An error catastrophe in cancer?

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Abstract

A comparison between the evolution of cancer cell populations and RNA viruses reveals a number of remarkable similarities. Both display high levels of plasticity and adaptability as a consequence of high degrees of genetic variation. It has been suggested that, as it occurs with RNA viruses, there is a threshold in the levels of genetic instability affordable by cancer cells in order to be able to overcome selection barriers (Trends Genet. 15 (1999) M57). Here we explore this concept by means of a simple mathematical model. It is shown that an error threshold exists in this model, which investigates both competition between cancer cell populations and its impact on overall tumor growth dynamics. Once the threshold is reached, the highly unstable tumor cell populations, which were sustaining malignant growth, become unable to maintain their genetic information, which in turn triggers a slowed down overall tumor growth regime.

Introduction

A hallmark of cancer cells is their underlying genetic instability. Often, this term is used to describe a state, i.e., the occurrence of either small genetic alterations such as nucleotide deletions or insertions or larger ones such as alterations in the chromosomal number per se, termed aneuploidy. Nonetheless, as Lengauer et al. (1998) already pointed out, genetic instability should denote a rate more than a state, hence the occurrence of a particular mutation in the genome of the cell over time. Such hypermutability has been liked to chemical carcinogens (Bardelli et al., 2001) as well as non-DNA damaging stress (Li et al., 2001). Different aspects of hypermutation and its impact on cancer development have been analysed from mathematical models (Wodarz and Krakauer, 2001; Frank et al., 2003; Gatenby and Frieden, 2002; Plotkin and Nowak, 2002).

Given the common conception of tumorigenesis as a multistep process (Fearon and Vogelstein, 1990), with continually accumulating mutations, and based on the calculation that the normal, somatic mutation rate accounts for only 1.4×10−10mutations/basepair/cellgeneration, Loeb (1991) postulated the existence of a so-called mutator phenotype. As the cited background mutation rate cannot account for the marked heterogeneity seen in most solid cancers, he further argues that “cancer cells must exhibit or have exhibited a mutator phenotype” (Loeb, 1994). Loeb concludes that this mutator hypothesis as well as Novell's generally accepted concept of clonal evolution as the driving force for tumor progression are not exclusive (Novell, 1976). Others, however, have argued that selection without an increased mutation rate is both necessary and sufficient to explain tumorigenesis (Tomlinson et al., 1996) and to account for the mutations seen in tumors, especially if the process of aging were to increase the selective conditions for clonal expansion (Chow and Rubin, 2000).

As discussed by Cahill et al., genetic instability in cancer allows to overcome selection barriers, a process which fosters further tumor progression (Cahill et al., 1999; see also Jackson and Loeb, 1998). Normal cells display low levels of instability and tumor progression will benefit from genetic instability by generating cellular diversity. Such heterogeneous populations will include genetic alterations to overcome the barriers and tumor progression will continue (see for example Wodarz and Krakauer, 2001). Although this situation is known to play a key role in the initial stages of tumorigenesis, genetic instability will be observable at late stages: it is carried along with the clonally selected alterations.

A relevant point is the fact that too high levels of instability might be harmful because of accumulated damage. In other words, a limit to instability must exist (Cahill et al., 1999). Such a threshold is actually very similar to the so-called error catastrophe (or error threshold) displayed by RNA viruses (Domingo and Holland, 1994; Domingo et al., 1995; Nowak and May, 2000). These viruses are known to mutate at very high rates. As predicted by Eigen and Schuster's theory of quasispecies, a critical mutation rate exists beyond the genomic information is lost i.e. no Darwinian selection operates (Eigen, 1971; Schuster, 1994). This actually corresponds to an example of a phase transition in a complex biosystem and as such it allows to develop powerful theoretical approximations (Solé et al., 1996; Solé and Goodwin, 2001).

RNA viruses are known to replicate close to their error threshold. Several theoretical approaches to this problem have been developed in order to understand the presence and implications of this threshold (Swetina and Schuster, 1982; Eigen 1987, Eigen 1988; Pastor-Satorras and Solé, 2001; Kamp and Bornholdt, 2002; Kamp et al., 2003). The evolutionary success of RNA viruses is due to their enormous plasticity and adaptability to changing environments. The high mutation rate generates a highly heterogeneous population, so-called molecular quasispecies. The quasispecies structure provides an extraordinary reservoir of variants with potentially useful phenotypes in the face of environmental change.

How strong are the similarities between unstable tumors and RNA populations? Several features are clearly shared by both, at least qualitatively. One is the presence of high levels of heterogeneity, both at the genotype and phenotype levels. Different replication and infection mechanisms in RNA viruses are matched by wide levels of variability in cancer cells, affecting cell communication, growth and apoptosis. Accordingly, escape from the immune system (and other selection barriers) operates in both systems. Viruses use antigenic diversity whereas tumors evade the immune system by loosing their antigens through mutation, or making use of antigenic modulation and/or tumor-induced immune suppression (Rosenberg, 2001).

Increased mutagenesis beyond the error catastrophe can destroy the virus, since beyond the threshold no Darwinian selection is at work (Schuster, 1994). The exceptionally high mutation rates in RNA viruses is illustrated by the finding that most HIV virions in blood appear to be non-viable (Coffin, 1995). Similarly, genetic instability in cancer cells will have detrimental effects on cell's fitness, since most random mutations are likely to be harmful (see Gatenby and Frieden, 2002). Effective experimental strategies have shown that the error threshold can actually be exploited in antiviral therapy (Holland et al., 1999; Loeb et al., 1999; Cottry et al., 2001). Within the context of HIV treatment, using promutagenic nucleoside analogs, viral replication of HIV has been shown to be abolished in vitro (Loeb et al., 1999). As indicated by Cahill et al., the best chance of cure advanced cancers might be a result of tumor genetic instability (Cahill et al., 1999; Loeb et al., 2003): cancer cells are more sensitive to stress-inducing agents. Cancer, it is argued, would provide a good target for direct attack by drugs promoting genetic instability selectively in tumor cells.

To elucidate the possible implications of the error threshold in cancer from a theoretical standpoint, we present a simple mathematical model, which investigates the interplay between cell proliferation and mutation rate within a simple tumor growth model. The results support the notion of the existence of an error-threshold in tumor systems, which corresponds to a “critical” value of genetic instability, which, once exceeded, will trigger a concomitant sharp decrease in the tumor's proliferation rate. This concept of a trade-off between two of the tumor's key features therefore combines for the first time the still controversial “mutator phenotype” hypothesis with the generally accepted, clonal selection-driven optimization process. Important implications of this work for both experimental studies and future clinical work are discussed.

Section snippets

The error threshold in quasispecies

In this section we shortly review the simplest model of quasispecies dynamics, the so-called Swetina–Schuster model (1982). The starting point is the general Eigen–Schuster quasispecies model, defined by the following set of equations:dxidt=j=1nxjfjQji−Φ(x)xi,where xi indicates the fraction of the population associated to the i-th mutant genome (here i=1,…,n, where n is very large) so that j=1nxj=1. Here fj is the growth rate of the j-th mutant, Qij is the probability of having a mutation ij

The error threshold in cancer

In neoplastic cells, genetic alterations can arise from a disparate source of mechanisms, e.g. from inaccurate DNA replication to failure of DNA repair systems. And indeed, the latter has been recently discussed in the context of a biological equivalent to the mutator phenotype as Fishel (2001) linked the selection for mismatch repair defect in hereditary non-polyposis colon cancer to resistance to DNA damage-induced apoptosis. Previous models of cancer growth and evolution have considered

Discussion

In recent years, it has become increasingly clear that many diseases cannot be treated without taking into account their multifactorial character. This recognition led to the coining of a new term, complex disease to label this family of illnesses where many different factors or genes are involved. Cancer belongs to this family of complex diseases, thus needs to be investigated as such and targeted accordingly. Based on PCR analysis of samples from colorectal premalignant polyp and carcinoma

Acknowledgements

We thank Isabel González-Garcia (who suggested interesting links between RNA viruses and cancer) and to Josep Costa for useful discussions. This work has been supported by grants MCYT BFM 2001-2154 and by the Santa Fe Institute (RVS) and by the Harvard-MIT (HST) Athinoula A. Martinos Center for Biomedical Imaging, the Department of Radiology and the Molecular Neuro-Oncology Laboratory at Massachusetts General Hospital (TSD).

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