Punctuated mutagenesis promotes multi-step evolutionary adaptation in human cancers

Reviewer #1 (Public review):

Summary:

Grasper et al. present a combined analysis of the role of temporal mutagenesis in cancer, which includes both theoretical investigation and empirical analysis of point mutations in TCGA cancer patient cohorts. They find that temporally elevated mutation rates contribute to cancer fitness by allowing fast adaptation when the fitness drops (due to previous deleterious mutations). This may be relevant in the case of tumor suppressor genes (TSG), which follow the 2-hit hypothesis (i.e., biallelic 2 mutations are necessary to deactivate TS), and in cases where temporal mutagenesis occurs (e.g., high APOBEC, ROS). They provide evidence that this scenario is likely to occur in patients with some cancer types. This is an interesting and potentially important result that merits the attention of the target audience. Nonetheless, I have some questions (detailed below) regarding the design of the study, the tools and parametrization of the theoretical analysis, and the empirical analysis, which I think, if addressed, would make the paper more solid and the conclusion more substantiated.

Strengths:

Combined theoretical investigation with empirical analysis of cancer patients.

Weaknesses:

Parametrization and systematic investigation of theoretical tools and their relevance to tumor evolution.

Reviewer #2 (Public review):

This work presents theoretical results concerning the effect of punctuated mutation on multistep adaptation and empirical evidence for that effect in cancer. The empirical results seem to agree with the theoretical predictions. However, it is not clear how strong the effect should be on theoretical grounds, and there are other plausible explanations for the empirical observations.

For various reasons, the effect of punctuated mutation may be weaker than suggested by the theoretical and empirical analyses:

(1) The effect of punctuated mutation is much stronger when the first mutation of a two-step adaptation is deleterious (Figure 2). For double inactivation of a TSG, the first mutation--inactivation of one copy--would be expected to be neutral or slightly advantageous. The simulations depicted in Figure 4, which are supposed to demonstrate the expected effect for TSGs, assume that the first mutation is quite deleterious. This assumption seems inappropriate for TSGs, and perhaps the other synergistic pairs considered, and exaggerates the expected effects.

(2) More generally, parameter values affect the magnitude of the effect. The authors note, for example, that the relative effect decreases with mutation rate. They suggest that the absolute effect, which increases, is more important, but the relative effect seems more relevant and is what is assessed empirically.

(3) Routes to inactivation of both copies of a TSG that are not accelerated by punctuation will dilute any effects of punctuation. An example is a single somatic mutation followed by loss of heterozygosity. Such mechanisms are not included in the theoretical analysis nor assessed empirically. If, for example, 90% of double inactivations were the result of such mechanisms with a constant mutation rate, a factor of two effect of punctuated mutagenesis would increase the overall rate by only 10%. Consideration of the rate of apparent inactivation of just one TSG copy and of deletion of both copies would shed some light on the importance of this consideration.

Several factors besides the effects of punctuated mutation might explain or contribute to the empirical observations:

(1) High APOBEC3 activity can select for inactivation of TSGs (references in Butler and Banday 2023, PMID 36978147). This selective force is another plausible explanation for the empirical observations.

(2) Without punctuation, the rate of multistep adaptation is expected to rise more than linearly with mutation rate. Thus, if APOBEC signatures are correlated with a high mutation rate due to the action of APOBEC, this alone could explain the correlation with TSG inactivation.

(3) The nature of mutations caused by APOBEC might explain the results. Notably, one of the two APOBEC mutation signatures, SBS13, is particularly likely to produce nonsense mutations. The authors count both nonsense and missense mutations, but nonsense mutations are more likely to inactivate the gene, and hence to be selected.

Author response:

eLife Assessment

This valuable study presents a theoretical model of how punctuated mutations influence multistep adaptation, supported by empirical evidence from some TCGA cancer cohorts. This solid model is noteworthy for cancer researchers as it points to the case for possible punctuated evolution rather than gradual genomic change. However, the parametrization and systematic evaluation of the theoretical framework in the context of tumor evolution remain incomplete, and alternative explanations for the empirical observations are still plausible.

We thank the editor and the reviewers for their thorough engagement with our work. The reviewers’ comments have drawn our attention to several important points that we have addressed in the updated version. We believe that these modifications have substantially improved our paper.

There were two major themes in the reviewers’ suggestions for improvement. The first was that we should demonstrate more concretely how the results in the theoretical/stylized modelling parts of our paper quantitatively relate to dynamics in cancer.

To this end, we have now included a comprehensive quantification of the effect sizes of our results across large and biologically-relevant parameter ranges. Specifically, following reviewer 1’s suggestion to give more prominence to the branching process, we have added two figures (Fig S3-S4) quantifying the likelihood of multi-step adaptation in a branching process for a large range of mutation rates and birth-death ratios. Formulating our results in terms of birth-death ratios also allowed us to provide better intuition regarding how our results manifest in models with constant population size vs models of growing populations. In particular, the added figure (Fig S3) highlights that the effect size of temporal clustering on the probability of successful 2-step adaptation is very sensitive to the probability that the lineage of the first mutant would go extinct if it did not acquire a second mutation. As a result, the phenomenon we describe is biologically likely to be most effective in those phases during tumor evolution in which tumor growth is constrained. This important pattern had not been described sufficiently clearly in the initial version of our manuscript, and we thank both reviewers for their suggestions to make these improvements.

The second major theme in the reviewers’ suggestions was focused on how we relate our theoretical findings to readouts in genomic data, with both reviewers pointing to potential alternative explanations for the empirical patterns we describe.

We have now extended our empirical analyses following some of the reviewers’ suggestions. Specifically, we have included analyses investigating how the contribution of reactive oxygen species (ROS)-related mutation signatures correlates with our proxies for multi-step adaptation; and we have included robustness checks in which we use Spearman instead of Pearson correlations. Moreover, we have included more discussion on potential confounds and the assumptions going into our empirical analyses as well as the challenges in empirically identifying the phenomena we describe.

Below, we respond in detail to the individual comments made by each reviewer.

Public Reviews:

Reviewer #1 (Public review):

Summary:

Grasper et al. present a combined analysis of the role of temporal mutagenesis in cancer, which includes both theoretical investigation and empirical analysis of point mutations in TCGA cancer patient cohorts. They find that temporally elevated mutation rates contribute to cancer fitness by allowing fast adaptation when the fitness drops (due to previous deleterious mutations). This may be relevant in the case of tumor suppressor genes (TSG), which follow the 2-hit hypothesis (i.e., biallelic 2 mutations are necessary to deactivate TS), and in cases where temporal mutagenesis occurs (e.g., high APOBEC, ROS). They provide evidence that this scenario is likely to occur in patients with some cancer types. This is an interesting and potentially important result that merits the attention of the target audience. Nonetheless, I have some questions (detailed below) regarding the design of the study, the tools and parametrization of the theoretical analysis, and the empirical analysis, which I think, if addressed, would make the paper more solid and the conclusion more substantiated.

Strengths:

Combined theoretical investigation with empirical analysis of cancer patients.

Weaknesses:

Parametrization and systematic investigation of theoretical tools and their relevance to tumor evolution.

We sincerely thank Reviewer 1 for their comments. As communicated in more detail in the point-by-point replies to the “Recommendations for the authors”, we have revised the paper to address these comments in various ways. To summarize, Reviewer 1 asked for (1) more comprehensive analyses of the parameter space, especially in ranges of small fitness effects and low mutation rates; (2) additional clarifications on details of mechanisms described in the manuscript; and (3) suggested further robustness checks to our empirical analyses. We have addressed these points as follows: we have added detailed analyses of dynamics and effect sizes for branching processes (see Sections SI2 and SI3 in the Supplementary Information, as well as Figures S3 and S4). As suggested, these additions provide characterizations of effect sizes in biologically relevant parameter ranges (low mutation rates and smaller fitness effect sizes), and extend our descriptions to processes with dynamically changing population sizes. Moreover, we have added further clarifications at suggested points in the manuscript, e.g. to elaborate on the non-monotonicities in Fig 3. Lastly, we have undertaken robustness checks using Spearman rather than Pearson correlation coefficients to quantify relations between TSG deactivation and APOBEC signature contribution, and have performed analyses investigating dynamics of reactive oxygen species-associated mutagenesis instead of APOBEC.

Reviewer #2 (Public review):

This work presents theoretical results concerning the effect of punctuated mutation on multistep adaptation and empirical evidence for that effect in cancer. The empirical results seem to agree with the theoretical predictions. However, it is not clear how strong the effect should be on theoretical grounds, and there are other plausible explanations for the empirical observations.

Thank you very much for these comments. We have now substantially expanded our investigations of the parameter space as outlined in the response to the “eLife Assessment” above and in the detailed comments below (A(1)-A(3)) to convey more quantitative intuition for the magnitude of the effects we describe for different phases of tumor evolution. We agree that there could be potential additional confounders to our empirical investigations besides the challenges regarding quantification that we already described in our initial version of the manuscript. We have thus included further discussion of these in our manuscript (see replies to B(1)-B(3)), and we have expanded our empirical analyses as outlined in the response to the “eLife Assessment”.

For various reasons, the effect of punctuated mutation may be weaker than suggested by the theoretical and empirical analyses:

(A1) The effect of punctuated mutation is much stronger when the first mutation of a two-step adaptation is deleterious (Figure 2). For double inactivation of a TSG, the first mutation--inactivation of one copy--would be expected to be neutral or slightly advantageous. The simulations depicted in Figure 4, which are supposed to demonstrate the expected effect for TSGs, assume that the first mutation is quite deleterious. This assumption seems inappropriate for TSGs, and perhaps the other synergistic pairs considered, and exaggerates the expected effects.

Thank you for highlighting this discrepancy between Figure 2 and Figure 4. For computational efficiency and for illustration purposes, we had opted for high mutation rates and large fitness effects in Figure 2; however, our results are valid even in the setting of lower mutation rates and fitness effects. To improve the connection to Figure 4, and to address other related comments regarding parameter dependencies, we have now added more detailed quantification of the effects we describe (Figures SF3 and SF4) to the revised manuscript. These additions show that the effects illustrated in Figure 2 retain large effect sizes when going to much lower mutation rates and much smaller fitness effects. Indeed, while under high mutation rates we only see the large relative effects if the first mutation is highly deleterious, these large effects become more universal when going to low mutation rates.

In general, it is correct that the selective disadvantage (or advantage) conveyed by the first mutation affects the likelihood of successful 2-step adaptations. It is also correct that the magnitude of the ‘relative effect’ of temporal clustering on valley-crossing is highest if the lineage with only the first of the two mutations is vanishingly unlikely to produce a second mutant before going extinct. If the first mutation is strongly deleterious, the lineage of such a first mutant is likely to quickly go extinct – and therefore also more likely to do so before producing a second mutant.

However, this likelihood of producing the second mutant is also low if the mutation rate is low. As our added figure (Figure SF3) illustrates, at low mutation rates appropriate for cancer cells, is insensitive to the magnitude of the fitness disadvantage for large parts of the parameter space. Especially in populations of constant size (approximated by a birth/death ratio of 1), the relative effects for first mutations that reduce the birth rate by 0.5 or by 0.05 are indistinguishable (Figure SF3f).

Moreover, the absolute effect (f_k - f₁), as we discuss in the paper (Figures SF2 and SF3) is largest in regions of the parameter space in which the first mutant is not infinitesimally unlikely to produce a second mutant (and f_k and f₁ would be infinitesimally small), but rather in parameter regions in which this first mutant has a non-negligible chance to produce a second mutant. The absolute effect (f_k - f₁) therefore peaks around fitness-neutral first mutations. While the next comment (below) says that our empirical investigations more closely resemble comparisons of relative effects and not absolute effects, we would expect that the observations in our data come preferentially from multi-step adaptations with large absolute effect since the absolute effect is maximal when both f_k and f₁ are relatively high.

In summary, we believe Figure 2, while having exaggerated parameters for very defendable reasons, is not a misleading illustration of the general phenomenon or of its applicability in biological settings, as effect sizes remain large when moving to biologically realistic parameter ranges. To clarify this issue, we have largely rewritten the relevant paragraphs in the results section and have added two additional figures (Figures SF3 and SF4) as well as a section in the SI with detailed discussion (SI2).

(A2) More generally, parameter values affect the magnitude of the effect. The authors note, for example, that the relative effect decreases with mutation rate. They suggest that the absolute effect, which increases, is more important, but the relative effect seems more relevant and is what is assessed empirically.

Thank you for this comment. As noted in the replies to the above comments, we have now included extensive investigations of how sensitive effect sizes are to different parameter choices. We also apologize for insufficiently clearly communicating how the quantities in Figure 4 relate to the findings of our theoretical models.

The challenge in relating our results to single-timepoint sequencing data is that we only observe the mutations that a tumor has acquired, but we do not directly observe the mutation rate histories that brought about these mutations. As an alternative readout, we therefore consider (through rough proxies: TSGs and APOBEC signatures) the amount of 2-step adaptations per acquired/retained mutation. While we unfortunately cannot control for the average mutation rate in a sample, we motivate using this “TSG-deactivation score” by the hypothesis that for any given mutation rate, we expect a positive relationship between the amount of temporal clustering and the amount of 2-step adaptations per acquired/retained mutation. This hypothesis follows directly from our theoretical model where it formally translates to the statement that for a fixed μ, f_k is increasing in k.

However, while both quantities f_k/f₁ or f_k - f₁ from our theoretical model relate to this hypothesis – both are increasing in k –, neither of them maps directly onto the formulation of our empirical hypothesis.

We have now rewritten the relevant passages of the manuscript to more clearly convey our motivation for constructing our TSG deactivation score in this form (P. 4-6).

(A3) Routes to inactivation of both copies of a TSG that are not accelerated by punctuation will dilute any effects of punctuation. An example is a single somatic mutation followed by loss of heterozygosity. Such mechanisms are not included in the theoretical analysis nor assessed empirically. If, for example, 90% of double inactivations were the result of such mechanisms with a constant mutation rate, a factor of two effect of punctuated mutagenesis would increase the overall rate by only 10%. Consideration of the rate of apparent inactivation of just one TSG copy and of deletion of both copies would shed some light on the importance of this consideration.

This is a very good point, thank you. In our empirical analyses, the main motivation was to investigate whether we would observe patterns that are qualitatively consistent with our theoretical predictions, i.e. whether we would find positive associations between valley-crossing and temporal clustering. Our aim in the empirical analyses was not to provide a quantitative estimate of how strongly temporally clustered mutation processes affect mutation accumulation in human cancers. We hence restricted attention to only one mutation process which is well characterized to be temporally clustered (APOBEC mutagenesis) and to only one category of (epi)genomic changes (SNPs, in which APOBEC signatures are well characterized). Of course, such an analysis ignores that other mutation processes (e.g. LOH, copy number changes, methylation in promoter regions, etc.) may interact with the mechanisms that we consider in deactivating Tumor suppressor genes.

We have now updated the text to include further discussion of this limitation and further elaboration to convey that our empirical analyses are not intended as a complete quantification of the effect of temporal clustering on mutagenesis in-vivo (P. 10,11).

Several factors besides the effects of punctuated mutation might explain or contribute to the empirical observations:

(B1) High APOBEC3 activity can select for inactivation of TSGs (references in Butler and Banday 2023, PMID 36978147). This selective force is another plausible explanation for the empirical observations.

Thank you for making this point. We agree that increased APOBEC3 activity, or any other similar perturbation, can change the fitness effect that any further changes/perturbations to the cell would bring about. Our empirical analyses therefore rely on the assumption that there are no major confounding structural differences in selection pressures between tumors with different levels of APOBEC signature contributions. We have expanded our discussion section to elaborate on this potential limitation (P. 10-11).

While the hypothesis that APOBEC3 activity selects for inactivation of TSGSs has been suggested, there remain other explanations. Either way, the ways in which selective pressures have been suggested to change would not interfere relevantly with the effects we describe. The paper cited in the comment argues that “high APOBEC3 activity may generate a selective pressure favoring” TSG mutations as “APOBEC creates a high [mutation] burden, so cells with impaired DNA damage response (DDR) due to tumor suppressor mutations are more likely to avert apoptosis and continue proliferating”. To motivate this reasoning, in the same passage, the authors cite a high prevalence of TP53 mutations across several cancer types with “high burden of APOBEC3-induced mutations”, but also note that “this trend could arise from higher APOBEC3 expression in p53-mutated tumors since p53 may suppress APOBEC3B transcription via p21 and DREAM proteins”.

Translated to our theoretical framework, this reasoning builds on the idea that APOBEC3 activity increases the selective advantage of mutants with inactivation of both copies of a TSG. In contrast, the mechanism we describe acts by altering the chances of mutants with only one TSG allele inactivated to inactivate the second allele before going extinct. If homozygous inactivation of TSGs generally conveys relatively strong fitness advantages, lineages with homozygous inactivation would already be unlikely to go extinct. Further increasing the fitness advantage of such lineages would thus manifest mostly in a quicker spread of these lineages, rather than in changes in the chance that these lineages survive. In turn, such a change would have limited effect on the “rate” at which such 2-step adaptations occur, but would mostly affect the speed at which they fixate. It would be interesting to investigate these effects empirically by quantifying the speed of proliferation and chance of going extinct for lineages that newly acquired inactivating mutations in TSGs.

Beyond this explicit mention of selection pressures, the cited paper also discusses high occurrences of mutations in TSGs in relation to APOBEC. These enrichments, however, are not uniquely explained by an APOBEC-driven change in selection pressures. Indeed, our analyses would also predict such enrichments.

(B2) Without punctuation, the rate of multistep adaptation is expected to rise more than linearly with mutation rate. Thus, if APOBEC signatures are correlated with a high mutation rate due to the action of APOBEC, this alone could explain the correlation with TSG inactivation.

Thank you for making this point. Indeed, an identifying assumption that we make is that average mutation rates are balanced between samples with a higher vs lower APOBEC signature contribution. We cannot cleanly test this assumption, as we only observe aggregate mutation counts but not mutation rates. However, the fact that we observe an enrichment for APOBEC-associated mutations among the set of TSG-inactivating mutations (see Figure 4F) would be consistent with APOBEC-mutations driving the correlations in Fig 4D, rather than just average mutation rates. We have now added a paragraph to our manuscript to discuss these points (P. 10-11).

(B3) The nature of mutations caused by APOBEC might explain the results. Notably, one of the two APOBEC mutation signatures, SBS13, is particularly likely to produce nonsense mutations. The authors count both nonsense and missense mutations, but nonsense mutations are more likely to inactivate the gene, and hence to be selected.

Thank you for making this point. We have included it in our discussion of potential confounders/limitations in the revised manuscript (P. 10-11).