## Info

Probability to arrest upon damage, ri Probability to arrest upon damage, r]

Fig. 8.3 Relationship between checkpoint competence (probability to arrest upon damage, 77) and the time it takes for the tumor to reach a critical size (first stage size). We observe similar patterns with two mechanisms, (a) The duration of cell cycle arrest (expressed in the variable 7) is varied. Parameter values were chosen as follows: p=2; r=2; u=0.3; a=0.9; /3=10~7;d = 0.1; targetsize = 1012. (b) The amount of tissue induced tumor cell inhibition, p, is varied. Parameter values were chosen as follows: p=2; r=2; u=0.3; a=0.5; f3=10~7;d = 0.1; tar getsize = 1012.

point deficient organisms is outweighed by the disadvantage of increased cell death in the absence of repair. Overall, this leads to a reduced initial growth rate of tumor cells in the checkpoint deficient scenario. Note that the time it takes for the tumor to reach the threshold size tends towards infinity as 77 —>1. This is because for r]—l, genome surveillance is 100% efficient and no mutants are ever created. This is clearly unrealistic.

While a reduction in checkpoint competence can lead to a slower initial growth rate of the tumor cells in this parameter region, a reduction in checkpoint competence always results in a higher mutation rate of the tumor cells (Figure 8.4), and thus in an enhanced ability of the tumor to progress.

Probability to arrest upon damage, T]

Fig. 8.4 Relationship between checkpoint competence (probability to arrest upon damage, rj) and the mutation rate of cells. The same relationship is observed irrespective of the duration of cell cycle arrest or the rate of tissue-mediated tumor cell inhibition. Parameter values were chosen as follows: p=2; r=2; u=0.3; a=0.9; 0=1O~7\ d = 0.1.

Probability to arrest upon damage, T]

Fig. 8.4 Relationship between checkpoint competence (probability to arrest upon damage, rj) and the mutation rate of cells. The same relationship is observed irrespective of the duration of cell cycle arrest or the rate of tissue-mediated tumor cell inhibition. Parameter values were chosen as follows: p=2; r=2; u=0.3; a=0.9; 0=1O~7\ d = 0.1.

Therefore, if the cost of cell death is high compared to the cost of cell cycle arrest, the model gives rise to the counter-intuitive observation that a reduction in checkpoint competence can lead to the generation of fewer firststage tumors during a defined time frame; however, the tumors which do arise are expected to accumulate further carcinogenic mutations faster and therefore have the potential to progress faster. It remains to be determined how relevant this result is. While these conditions could hold for checkpoint genes which are solely responsible for DNA repair, they might not hold for checkpoints which are responsible for apoptosis, or for both senescence and apoptosis (such as p53). If a reduction in the checkpoint leads to reduced apoptosis, cell death in not likely to be the dominant fitness cost.

### 8.6 Tumor growth and the microenvironment

Now we examine how tissue-mediated tumor cell inhibition influences the effect of checkpoint competence on the initial growth rate of the tumor and the mutation rate of tumor cells. The dynamics depend on the degree with which healthy tissue exerts inhibitory activity on the tumor cells, p. This is shown in Figure 8.3b, and also summarized by time-series simulations in Figure 8.5.

First, assume that the tissue-mediated inhibitory activity is relatively small and lies below a threshold (small value of p). Now the behavior of the model is identical to the one described in the last section. We concentrate on the parameter region in which a reduction in checkpoint competence leads to an increased initial growth rate of the tumor cells, and to an increased mutation rate (shown again in Figure 8.3b for reference). In other words, senescence represents an important cost for the cells. As explained above, reduced checkpoint competence allows cancer cells to proceed through the cell cycle without delay following genomic alterations (Figure 8.5a). Again, at values of rj close to 1, the time it takes the tumor to reach the threshold size becomes rapidly longer and goes to infinity for r}=l because genomic surveillance is 100% efficient (Figure 8.3b).

As the rate of tumor cell inhibition, p, is increased, these patterns change (Figure 8.3b). Now, a reduction of checkpoint competence results in a slower growth rate of the tumor (summarized by a time-series graph in Figure 8.5b). The higher the checkpoint competence, the faster the initial growth rate of the tumor. As the rate of tissue-mediated inhibition of cancer cells is increased further, the more pronounced this relationship becomes (Figure 8.3b). This is the same counter-intuitive result observed above, and is explained as follows in the current context. A checkpoint has two opposite effects on cancer cells in the model. On the one hand, it sends tumor cells into cell cycle arrest and this slows down tumor growth. On the other hand, it reduces the inhibitory effect exerted by tissue cells, and this enhances tumor growth. Tissue mediated inhibitory effects are reduced because the tissue cells frequently enter cell cycle arrest during which they do not function at normal levels. If tissue-mediated inhibition plays a sufficiently important role in the dynamics of tumor initiation (high values of p), the advantage gained by reduced tissue-mediated inhibition in the presence of a checkpoint outweighs the cost the cancer cells have to pay as a result of checkpoint competence. As before, we observe that as the value of t] approaches 1, the time it takes for the tumor to grow to the threshold size

— Checkpoint competent Checkpoint deficient

(b )p=25

Time (arbitrary units)

Fig. 8.5 Time series depicting the average initial growth of the first stage tumor in checkpoint competent organisms (solid line) and checkpoint deficient organisms (dashed line), (a) Rate of tissue-mediated tumor cell inhibition is zero, (b) Rate of tissue-mediated tumor cell inhibition is relatively high. Parameter values were chosen as follows: p—2; r=2 1=0.1; u=0.3; a=0.5; f3=10~'7;d = 0.1. Checkpoint competent organisms have r)=0.9, and checkpoint deficient organisms have r)=0.1.

Time (arbitrary units)

Fig. 8.5 Time series depicting the average initial growth of the first stage tumor in checkpoint competent organisms (solid line) and checkpoint deficient organisms (dashed line), (a) Rate of tissue-mediated tumor cell inhibition is zero, (b) Rate of tissue-mediated tumor cell inhibition is relatively high. Parameter values were chosen as follows: p—2; r=2 1=0.1; u=0.3; a=0.5; f3=10~'7;d = 0.1. Checkpoint competent organisms have r)=0.9, and checkpoint deficient organisms have r)=0.1.

goes towards infinity because genomic surveillance prevents the generation of any tumor cells (Figure 8.3b). In contrast to the rate of tumor growth, an increase in the level of tissue-mediated tumor cell inhibition does not change the relationship between checkpoint competence and the mutation rate of the cells (ability of the tumor to progress). Regardless of the value of p, a reduction in checkpoint competence is predicted to result in a faster rate of mutation (Figure 8.4). Therefore while reduced checkpoint competence is expected to result in the establishment of fewer tumors within a given time frame, the tumors which do develop are predicted to progress faster. This is the same outcome as observed in the last section, but is brought about by a different mechanism.

The only case where these relationships do not hold is at very high rates of DNA damage (u —> 1). In this case, most tissue cells will be non-functional or dead and tumor cell inhibition is not a significant factor anymore. This parameter region is, however, biologically unrealistic because such a scenario would correspond to death of the organism as a result of senescence or tissue destruction.

While not considered explicitly, the same considerations should apply to checkpoints which induce apoptosis. Higher levels of apoptosis can reduce the number of tissue cells, and this can lead to a compromised ability of the tissue to inhibit tumor cells. If tissue-mediated inhibition of tumor cells is a sufficiently significant component in the dynamics of tumor initiation, then apoptosis deficiency can lead to reduced tumor incidence, but in faster progression of the tumors which do develop. Whether this argument holds depends on how exactly apoptosis influences tissue size and the process of aging [Campisi (2003a); Camplejohn et al. (2003); Gilhar et al. (2004); Jansen-Durr (2002)].

8.7 Theory and data

The following relationships between checkpoint competence, senescence, and the development of cancer were found.

(1) The higher the checkpoint competence, the lower the rate of cancer incidence and progression, but the earlier the onset of aging (level of senescence is higher in the face of DNA damage). Lower checkpoint competence prevents an early onset of aging, but promotes cancers. This outcome is brought about by the following conditions. First, the advantage derived from avoiding cell cycle arrest upon damage must be higher than the cost derived from cell death in the absence of repair. In addition it requires that tissue cells exert no (or only little) inhibitory activity on tumor cells. These arguments might only apply to checkpoints which induce cell cycle arrest, and not to checkpoints which induce apoptosis.

(2) A reduction in checkpoint competence can result both in fewer aging symptoms and in fewer cancers; however, the cancers which do become established are characterized by accelerated progression. This is promoted by the following conditions (for a schematic explanation see Figure 8.6). First, it may occur because the cost derived from increased cell death in the absence of repair is higher than the benefit derived from avoiding cell cycle arrest upon damage. Whether this argument applies depends on the details of the checkpoint mediated activity, and requires that cell death (and thus apoptosis) occurs efficiently. However, a separate mechanism can lead to the same observation. It involves tissue-mediated tumor cell inhibition as a significant factor in the dynamics of tumor initiation. Reduced checkpoint competence prevents tissue aging and preserves the inhibitory function. This in turn leads to the development of fewer tumors. In contrast, higher checkpoint competence promotes tissue aging and compromises inhibitory function. In this parameter region, the advantage which the tumor cells gain from impaired inhibition outweighs the cost derived from the disruption of the tumor cell cycle; this leads to the generation of more cancers. This effect of tissue-mediated tumor cell inhibition is summarized by computer simulations in Figure 8.5. Since this mechanism requires that checkpoint-induced aging plays a dominant role in the dynamics of tissue cells, it is promoted by relatively high levels of DNA damage which can potentially trigger the checkpoints. It is unlikely to work if DNA damage is a relatively rare event. This mechanism may also be relevant to the induction of apoptosis if apoptosis contributes to tissue aging and a decline of tissue function.

In the following, these notions will be discussed in the context of mice which have varying competence to mount p53 responses upon genomic damage.

A recent study has demonstrated that p53 might be an important factor which contributes to senescence and aging [Donehower (2002); Tyner et al. (2002)], and this has sparked much discussion [Kirkwood (2002); Sharp-less and DePinho (2002)]. Tyner et al. developed a genetically altered mouse that can express a truncated form of p53 which augments wild-type p53 activity. Survival of these super-p53 mice was compared to wild-type (p53+/+) animals as well as p53 deficient animals (p53-/+, p53-/-). The experiments demonstrated that p53+/+ mice showed best survival, followed by the super-p53 mice. The p53 deficient animals were characterized

Cost of cell death in absence of repair, a, relative to cost of cell cycle arrest upon repair, 1/y. ^

Fig. 8.6 Schematic summary of the counter-intuitive mathematical result regarding checkpoint competence and tumor incidence. This is not based on numerical simulation, but is a graphical summary to aid understanding.

by an even lower survival rate because of the early development of certain cancers. It turned out that the super-p53 animals had reduced survival compared to wild-type mice because they experienced an accelerated onset of aging. On the other hand, tumor incidence in super-p53 mice was greatly reduced. These experiments support the notion that p53 activity represents a tradeoff between preventing senescence and preventing the development of cancer. This corresponds to one of the parameter regions observed in the model, and the conditions of the experiments are consistent with this parameter region. Two aspects are likely to be responsible. First, the study looked for the spontaneous development of tumors and did not induce them with carcinogenic agents. This means that especially at relatively early ages of the mice, DNA damage and the induction of checkpoints are rare events in healthy tissue cells. Consequently, the amount of tissue-mediated tumor cell inhibition is not likely to differ significantly between p53 competent and p53 deficient mice during this phase. The only effect of p53 deficiency is to allow the tumor cells to progress faster through the cell cycle in the face of oncogenic mutations. Therefore, p53 deficient mice are expected to show an elevated onset of tumors during early life. In addition, it is possible that the cancers which developed in the p53 deficient mice are not significantly inhibited by tissue cells. The amount of tissue-mediated inhibition of tumor cells can vary between different tissues. In this context, it is interesting to note that the cancers which developed in p53 deficient animals in this study were specific cases, mostly sarcomas and lymphomas. Other cancers in which the deletion of p53 is an important step did not occur at elevated levels. In fact, lung cancers were observed in p53 competent but not in p53 deficient animals.

Another interesting study compared the rate of skin cancer initiation and progression in p53+/+, p53+/-, and p53-/- mice [Kemp et al. (1993)]. The rate of cancer initiation and progression was statistically similar in p53+/+ and p53+/- heterozygotes. Double knockout mice (p53-/-), however, showed a reduced incidence of papillomas compared to wild-type animals. On the other hand, the tumors which were generated in p53-/-mice were characterized by more rapid malignant progression compared to p53+/+ animals. This is the second type of behavior predicted by the model. The reason that this behavior is observed in the Study by Kemp et al. could be as follows. First, the development of skin cancer is known to depend strongly on angiogenesis, and therefore inhibition of angiogenesis could ensure that tissue-mediated tumor cell inhibition is a significant force in the process of cancer initiation and progression. Moreover, in contrast to the study by Tyner et al., mice were treated with carcinogenic agents in order to induce tumors. This means that mice experience elevated levels of DNA damage and frequent induction of p53. This can result in elevated levels of tissue senescence in p53 competent animals, and this could result in reduced ability of tissue cells to display anti-tumor activity. Hence, tumors develop more often in p53 competent, compared to p53 deficient mice. According to the model, another explanation for this outcome could be that in the absence of repair, the cost derived from the production of lethal mutants outweighs the benefit derived from avoiding repair and cell cycle arrest. It is, however, not clear whether this is a likely explanation. Because p53 is also involved in the induction of apoptosis upon genomic damage or oncogenic mutations, it can be argued that p53 deficient organisms show reduced levels of apoptosis and cell death. Therefore, lethality in the absence of repair might not be a dominant factor.

This work also has implications for understanding the pattern of cancer incidence in patients which have a familial genetic defect in checkpoint genes. An interesting example is Li-Fraumeni syndrome which is characterized by lack of functional p53 in every cell of the body [Evans and Lozano (1997)]. Interestingly, patients develop only certain types of cancers, most importantly sarcomas. Although other types of cancers, such as colon cancer, also involve p53 inactivation as a crucial event in progression, they do not occur at elevated rates in Li-Fraumeni patients. According to the modeling results presented here, the exact details involved in the process of carcinogenesis can determine whether reduced p53 activity (and reduced checkpoint competence in general) leads to a higher incidence of cancers or not.

Chapter 9

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