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Mutation load, functional overlap, and synthetic lethality in the evolution and treatment of cancer
ARTICLE IN PRESS
Journal of Theoretical Biology 223 (2003) 205–213
Mutation load, functional overlap, and synthetic lethality in the evolution and treatment of cancer Alexander Kamb* Deltagen Proteomics, Inc., 615 Arapeen Drive, Suite 300, Salt Lake City, UT 84108, USA Received 16 September 2002; received in revised form 4 February 2003; accepted 13 February 2003
Abstract The efficacy of conventional anti-cancer drugs is puzzling in view of the ubiquitous tissue distribution and vital nature of their targets. Differences in cell cycling rates are not thought sufficient to explain chemotherapeutic selectivity. I suggest an alternative possibility based on the combinatorial effects of mutations in cancer cells. This model incorporates the concepts of synthetic–lethal interactions and mutation loads to explain the drug sensitivity of cancer cells. From this perspective, drugs that target complex processes that utilize genetically redundant or overlapping components, such as DNA replication and chromosome segregation, offer attractive target opportunities. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Chemotherapy; Combinatorial; Genetic interaction; Model
1. Introduction The rationale behind cancer chemotherapy is that certain drugs are more toxic to malignant cells than normal cells. The mechanistic basis for chemotherapeutic selectivity, to the degree it exists, is far from clear in most cases. Some selectivity doubtless derives from differences in cell cycling rates. Indeed, one of the principal causes of side effects is sensitivity of rapidly dividing stem cells such as those that form intestinal epithelia (Hruban et al., 1989). But high mitotic index of malignant cells, a measure of rapid cell division, is often a negative prognostic indicator for cancer (Sinicrope et al., 1999). The targets of the most widely used anti-cancer drugs, such as microtubules, DNA and enzymes involved in nucleic acid metabolism, are common to all cells, including normal tissue. For this reason, chemotherapeutic agents have narrow therapeutic windows. Nonetheless, they can cause tumor regression and eradication (Balis, 1997). Cancer cells contain multiple types of genetic and epigenetic aberrations (Gupta et al., 1997; Jones and *Tel.: +1-801-303-0300; fax: +1-801-303-0333. E-mail address: [email protected] (A. Kamb).
Laird, 1999). In many cases, they display marked decreases in chromosome stability and replication fidelity (Loeb, 1991; Perucho et al., 1994; Tlsty et al., 1993). As a result, numerous tumorigenic alterations exist in malignant cells, including base substitutions and frameshifts, loss-of heterozygosity, homozygous deletion, and methylation. The best known are mutations in P53 and K-ras. These changes contribute directly to tumor growth (Donehower, 1996; Fisher et al., 2001; Johnson et al., 2001). In addition to adaptive changes, presumptive selectively neutral alterations occur in cancer cells, including microsatellite repeat variants (Perucho et al., 1994). Because of the increased mutation rate and cell division number that accompany tumorigenesis, it is likely that cancer cells accumulate mutations and epigenetic changes that affect the functions of nonessential genes. By inference from experiments in mice, flies, yeast and E. coli, normal human cells probably possess considerable overlap of genetic functions (Winzeler et al., 1999; Adams et al., 2000; Driever et al., 1996; Ross-Macdonald et al., 1999; www.shigen.nig.ac.jp/ecoli/PEC). Genetic lethal screens and assays of targeted disruptions of single genes yield the surprising result that less than a quarter of genes are essential. In principle, non-essential
0022-5193/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0022-5193(03)00087-0
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genes collectively present a large mutation target in neoplasia. Mutations in non-essential genes can render organisms inviable when combined with one another (Guarente, 1993; Tong et al., 2001). This phenomenon, known as synthetic lethality, has been documented in a variety of genetic settings, especially in yeast. The underlying basis for synthetic phenotypes has been explored in many instances. Typically, the synthetic–lethal gene pairs participate in the same cellular or biochemical process (Guarente, 1993). Therapeutic strategies based on synthetic lethality are especially appealing in cancer (Hartwell et al., 1997). A drug may achieve selectivity for malignant cells through the genetic interactions between its target and mutant genes resident in the tumor. These interactions may produce a synthetic–lethal phenocopy in cancer cells, leaving normal cells unharmed. Here I explore the conceptual significance of synthetic lethality in the context of cancer. I propose a model based on synthetic–lethal interactions that may explain the efficacy of conventional cancer therapies, and possibly point the way to new drug targets.
2. Methods 2.1. Calculation of combinations (as graphed in Fig. 1B) Points are calculated according to WT ðmÞ ¼
m X
w i ¼ 2m m 1
where wi ¼
i¼2
m i
2.2. Calculation of probability of death (L(m)) (as graphed in Fig. 2) Points on graph calculated according to
! :
Fig. 1. Model for mutant gene and chemotherapeutic interactions. (A) Sets of combinations within a total of four mutant genes (1–4) and a fifth mutation or specific drug-mediated inhibition. Pair-wise combinations, triples and a quadruple interaction with the added mutation/ drug are shown. (B) Roughly exponential increase in total combinations of mutations as a function of mutation number compared to increase of pair-wise combinations only (w2 ), triples (w3 ), or quadruples (w4 ).
(C) Pairs plus triples and quadruples, weighted at 1/20 pairs: Lðm 1Þ ¼ ð1 ðð1 p2 Þw2 ðmÞ
(A) All combinations: m Y Lðm 1Þ ¼ ð1 ð ð1 p2 ÞW ðiÞW ði1Þ ÞÞ i¼2
¼ ð1 ð1 P2 ÞW ðmÞ Þ; where W ðmÞ ¼ 2m 1; or, (B) Pairs only: Lðm 1Þ ¼ ð1 ð1 p2 Þw2 ðmÞ Þ where w2 ðiÞ ¼ or,
!
i ; 2
ð1 p3 Þw3 ðmÞ ð1 p4 Þw4 ðmÞ ÞÞ; where e.g. w3 ðmÞ ¼
m 3
! ;
or, (D) Pairs in two classes: Lðm 1Þ ¼ ð1 ðð1 p2 Þw2 ð0:9 mÞ Þðð1 pj2 Þw2 ð0:1 mÞ Þ: For Fig. 2D, the m mutations are apportioned into two categories (p2 ¼ 0:0001 and pj2 ¼ 0:1) in the ratio 1:9, by multiplying m by 0.9 and 0.1, and rounding to the nearest integer to compute w2 ðiÞ: Note that w2 ð1Þ ¼ w3 ð1Þ ¼ w3 ð2Þ ¼ w4 ð1Þ ¼ w4 ð2Þ ¼ w4 ð3Þ ¼ 0:
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2.3. Calculation of survival probability (P(m)) (as graphed in Fig. 3) We use the relation: (A)
PT ðmÞ ¼ ð1 p1 Þm
m Y
ð1 p2 ÞW ðiÞW ði1Þ
i¼2
¼ ð1 p1 Þm ð1 p2 ÞW ðmÞ ; or; (B)
PT ðmÞ ¼ ð1 p1 Þm
m Y
ð1 p2 Þw2 ðiÞ
i¼2
¼ ð1 p1 Þ ð1 p2 Þw2 ðmÞ ; m
where p1 is the probability that a mutation affects an essential gene (=0.2). 2.4. Calculation of equilibrium mutation distributions (as graphed in Figs. 4 and 5) We use matrix algebra to compute the equilibrium distribution of mutations in a population of tumor cells, so that: xðtÞ ¼ xð0ÞðSÞt ; where xðtÞ is a vector that contains the genotype (mutation) frequencies after t generations; S is a matrix
Fig. 2. Graph of probability of an additional lethal mutational/ epigenetic event (or lethal therapeutic event) as a function of mutation number in tumors ðLðmÞÞ: LðmÞ is computed as in Methods, using m þ 1: For A–C, different curves correspond to different values of p2 shown in the box: (A) with higher order gene groups weighted equivalently, (B) with gene pairs only, (C) with gene pairs, triples and quadruples, but with p3 ¼ p4 ¼ ð0:05Þp2 : (D) Under a model in which 10% of the genes have (p2 ¼ 0:1) and the remaining non-essential genes have p2 ¼ 0:0001; only pair-wise interactions are considered; one additional mutation or drug interaction (m þ 1) involves the (p2 ¼ 0:1) class (dashed line); (m þ 2) is the same except two further interactions/mutations occur. The steps in the curve are a result of the rounding procedure used (see Methods).
Fig. 3. Probability (PT ðmÞ) of having survived m random mutational/ epigenetic events in essential and non-essential genes. Different curves correspond to different values of p2 shown in the box: (A) under the all-combinations model, as in Fig. 2A; (B) under a pairs-only model, as in Fig. 2B.
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Fig. 4. Graph of population fraction at mmax : mmax is the value of m corresponding to the maximum population fraction at generation t ¼ 2; 000: Values are calculated for three different mutation rates (U) under an all-combinations model (A–C) or a pairs+triples and quadruples model, where triples and quadruples are weighted at ð0:05Þx of pairs (D–F). A and D, U ¼ 0:01: B and E, U ¼ 0:1: C and F, U ¼ 1:0: Different curves correspond to different values of p2 shown in the box.
that carries out the mutation operation, with elements corresponding to Poisson probabilities of mean=U=average number of dominant, hemi- or homozygous alterations/cell/generation, and accomplishes selection according to fitnesses of the various genotypes. pð0jUÞ 0 S ¼ 0 0
pð1jUÞ pð0jUÞ
pð2jUÞPðDW0;2 Þ pð1jUÞPðDW1;2 Þ
0
pð0jUÞ
0
0
pðNjUÞPðDW0;N Þ pðN 1jUÞPðDW1;N Þ ; pð1jUÞPðDW2;N Þ pð0jUÞ
where, e.g. w2 ðiÞ is the number of pair-wise combinations of i mutations; w3 ðiÞ is the number of triple combinations, etc. Calculations were performed for p2 ¼ 0:1; 0:01; 0:001; 0:0001: In case (2), values of p3 ¼ p4 ¼ ð0:05Þp2 were used.
3. Results 3.1. Model
where pðjjUÞ ¼ eU U j =j! is the Poisson probability with mean=U of j mutations in non-essential genes/cell/division, and (1) PðDWi;j Þ ¼ ð1 p2 ÞðW ðjÞW ðiÞÞ ; or; (2) PðDWi;j Þ ¼ ðð1 p2 Þðw2 ðjÞw2 ðiÞÞ ð1 p3 Þðw3 ðjÞw3 ðiÞÞ ð1 p4 Þðw4 ðjÞw4 ðiÞÞ Þ:
Suppose that a tumor cell has endured mutational events or epigenetic alterations in m non-essential genes. We treat these as either dominant, homo- or hemizygous, so their effects are not masked by diploidy. Each mutation compromises gene function, but the combination is non-lethal. We seek to establish a framework to analyse the probability of synthetic–lethal interactions with a targetselective inhibitory drug. In a formal sense, the drug acts as a gene-disabling mutation. Thus, we look at possible
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Fig. 5. Graph of genotype (xðtÞ) distribution at t ¼ 2; 000: Calculations of xðtÞ and panels A–F are as in Fig. 4. Different curves correspond to different values of p2 shown in the box.
synthetic–lethal interactions that may ensue between the m mutations and an additional disruptive genetic or chemical event. In the standard synthetic–lethal case, there are m possible new pair-wise lethal interactions between the existing mutant genes and the additional one. The total probability of a synthetic–lethal event is the per gene probability, p2 ; multiplied by m: However, we need not restrict the potential synthetic interactions to pairs of loci, but may also consider higher order interactions. These involve triple and quadruple mutant sets, and possibly even larger groups. Therefore, for triple gene interactions, we take all double mutant combinations within the group of m genes combined with the additional gene or drug interaction. For quadruple mutants, we take all combinations of triples within the m genes, and so on (Fig. 1A). This leads to an approximately exponential increase in the number of possible genetic interactions (Fig. 1B). The probability of higher order interactions could be the same as p2 : Alternatively, it could be higher than p2 ;
or lower. It is difficult to know p2 ; and more difficult to guess the appropriate probabilities for higher order interactions. As a starting point, we may assume a constant probability of synthetic–lethal interaction that applies to all mutation groups, irrespective of size. In what follows, I take this as one extreme and ignore possible models where p2 op3 ; p4 ; etc., because these may be unrealistic (see Discussion). At the other extreme, I consider models that include only pair-wise interactions. I also consider models in which higher order interactions are less important (i.e. p2 > p3 ; p4 ; etc.). 3.2. Relation between mutation number and synthetic– lethal occurrence For the case where all groups of interactions have the same synthetic–lethal probability, we can compute the chance (LðmÞ) that a cell that carries m mutations will survive another (m þ 1) change. We assume that all interactions are independent and have the same individual probability (p2 ) of producing a synthetic–lethal
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interaction. The combinatorial genetic interactions create a threshold, above which the probability of survival is extremely low (Figs. 1B, 2A). Within a broad range of p2 values, the mutation number (m) at which survival becomes very improbable is approximately 5–15. We can compare the survival probability calculated from all combinations to that computed using only pairwise gene combinations (Fig. 2B). The difference is dramatic, and more mutations are tolerated in a model that considers only pair-wise genetic interactions, especially for small p2 : This result follows from the much more rapid increase in total combinations (WT ) compared to combinations of only two mutant loci (Fig. 1B). Thus, inclusion of higher order interactions, though not an essential feature of the model, creates a more precipitous decline in survival probability as a function of mutation number. We can also look at slightly more complicated, but possibly more realistic, models. One of these involves synthetic–lethal probabilities that are lower for triples and quadruples than for pair-wise interactions (Fig. 2C). The rationale for such a model is that probabilities of combining two mutations within a single pathway may be considerably higher than for three, etc. (see Discussion). Based on the ratio between the fraction of essential genes (0.2) and the fraction of synthetic–lethal pairs estimated from Tong et al (B0.01), we use p3 ¼ p4 ¼ ð0:05Þp2 (Tong et al., 2001). This model makes predictions that are fairly similar to the pairs-only model (Fig. 2B). Another model type postulates two groups of nonessential genes: a group that has a high probability of synthetic–lethal interaction (e.g. p2 ¼ 0:1), amounting in this case to 10% of the non-essential gene fraction; and a second group that has a low probability of interaction (e.g. p2 ¼ 0:0001). This sort of model attempts to describe a scenario where a subset of genes involved in complex processes such as cytokinesis or protein secretion displays a high degree of synthetic–lethal interaction, whereas the rest of the non-essential genes are much more insulated from one another. The model reduces in essence to the pairs-only model, but is included to underscore its conceptual difference. In the case where one additional (m þ 1) mutation or druginduced inhibition involves the (p2 ¼ 0:1) subset, and only pair-wise interactions are included, the probability of lethal interaction is a blend between the curves for p2 ¼ 0:1 and 0:0001 (Fig. 2D, dashed line). Interestingly, if we look at the case where two additional mutations or drug interactions (m þ 2) occur in the (p2 ¼ 0:1) subset, we see a very dramatic difference (Fig. 2D, solid line). Virtually no cells survive beyond mB5: This situation may occur when an inhibitory drug cross-reacts with one or more molecules; that is, the drug inhibits the function of at least
two targets involved in similar complex processes in the cell. 3.3. Equilibrium number of non-essential gene mutations We can compute the probability PðmÞ that a particular cell will sustain m mutations in either nonessential or essential genes by multiplying the individual probabilities at each step of the process from one to m (Fig. 3). The probability of traversing the steps from zero to 10–15 is very low over a range of p2 values. This result holds for both of the extreme models (all combinations weighted equally as in Fig. 2A, or pairsonly as in Fig. 2B). The reason is that mutations in essential genes ultimately limit survival. Nevertheless, the subpopulation that survives accumulates mutations in non-essential genes. Because of the constant input of mutations, the total number of mutations builds up in asexual organisms. The high mutation rates will push the mutation load in tumors to the point where it makes a significant negative impact on fitness. At this equilibrium, the mutation rate balances the rate of elimination. We can determine the equilibrium distribution of nonessential-gene mutations, assuming a certain mutation rate U (number of dominant, hemi- or homozygous deleterious mutations in non-essential genes/cell/division) and a particular value of p2 : We approximate U as constant, though the homozygous component increases with increasing mutation number due to the quadratic dependence on mutant allele frequency (i.e. with higher m; there is a higher probability of mutation of both alleles because homozygous mutation frequencies are the square of the single-mutant allele frequency). Considering only two of the models (all combinations or pairs+triples and quadruples weighted at 1/20 of pairs), we use matrix algebra to calculate the equilibrium genotypes (see Methods). Convergence requires a substantial number of generations, but mmax becomes populated between t ¼ 100 and 1200 in all cases (Fig. 4). The equilibrium value of m corresponding to the highest population fraction (mmax ) is affected by U and by p2 (Fig. 5). mmax is higher when U is higher, and when p2 is lower. mmax at equilibrium varies considerably, from 7– 16 for the all-combinations model and 14–147 for the pairs-only model, depending on the values of U and p2 (Table 1).
4. Discussion There are numerous examples of synthetic lethality in model organisms. In yeast, for instance, various screens and selections have uncovered over 1400 synthetic–lethal gene pairs (http://mips.gsf.de/proj/ yeast/tables/interaction/genetic interact.html). Recently,
ARTICLE IN PRESS A. Kamb / Journal of Theoretical Biology 223 (2003) 205–213 Table 1 Value of m for the maximum population fraction (mmax ) at t ¼ 2000: U is the average number of new alterations/cell/generation. (1) is calculated according to a model that weighs all combinations equally; (2) according to a model that includes pairs, triples and quadruples, and weighs the triple and quadruple combinations at 1/20 of the pair synthetic-lethal probability (p2 ) U
p2
ð1Þmmax
ð2Þmmax
0.01 0.01 0.01 0.1 0.1 0.1 1.0 1.0 1.0
0.01 0.001 0.0001 0.01 0.001 0.0001 0.01 0.001 0.0001
7 10 13 9 12 15 10 13 16
14 18 19 28 54 96 36 73 147
a genome-wide synthetic–lethal scan using 8 distinct mutant genes yielded a total of 300 lethal double-mutant combinations, for an average of about 30 lethal partners per gene (Tong et al., 2001). The set of eight genes was chosen partly to increase the odds of recovery, and likely represents a biased group. Nonetheless, it is probable that synthetic lethality is not a rare event. It is difficult to know the probability for the average gene, but clearly some genes have large numbers of partners. Notably, in the yeast genomic analysis, 37,376 (8 4672) double mutant combinations were examined and 99.2% of these grew normally (Tong et al., 2001). Thus, we observe high levels of functional redundancy through single-gene disruptions; but in a sense, even more dramatic redundancy when we explore double mutants of non-essential genes. The percentage of inviable double-mutant combinations is lower than the percentage of lethal single-gene mutations. Several plausible models for mutation/drug interaction can be imagined. Here I have explored four types of model: (1) a model based on the equivalence of all viable mutation groups, where the probability of synthetic– lethal interactions within groups of double mutants, triple mutants, etc. is the same; (2) a model in which only interaction pairs count (i.e. p3 ¼ p4 ; etc. =0); (3) a model where the combinations are differentially weighted so that p3 ¼ p4 =(0.05)p2 ; and (4) a model that considers pair-wise interactions of two kinds: those between a 90% fraction of non-essential genes that interact rarely (p2 ¼ 0:0001), and those between the remaining non-essential genes that interact strongly (p2 ¼ 0:1). This last model is the most complex, a variant of the second model, but possibly the most realistic. For a given gene, the probability (p2 ) of synthetic–lethal interaction depends on two major factors: the number of genes that participate in the same cellular pathway or process (Guarente, 1993), and the probability that a
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given mutant gene pair within this pathway is synthetic lethal. For this last model, I have assumed that 10% of non-essential genes (of the total 80%) are in a class that has a high probability of interaction (0.1). This assumption conforms with Tong et al. (i.e. (0.1)(0.1)=0.01) (Tong et al., 2001). The assumptions explored here vary widely. For instance, for p2 I have included values from 0.1 to 0.00001; and p3 values that range from 0 to p2 : Though these assumptions have not been tested, the technology exists to provide some estimates for the probabilities of synthetic–lethal interaction among, for example, triple mutants (Tong et al., 2001). Tumors are rife with genetic change, and may well contain disruptive mutations in non-essential genes. In support of this view, experiments that compare fitness levels of two yeast strains, one wild type and one deficient in DNA repair, show that mutations accumulate under mild selection conditions that compromise growth and viability only under stress (Szafraniec et al., 2001). Under normal growth conditions, the wild-type and mutant strains display similar properties. Interestingly, the yeast strains used were diploid. Thus, heterozygous mutations may be sufficient to generate declines in fitness, manifested only when cells must endure difficult circumstances such as growth at high temperature. Temperature increases may destroy the function of particular allelic forms of proteins, thereby boosting the number of effective synthetic–lethal interactions. Presumably, hemi- and homozygous mutations would produce more severe effects on fitness. Thus, stress actualizes the cryptic mutation load in cells grown under mild conditions. If one or more of the models discussed here approximates the situation in tumors, we may expect that tumors accumulate dominant, homo- or hemizygous alterations until they near a threshold for m, at which point they are under considerable pressure to eliminate new ones that arise. These ideas suggest that malignancies may carry a significant mutation load, and therefore, may produce inviable daughter cells at high frequency. Such behavior provides one possible explanation for high apoptotic rates in tumors. Tumors may partly suppress the impact of mutations by inhibiting apoptotic programs. But despite these steps, tumor cells may remain poised on the brink of catastrophe (Symonds et al., 1994; Yu et al., 2002). The mutation load in tumors also allows rationalization of chemotherapeutic efficacy. Complex processes, especially those involved in DNA replication and the cytoskeleton, may engender higher levels of synthetic– lethal interaction (Tong et al., 2001). Therefore, drugs that interfere with these cellular processes may be more likely to produce lethal effects in tumors than in normal cells, in spite of the tumor’s tendency to forestall apoptosis (Symonds et al., 1994; Yu et al., 2002). The
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probability is that a given malignant cell, regardless of how different it is from other cells in the mass or from other tumors, will contain enough mutations that affect, for example, chromosome segregation, to ensure a synthetic–lethal interaction with the drug. Drugs that target other complex, vital processes, including proteosome inhibitors, may act at least partially through this mechanism (Garber, 2002). Many chemotherapeutic drugs display only limited molecular specificity. For instance, the microtubule inhibitors such as colchicine and vinblastine bind several tubulin paralogs (Jordan et al., 1998). Even topoisomerase inhibitors such as doxorubicin and etoposide fail to distinguish between the two homologous forms (Patel et al., 2000). Such cross-reaction may be an important feature of their efficacy. Indeed, novel anti-cancer therapeutic strategies that exploit targets with many potential synthetic–lethal partners may prove fruitful.
Acknowledgements I thank Dr. Joshua Cherry for helpful discussions and Chunwei Wang for computing assistance.
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Fisher, G.H., Wellen, S.L., Klimstra, D., Lenczowski, J.M., Tichelaar, J.W., Lizak, M.J., Whitsett, J.A., Koretsky, A., Varmus, H.E., 2001. Induction and apoptotic regression of lung adenocarcinomas by regulation of a K-Ras transgene in the presence and absence of tumor suppressor genes. Genes Dev. 15, 3249–3262. Garber, K., 2002. Cancer research. Taking garbage in, tossing cancer out? Science 295, 612–613. Guarente, L., 1993. Synthetic enhancement in gene interaction: a genetic tool come of age. Trends Genet. 9, 362–366. Gupta, P.K., Sahota, A., Boyadjiev, S.A., Bye, S., Shao, C., O’Neill, J.P., Hunter, T.C., Albertini, R.J., Stambrook, P.J., Tischfield, J.A., 1997. High frequency in vivo loss of heterozygosity is primarily a consequence of mitotic recombination. Cancer Res. 57, 1188–1193. Hartwell, L.H., Szankasi, P., Roberts, C.J., Murray, A.W., Friend, S.H., 1997. Integrating genetic approaches into the discovery of anticancer drugs. Science 278, 1064–1068. Hruban, R.H., Yardley, J.H., Donehower, R.C., Boitnott, J.K., 1989. Taxol toxicity. Epithelial necrosis in the gastrointestinal tract associated with polymerized microtubule accumulation and mitotic arrest. Cancer 63, 1944–1950. Johnson, L., Mercer, K., Greenbaum, D., Bronson, R.T., Crowley, D., Tuveson, D.A., Jacks, T., 2001. Somatic activation of the K-ras oncogene causes early onset lung cancer in mice. Nature 410, 1111–1116. Jones, P.A., Laird, P.W., 1999. Cancer epigenetics comes of age. Nat. Genet. 21, 163–167. Jordan, A., Hadfield, J.A., Lawrence, N.J., McGown, A.T., 1998. Tubulin as a target for anticancer drugs: agents which interact with the mitotic spindle. Med. Res. Rev. 18, 259–296. Loeb, L.A., 1991. Mutator phenotype may be required for multistage carcinogenesis. Cancer Res. 51, 3075–3079. Patel, S., Keller, B.A., Fisher, L.M., 2000. Mutations at arg486 and glu571 in human topoisomerase IIalpha confer resistance to amsacrine: relevance for antitumor drug resistance in human cells. Mol. Pharmacol. 57, 784–791. Perucho, M., Peinado, M.A., Ionov, Y., Casares, S., Malkhosyan, S., Stanbridge, E., 1994. Defects in replication fidelity of simple repeated sequences reveal a new mutator mechanism for oncogenesis. Cold Spring Harb. Symp. Quant. Biol. 59, 339–348. Ross-Macdonald, P., Coelho, P.S., Roemer, T., Agarwal, S., Kumar, A., Jansen, R., Cheung, K.H., Sheehan, A., Symoniatis, D., Umansky, L., Heidtman, M., Nelson, F.K., Iwasaki, H., Hager, K., Gerstein, M., Miller, P., Roeder, G.S., Snyder, M., 1999. Large-scale analysis of the yeast genome by transposon tagging and gene disruption. Nature 402, 413–418. Sinicrope, F.A., Hart, J., Hsu, H.A., Lemoine, M., Michelassi, F., Stephens, L.C., 1999. Apoptotic and mitotic indices predict survival rates in lymph node- negative colon carcinomas. Clin Cancer Res 5, 1793–1804. Symonds, H., Krall, L., Remington, L., Saenz-Robles, M., Lowe, S., Jacks, T., Van Dyke, T., 1994. P53-dependent apoptosis suppresses tumor growth and progression in vivo. Cell 78, 703–711. Szafraniec, K., Borts, R.H., Korona, R., 2001. Environmental stress and mutational load in diploid strains of the yeast Saccharomyces cerevisiae. Proc. Natl Acad. Sci. USA 98, 1107–1112. Tlsty, T.D., Jonczyk, P., White, A., Sage, M., Hall, I., Schaefer, D., Briot, A., Livanos, E., Roelofs, H., Poulose, B., et al., 1993. Loss of chromosomal integrity in neoplasia. Cold Spring Harb. Symp. Quant. Biol. 58, 645–654. Tong, A.H., Evangelista, M., Parsons, A.B., Xu, H., Bader, G.D., Page, N., Robinson, M., Raghibizadeh, S., Hogue, C.W., Bussey, H.,
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Journal of Theoretical Biology 223 (2003) 205–213
Mutation load, functional overlap, and synthetic lethality in the evolution and treatment of cancer Alexander Kamb* Deltagen Proteomics, Inc., 615 Arapeen Drive, Suite 300, Salt Lake City, UT 84108, USA Received 16 September 2002; received in revised form 4 February 2003; accepted 13 February 2003
Abstract The efficacy of conventional anti-cancer drugs is puzzling in view of the ubiquitous tissue distribution and vital nature of their targets. Differences in cell cycling rates are not thought sufficient to explain chemotherapeutic selectivity. I suggest an alternative possibility based on the combinatorial effects of mutations in cancer cells. This model incorporates the concepts of synthetic–lethal interactions and mutation loads to explain the drug sensitivity of cancer cells. From this perspective, drugs that target complex processes that utilize genetically redundant or overlapping components, such as DNA replication and chromosome segregation, offer attractive target opportunities. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Chemotherapy; Combinatorial; Genetic interaction; Model
1. Introduction The rationale behind cancer chemotherapy is that certain drugs are more toxic to malignant cells than normal cells. The mechanistic basis for chemotherapeutic selectivity, to the degree it exists, is far from clear in most cases. Some selectivity doubtless derives from differences in cell cycling rates. Indeed, one of the principal causes of side effects is sensitivity of rapidly dividing stem cells such as those that form intestinal epithelia (Hruban et al., 1989). But high mitotic index of malignant cells, a measure of rapid cell division, is often a negative prognostic indicator for cancer (Sinicrope et al., 1999). The targets of the most widely used anti-cancer drugs, such as microtubules, DNA and enzymes involved in nucleic acid metabolism, are common to all cells, including normal tissue. For this reason, chemotherapeutic agents have narrow therapeutic windows. Nonetheless, they can cause tumor regression and eradication (Balis, 1997). Cancer cells contain multiple types of genetic and epigenetic aberrations (Gupta et al., 1997; Jones and *Tel.: +1-801-303-0300; fax: +1-801-303-0333. E-mail address: [email protected] (A. Kamb).
Laird, 1999). In many cases, they display marked decreases in chromosome stability and replication fidelity (Loeb, 1991; Perucho et al., 1994; Tlsty et al., 1993). As a result, numerous tumorigenic alterations exist in malignant cells, including base substitutions and frameshifts, loss-of heterozygosity, homozygous deletion, and methylation. The best known are mutations in P53 and K-ras. These changes contribute directly to tumor growth (Donehower, 1996; Fisher et al., 2001; Johnson et al., 2001). In addition to adaptive changes, presumptive selectively neutral alterations occur in cancer cells, including microsatellite repeat variants (Perucho et al., 1994). Because of the increased mutation rate and cell division number that accompany tumorigenesis, it is likely that cancer cells accumulate mutations and epigenetic changes that affect the functions of nonessential genes. By inference from experiments in mice, flies, yeast and E. coli, normal human cells probably possess considerable overlap of genetic functions (Winzeler et al., 1999; Adams et al., 2000; Driever et al., 1996; Ross-Macdonald et al., 1999; www.shigen.nig.ac.jp/ecoli/PEC). Genetic lethal screens and assays of targeted disruptions of single genes yield the surprising result that less than a quarter of genes are essential. In principle, non-essential
0022-5193/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0022-5193(03)00087-0
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genes collectively present a large mutation target in neoplasia. Mutations in non-essential genes can render organisms inviable when combined with one another (Guarente, 1993; Tong et al., 2001). This phenomenon, known as synthetic lethality, has been documented in a variety of genetic settings, especially in yeast. The underlying basis for synthetic phenotypes has been explored in many instances. Typically, the synthetic–lethal gene pairs participate in the same cellular or biochemical process (Guarente, 1993). Therapeutic strategies based on synthetic lethality are especially appealing in cancer (Hartwell et al., 1997). A drug may achieve selectivity for malignant cells through the genetic interactions between its target and mutant genes resident in the tumor. These interactions may produce a synthetic–lethal phenocopy in cancer cells, leaving normal cells unharmed. Here I explore the conceptual significance of synthetic lethality in the context of cancer. I propose a model based on synthetic–lethal interactions that may explain the efficacy of conventional cancer therapies, and possibly point the way to new drug targets.
2. Methods 2.1. Calculation of combinations (as graphed in Fig. 1B) Points are calculated according to WT ðmÞ ¼
m X
w i ¼ 2m m 1
where wi ¼
i¼2
m i
2.2. Calculation of probability of death (L(m)) (as graphed in Fig. 2) Points on graph calculated according to
! :
Fig. 1. Model for mutant gene and chemotherapeutic interactions. (A) Sets of combinations within a total of four mutant genes (1–4) and a fifth mutation or specific drug-mediated inhibition. Pair-wise combinations, triples and a quadruple interaction with the added mutation/ drug are shown. (B) Roughly exponential increase in total combinations of mutations as a function of mutation number compared to increase of pair-wise combinations only (w2 ), triples (w3 ), or quadruples (w4 ).
(C) Pairs plus triples and quadruples, weighted at 1/20 pairs: Lðm 1Þ ¼ ð1 ðð1 p2 Þw2 ðmÞ
(A) All combinations: m Y Lðm 1Þ ¼ ð1 ð ð1 p2 ÞW ðiÞW ði1Þ ÞÞ i¼2
¼ ð1 ð1 P2 ÞW ðmÞ Þ; where W ðmÞ ¼ 2m 1; or, (B) Pairs only: Lðm 1Þ ¼ ð1 ð1 p2 Þw2 ðmÞ Þ where w2 ðiÞ ¼ or,
!
i ; 2
ð1 p3 Þw3 ðmÞ ð1 p4 Þw4 ðmÞ ÞÞ; where e.g. w3 ðmÞ ¼
m 3
! ;
or, (D) Pairs in two classes: Lðm 1Þ ¼ ð1 ðð1 p2 Þw2 ð0:9 mÞ Þðð1 pj2 Þw2 ð0:1 mÞ Þ: For Fig. 2D, the m mutations are apportioned into two categories (p2 ¼ 0:0001 and pj2 ¼ 0:1) in the ratio 1:9, by multiplying m by 0.9 and 0.1, and rounding to the nearest integer to compute w2 ðiÞ: Note that w2 ð1Þ ¼ w3 ð1Þ ¼ w3 ð2Þ ¼ w4 ð1Þ ¼ w4 ð2Þ ¼ w4 ð3Þ ¼ 0:
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2.3. Calculation of survival probability (P(m)) (as graphed in Fig. 3) We use the relation: (A)
PT ðmÞ ¼ ð1 p1 Þm
m Y
ð1 p2 ÞW ðiÞW ði1Þ
i¼2
¼ ð1 p1 Þm ð1 p2 ÞW ðmÞ ; or; (B)
PT ðmÞ ¼ ð1 p1 Þm
m Y
ð1 p2 Þw2 ðiÞ
i¼2
¼ ð1 p1 Þ ð1 p2 Þw2 ðmÞ ; m
where p1 is the probability that a mutation affects an essential gene (=0.2). 2.4. Calculation of equilibrium mutation distributions (as graphed in Figs. 4 and 5) We use matrix algebra to compute the equilibrium distribution of mutations in a population of tumor cells, so that: xðtÞ ¼ xð0ÞðSÞt ; where xðtÞ is a vector that contains the genotype (mutation) frequencies after t generations; S is a matrix
Fig. 2. Graph of probability of an additional lethal mutational/ epigenetic event (or lethal therapeutic event) as a function of mutation number in tumors ðLðmÞÞ: LðmÞ is computed as in Methods, using m þ 1: For A–C, different curves correspond to different values of p2 shown in the box: (A) with higher order gene groups weighted equivalently, (B) with gene pairs only, (C) with gene pairs, triples and quadruples, but with p3 ¼ p4 ¼ ð0:05Þp2 : (D) Under a model in which 10% of the genes have (p2 ¼ 0:1) and the remaining non-essential genes have p2 ¼ 0:0001; only pair-wise interactions are considered; one additional mutation or drug interaction (m þ 1) involves the (p2 ¼ 0:1) class (dashed line); (m þ 2) is the same except two further interactions/mutations occur. The steps in the curve are a result of the rounding procedure used (see Methods).
Fig. 3. Probability (PT ðmÞ) of having survived m random mutational/ epigenetic events in essential and non-essential genes. Different curves correspond to different values of p2 shown in the box: (A) under the all-combinations model, as in Fig. 2A; (B) under a pairs-only model, as in Fig. 2B.
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Fig. 4. Graph of population fraction at mmax : mmax is the value of m corresponding to the maximum population fraction at generation t ¼ 2; 000: Values are calculated for three different mutation rates (U) under an all-combinations model (A–C) or a pairs+triples and quadruples model, where triples and quadruples are weighted at ð0:05Þx of pairs (D–F). A and D, U ¼ 0:01: B and E, U ¼ 0:1: C and F, U ¼ 1:0: Different curves correspond to different values of p2 shown in the box.
that carries out the mutation operation, with elements corresponding to Poisson probabilities of mean=U=average number of dominant, hemi- or homozygous alterations/cell/generation, and accomplishes selection according to fitnesses of the various genotypes. pð0jUÞ 0 S ¼ 0 0
pð1jUÞ pð0jUÞ
pð2jUÞPðDW0;2 Þ pð1jUÞPðDW1;2 Þ
0
pð0jUÞ
0
0
pðNjUÞPðDW0;N Þ pðN 1jUÞPðDW1;N Þ ; pð1jUÞPðDW2;N Þ pð0jUÞ
where, e.g. w2 ðiÞ is the number of pair-wise combinations of i mutations; w3 ðiÞ is the number of triple combinations, etc. Calculations were performed for p2 ¼ 0:1; 0:01; 0:001; 0:0001: In case (2), values of p3 ¼ p4 ¼ ð0:05Þp2 were used.
3. Results 3.1. Model
where pðjjUÞ ¼ eU U j =j! is the Poisson probability with mean=U of j mutations in non-essential genes/cell/division, and (1) PðDWi;j Þ ¼ ð1 p2 ÞðW ðjÞW ðiÞÞ ; or; (2) PðDWi;j Þ ¼ ðð1 p2 Þðw2 ðjÞw2 ðiÞÞ ð1 p3 Þðw3 ðjÞw3 ðiÞÞ ð1 p4 Þðw4 ðjÞw4 ðiÞÞ Þ:
Suppose that a tumor cell has endured mutational events or epigenetic alterations in m non-essential genes. We treat these as either dominant, homo- or hemizygous, so their effects are not masked by diploidy. Each mutation compromises gene function, but the combination is non-lethal. We seek to establish a framework to analyse the probability of synthetic–lethal interactions with a targetselective inhibitory drug. In a formal sense, the drug acts as a gene-disabling mutation. Thus, we look at possible
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Fig. 5. Graph of genotype (xðtÞ) distribution at t ¼ 2; 000: Calculations of xðtÞ and panels A–F are as in Fig. 4. Different curves correspond to different values of p2 shown in the box.
synthetic–lethal interactions that may ensue between the m mutations and an additional disruptive genetic or chemical event. In the standard synthetic–lethal case, there are m possible new pair-wise lethal interactions between the existing mutant genes and the additional one. The total probability of a synthetic–lethal event is the per gene probability, p2 ; multiplied by m: However, we need not restrict the potential synthetic interactions to pairs of loci, but may also consider higher order interactions. These involve triple and quadruple mutant sets, and possibly even larger groups. Therefore, for triple gene interactions, we take all double mutant combinations within the group of m genes combined with the additional gene or drug interaction. For quadruple mutants, we take all combinations of triples within the m genes, and so on (Fig. 1A). This leads to an approximately exponential increase in the number of possible genetic interactions (Fig. 1B). The probability of higher order interactions could be the same as p2 : Alternatively, it could be higher than p2 ;
or lower. It is difficult to know p2 ; and more difficult to guess the appropriate probabilities for higher order interactions. As a starting point, we may assume a constant probability of synthetic–lethal interaction that applies to all mutation groups, irrespective of size. In what follows, I take this as one extreme and ignore possible models where p2 op3 ; p4 ; etc., because these may be unrealistic (see Discussion). At the other extreme, I consider models that include only pair-wise interactions. I also consider models in which higher order interactions are less important (i.e. p2 > p3 ; p4 ; etc.). 3.2. Relation between mutation number and synthetic– lethal occurrence For the case where all groups of interactions have the same synthetic–lethal probability, we can compute the chance (LðmÞ) that a cell that carries m mutations will survive another (m þ 1) change. We assume that all interactions are independent and have the same individual probability (p2 ) of producing a synthetic–lethal
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interaction. The combinatorial genetic interactions create a threshold, above which the probability of survival is extremely low (Figs. 1B, 2A). Within a broad range of p2 values, the mutation number (m) at which survival becomes very improbable is approximately 5–15. We can compare the survival probability calculated from all combinations to that computed using only pairwise gene combinations (Fig. 2B). The difference is dramatic, and more mutations are tolerated in a model that considers only pair-wise genetic interactions, especially for small p2 : This result follows from the much more rapid increase in total combinations (WT ) compared to combinations of only two mutant loci (Fig. 1B). Thus, inclusion of higher order interactions, though not an essential feature of the model, creates a more precipitous decline in survival probability as a function of mutation number. We can also look at slightly more complicated, but possibly more realistic, models. One of these involves synthetic–lethal probabilities that are lower for triples and quadruples than for pair-wise interactions (Fig. 2C). The rationale for such a model is that probabilities of combining two mutations within a single pathway may be considerably higher than for three, etc. (see Discussion). Based on the ratio between the fraction of essential genes (0.2) and the fraction of synthetic–lethal pairs estimated from Tong et al (B0.01), we use p3 ¼ p4 ¼ ð0:05Þp2 (Tong et al., 2001). This model makes predictions that are fairly similar to the pairs-only model (Fig. 2B). Another model type postulates two groups of nonessential genes: a group that has a high probability of synthetic–lethal interaction (e.g. p2 ¼ 0:1), amounting in this case to 10% of the non-essential gene fraction; and a second group that has a low probability of interaction (e.g. p2 ¼ 0:0001). This sort of model attempts to describe a scenario where a subset of genes involved in complex processes such as cytokinesis or protein secretion displays a high degree of synthetic–lethal interaction, whereas the rest of the non-essential genes are much more insulated from one another. The model reduces in essence to the pairs-only model, but is included to underscore its conceptual difference. In the case where one additional (m þ 1) mutation or druginduced inhibition involves the (p2 ¼ 0:1) subset, and only pair-wise interactions are included, the probability of lethal interaction is a blend between the curves for p2 ¼ 0:1 and 0:0001 (Fig. 2D, dashed line). Interestingly, if we look at the case where two additional mutations or drug interactions (m þ 2) occur in the (p2 ¼ 0:1) subset, we see a very dramatic difference (Fig. 2D, solid line). Virtually no cells survive beyond mB5: This situation may occur when an inhibitory drug cross-reacts with one or more molecules; that is, the drug inhibits the function of at least
two targets involved in similar complex processes in the cell. 3.3. Equilibrium number of non-essential gene mutations We can compute the probability PðmÞ that a particular cell will sustain m mutations in either nonessential or essential genes by multiplying the individual probabilities at each step of the process from one to m (Fig. 3). The probability of traversing the steps from zero to 10–15 is very low over a range of p2 values. This result holds for both of the extreme models (all combinations weighted equally as in Fig. 2A, or pairsonly as in Fig. 2B). The reason is that mutations in essential genes ultimately limit survival. Nevertheless, the subpopulation that survives accumulates mutations in non-essential genes. Because of the constant input of mutations, the total number of mutations builds up in asexual organisms. The high mutation rates will push the mutation load in tumors to the point where it makes a significant negative impact on fitness. At this equilibrium, the mutation rate balances the rate of elimination. We can determine the equilibrium distribution of nonessential-gene mutations, assuming a certain mutation rate U (number of dominant, hemi- or homozygous deleterious mutations in non-essential genes/cell/division) and a particular value of p2 : We approximate U as constant, though the homozygous component increases with increasing mutation number due to the quadratic dependence on mutant allele frequency (i.e. with higher m; there is a higher probability of mutation of both alleles because homozygous mutation frequencies are the square of the single-mutant allele frequency). Considering only two of the models (all combinations or pairs+triples and quadruples weighted at 1/20 of pairs), we use matrix algebra to calculate the equilibrium genotypes (see Methods). Convergence requires a substantial number of generations, but mmax becomes populated between t ¼ 100 and 1200 in all cases (Fig. 4). The equilibrium value of m corresponding to the highest population fraction (mmax ) is affected by U and by p2 (Fig. 5). mmax is higher when U is higher, and when p2 is lower. mmax at equilibrium varies considerably, from 7– 16 for the all-combinations model and 14–147 for the pairs-only model, depending on the values of U and p2 (Table 1).
4. Discussion There are numerous examples of synthetic lethality in model organisms. In yeast, for instance, various screens and selections have uncovered over 1400 synthetic–lethal gene pairs (http://mips.gsf.de/proj/ yeast/tables/interaction/genetic interact.html). Recently,
ARTICLE IN PRESS A. Kamb / Journal of Theoretical Biology 223 (2003) 205–213 Table 1 Value of m for the maximum population fraction (mmax ) at t ¼ 2000: U is the average number of new alterations/cell/generation. (1) is calculated according to a model that weighs all combinations equally; (2) according to a model that includes pairs, triples and quadruples, and weighs the triple and quadruple combinations at 1/20 of the pair synthetic-lethal probability (p2 ) U
p2
ð1Þmmax
ð2Þmmax
0.01 0.01 0.01 0.1 0.1 0.1 1.0 1.0 1.0
0.01 0.001 0.0001 0.01 0.001 0.0001 0.01 0.001 0.0001
7 10 13 9 12 15 10 13 16
14 18 19 28 54 96 36 73 147
a genome-wide synthetic–lethal scan using 8 distinct mutant genes yielded a total of 300 lethal double-mutant combinations, for an average of about 30 lethal partners per gene (Tong et al., 2001). The set of eight genes was chosen partly to increase the odds of recovery, and likely represents a biased group. Nonetheless, it is probable that synthetic lethality is not a rare event. It is difficult to know the probability for the average gene, but clearly some genes have large numbers of partners. Notably, in the yeast genomic analysis, 37,376 (8 4672) double mutant combinations were examined and 99.2% of these grew normally (Tong et al., 2001). Thus, we observe high levels of functional redundancy through single-gene disruptions; but in a sense, even more dramatic redundancy when we explore double mutants of non-essential genes. The percentage of inviable double-mutant combinations is lower than the percentage of lethal single-gene mutations. Several plausible models for mutation/drug interaction can be imagined. Here I have explored four types of model: (1) a model based on the equivalence of all viable mutation groups, where the probability of synthetic– lethal interactions within groups of double mutants, triple mutants, etc. is the same; (2) a model in which only interaction pairs count (i.e. p3 ¼ p4 ; etc. =0); (3) a model where the combinations are differentially weighted so that p3 ¼ p4 =(0.05)p2 ; and (4) a model that considers pair-wise interactions of two kinds: those between a 90% fraction of non-essential genes that interact rarely (p2 ¼ 0:0001), and those between the remaining non-essential genes that interact strongly (p2 ¼ 0:1). This last model is the most complex, a variant of the second model, but possibly the most realistic. For a given gene, the probability (p2 ) of synthetic–lethal interaction depends on two major factors: the number of genes that participate in the same cellular pathway or process (Guarente, 1993), and the probability that a
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given mutant gene pair within this pathway is synthetic lethal. For this last model, I have assumed that 10% of non-essential genes (of the total 80%) are in a class that has a high probability of interaction (0.1). This assumption conforms with Tong et al. (i.e. (0.1)(0.1)=0.01) (Tong et al., 2001). The assumptions explored here vary widely. For instance, for p2 I have included values from 0.1 to 0.00001; and p3 values that range from 0 to p2 : Though these assumptions have not been tested, the technology exists to provide some estimates for the probabilities of synthetic–lethal interaction among, for example, triple mutants (Tong et al., 2001). Tumors are rife with genetic change, and may well contain disruptive mutations in non-essential genes. In support of this view, experiments that compare fitness levels of two yeast strains, one wild type and one deficient in DNA repair, show that mutations accumulate under mild selection conditions that compromise growth and viability only under stress (Szafraniec et al., 2001). Under normal growth conditions, the wild-type and mutant strains display similar properties. Interestingly, the yeast strains used were diploid. Thus, heterozygous mutations may be sufficient to generate declines in fitness, manifested only when cells must endure difficult circumstances such as growth at high temperature. Temperature increases may destroy the function of particular allelic forms of proteins, thereby boosting the number of effective synthetic–lethal interactions. Presumably, hemi- and homozygous mutations would produce more severe effects on fitness. Thus, stress actualizes the cryptic mutation load in cells grown under mild conditions. If one or more of the models discussed here approximates the situation in tumors, we may expect that tumors accumulate dominant, homo- or hemizygous alterations until they near a threshold for m, at which point they are under considerable pressure to eliminate new ones that arise. These ideas suggest that malignancies may carry a significant mutation load, and therefore, may produce inviable daughter cells at high frequency. Such behavior provides one possible explanation for high apoptotic rates in tumors. Tumors may partly suppress the impact of mutations by inhibiting apoptotic programs. But despite these steps, tumor cells may remain poised on the brink of catastrophe (Symonds et al., 1994; Yu et al., 2002). The mutation load in tumors also allows rationalization of chemotherapeutic efficacy. Complex processes, especially those involved in DNA replication and the cytoskeleton, may engender higher levels of synthetic– lethal interaction (Tong et al., 2001). Therefore, drugs that interfere with these cellular processes may be more likely to produce lethal effects in tumors than in normal cells, in spite of the tumor’s tendency to forestall apoptosis (Symonds et al., 1994; Yu et al., 2002). The
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probability is that a given malignant cell, regardless of how different it is from other cells in the mass or from other tumors, will contain enough mutations that affect, for example, chromosome segregation, to ensure a synthetic–lethal interaction with the drug. Drugs that target other complex, vital processes, including proteosome inhibitors, may act at least partially through this mechanism (Garber, 2002). Many chemotherapeutic drugs display only limited molecular specificity. For instance, the microtubule inhibitors such as colchicine and vinblastine bind several tubulin paralogs (Jordan et al., 1998). Even topoisomerase inhibitors such as doxorubicin and etoposide fail to distinguish between the two homologous forms (Patel et al., 2000). Such cross-reaction may be an important feature of their efficacy. Indeed, novel anti-cancer therapeutic strategies that exploit targets with many potential synthetic–lethal partners may prove fruitful.
Acknowledgements I thank Dr. Joshua Cherry for helpful discussions and Chunwei Wang for computing assistance.
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