Quantification of the Selective Advantage of Driver Mutations Is Dependent on the Underlying Model and Stage of Tumor Evolution

Detecting and quantifying selection in cancer is one of the key goals of cancer genomics, as positively selected driver gene mutations present viable targets for development of novel cancer therapies (1). Measuring the selective growth advantage provided by driver mutations could lead to a precise quantitative understanding of cancer evolution, allow for prognostication of cancer progression in patients, and facilitate precision oncology.

Early works (2) reported small average selective advantage of driver mutations in pancreatic cancer and glioblastoma, on the order of 1%, with similar estimates obtained more recently for driver mutations in seemingly normal esophagus and skin (3). On the other hand, some newer works report much larger selective advantages of driver mutations, on the order of 20% to 80% in multiple cancer types (4) and recently as high as 1,200% in pancreatic cancer and even higher in thyroid and liver hepatocellular carcinoma (5). Are the early estimates wrong? Are the new estimates too high? We demonstrate here that selective advantage of cancer drivers depends on the underlying model and stage of tumor evolution, and that comparison of numerical values of selective advantage across studies should be taken with care and regard to these issues. We will focus here mostly on the example of the KRAS oncogene in colorectal cancer, and show that its selective advantage can vary by two orders of magnitude, depending on the stage of colorectal tumor evolution in which the driver mutation is acquired. We will also demonstrate that different definitions of selective advantage across various studies can lead to an equally large variation in the reported selective advantage of driver mutations.

Initial stages of tumor evolution in many tissues are thought to occur in a stem cell compartment, such as within stem cells at the base of an intestinal crypt (Fig. 1A, top). The evolutionary dynamics of driver mutations in intestinal crypts were studied by Vermeulen and colleagues (6), who used experimental visualization of stem cell clones together with mathematical modeling to quantify the competitive advantage of common colorectal cancer driver mutations. They presented a model of stem cell dynamics in a crypt, which can be thought of as a ring of N stem cells replacing their neighbors in a random fashion (6). In this model, a wild-type stem cell has 50% chance of replacing a neighboring wild-type stem cell (6). On the other hand, a stem cell with a mutation in Kras has been shown to have a 78% chance of replacing an adjacent wild-type stem cell (and 22% chance of being replaced by a wild-type stem cell; ref. 6). In this setting, selective advantage of Kras can be defined as the relative increase in the chance of being chosen to replace a neighboring wild-type stem cell (rather than vice versa) conferred by the driver. Thus, selective advantage that Kras provides to a colorectal stem cell is equal to s = 0.78/0.22–1 = 255%.

Oncogenic mutations lead not only to expansion of mutant stem cells within a single crypt, but also to increased levels of crypt fission (Fig. 1A, bottom; ref. 7). Wild-type crypt fission (division) rate in healthy human colonic tissue is measured to be 0.007/year (7), balanced by the rate of crypt fusion (8). Division rate of KRAS-mutant crypts is increased to 0.07 per year (7), ten times higher than for wild-type crypts. Various models define selective advantage of cancer drivers as the relative decrease in death rate (2), relative increase in division rate (5) of relative increase in the net growth rate (division - death; ref. 4). Defining selective advantage of KRAS as the relative increase in net growth rate of KRAS-mutant crypts over wild-type crypts would lead to an infinite selective advantage, as the net growth rate of wild-type crypts is practically 0 in adult tissue. Defining selective advantage as the relative increase in crypt division (fission) rate would lead to selective advantage of KRAS of 900%.

Furthermore, KRAS often occurs as a second driver mutation on the way to colorectal cancer, following APC inactivation. It has been recently estimated (9) that KRAS typically increases the division (fission) rate of colorectal crypts that have previously inactivated APC by 35%. Lahouel and colleagues recently reported an even smaller estimate for relative increase in division rate provided by KRAS as the second driver in colorectal cancer (5), of up to 15%. The examples above indicate that when KRAS is activated in previously normal colorectal stem cells, it provides selective advantage to the stem cells and colorectal crypts that is on the order of 100% to 1,000%. However, when it appears as the second driver in colorectal cancer, the typical selective advantage it provides is on the order of 10%.

We focused on the example of the KRAS mutation acquired during various stages of colorectal tumor evolution. Even though KRAS is typically thought to be the second driver mutation acquired on the way to colorectal cancer, it has been shown to also provide selective growth advantage at the earliest stages of colorectal tumor evolution (6, 7), as discussed in the previous sections. This may seem in contrast with experimental findings that individual KRAS-mutated lesions are unlikely to progress to colorectal cancer (10). Indeed, although the relative increase in the fission rate of KRAS-mutated crypts is large, their absolute fission rate remains fairly small (0.07 per year, corresponding to a doubling time of ∼10 years; ref. 7). Thus, an individual KRAS- mutated lesion is expected to remain microscopic, and unlikely to obtain subsequent driver mutations necessary for malignant transformation within a human lifetime. However, recent work (9) helps quantify the expected number of KRAS-mutated lesions in the entire human colon and demonstrates that, due to the high estimated number of such lesions, KRAS may be the first driver mutation in up to a third of colorectal cancer patients whose cancers harbor the mutation.

When discussing selective advantage of cancer drivers, it is important to note that many mathematical models of cancer evolution disregard tissue hierarchy (2, 4) and include populations of cells that can divide and die with some rates (Fig. 1B; refs. 2, 4). Such models are more suitable for later stages of cancer progression, when cancer cells are poorly differentiated or dedifferentiated, or for early stages of tumor evolution in tissues that are maintained by a single type of progenitor cells (such as skin; ref. 11) or well-mixed stem cells (e.g., hematopoietic; ref. 12).

Healthy tissues are at homeostasis and have balanced overall division and death rates (b = d), leading to a net growth rate of 0. For simplicity, we can assume that b = d = 1 (per some unit time). An oncogenic mutation can decrease cell death rate by s = 1% (d₁ = d * (1 − s) = 1 – s), leading to a clonal expansion with net growth rate equal to b − d₁ = s. This small decrease in the death rate (2) of 1% thus leads to a relative increase in the net growth rate (4) over homeostatic tissue that is infinite (as healthy tissue net growth rate is 0). A second mutation with the same decrease in death rate of s = 1% will lead to a clonal expansion with net growth rate 2s, which represents 100% relative increase in net growth rate over a single mutation. A third mutation with the same decrease in the death rate of 1% would correspond to the relative increase in the growth rate of 50% and so on. The seeming discrepancy between small selective advantage (on the order of 1%) reported previously for driver mutations in pancreatic cancer and glioblastoma (2) versus the much larger advantages (20%–80%) reported subsequently for late drivers in multiple cancer types (4) can be understood to stem from the difference in the models they were inferred with. The former model defined selective advantage as the relative decrease in the death rate of cells due to driver mutations, while the latter defined selective advantage as the relative increase in the net growth rate. Both studies (2, 4) assumed a well-mixed population of cells without tissue hierarchy.

The above examples demonstrate that the same driver mutation can have vastly different numerical values of selective advantage at different stages of tumor evolution and when using different underlying models, and that selective advantage of 1% defined in one way (e.g., as the relative decrease in the death rate) can correspond to virtually any value of selective advantage if it is defined as the relative increase in the net growth rate. Similarly, some model settings do not allow selective advantages greater than 100%. This occurs, for example, when selective advantage is defined as the relative decrease in the death rate of cells provided by a driver mutation (2); or when selective advantage is defined as an increase in proliferative bias of stem cells towards symmetric renewal (3). In contrast, in other settings selective advantage is theoretically unbounded, such as when drivers increase division rate (5) or net growth rate (4).

It is important to note that the confusion in reporting and comparing the magnitude of selective advantage across studies often arises when increases in fitness (or a similar quantity) are expressed in relative rather than absolute terms. Furthermore, knowledge of selective advantage expressed as a single number is insufficient for the full quantitative understanding of the population dynamics, which requires knowledge of parameters governing the growth of both populations, wild-type and mutant. The easiest way to avoid confusion is to report absolute growth rates (or fitness) of both wild-type and mutant populations.

In addition to the stage of tumor evolution and the specific model employed, selective advantage of a driver mutation will also depend on the tissue in question (5). Some drivers are frequently mutated in cancers of a single or a small number of tissues, while being infrequently mutated in most other cancer types, which may suggest that such mutations provide significant selective advantage only in specific tissues. An example of such a driver is the tumor suppressor APC, which is mutated in more than 80% of colorectal cancers, but is infrequently mutated in most other cancer types. APC has been shown to provide a very large selective advantage to previously normal colorectal crypts: the fission rate of crypts that have inactivated APC is roughly three times larger than the fission rate of crypts with activated KRAS (7, 9), and it is likely that APC and KRAS are the two drivers that provide the largest advantage to previously normal colorectal crypts. The large selective advantage provided to colorectal crypts by APC inactivation seems to be behind both its frequency in colorectal cancer and the observation that it tends to be the first driver mutation in the majority of colorectal cancers (9).

On the other hand, some driver genes are mutated in many cancer types. KRAS and TP53 are examples of such drivers. For example, Lahouel and colleagues have recently estimated that KRAS increases the division rate of pancreatic stem cells by 1,200%, where it is typically the first driver mutation on the way to pancreatic cancer. This selective advantage is of a similar order of magnitude as when KRAS is the first driver in colorectal cancer.

TP53 tumor suppressor gene is the most commonly mutated gene in human cancer. Does that imply that it confers a large selective advantage? The answer again depends on the stage of tumor evolution. While TP53 does not seem to provide selective advantage as the first driver in colorectal cancer in normal conditions (6), it is crucial for transformation from benign to a malignant tumor, thus providing important advantage as a later driver. TP53 is also typically a late driver in chronic lymphocytic leukemia (CLL), where it has been shown to provide a large growth advantage as a late, subclonal driver (13).

Metastasis, the dissemination and subsequent growth of tumor cells in other tissues, is also expected to play a crucial role in shaping selection, as disseminated cells must survive and proliferate in new environments. Recent work demonstrates that different metastatic sites in colorectal cancer (lymph node versus distant) are subject to different levels of selection, with stronger selection associated with formation of distant metastases (14). Hu and colleagues report relaxed selective pressures in metastases relative to early cancer development in colorectal and breast cancer, but not in lung cancer (15).

Selective fitness advantage of a driver mutation also depends on possible competition or interaction between the populations of cells with and without the driver. Although quantitative data on competition between different clonal populations are scarce in human tumor settings, there is recent evidence that intestinal crypts carrying oncogenic mutations outcompete neighboring normal stem cells by secreting factors that promote their dedifferentiation (16).

Tumor suppressor TP53 is also a prime example of a driver gene that provides different selective advantage under different microenvironmental conditions. Vermeulen and colleagues showed that while mutated P53 does not provide advantage to previously wild-type colorectal stem cells under normal conditions, it does provide significant selective advantage when the microenvironment shows signs of inflammation, such as in colitis (6). These findings are similar to those of Klein and colleagues who only find advantage for P53 mutation in irradiated skin, and not under normal conditions (11). Virus infections such as HPV and mutational processes such as APOBEC mutagenesis have also been shown to affect selective advantage of driver mutations (17).

Aging is another process that can lead to significant changes in the tissue and tumor microenvironment, and that can have an effect on selective advantage of driver mutations. For example, there is experimental evidence that the same oncogenic mutations that are not selected in young organisms can become selected in older animals (18). Immune cells represent an important part of the tumor microenvironment, potentially leading to negative selection of certain tumor clones (immunoediting) and exerting selective pressure on tumors to evolve immune-escape mechanisms (19).

Finally, therapy typically radically alters the fitness landscape of cancer. This is particularly evident in the case of targeted therapies, which often succeed in eradicating many if not most tumor subpopulations, but ultimately fail due to survival and proliferation of treatment-resistant cells, which often carry well-defined resistance mutations (20, 21).

Quantifying parameters of cancer evolution in individual patients, including selective growth advantages of individual and combinatorial driver lesions, holds great promise for prognosticating individual tumor trajectories, which could facilitate personalized treatment selection and precision oncology. However, care must be taken that, when dealing with estimates of selective growth advantages of driver mutations, the underlying model is clearly stated, as well as the stage of tumor evolution that it applies to, which includes any genetic background upon which the driver mutation may appear. Otherwise, comparison of values of selective advantage across studies without careful consideration of these issues can lead to unnecessary confusion and unjustified conclusions.

I. Bozic reports grants from National Science Foundation during the conduct of the study, Johnson & Johnson outside the submitted work, as well as a patent for use of clonal evolution analysis for ibrutinib resistance in chronic lymphocytic leukemia patients pending.

The author thanks Bert Vogelstein for careful reading and comments on the manuscript. This work is supported by the National Science Foundation grant DMS-2045166.