A₃/S₃ > A₂/S₂, A₂/S₂ > A₁/S₁, and A₁/S₁ > A₀/S₀ are almost always observed in Table 1 with 32 (3 × 8 + 2 × 4) out of 36 such relationships. The use of A/S ratios may still under-estimate the selective advantages of A_1∼3 mutations because S_1∼3 may have slight advantages as well (see supplement File S2). Assuming S₁ is truly neutral, we use S₀ to S₁ as the basis to calculate the excess of A_1∼3 in Table 2 where 35 of the 36 Obs(A_i) > Exp(A_i) relationships can be observed. The implication is that hundreds and, likely low thousands, of A₁’s and A₂’ should be CDNs whereas we have only confidently identified ∼76 strong CDNs, on average, for a cancer type. (Note that A₁ excesses are less reliable since a 1% error in the calculation would mean 566 CDNs.)

Table 2

2. CDNs and the amino acids affected

We now ask whether the amino acid changes associated with CDNs bear the signatures of positive selection. Amino acids that have divergent physico-chemical properties have been shown to be under strong selection, both positive and negative (Chen, He, et al. 2019; Chen, Lan, et al. 2019). We note that, in almost all cases in cancer evolution, when a codon is altered, only one nucleotide of the triplet codon is changed. Among the 190 amino acid (AA, 20×19/2) pairs, only 75 of the pairs differ by one bp (Tang et al. 2004). For example, Pro (CCN) and Ala (GCN) may differ by only one bp but Pro and Gly (GGN) must differ by at least 2 bp. These 75 AA changes, referred to as the elementary AA changes (Grantham 1974; Li et al. 1985; Yang et al. 2003; Meyer et al. 2021), account for almost all AA substitutions in somatic evolution.

In a series of studies (Tang et al. 2004; Chen, He, et al. 2019; Chen, Lan, et al. 2019), we have defined the physico-chemical distances between AAs of the 75 elementary pairs as ΔUi, where i = 1 to 75. ΔUi reflects 47 measures of AA differences including hydrophobicity, size, charge etc. and ranges between 0 and 1. The most similar pair, Ser and Thr, has ΔUi = 0 and the most dissimilar pair is Asp and Try with ΔUi = 1. These studies show that ΔUi is a strong determinant of the evolutionary rates of DNA sequences and that large-step changes (i.e., large ΔUi’s) are more acutely “recognized” by natural selection. These large-step changes are either highly deleterious or highly advantageous. Most strikingly, advantageous mutations are enriched with AA pairs of ΔUi > 0.8 (Chen, He, et al. 2019).

To analyze the properties of CDNs, we choose 6 cancer types from Table 1 that have the largest sample sizes (n > 500) but leap over kidney since kidney cancers have unusually low CDN counts. In Fig. 2, we divide the CDNs into groups according to the number of recurrences, i. CDNs of similar i’s are merged into the same group in the descending order of i, until there are at least 10 CDNs in the group. The 6 cancer types show two clear trends: 1) the proportion of CDNs with ΔUi > 0.8 (red color segments) increases in groups with higher recurrences; 2) in contrast, the proportion of CDNs with ΔUi < 0.4 (green segments) decreases as recurrences increase. These two trends would mean that highly recurrent CDNs tend to involve larger AA distances (ΔUi > 0.8) and similar AAs tend not to manifest strong fitness increases. In general, CDNs alter amino acids in ways that expose the changes to strong selection.

Figure 2:

3. CDNs in relation to the genes harboring them

We shall use the term “CDN genes” for genes having at least one CDN site. Since CDN genes contribute to tumorigenesis when harboring a CDN mutation, they should be considered cancer drivers as well. CDN genes have two desirable qualities for recognition as driver genes. First, CDNs are straightforward and unambiguous to define (e.g., i ≥ 3 for n < 1000). In the literature, there have been multiple definitions of cancer driver genes (Reimand and Bader 2013; Porta-Pardo and Godzik 2014; Mularoni et al. 2016; Arnedo-Pac et al. 2019), resulting in only modest overlaps among cancer gene lists (see Fig. S3). Second, the evolutionary fitness of CDN, and hence the tumorigenic potentials of CDN genes, can be computed (supplement File S1).

We now present the analyses of CDN genes, using the same 6 cancers of Fig. 2. Two types of CDN genes are shown in Table 3. Type I genes fulfill the conventional criterion of fast evolution with the whole-gene Ka/Ks (or dN/dS) significantly larger than 1 (Martincorena et al. 2017). Averaged across cancer types, Type I overlaps by 95.7% with the canonical CDG list, which is the union of three popular lists (Bailey et al. 2018; Sondka et al. 2018; Martínez-Jiménez et al. 2020). Type I genes are mostly well-known canonical CDGs (e.g., TP53, PIK3CA, and EGFR).

Table 3

Type II (CDN genes) is the new class of cancer driver genes. These genes have CDNs but do not meet the conventional criteria of whole-gene analysis. Obviously, if a gene has only one or two CDNs plus some sporadic hits, the whole-gene Ka/Ks would not be significantly greater than 1. As shown in Table 3, over 80% of CDN genes have only 1∼2 CDN sites. The salient result is that Type II genes outnumber Type I genes by a ratio of 5 : 1 (229 : 45, column 8, Table 3). Furthermore, Type II genes overlap with the canonical CDG list by only 23%.

Type II genes represent a new class of cancer drivers that concentrate their tumorigenic strength on a small number CDN sites. They have been missed by the conventional whole-gene definition of cancer drivers. One such example is the FGFR3 gene in lung cancer. This gene of 809 codons has only 8 hits, among which one is a CDN (i = 3) in lung cancer. It is noticed solely for this CDN. In the supplemental text, we briefly annotate these new cancer driver genes for comparisons with the canonical driver genes (supplement File S1). Possible functional tests in the future can be found in Discussion.

We now briefly discuss the driver genes listed in previous studies as shown at the lower part of Table 3 (Bailey et al. 2018; Sondka et al. 2018; Martínez-Jiménez et al. 2020). From the total number of CDGs listed, it is clear that the overlaps are limited. As analyzed before (Wu et al. 2016), conventional gene lists overlap mainly by a core set of high Ka/Ks genes. This core set has not changed much as various criteria such the replication timing, expression profiles, epigenetic features are introduced. These criteria are the reasons for the many CDGs recognized by only a small subset of CDG lists. CDN genes, in contrast, can be objectively defined as CDN mutations (i recurrences in n samples) themselves are unambiguous.

Variation in CDN number and tumorigenic contribution among genes

By and large, the distribution of CDNs among genes is very uneven. Fig. 3A shows 10 genes with at least 6 CDNs whereas 87 genes have only one CDN. Two genes stand out for the number of CDNs they harbor, TP53 and PIK3CA, which also happen to be the only genes mutated in >15% of all cancer patients surveyed (Kandoth et al. 2013). Clearly, the prevalence of mutations in a gene is a function of the number of strong CDNs it harbors.

Figure 3:

Although a small number of genes have unusually high number of CDNs, these genes may not drive the tumorigenesis in proportion to their CDN numbers in individual patients. Fig. 3B shows the number of CDN mutations on TP53 that occur in any single patient. Usually, only one CDN change is observed in a patient whereas 2 or 3 CDN mutations are expected. It thus appears that CDNs on the same genes are redundant in their tumorigenic effects such that the second hit may not yield additional advantages. This pattern of disproportionally lower contribution by CDN-rich genes is true in other genes such as EGFR and KRAS. Consequently, the large number of genes with only 1 or 2 CDN sites are disproportionately important in driving the tumorigenesis of individual patients.

4. CDNs in relation to the cancer types - The pan-cancer properties

In the current literature, cancer driver genes (however they are defined) generally meet the statistical criteria for driver genes in only one or a few cancer types. However, genes may in fact contribute to tumorigenesis but are insufficiently prevalent to meet the statistical requirements for CDGs. Many genes are indeed marginally qualified as drivers in some tissues and barely miss the statistical cutoff in others. To see if genes that drive tumorigenesis in multiple tissues are more common than currently understood, we need to raise the sensitivity of cancer driver detection. Thus, CDNs may provide the resolution.

To test the pan-cancer driving capacity of CDNs, we define i_max as the largest i values among the 12 cancer types for each CDN. The number of cancer types where the said mutation can be detected (i.e., i > 0) is designated NC12. Fig. 4 presents the relationship between the observed NC12 of each CDN against i_max of that CDN. Clearly, many CDNs are observed in multiple cancer types (NC12 > 3), even though they do not qualify as a driver gene in all but a single cancer type. It happens frequently when a mutation has i > 3 in one cancer type but has i < 3 in others. One extreme example is C394 and G395 in IDH1. In CNS, both sites show i ≫ 3, while in 6 other cancer types (lung, breast, large intestine, prostate, urinary tract, liver), their hits are i < 3 but > 0. Conditional on a specific site informed by a cancer type, a mutation in another cancer type should be very unlikely if the mutation is not tumorigenic in multiple tissues. Hence, the pattern in Fig. 4 is interpreted to be drivers in multiple cancer types, but with varying statistical strength.

Figure 4:

Examining Fig. 4 more carefully, we could see that CDNs with a larger i_max in one cancer type are more likely to be identified as CDNs in multiple cancer types (red dots, r = 0.97, p = 9.23×10⁻⁵, Pearson’s correlation test). Of 22 sites with i_max > 20, 15 are identified as CDNs (i ≥ 3) in multiple cancer types, with a median NC12 of 9. On the opposite end, 2 CDNs with i_max > 20 are observed in only one cancer type (EGFR: T2573 in lung and FGFR2: C755 in endometrium cancer). The bimodal pattern suggests that a few cancer driver mutations are tissue specific whereas most others appear to have pan-cancer driving potentials.

To conclude, when a driver is observed in more than one cancer type, it is often a cancer driver in many others, but insufficiently powerful to meet the statistical criteria for driver mutations. This pan-cancer property can be seen at the higher resolution of CDN, but is often missed at the whole-gene level. Cancers of the same tissue in different patients, often reported to have divergent mutation profiles (Nik-Zainal et al. 2012; Roberts and Gordenin 2014), should be a good test of this hypothesis.

5. CDNs in relation to individual patients and therapeutic strategies

In previous sections, the focus is on the population of cancer patients; for example, how many in the patient population have certain mutations. We now direct the attention to individual patients. It would be necessary to pinpoint the CDN mutations in each patient in order to delineate the specific evolutionary path and to devise the treatment strategy. We shall first address the cancer driving power of CDN vs. non-CDN mutations in the same gene.

1) Efficacy of targeted therapy against CDNs vs non-CDNs

In general, a patient would have many point mutations, only a few of which are strong CDNs. We may ask whether most mutations on the canonical genes, such as EGFR, are CDNs. Presumably, synonymous, and likely many nonsynonymous, mutations on canonical genes may not be CDNs. It would be logical to hypothesize that patients whose EGFR has a CDN mutation (Group1 patients) should benefit from the gene-targeted therapy more than patients with a non-CDN mutation on the same gene (Group2 patients). In the second group, EFGR may be a non-driver of tumorigenesis.

Published data (AACR Project GENIE Consortium 2017; Choudhury et al. 2023) are re-analyzed as shown in Fig. 5. The hypothesis that patients of Group2 would not benefit as much as those of Group1 is supported by the analysis. This pattern further strengthens the underlying assumption that non-CDN mutations, even on canonical genes, are not cancer drivers.

Figure 5.

2) Number of CDNs in each patient

We postulate that a full set of CDNs should be able to inform about the cause of each cancer as well as the design of gene-targeted therapy. In Table 4, the known CDNs based on TCGA are tallied. Note that only a few CDNs fall on the canonical driver genes whereas most CDNs fall on the non-conventional ones.

Table 4

In most cancer types, 10%∼30% of patients, shown in the n₀ row of Table 4, have no known CDNs (and >50% among breast cancer patients). Hence, the current practice is to rely on missense mutations, regardless of CDNs or non-CDNs, on the canonical genes. The CDN column vs. the gene column in Table 4 address this issue. For example, the CDN column suggests that 33% of lung cancer patients (the n₀ row) would not respond well to gene-targeted therapy whereas the gene column show only 5.3%. The difference is due to a higher, and likely inflated, detection rate of candidate drivers in the gene column. We suggest that patients who have a non-CDN mutation on a driver gene would not respond to the targeted therapy against that gene, as demonstrated in Fig. 5. In the above example, 27.7% (33%∼5.3%) of patients may be subjected to the targeted treatment but may not respond well.

3) Prevalence vs. potency of CDN-bearing genes in driving tumorigenesis

The last question is the relationship between mutation prevalence and tumorigenic strength (or potency) among CDN-bearing genes. For example, when a patient is diagnosed to have 5 CDNs in 5 genes, what may be their relative contributions to the tumorigenesis? Are they equally valid candidates for targeted therapy? It would seem logical that canonical CDGs with many CDNs should be the targets. However, because these genes would contribute at most one CDN to the tumorigenesis (Fig. 3B), targeting a high prevalence gene may not yield more benefits to the patients than targeting a low prevalence gene that has a CDN.

The implication is that prevalence and potency of CDNs may not be strongly correlated. Some genes may be prevalently mutated in the patient population but, in each affected patient, these genes may not be more potent than the less prevalent genes with a CDN mutation. Potency can be tested in vitro by gene editing or in vivo by targeting treatment. In this interpretation, targeting a CDN of low prevalence (say, i = 3) may be as effective in treatment as targeting a high prevalence CDN with i = 20. The model and Table 5 present this hypothesis based on cancer hallmarks.

Table 5

The hallmarks of cancer were first proposed by (Hanahan and Weinberg 2000) with several updates (Hanahan and Weinberg 2011; Hanahan 2022). Each hallmark is a cancer phenotype shown in Table 5 that lists the number of genes involved in each particular hallmark (see Methods). While each hallmark may be associated with a number of genes, many genes are also involved in multiple hallmarks. As even the highly prevalent genes would usually have at most one mutation in each patient, we assume that each gene is associated with one hallmark in each patient.

Suppose that tumorigenesis requires a mutation in most (but perhaps not all) of the hallmarks, then the number of mutation combinations would be the product of all numbers in the corresponding column. For breast cancer, it would be 8 × 12 × 4 …. × 11 × 2 ∼ 1.7 × 10¹¹. In other words, the possible mutation combinations that can drive breast cancer is over a billion. Hence, two breast cancers are unlikely to have the same set of CDGs or CDNs. In this view, the prevalence of a gene would be inversely proportional to the hallmark gene number. For example, genes of “invasion and metastasis” in breast cancer would have a prevalence of < 1/52. In contrast, the potency in tumorigenesis should depend on the hallmark phenotype itself, and independent of gene number for that hallmark. In this example, each gene of “invasion and metastasis” may be lowly prevalent, but could also be highly potent in each patient.

In short, the prevalence and potency of CDNs may be poorly correlated. The hypothesis can be functionally tested (by gene-editing in vitro or targeting treatment in vivo) in conjunction with the data on the attraction (i.e., co-occurrences) vs repulsion (lack of co-occurrences) of CDNs.

Discussion

The companion study presents the theory that computes the limit of recurrences (i/n, i times in n patients) of reachable by neutral mutations. Above the cutoff (e.g., 3/1000), a recurrent mutation is deemed an advantageous CDN. At present, the power of CDN analysis is hampered by the still small sample sizes, generally between 300 and 3000. We show that, when n reaches 10⁵, a mutation only has to recur 12 times to be shown as a CDN, i.e., 25 times more sensitive than 3/1000. In short, nearly all CDNs should be discovered with n ≥ 10⁵.

In this study, we apply the theory on existing data to characterize the discovered CDNs. Based on the TCGA data, this study concludes that each cancer patient carries only 1∼2 CDNs, whereas 6∼10 drivers are usually hypothesized to be present in each cancer genome (Hanahan and Weinberg 2011; Vogelstein et al. 2013; Campbell et al. 2020). This deficit signifies the current incomplete understanding of cancer driving potentials. Across patients of the same cancer type, about 50 to 150 CDNs have been discovered for each cancer type, representing perhaps only 10% of all possible CDNs. Given a complete set of CDNs, it should be possible to delineate the path of tumor evolution for each individual patient.

Direct functional test of CDNs would be to introduce putative cancer-driving mutations and observe the evolution of tumors. Such a task of introducing multiple mutations that are collectively needed to drive tumorigenesis has been done only recently, and only for the best-known cancer driving mutations (Ortmann et al. 2015; Takeda et al. 2015; Hodis et al. 2022). In most tumors, the correct combination of mutations needed is not known. Clearly, CDNs, with their strong tumorigenic strength, are suitable candidates.

Many CDNs in a patient may not fall on conventional CDGs, whereas these conventional CDGs may have passenger or weak mutations. Therefore, the efforts in gene-targeting therapy may well be shifted to the CDN-harboring genes. Given a complete set of CDNs, many more driver genes can be identified. Since many driver genes cannot be targeted for biological or technical reasons (Dang et al. 2017; Danesi et al. 2021; Waarts et al. 2022), a large set of CDGs will be desirable. The goal is that each cancer patient would have at least one targetable CDG driven by its CDN. In fact, it would be most beneficial if patients can have multiple targetable CDGs. In that case, the probability that resistant mutations eluding multiple targeting drugs should be diminished.

Another interesting insight revealed may be the distributions of CDNs across different cancer types. It suggests that CDNs previously identified to be cancer-specific may have pan-cancer effects. Such recurrences across cancer types are likely selection-driven but, in many cancer types, the strength is not sufficient to rise above the statistical threshold. While tumorigenesis in the same tissue type is a process of massively repeated evolution, cancer evolution in different tissues represents massive parallel evolution. The parallelism represents processes driven by the same selective forces (for cell proliferation) under different ecological conditions.

CDNs can also be used in cancer screening with the advantage of efficiency as the targeted mutations are fewer. Being efficient, the false negative rate should be lower too. Most interesting of all, the false positive rate should be far lower than the gene-based screen which often shows a false positive rate of >50% (supplement File S1).

Cancer evolution falls within the realm of ultra-microevolution (Wu et al. 2016). The repeated evolution addresses the single most severe criticism of evolutionary studies, namely all evolutionary events have a sample size of one. Individual advantageous mutations should repeat themselves as CDNs. Mutations that have been favored by positive selection in each individual patient are also the most fruitful targets in cancer therapy. The two studies thus unite evolutionary biology and cancer medicine.

Methods

Data preparation

Single-nucleotide variant (SNV) data for TCGA patients were downloaded from the GDC Data Portal (https://portal.gdc.cancer.gov/). Mutations exceeding a 1‰ frequency in the Genome Aggregation Database (gnomAD) were excluded to minimize potential false positives arising from germline variants. Patients with more than 3000 coding region point mutations were filtered out as potential hypermutator phenotypes. This filtering process yielded a final analysis set encompassing 7369 patients across 12 diverse cancer types for subsequent analysis. The calculation of A_i and S_i follows the same method as described in the companion paper.

For CDN analysis in non-cancerous tissues, mutation profiles for normal tissues were retrieved from SomaMutDB (Sun et al. 2022). Mutations from different samples originating from the same individual were consolidated. Donners above the age of 80 were excluded from our dataset. The mutation processing followed the same pipeline as previously described. In total, we have mutation profiles from 487 donners serving as a negative control.

The canonical lists of cancer driver genes were obtained from three distinct data sources. The CGC Tier 1 genes, encompassing genes with the highest confidence of driver status, were retrieved from the COSMIC Cancer Gene Census (https://cancer.sanger.ac.uk/census) (Sondka et al. 2018). The IntOGen driver gene list, which employs an integrated pipeline for gene discovery, was downloaded from https://www.intogen.org/download (Martínez-Jiménez et al. 2020). Bailey’s driver gene list comprises 299 cancer driver genes identified through a PanSoftware strategy, with further experimental validation confirming their role in driving cell lines (Bailey et al. 2018). The consistency of cancer types across all studies was manually verified using oncotree (https://oncotree.mskcc.org/#/home). For the analysis of driver gene overlap, only drivers from the same cancer type were compared.

The hallmark annotation of genes is downloaded from COSMIC (https://cancer.sanger.ac.uk/cosmic/download), encompassing 331 genes with annotated dysregulated biological processes. It is important to note that these hallmarks are manually annotated as part of an ongoing effort to characterize the role of genes in cancer based on literature evidence. The actual scale of hallmark genes may be substantially larger than the current version.

For gene-level selection analysis, we utilized the R package ‘dndscv’ to quantify selection signals for missense and nonsense mutations in a given gene (Martincorena et al. 2017). Specifically, the package calculates the Ka/Ks ratio, denoted as ‘w’ in the final results, for a given mutation impact (missense or nonsense). The significance of selection is presented as q values after Benjamini-Hochberg (BH) adjustment. Genes with w > 1 and q < 0.1 were identified as being significantly under positive selection.

We employ i* = 3 as a cutoff for identifying Cancer Driving Nucleotides (CDNs) across various cancer types. The specific value of i* is detailed in Eq. 10 of the companion paper (supplement File S2). Here, i* = 3 is chosen consistently across all cancer types, taking into account the abundance of sites under positive selection given i = 3 in Table 2. Throughout our analysis, emphasis is placed on CDNs of the missense category, where missense mutations with a recurrence ≥3 are identified as CDNs. For ΔUi analysis, the reference table for 75 single-step amino acid changes was obtained from (Chen, He, et al. 2019), and the ΔUi for each CDN is derived by mapping the amino acid change to the reference table.

Calculation of A_i_e

We employ Eq. 9 from the companion paper to calculate the expected value for A_i under neutrality. For a given site, the cumulative probability for recurrence x ≤ i − 1 could be expressed as:

where n is the population size of a given cancer type, and E(u) is the mutation rate per site per patient derived from singleton synonymous mutations:

Then by expectation, site number of recurrence i (A_x≥i) could be represented by:

Following the same logic, we’ll have A_x≥i+1 as:

Then the expected value for A_i_e is then:

L_A and L_S are missense and synonymous sites, respectively. The calculation procedure is described in methods of the companion paper (supplement File S2).

With Eqs. S1∼S3, we could solve for the expected number of sites with missense mutation recurrence i.

Survival analysis of EGFR-targeted therapy

The mutation and clinical profiles of 23,253 patients were retrieved from the GENIE project (Cerami et al. 2012; de Bruijn et al. 2023), with 7,216 patients harboring EGFR mutations. Survivor months were calculated as the time elapsed between the date of sequencing and the date of the last contact (or day of death). In cases where patients had multiple sequencing reports, the earliest one was selected. For CDN calling, we applied Eq. 10 from the companion paper (supplement File S2). With ε = 0.01, we set the CDN cutoff i* = 14. To mitigate potential biases from other common drivers in lung cancer, patients with indels in exon 19 and 20 of EGFR, G12/13 mutations in KRAS, V600 mutations in BRAF, exon 20 insertions in HER2, fusions in MET, ALK, ROS1, RET, NTRK, and MET were filtered out. The final survival analysis was conducted using GraphPad Prism 8.

Annotation for non-canonical CDN genes

We conducted functional annotation and enrichment analysis for newly identified non-canonical CDN genes using four independent databases (Gene Ontology, KEGG, Disease Ontology, and Reactome) with R packages (clusterProfiler, DOSE, ReactomePA). For each analysis, we set a p-value cutoff of 0.05 and a q-value cutoff of 0.2, with p value adjustment method set to “BH”. To explore the connections between non-canonical CDN genes and canonical cancer driver genes (CDGs), enrichment analyses were performed alongside cancer drivers from IntOGen. Specifically, for enrichment annotations related to cancer hallmarks, the corresponding genes were subjected to manual confirmation using CancerGeneNET (https://signor.uniroma2.it/CancerGeneNet/).

Acknowledgements

We wish to acknowledge the supports from the First Affiliated Hospital, the Seventh Affiliated Hospital of Sun Yat-sen University, Cancer Center of Clifford Hospital, Jinan University, Cancer Hospital Chinese Academy of Medical Sciences, Shenzhen Center, and Guangdong Academy of Medical Sciences, Guangdong Provincial People’s Hospital on the startup of the Cancer Driving Nucleotide (CDN) project. We would like to acknowledge Kunming Institute of Zoology for discussing the ideas of CDN. We thank Weiwei Zhai, Qianfei Wang, and Weini Huang for insightful comments and suggestions. We would also like to acknowledge the American Association for Cancer Research (AACR) and The Cancer Genome Atlas (TCGA) project, which have provided invaluable datasets and resources that have significantly enriched our understanding of cancer biology and improved patient outcomes. This work was supported by the National Natural Science Foundation of China (32293193/32293190 and 32150006 to C.I.W.), the National Key Research and Development Projects of the Ministry of Science and Technology of China (2021YFC2301300), National Key R&D Program of China (2021YFC0863400), and the Innovation Group Project of Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai; No. 311021006).

Declaration of interests

The authors declare no competing interests.