Background
==========

The study of cost-effectiveness comparisons between competing medical interventions has led to a variety of proposals for quantifying cost-effectiveness. Although the most widely used measure is still the incremental cost-effectiveness ratio (ICER), there is increasing preference for the cost-effectiveness acceptability curve (CEAC). Willan \[[@B1]\] has recently proposed an alternative that he calls the probability of cost-effectiveness.

The differences between these various approaches can be subtle, and further complexity is introduced by some authors preferring a Bayesian formulation over more traditional frequentist analysis. One purpose of this article is to clarify some important issues, concerning (a) the perspectives of different decision makers and (b) the distinction between the true value of an unknown parameter and a statistical inference about that parameter.

Discussion
==========

We first review various approaches to measuring cost-effectiveness, including the ICER, the mean incremental net benefit, and the measure proposed by Willan \[[@B1]\]. We then contrast these measures and argue that Willan\'s proposal is of only secondary interest to a health care provider. All of the cost-effectiveness measures are in practice unknown parameters that must be estimated from data, and we next consider inference about these measures from both the frequentist and Bayesian approaches. Finally, a fundamental flaw in the estimator proposed by Willan \[[@B1]\] for his probability of cost-effectiveness is exposed.

Measures of cost-effectiveness
------------------------------

We consider two competing treatments, drugs, or other health technologies, which we refer to as Treatment 1 and Treatment 2. Conventionally, Treatment 1 is often the standard treatment whereas Treatment 2 is a new or comparator treatment. In reality there will usually be far more than two competing treatments for any condition, but for the purpose of this article it is enough to consider, like Willan \[[@B1]\], just two treatments.

A little notation is necessary. Let *C*~i~ be the cost associated with an individual patient when given Treatment *i*, and let *E*~i~ be the value of an appropriate effectiveness measure associated with that patient when given Treatment *i.* Now it is important to recognise variation between patients. One patient will incur different costs and experience different effectiveness from another. Therefore, *C*~i~ and *E*~i~ are random quantities, which we interpret as the cost and effectiveness under Treatment *i* for an individual patient *randomly* drawn from the population of all patients under consideration. The probability distributions of these random quantities describes how they vary over the population.

In order to compare cost-effectiveness between the two treatments, we require a way to link costs to effectiveness, and this is done through a decision-maker\'s *willingness to pay* coefficient *K.* Formally, the decision-maker is prepared to pay *K* units of money to obtain one unit of effectiveness. Therefore, the *net benefit* of Treatment *i* for an individual (random) patient is

*B*~i~(*K*) = *K E*~i~ - *C*~i~.

This expresses net benefit on the monetary scale by converting the *E*~i~ units of effectiveness into *K E*~i~ units of money before subtracting the cost *C*~i~. (We could equally express net benefit on the effectiveness scale as *E*~i~ - *C*~i~/*K*, but the two approaches are clearly formally equivalent.) The notation also emphasises the dependence of the net benefit on the decision-maker\'s willingness to pay coefficient *K.*

Treatment 2 would be clearly more cost-effective than Treatment 1 for an individual (random) patient if *B*~2~(*K*) \>*B*~1~(*K*). This can be expressed simply in terms of the *individual incremental net benefit* (individual INB)

*D*~B~(*K*) = *B*~2~(*K*) - *B*~1~(*K*) = *K D*~E~ - *D*~C~,

where *D*~E~ = *E*~2~ - *E*~1~ and *D*~C~ = *C*~2~ - *C*~1~ are the increments in effectiveness and cost, respectively.

If all patients were the same, and experienced the same costs and effectiveness, then the individual INB would be the same for all patients, and could then be called *the* INB. Then the comparison of treatments would become trivial. The INB would quantify the gain (if positive) or loss (if negative) per patient that would result from switching from Treatment 1 to Treatment 2. Treatment 2 would clearly be more cost-effective than Treatment 1 if, and only if, the INB was positive.

However, patients will vary, and the consequence of this is that individual INB will vary between patients, and there is no single value to represent the comparison between the two treatments. Across the population, there is a probability distribution of individual INB.

The measures of cost-effectiveness that are in widespread use in health economics are based on the *mean* of this distribution. We denote the population *mean incremental net benefit* (mean INB) by Δ~B~(*K*). The standard notation in probability theory for a mean or *expected* value is ![](1471-2288-2-5-i1.gif), so the mean incremental net benefit is

Δ~B~(*K*) = ![](1471-2288-2-5-i2.gif)(*D*~B~(*K*)) = *K* Δ~E~ - Δ~C~,

where Δ~E~ = ![](1471-2288-2-5-i3.gif)(*D*~E~) and Δ~C~ = ![](1471-2288-2-5-i4.gif)(*D*~C~) are the population mean increments in effectiveness and cost. Then Treatment 2 is defined to be more cost-effective than Treatment 1, in terms of the population mean, if Δ~B~(*K*) \> 0.

The *incremental cost-effectiveness ratio* (ICER) can be expressed as

ρ = Δ~C~/Δ~E~,

and we can see that Δ~B~(*K*) \> 0, i.e. Treatment 2 is more cost-effective than Treatment 1, if ρ \<*K* and Δ~E~ \> 0, or if ρ \>*K* and Δ~E~ \< 0.

The probability of cost-effectiveness as proposed by Willan \[[@B1]\] is the probability that an individual (random) patient will have a positive individual INB. We can denote this by θ(*K*) = *Pr*(*D*~B~(*K*) \> 0). It can also be seen as the proportion of all patients in the population who have positive individual INBs.

Δ~B~(*K*) and θ(*K*) are just two summary measures of the distribution of net benefit in the population. If the distribution is symmetric about its mean, as shown for instance in Figure [1](#F1){ref-type="fig"}, then the two measures will be in agreement, in the sense that Δ~B~(*K*) will be positive if and only if θ(*K*) is greater than 0.5.

![Two symmetric distributions of net benefit.](1471-2288-2-5-1){#F1}

Thus, the distribution represented by the solid curve in Figure [1](#F1){ref-type="fig"} has mean Δ~B~(*K*) = 1.3 and θ(*K*) = 0.903, so that Treatment 2 is more cost-effective in terms of having a higher mean INB and the proportion of patients who will achieve a higher individual INB under Treatment 2 is 90.3%. Conversely, the distribution represented by the dashed curve has Δ~B~(*K*) = -0.7 and θ(*K*) = 0.242, so the mean INB under Treatment 2 is now less than under Treatment 1, and only 24.2% of patients will obtain a higher individual INB under Treatment 2.

If, however, the distribution is not symmetric, then it is quite possible for the two measures to give apparently contradictory indications of relative cost-effectiveness. Figure [2](#F2){ref-type="fig"} shows another two possible distributions. In the distribution shown as a solid line, Δ~B~(*K*) = 0.2 and θ(*K*) = 0.414, so the mean INB is positive but only 41.4% of patients actually have a higher individual INB under Treatment 2. This is because those 41.4% include an appreciable proportion who obtain large positive individual INBs of 2 or more, whereas although the other 58.6% have negative individual INBs they never experience a value beyond -1. Conversely, in the distribution shown as a dashed line in Figure [2](#F2){ref-type="fig"}, Δ~B~(*K*) = -1 and θ(*K*) = 0.682, so that the mean INB is negative but 68.2% of patients have a positive individual INB.

![Two skewed distributions of net benefit.](1471-2288-2-5-2){#F2}

Which measure is best?
----------------------

It is well-known in health economics that, from the perspective of a health care provider needing to decide which treatment to apply to the population of patients in their care, it is the mean cost and effectiveness over the whole population that matters \[[@B2]\]. This is because the decision is to apply to the whole population. The health care provider will have to pay a cost equal to the total of all the costs for individual patients under the chosen treatment, and when expressed on a per-patient basis this is the population mean cost. For a similar reason, the per-patient mean effectiveness under the chosen treatment measures the benefit that the health care provider obtains for that cost in terms of improved health for the patients in its care. If the health care provider\'s willingness to pay coefficient is *K*, then the appropriate measure of relative cost-effectiveness is the mean INB Δ~B~(*K*), and the correct decision is to fund Treatment 2 if Δ~B~(*K*) \> 0 or Treatment 1 if Δ~B~(*K*) \< 0 \[[@B3]\].

As discussed in the previous section, this can be expressed in terms of comparing the ICER ρ with *K*, but that approach is more complex, since the comparison depends on the sign of Δ~E~.

From the perspective of a health care provider, then, needing to make a decision between two treatments, the decision rests on mean INB, and in fact only on its *sign.* There is no role for Willan\'s θ(*K*). As we have seen in Figure [2](#F2){ref-type="fig"}, the wrong decision could be made if it were based on θ(*K*).

Willan \[[@B1]\] says, \"The use of θ(*K*) should be helpful to policy-makers\". We agree, in the sense that it does give extra information about the distribution of individual INBs in the population, but as such it is of secondary interest, only. It should not be used as the basis of the actual decision. Nevertheless, we believe that in general an understanding of the distribution of individual INBs in the population is useful ancillary information that may be helpful to a decision-maker in the subsequent implementation of the decision.

The perspective of a health care provider is not necessarily the only one of interest. An individual clinician wishing to decide how to treat an individual patient may be willing to regard that patient as randomly drawn from a large population, and might be interested in θ(*K*). However, the situations shown in Figure [2](#F2){ref-type="fig"} argue for caution. Consider for instance the dashed curve. The patient is substantially more likely to have a positive individual INB than a negative one, and this may seem to suggest prescribing Treatment 2. There is, however, a risk of a large negative INB, corresponding to the patient having a very much worse outcome with Treatment 2 than with Treatment 1. In our opinion, the mean INB is as relevant to an individual decision as to the group decision of a health care provider.

Inference about cost-effectiveness
----------------------------------

The measures of cost-effectiveness described in the preceding section are all unknown in practice because they depend on the unknown distribution of individual INBs for patients in the population. From the statistical point of view they are unknown parameters. In order to learn about them, we will need to obtain some relevant evidence. This might, for instance, as supposed in Willan \[[@B1]\], consist of observations of actual costs and effectiveness for a sample of patients in a clinical trial.

We then need to construct appropriate methods of statistical inference for parameters of interest, based on the data. There is a substantial literature on this topic. Based on data from a clinical trial, various authors have presented estimators and confidence intervals for the ICER \[[@B4]-[@B12]\], and comparable inferences for the mean INB \[[@B3],[@B13]\]. All of these references employ the frequentist approach to statistical inference. Analyses under a Bayesian approach have also been given \[[@B14]-[@B18]\]. The fact that the ICER is a ratio, together with the way its interpretation changes as the sign of Δ~E~ changes, mean that inference about the mean INB is generally much more straightforward \[[@B17],[@B18]\].

Inference about the mean INB is generally presented by means of a *Cost-Effectiveness Acceptability Curve* (CEAC) \[[@B16]-[@B22]\]. As introduced by van Hout et al \[[@B19]\], the CEAC plots the probability that mean INB is positive against *K.* The value of such a graph lies partly in the difficulty of specifying *K* in practice. Decision-makers are generally reluctant to commit themselves to an explicit willingness to pay, and plotting against *K* allows them to assess the relative cost-effectiveness of the two treatments over a range of values of *K.* Strictly, the probability that Δ~B~(*K*) is positive can only be a Bayesian inference, since only in the Bayesian approach is it possible to assign probability distributions to unknown parameters. The frequentist analogue is to consider the P-value of a significance test of the null hypothesis that Δ~B~(*K*) \< 0 \[[@B17],[@B23]\]. It is important to remember, as always, that the interpretation of a P-value for a null hypothesis is much less direct and meaningful than the Bayesian probability that the hypothesis is true.

In its more natural Bayesian form, the CEAC states, for given *K*, the probability, *based on the available evidence*, that the true value of the unknown parameter Δ~B~(*K*) is positive. It therefore states, for given *K*, the probability, *based on the available evidence*, that Treatment 2 is more cost-effective than Treatment 1, from the perspective of a health care provider needing to make a decision between the two treatments. In presenting the CEAC in practice, authors have tended to assert that the CEAC states, for given *K*, the probability that Treatment 2 is more cost-effective than Treatment 1, omitting to refer to the fact that this probability is based on available evidence, and omitting to state the decision context. Willan \[[@B1]\] objects to this presentation of the CEAC as giving \'the probability of cost-effectiveness\'. He writes:

\"The interpretation that the acceptability curve is the probability that the intervention is cost-effective is not entirely accurate and could easily be misunderstood by policy makers. Consider the situation in which the observed INB for treatment is very small, but due to a very large sample size the acceptability curve at the value of λ \[our *K*\] of interest is 0.99. Attaching the label \"the probability that the intervention is cost-effective\" to this quantity could mislead policy makers into thinking that treatment is highly beneficial compared to the standard. What, in fact, is high is our confidence that the INB, however small, is not zero.\"

We agree that to refer to the CEAC as simply \'the probability of cost-effectiveness\', or \'the probability that Treatment 2 is more cost-effective than Treatment 1\', is potentially misleading if its dependence on the available evidence and on the decision context is not clear. We advocate that the phrase \'based on available evidence\' should be used to emphasise the first point, or for a technical audience the Bayesian formulation of \'the posterior probability of cost-effectiveness\' would be appropriate. It might be helpful also to emphasise that we are judging cost-effectiveness from the perspective of a health care provider needing to decide between two treatments, although this context has been so pervasively adopted in health economics that we believe it can be taken as understood.

Willan proposes that θ(*K*) should more properly be called \'the probability of cost-effectiveness\', but to use the phrase for θ(*K*) without further qualification would be *equally* misleading to policy makers. To parallel the above quotation from Willan \[[@B1]\], consider the situation in which the mean INB is positive but small, but due to there being very little between-patient variation we find θ(*K*) = 0.99. Attaching the label \'the probability that the intervention is cost-effective\' to this quantity could mislead policy makers into thinking that treatment is highly beneficial compared to the standard. What, in fact, is high is the proportion of patients in the population for whom the individual INB, however small, is positive.

*Neither* measure asserts the degree to which one treatment is \'highly beneficial\' compared to the other. *Both* are concerned only with the sign of INB. The CEAC gives the probability, based on available evidence, that the mean INB is positive, while θ(*K*) gives the probability that an individual INB is positive.

Willan \[[@B1]\] further objects to the fact that the CEAC changes as we get more information, because it is a statistical inference. As we get more evidence, our uncertainty about the sign of Δ~B~(*K*) for a given value of *K* will decrease until we become certain either that Δ~B~(*K*) is positive (whereupon the CEAC will tend to 1) or that it is negative (in which case the CEAC will tend to 0). This is entirely natural, and we do not understand this objection.

Willan\'s θ(*K*) is a probability in a different sense, because it is a population parameter, not an inference about a population parameter. Inferences change as we get more data, while the true values of the underlying parameters remain fixed, but unknown. This does not make θ(*K*) in any sense a superior kind of probability. It happens that Willan is interested in inference about a parameter that can itself be considered as a probability (although we believe it would be more helpful to call it a proportion, i.e. the proportion of patients in the population with positive individual INBs). To make inference about it, he provides an estimator (although, as we shall see below, that estimator is logically flawed), but he could have considered calculating a P-value for the null hypothesis that θ(*K*) \> 0.5. That would be analogous to the CEAC, and would change with the available data in the same way.

Willan\'s estimator
-------------------

Willan proposes an estimator of θ(*K*) based on data comprising observed costs and effectiveness values for a sample of *n*~S~ patients given the standard, treatment 1, and another sample of *n*~T~ patients given the intervention, treatment 2. Now since these data do not include any observations in which the same patient is given both treatments, it is completely impossible to learn the true value of θ(*K*), no matter how large *n*~S~ and *n*~T~ might be.

It is easy to demonstrate this impossibility with a simple example. Suppose that we have enormous samples such that we learn the true distribution in the population of costs and effects for treatment 1 and the true distribution of costs and effects for treatment 2. In particular, we will also learn the true distribution of net benefits *B*~i~(*K*) for each treatment. Suppose that the value of *K* is given and that the distribution of the net benefit *B*~1~(*K*) under treatment 1 is *N*(0,1) (i.e. normal with mean 0 and variance 1), while the distribution of net benefit *B*~2~(*K*) under treatment 2 is *N*(1,1). With all this information we know these distributions, and so we know exactly that Δ~B~(*K*) = 1. We therefore know with certainty that treatment 2 is more cost-effective than treatment 1 for a health care provider with the given value of *K.*

Even with all this information we do not know θ(*K*), because this depends on how correlated *B*~1~(*K*) and *B*~2~(*K*) are in the population. At one extreme, they might be perfectly positively correlated, such that for every individual in the population it is true that *B*~2~(*K*) = *B*~1~(*K*) + 1. Then θ(*K*) = 1, because the individual INB is positive for *every* patient. At the other extreme we might have perfect negative correlation, so that for every individual in the population we have *B*~2~(*K*) = 1 - *B*~1~(*K*). Then treatment 2 is more cost-effective for all those individuals for whom *B*~1~(*K*) \< 0.5. The proportion of such individuals in the population is 69.15%, and so θ(*K*) = 0.6915.

Willan\'s estimator effectively assumes that *B*~1~(*K*) and *B*~2~(*K*) are independent in the population, and for our example this implies that *D*~B~(*K*) is distributed as *N*(1,2), with the result that θ(*K*) = 0.7633. The assumption is arbitrary and completely unsupported. Indeed one might imagine that in practice there would be quite strong correlations, on the basis that a patient who responds well to one treatment might respond relatively well to the other, and similarly for costs. But we reiterate that there is absolutely no evidence about this correlation in the data which Willan supposes are available. Indeed for most kinds of intervention it is impractical to test two treatments on the same patient, and even when this is possible we must expect the picture to be complicated by cross-over effects.

What Willan \[[@B1]\] actually estimates is the probability that a randomly chosen patient given treatment 1 will obtain a higher net benefit than *another* randomly chosen patient given treatment 2. This is an entirely different measure from θ(*K*) and we cannot imagine that it is of fundamental interest to any policy maker.

Summary
=======

1\. From the perspective of a health care provider needing to decide which of two treatments to fund, it is the mean cost and mean effectiveness, over the whole population of patients within the provider\'s remit, that are of primary concern. This leads to the mean INB Δ~B~(*K*) as the appropriate measure of cost-effectiveness, and to the specific question of whether Δ~B~(*K*) is positive.

2\. Any measure of cost-effectiveness is a property of the population of patients under consideration, and is an unknown parameter. We make statistical inferences about parameters, based on available evidence. The true value of the parameter is fixed, independent of the available evidence, but unknown. Any statistical inference statement about the parameter is liable to change as the evidence changes. The CEAC plots the probability, based on available evidence, that Δ~B~(*K*) \> 0, and is the most relevant inference for a health care provider needing to decide between two treatments. Because it is an inference, the CEAC depends on the data.

3\. When reporting the CEAC in practice, its dependence on the data should be made clear by referring to it in such phrases as \'the probability of cost-effectiveness based on available evidence\' or \'the posterior probability of cost-effectiveness\'. It may also be useful to emphasise that cost-effectiveness is being judged from the perspective of a health care provider needing to decide which of two treatments to fund.

4\. Willan\'s probability of cost-effectiveness θ(*K*) may be useful to a decision maker in the same way as knowing other aspects of the distribution of individual INBs in the population would be useful, but it will generally be of secondary importance to the sign of Δ~B~(*K*). Since θ(*K*) is a parameter it does not depend on the data, but it is unknown, and any statistical inference about it will depend on the data.

5\. θ(*K*) should not be referred to simply as \'the probability of cost-effectiveness\' either, and we advise calling it, for example, \'the proportion of patients for whom the treatment is cost-effective\'. The fact that it is an unknown parameter should be emphasised, by a formulation such as \'based on available evidence, the proportion \... is estimated to be \...\'

6\. The proposed estimator of θ(*K*) given by Willan \[[@B1]\] is flawed. This parameter cannot be estimated consistently from the kind of data considered by Willan. His proposed estimate is in fact a probability concerning two randomly selected future patients, and is of doubtful interest to any decision maker.

Conclusion
==========

In conclusion, therefore, we reiterate the appropriateness of the CEAC as the primary comparator of relative cost-effectiveness between two treatments from the perspective of a health care provider. Willan\'s \'probability of cost-effectiveness\' would be of only secondary value in evidence presented to policy makers, and his proposed estimator of that probability is fatally flawed. However, we agree with Willan that assessments of cost-effectiveness should be more clearly stated, avoiding the unqualified phrase \'the probability of cost-effectiveness\'.

Competing interests
===================

None declared.

Pre-publication history
=======================

The pre-publication history for this paper can be accessed here:

<>


Background
==========

For over ten years chemo-radiotherapeutic combinations have evolved as prevalent modalities in the cure of solid tumors. The rationale for these treatments relies mostly on the drugs\' ability to sterilize disseminated metastases (spatial cooperation) and on radiation-drug interaction for improved local control of the primary tumor. Supraadditive interaction, often resulting from impaired repair of radiation-induced sublethal damage, may lead to limiting toxicities. In contrast, pure additivity of the treatments may conceivably be turned to advantage because the dose-dependent response of cells to radiation includes a quadratic term. This is of concern, for example, to farnesyl transferase inhibitors (FTIs) of which six have already been tested in phase I clinical trials \[[@B1],[@B2]\] with most attention being paid to the non-peptidomimetic R115777 \[[@B3]-[@B5]\]. As one may expect a cytostatic rather than a cytotoxic effect from FTIs, assays of combined modality treatment with cytotoxic agents applied in close temporal proximity should be performed. This prompted us to investigate the cells\' response to RPR-130401 (Scheme [1](#F1){ref-type="fig"}), a non-peptidomimetic FTI issued from chemical optimization from series selected by random screening at Rhône-Poulenc-Rorer Co. \[[@B6]\], both alone or in concomitant association with ionizing radiation.

A comprehensive approach to these problems requires an insight into the molecular targets of drug action. Together with mutation or deletion of the *p53* tumor suppressor gene, mutations in one of the four *Ras* genes (*H-, N-, K*~*A*~- and *K*~*B*~-*Ras*) represent the most frequent genetic alterations in human cancers \[[@B7]\] with predominance in pancreatic (90%), colorectal (50%) and lung (20%) tumors (for a review on ras mutations in relation to oncogenic transformation see \[[@B2]\]). Activation of Ras proteins requires prenylation of the CAAX sequence at their C-terminus, to ultimately permit their association with other proteins \[[@B8]\] or with the inner face of the plasma membrane \[[@B9]\]. A key step in this process is catalyzed by farnesyltransferase (FTase). The K-Ras protein can alternatively be prenylated by type I geranylgeranyltransferase (GGTase I), a closely related enzyme \[[@B10]\].

FTase has been a very attractive target for antitumor drug discovery because prenylation is required for oncogenic Ras to transform cells \[[@B11]-[@B13]\]. Numerous inhibitors have been developed, including FPP analogs, CAAX peptide analogs, bisubstrate analogs \[[@B14],[@B15]\] and more recently GGTase I inhibitors \[[@B16]\]. However, it is now known that a range of non-Ras proteins are targets for prenylation \[[@B17]-[@B19]\]. In spite of this, the quest for specific FTase-targeting drugs that would not affect GGTase is still pertinent, because geranylgeranylation of normal cellular proteins is five to ten times more prevalent than farnesylation \[[@B20],[@B21]\].

RPR-130401 acts as a competitive inhibitor of the FPP substrate with respect to the farnesylated proteins, with an IC~50~ of 28 nM for the inhibition of K-Ras prenylation *in vitro*\[[@B6]\], and has demonstrated *in vivo* antitumor activity in mice bearing human carcinoma xenografts \[[@B22]\]. RPR-130401 is highly selective (more than 300-fold) for FTase with regards to GGTase, an unexpected result since GGTase can accommodate and transfer both FPP and geranylgeranyl pyrophosphate to CAAX-motifs in proteins \[[@B23]\]. Consistently, RPR-130401 efficiently inhibits Ras farnesylation in cells but does not block geranylgeranyl transfer to Ras \[[@B24]\]. RPR-130401 is also very efficient in inhibiting lamin B farnesylation \[[@B6]\]. The lack of protein substrate specificity is of particular interest for the development of this series of FTIs, as non-Ras farnesylated proteins may participate in transformation by Ras-dependent or -independent pathways. The discovery of prenylation-dependent oncogenic protein tyrosine phosphatases harboring a CAAX-box \[[@B25]\] strengthens the interest for such FTIs as RPR-130401.

For studies with RPR-130401 we chose three cell lines bearing a *K-Ras* allele with a point mutation, namely, the human colon adenocarcinoma HCT-116 with mutation at codon 13 \[[@B26]\], the human pancreatic carcinoma MiAPaCa-2 with mutation at codon 12 \[[@B27]\], and the human lung carcinoma A-549 with another mutation at codon 12 \[[@B28]\]. Cell growth or survival, cell cycle progression, ploidy, lamin B structure in nuclear lamina, cytoskeleton framework, and lamin B fragmentation were taken as an endpoint in single or combined treatment with ionizing radiation. The data show that RPR-130401 affects the integrity of the lamin B network, resulting in an aberrant onset of mitosis and cytokinesis and ensuing hyperploidy without significant changes in radiation susceptibility.

Results
=======

Growth inhibition by RPR-130401
-------------------------------

The response of HCT-116, A-549 and MiAPaCa-2 cells to RPR-130401 was investigated through growth inhibition assays with exponentially growing subcultures. Cells were exposed to the drug for up to 7-days at concentrations in the range 2.5--7,000 nM. RPR-130401 was found to inhibit cell growth with an IC~50~ of 50 nM for HCT-116, 120 nM for MiAPaCa-2 and 710 nM for A-549 cells. The effect correlated with a pronounced lengthening of the cells\' doubling time (Figure [2](#F2){ref-type="fig"}).

![Chemical Structure of RPR-130401](1471-2210-2-2-1){#F1}

Altered cell cycle progression by RPR-130401 and radiation
----------------------------------------------------------

To investigate cell cycle redistribution by RPR-130401, HCT-116, MiAPaCa-2 and A-549 cells were exposed for 5-days to 1 × IC~50~ or 10 × IC~50~ FTI (relative to the cell line of interest) and submitted or not to γ-rays 24-h before harvest. BrdUrd was incorporated at the end of treatment for S-phase cell labeling. The three cell lines were not equally responsive to drug (Figure [3](#F3){ref-type="fig"}). RPR-130401 induced accumulation of HCT-116 cells in G2-M phase, with a concentration-dependent increase in the ploidy number and a decline in the normodiploid G1- and S-phase content. These observations correlate those made by other authors using Ras-mutated human pancreatic cells and L-744,832 \[[@B29]\] or human lung cancer cells and FTI-2153 \[[@B30]\]. MiAPaCa-2 cells showed a similar response at low (1 × IC~50~) drug concentration. However, with this cell line both the G1 phase depletion and the increase in the ploidy number, were substantially less pronounced at high (10 × IC~50~) than at low (1 × IC~50~) drug concentration. Finally, with the exception of the pre-mitotic arrest, the effect of RPR-130401 on cell cycle progression and ploidy change was comparatively minor in A-549 cells. Irradiation promoted drug-induced effects. Incidentally, flow cytometric analysis did not provide evidence of a significant amount of the sub-G1 DNA fragments expected from apoptosis.

![Growth inhibition by RPR-130401 in asynchronously growing HCT-116, A-549 and MiAPaCa-2 cells. Mid-log phase cells were seeded (2 × 10^5^ cells in 25 cm^2^ flasks) and incubated for 24-h prior to introduction of RPR-130401. The drug was present for up to the time of trypsinization and cell scoring. RPR-130401 induced a pronounced lengthening of the cell doubling time, namely, for HCT-116 cells, 23-h (50 nM drug = 1 × IC~50~) or 30-h (500 nM drug) *vs.* 18-h in drug-free controls; for A-549 cells, 30-h (0.71 μM drug = 1 × IC~50~) or 35-h (7.1 μM drug) *vs.* 22-h in drug-free controls; for MiAPaCa- 2 cells, 35-h (0.12 μM drug = 1 × IC~50~) or 40-h (1.2 μM drug) *vs*. 23-h in drug-free controls.](1471-2210-2-2-2){#F2}

Radiation survival in the presence of RPR-130401
------------------------------------------------

Two methods were used to determine whether RPR-130401 resulted or not in an altered radiation survival. For lengths of drug exposure in excess of 12-h (1- to 5-days), cells were trypsinized and plated following treatment to preclude artifacts due to cell multiplicity. Short contact with drug (1-, 2-, 3- or 12-h) was performed in the most sensitive cell line only, i.e., in HCT-116 cells. In that case, cells were plated prior to treatment and the data corrected for changes in cell multiplicity (see Materials and Methods) where necessary. A total of 78 survival curves were generated and fitted to eq. (2) (see Materials and Methods) for data analysis. Irrespective of the method used, exposure of cells to RPR-130401 did not produce any significant modification of radiation sensitivity relative to controls, even with the largest drug concentration and the longest length of drug exposure (Figure [4](#F4){ref-type="fig"}).

![Effect of RPR-130401 on cell cycle progression. Cells were grown for a total of 5-days without or with 1 × IC~50~ or 10 × IC~50~ RPR-130401. At day 4, part of samples was irradiated to the dose indicated and allowed to rest in the incubator for an additional 24-h prior to harvest. The DNA content was determined from flow cytometric analysis of propidium iodide staining and BrdUrd incorporation. 10^4^ nuclei were analysed for each sample. 2C, 4C and 8C, diploid, tetraploid and octoploid cells. Sq, quiescent (arrested in synthesis) S-phase cells.](1471-2210-2-2-3){#F3}

Effects of RPR-130401 on lamin B distribution
---------------------------------------------

Altered distribution of lamin B following exposure to the FTI was investigated in HCT-116, A-549 and MiaPaCa-2 cells. Cells were exposed for 5-days to 1 × IC~50~ or 10 × IC~50~ RPR-103401, submitted or not to γ-rays 24-h before harvest and lamin B was subsequently probed by immunofluorescence. Typical results are shown in Figure [5](#F5){ref-type="fig"}.

![Typical radiation survival curves for asynchronous growing cells without (•) or with exposure to 1 × IC~50~ (○) or 10 × IC~50~ (□) RPR-130401. Cells were plated, exposed to the drug for 3-days and irradiated. Each flask was trypsinized immediately after irradiation and 800 to 1,000 cells were replated in drug-free medium for colony formation assays. To account for the loss of plating efficiency du to drug exposure, survival values were normalized relative to the surviving fraction for drug alone. The curves were drawn for best fit to a linear quadratic equation (eq. (2), see Materials and Method) taking all data points into consideration. Found: α = 0.518 ± 0.036 Gy^-1^, β = 0.044 ± 0.016 Gy^-2^ for HCT-116 cells; α = 0.193 ± 0.036 Gy^-1^, β = 0.065 ± 0.014 Gy^-2^ for A-549 cells; α = 0.189 ± 0.058 Gy^-1^, β = 0.086 ± 0.026 Gy^-2^ for MiAPaCa-2 cells. Each data point came from an average over three flasks or more. *Bars, SD.* The figure at bottom right shows the surviving fraction at 2 Gy (SF~2~) of HCT-116 cells in the presence of RPR-130401. The conditions were the same as above. Data were corrected for the expression of potentially lethal damage \[82\].](1471-2210-2-2-4){#F4}

Control cells (Figure [5](#F5){ref-type="fig"}A,[5](#F5){ref-type="fig"}D &[5](#F5){ref-type="fig"}G) showed a nuclear distribution of lamin B with localization to the nuclear lamina as indicated by a ring-like staining at the nuclear periphery. During mitosis the lamin was either cytoplasmic (Figure [5](#F5){ref-type="fig"}D) or poorly detectable (Figure [5](#F5){ref-type="fig"}G &[5](#F5){ref-type="fig"}H). The pattern of lamin B distribution was markedly altered following incubation with RPR-130401, depending on the cell line. For HCT-116 (Figure [5](#F5){ref-type="fig"}B,[5](#F5){ref-type="fig"}C) and A-549 cells (Figure [5](#F5){ref-type="fig"}E,[5](#F5){ref-type="fig"}F), the lamin B staining was still nuclear with the characteristic ring-like structure but, in addition to giant nuclei typical of treated HCT-116 cells (Figure [5](#F5){ref-type="fig"}C), cell doublets with no proper separation of the daugther nuclei after telophase were observed (Figure [5](#F5){ref-type="fig"}F). MiAPaCa-2 cells showed a different pattern in response to RPR-130401 (Figure [5](#F5){ref-type="fig"}H,[5](#F5){ref-type="fig"}H\'). With these cells, lamin B was not strictly confined in the nucleus as indicated by cytoplasmic patches (Figure [5](#F5){ref-type="fig"}H). Examination of DAPI-stained nuclei confirmed the absence of DNA in these patches (Figure [5](#F5){ref-type="fig"}). Lamin B figures were not appreciably modified by exposure to ionizing radiation; however, radiation induced the formation of micronuclei in relation to mitotic cell death (data not shown).

Effects of RPR-130401 on actin and tubulin networks in HCT-116 cells
--------------------------------------------------------------------

Some FTIs reportedly affect the actin cytoskeleton *via* the Rho (a Ras-related GTP-binding protein) pathway \[[@B31]\] and Rho-B, an endosomal Rho protein involved in receptor trafficking, has recently been suggested as an important mediator of the antineoplastic potential of FTIs \[[@B19],[@B32]\]. We therefore sought to investigate the effects of 50 nM or 500 nM RPR-130401 on the distribution of actin and tubulin networks in HCT-116-cells exposed to RPR-130401 and/or radiation. Pictures obtained using rhodamine-phalloidin and immunofluorescent labeling of isothiocyanate-conjugated tubulin in control and treated cells, are shown in Figure [6](#F6){ref-type="fig"}.

![Immunofluorescent detection of lamin B in control (A, D, G) and treated (B, C, E, F, H, H\') HCT-116 (B, C), A-549 (E, F) and MiAPaCa-2 cells (H, H\'). Cells were grown on coverslips for 5-days without or with 1 × IC~50~ (B, E, H, H\') or 10 × IC~50~ (C, F) RPR-130401. Cells were then fixed and incubated with an anti-lamin B monoclonal antibody, then with an Alexa^®^-conjugated secondary antibody. To visualize nuclei, the cells were counter-stained with DAPI (H\'). Cells were viewed on a Zeiss microscope and photographed with Ilford HP-5 film. m, mitosis; p, cytoplasmic patches. The bar (B) represents 20 μm.](1471-2210-2-2-5){#F5}

L-739,749, another FTI, was earlier shown to induce rapid morphological reversion of rat fibroblasts (Rat1-ras) transformed with H-ras \[[@B33]\]. Such phenotypic reversion was not observed using RPR-130401 in HCT-116 cells. Normal membrane ruffles, circumferential actin bundles and focal adhesions as seen in control HCT-116 cells (Figure [6](#F6){ref-type="fig"}A), were still present in cells incubated for as long as 5-days in the presence of RPR-130401 (Figure [6](#F6){ref-type="fig"}B). The size of the nuclei and the number of giant cells grew in parallel in the presence of the drug, up to threefold relative to controls. The stress fibers and the tubulin network were normal in these cells (Figure [6](#F6){ref-type="fig"}B &[6](#F6){ref-type="fig"}D). Examination of bisbenzimide-stained nuclei showed the absence of apoptotic bodies (Figure [6](#F6){ref-type="fig"}A\' &[6](#F6){ref-type="fig"}B\'), and no vesicles were formed in the cytoplasm of treated cells.

RPR-130401-induced modification of the HCT-116 karyotype
--------------------------------------------------------

Activation of Ha-ras gene expression in mouse NIH3T3 cells is known to result in genomic instability, identified from chromosome aberrations including acentric fragments, multicentric and double-minute chromosomes \[[@B34],[@B35]\]. We therefore investigated the effects of 50 nM or 500 nM RPR-130401 on the ploidy and chromosome integrity in HCT-116-cells exposed to RPR-130401 and/or radiation. Figure [7](#F7){ref-type="fig"} shows the distribution of the chromosome score within individual metaphases of colcemid-treated cells after 1-day of contact with RPR-130401. Control cells showed a near-diploid karyotype with a modal number of chromosomes of 45. Excess ploidy increased with the drug concentration, the radiation dose and the length of drug exposure. The mitotic index decreased during treatment (data not shown), thus confirming that the accumulation of HCT-116 cells was in the G2 phase.

![Immunofluorescent visualization of cytoskeleton components in control (A, A\', C) and treated (B, B\', D) HCT-116 cells. Cells were grown on coverslips for 5-days without or with 500 nM RPR-130401. The cells were subsequently given 3.5 Gy γ-rays and allowed to rest in the incubator for 24-h. Cells were then fixed and incubated with TRITC-labeled phalloidin (A, B), or with an anti-α tubulin FTIC-conjugated antibody (C, D). Nuclei were counter-stained with bisbenzimide (A\', B\'). Cells were viewed as in Figure [5](#F5){ref-type="fig"}. The bar (C) represents 20 μm.](1471-2210-2-2-6){#F6}

However, no chromosome aberration was seen at this stage using FISH analysis with all human centromeres probes. All chromosomes in the metaphases examined displayed one unique centromere, even in metaphases containing up to 200 chromosomes (data not shown).

Western blot analysis of lamin B in treated cells
-------------------------------------------------

Flow cytometry (Figure [3](#F3){ref-type="fig"}) and DAPI fluorescence of nuclei (Figure [5](#F5){ref-type="fig"}), did not provide evidence of a significant level of apoptosis in cells exposed to RPR-130401. In some instances, however, the pictures obtained from immunofluorescence analysis of the lamin B status in cells exposed for 5-days to RPR-130401, suggested breakdown of nuclear lamina, and it has been shown recently that inhibition of protein prenylation may cause apoptotic cell death in pancreatic cells \[[@B36]\]. As lamin B cleavage into 46 kDa fragments is a hallmark of apoptosis \[[@B37]\], we performed a Western blot determination of lamin B in extracts from HCT-116, A-549 and MiAPaCa-2 cells exposed for 5-days to 10 × IC~50~ RPR-130401. The results (Figure [8](#F8){ref-type="fig"}) unambiguously show complete absence of lamin B cleavage.

![Effect of RPR-130401 exposure on the chromosome number distribution in individual metaphases. HCT-116 cells were grown for 4-days without (A, B) or with 50 nM (C, D) or 500 nM (E, F) RPR-130401. Cells were then given 3.5 Gy γ-rays (B, D, F) and returned to the incubator for 24-h prior to fixation and scoring. Each panel represents the counts from at least 50 metaphases.](1471-2210-2-2-7){#F7}

![Western blot analysis of lamin B in extracts from control and treated cells. Cells were incubated for 5-days in 75 cm^2^ flasks with 500 nM (HCT-116), 7.1 μM (A-549) or 1.2 μM (MiAPaCa-2) RPR-130401. A blank was also prepared for each cell line. The number of cells at the time of cell lysis, was in the range 10^7^. At the end of treatment, the flasks were rinsed twice with ice-cold PBS and cells lysed in PHEM buffer as described under Materials and Methods. An aliquot of each extract (20 μg total protein) was loaded in the wells of a 7.5% polyacrylamide gel and electrophoresis was performed under usual conditions with molecular weight standards, followed by transfer to a nitrocellulose membrane. The membrane was incubated with a mouse monoclonal antibody directed against human lamin B and revealed through chemiluminescence detection (see Materials and Methods).](1471-2210-2-2-8){#F8}

Discussion
==========

The main effects of RPR-130401 against the three K-Ras mutated cell lines used in this study were *(i)* a pronounced cytostatic effect, with an IC~50~ in the range 50--710 nM; *(ii)* accumulation of cells in G2 phase, with G1 and S phase depletion; *(iii)* induction of a large amount of hyperploid cells (HCT-116 and MiAPaCa-2) showing active S-phase DNA synthesis, together with some giant cells; *(iv)* profound alteration of the lamin B pattern, without cleavage of the protein; *(v)* no alteration of the microtubule and actin networks, even after prolonged incubation with a high drug concentration in the most sensitive cell line (500 nM, HCT-116 cells); *(vi)* strictly additive interaction with ionizing radiation with regard to cell kill, cell cycle redistribution and induction of hyperploidy.

Two alternative pathways should be taken into consideration in order to explain these observations, namely, inhibition of the farnesylation of p21^Ras^ or related proteins from the Ras superfamily, or inhibition of the farnesylation of other proteins resulting in disruption of the mitotic apparatus or cytokinesis traverse. These hypotheses are discussed below.

p21^Ras^ activation in normal and tumor cells is mandatory to the transition from cell quiescence to proliferation. However, it is generally agreed that inhibition of p21^Ras^ farnesylation does not suppress mitogenic functions in Ras-transformed cells \[[@B38]\]. Moreover, it has recently been shown that growth inhibition by FTIs does not necessarily proceed from inhibition of p21^Ras^ prenylation, and that various Ras-unrelated proteins may be important targets for FTI treatment \[[@B2],[@B19],[@B29],[@B39],[@B40]\]. Even though it results in an altered subcellular distribution of p21^Ras^\[[@B6]\], RPR-130401 is not able to block p21^Ras^ geranylgeranylation \[[@B24]\] in such a way that inhibition of p21^Ras^ farnesylation is not likely to account for the main effects of the drug. On the other hand, the peptidomimetic FTI L-739,749 has been reported to prevent Ras-induced transformation through inhibition of Rho-B prenylation \[[@B31]\] with a block in cell proliferation, increased apoptosis \[[@B41]\] and major changes in stress fiber formation, cell shape and mobility. None of these characteristic changes in cell morphology and architecture was observed upon prolonged exposure to RPR-130401 (Figure [6](#F6){ref-type="fig"}), which seems to rule out any member of the Rho family as a target for RPR-130401.

Considering the efficient pre-mitotic block and hyperploidy induced by RPR-130401, as also found with other FTIs \[[@B16],[@B29],[@B30],[@B42]\], it is tempting to postulate that the target of the drug is a protein involved at some stage in mitosis and/or cytokinesis, and whose farnesylation is required for proper activation. Indeed, protein isoprenylation is important at the G2/M transition in *Schizosaccharomyces pombe*\[[@B43]\] and nuclear lamins are major targets for FTase \[[@B18],[@B44]\]. Lamin B farnesylation, which is a very sensitive target for RPR-130401 *in vitro*\[[@B6]\], appears to deserve consideration as a candidate to this role. As a matter of fact, among the three major type A-C lamins, lamin A and lamin B are initially translated with a CAAX motif. This motif is cleaved upon post-translational maturation of lamin A but persists in lamin B, unless the C-terminal aminoacid residue is mutated \[[@B23]\]. Studies with mutant lamin deleted of the CAAX sequence have shown that the CAAX motif is essential to anchoring lamin B to the nuclear envelope \[[@B45],[@B46]\]; moreover, farnesylation is required for the integration of newly synthesized lamins into the pre-existing nuclear lamina during interphase, and GGTase is unable to substitute for FTase at this stage \[[@B47]\].

These data altogether suggest that inhibition of lamin B farnesylation could be an important target of RPR-130401, resulting in an aberrant onset of mitosis and cytokinesis and ensuing hyperploid cell generation. Strong support to this scheme is given by immunofluorescence experiments showing that the intranuclear distribution of lamin B is profoundly altered in cells exposed to RPR-130401 (Figure [5](#F5){ref-type="fig"}). This occurred without lamin B breakdown (Figure [8](#F8){ref-type="fig"}), consistent with lack of a significant level of apoptosis in the three cell lines used. Interestingly SCH-66336, another FTI, reportedly allows accumulation of unfarnesylated prelamin A in patients under phase I investigation \[[@B1]\] and in several cell lines in culture as well \[[@B48]\]. It has also been shown that SCH-66336 induces diruption of microtubule binding to the centromeric proteins CENP-E and CENP-F \[[@B17]\], thus evoking again faulty mitosis as an important outcome of FTI exposure.

Conclusions
===========

Oncogenic *Ras* expression has been reported to have different outcomes in rodent and human cells with regard to radiation susceptibility. Studies in mouse \[[@B49]-[@B52]\] or rat cells \[[@B51],[@B53]-[@B59]\] relied on transfection with *N-Ras*\[[@B49],[@B50]\], *H-Ras*\[[@B51],[@B53]-[@B58]\] or co-transfection with *H-Ras* and *myc*\[[@B53]-[@B55]\], \[[@B58]-[@B60]\]. Except in one study \[[@B51]\], the authors have conclusively shown that transformation of rodent cells with the *Ras* oncogenes results in enhanced radiation resistance. Co-transfection with *H-Ras* and *myc* was found to act synergistically with regard to induction of the radioresistant phenotype \[[@B53],[@B54],[@B58]-[@B60]\], possibly in relation to inhibition of *myc*-dependent apoptosis \[[@B58],[@B61]\].

With two exceptions in support of increased radioresistance \[[@B62],[@B63]\], early studies on human cells did not show any clear-cut relationship between radiation sensitivity and expression of oncogenic *Ras*\[[@B64]-[@B67]\]. In addition, a study involving a cohort of patients with stage II and III carcinoma of the uterine cervix, demonstrated the absence of a significant correlation between rearrangements or structure of the *Ha-ras-1* and/or *c-myc* genes and tumor response to radiotherapy \[[@B68]\]. However, the contribution of *N- or K-Ras* activation to intrinsic radioresistance in human cells has recently been adressed directly, i.e., without the perturbations introduced by cell transformation \[[@B69]\]. The mechanisms involved in *Ras*-related radioresistance are still open to question, but it might reasonably be proposed that it proceeds from constitutive activation of pathways dowstream from *Ras* in signal transduction, such as raf-1 \[[@B70]\] or phosphatidylinositol 3-kinase \[[@B71]\].

Whether and how FTase inhibition may affect the response of cells to ionizing radiation has also been a long-standing problem. The outcome appears to depend very much on the cell line and the specificity of the FTI used. The FTase inhibitor FTI-277 reportedly acted as a radiosensitizer in *H-Ras*-transformed rat embryo fibroblasts \[[@B72]\] and in human tumor cells harboring *H-Ras* mutation \[[@B73]\]. On the other hand, the radiation susceptibility of human tumor cells expressing the wild-type form of *Ras* was not altered by FTIs \[[@B73]\]. However, enhanced radiation response by FTI-277 has been described in human cells expressing wild-type *Ras* together with the 24-kDa isoform (FGF2) of basic fibroblast growth factor, a factor involved in acquired radioresistance \[[@B74]\]. This was taken as an indication that farnesylated proteins other than Ras might be involved in the modulation of radiation response by FTI-277 \[[@B74]\]. Weak radiosensitization only was obtained with FTI-277 in K-Ras mutants, unless FTI-277 was combined with GGTI-298 to hinder geranylgeranyl transfer to K-Ras \[[@B73]\]. Last but not least FTI-induced radiosensitization, when it occurs, seems to be independent on the growth inhibitory effect of the FTI \[[@B73]\].

We show here that RPR-130401 does not significantly alter the radiation susceptibility of human cells bearing K-Ras mutation. This occurs in spite of significant hyperploidization, accumulation of cells in G2 and depletion of S phase. Finally, impaired repair of radiation damage by RPR-130401, appears to be very unlikely to occur. This seems valuable in the prospect of combining RPR-130401 as an adjuvant to conventional radiotherapy, as it should provide strictly additive interaction without the local and systemic adverse effects inherent in treatments with radiation sensitizers \[[@B75]\]. In this respect it is very exciting to note that two farnesyltransferase inhibitors, FTI-276 and L-744,832, have recently proven to act synergistically with ionizing radiation *in vivo* for growth inhibition of xenotransplanted *H-Ras-*mutated human tumor cells, without increase in acute or long-term radiation-induced damage to healthy tissues \[[@B76]\].

Materials and methods
=====================

Reagents
--------

RPR-130401 was synthesized as described \[[@B77]\] and stored at -20°C as a 20 mM stock solution in DMSO. Prior to use, the solution was diluted first into medium containing 20% DMSO, then to the final concentration in culture medium. DMSO was kept below 0.1% so as not to alter cell growth or radiation response.

Colcemid and all products from cell culture were from Invitrogen (Cergy-Pontoise, France). BrdUrd, propidium iodide, bisbenzimide, DAPI, Giemsa stain, TRITC-phalloidin and mouse anti-α-tubulin monoclonal antibody (clone DM1A) came from Sigma-Aldrich (Saint-Quentin-Fallavier, France). Mouse monoclonal antibodies directed against lamin B was from Oncogene Research Products (San Diego, California). FITC-conjugated sheep anti-mouse IgG was from Sanofi-Synthélabo (Paris, France). Alexa^®^ 488 goat anti-mouse IgG conjugate was from Molecular Probes (Eugene, Oregon). Rat monoclonal antibody directed against BrdUrd was purchased from Harlan Sera-Lab (Loughborough, United Kingdom), and fluorescein isothiocyanate-conjugated goat anti-rat IgG (heavy chain specific) was from Southern Biotechnology Associates (Birmingham, Alabama). Human centromere probes for FISH was obtained from QBiogene (Illkirch, France). Solvents and chemicals were of the highest purity available and came from Merck Eurolab (Paris, France).

Cell culture
------------

HCT-116 human colon carcinoma (ATCC CCL-247), MiAPaCa-2 human pancreatic carcinoma (ATCC CRL-1420) and A-549 human lung carcinoma cells (ATCC CCL-185) were grown as monolayers in DMEM (HCT-116, MiAPaCa-2) or RPMI-1640 (A-549 cells) containing sodium pyruvate and Glutamax I, and supplemented with 10% foetal calf serum, 100 IU/ml penicillin, and 0.1 mg/ml streptomycin. Cells were routinely subcultured after trypsinization at a density of 6,000 cells/cm^2^ in culture flasks every 5-days and incubated at 37°C in a humidified atmosphere of 7% CO~2~ in air. Less than 9--10 passages of the same primary subculture were allowed. Prior to seeding, cells were rinsed twice with HBSS, harvested by trypsin-EDTA treatment and counted in an hemocytometer.

Survival assays
---------------

Radiation survival with or without combined drug exposure was determined by clonogenic assays. For determination of the response to radiation alone, cells from exponentially growing subcultures were seeded in 25 cm^2^ flasks at the suitable density, incubated for 3-h to allow cells to adhere and spread, and irradiated in culture medium at room temperature in an IBL-637 (^137^Cs) irradiator (CIS-Biointernational, Saclay, France) at a dose-rate of 0.92 Gy/min. All experiments were performed in triplicate or more.

Two protocols were used in single or combined treatment assays. For short lengths of drug exposure (≤ 12-h), 1,000 cells were plated in triplicate in 25 cm^2^ flasks and incubated for 3-h. Cells were then exposed to drug for 1-, 2-, 3-, 4- or 12-h, irradiated and returned to the incubator for 1-h in the presence of RPR-130401, followed by two washes with HBSS and feeding with drug-free medium. Colonies were allowed to grow for 8--11 days, then fixed with methanol, stained with Giemsa and scored. Small colonies (\< 30--50 cells) were disregarded. Results were corrected for cell multiplicity (see below).

Where the length of drug exposure was in excess of 12-h, cells were plated after treatments to avoid biases due to the formation of microcolonies. Typically, cells were plated in 25 cm^2^ flasks and exposed to drug for 1-, 2-, 3-, 4- or 5-days, and irradiated. Seeding was adjusted so as to obtain an equal number of cells at the time of irradiation, taking into consideration the cytostatic effect of the FTI and the length of drug exposure. Each flask was trypsinized immediately after irradiation, the cells were counted and 1,000 cells per flask were replated in drug-free medium for colony formation assays.

Flow cytometry and cytogenetic analysis
---------------------------------------

Cell cycle progression was monitored by dual parameter flow cytometry using a FACStar PLUS cytofluorometer (Becton Dickinson, Le Pont de Claix, France). Cells were grown for 3- to 6-days with or without RPR-130401. At that time, flasks were irradiated to 3.5 Gy (HCT-116), 5 Gy (A-549) or 5.5 Gy (MiAPaCa-2) and allowed to rest in the incubator for 24-h prior to fixation. 15-min before harvesting, cells were incubated with BrdUrd (10 μM) for pulse-labeling of S-phase cells, then collected, washed once with cold PBS and fixed in 70% ice-cold ethanol. Treatment of fixed cells for cytofluorimetric analysis, data acquisition and processing were done according to Demarcq *et al.*\[[@B78]\]. Cell cycle analysis was performed with ProCyt software (CEA-INSERM, Grenoble, France).

Alternatively, HCT-116 treated cells were incubated with 0.2 μg/ml colcemid for 1-h, washed twice with HBSS and allowed to swell for 30-min in 75 mM KCl hypotonic solution. Cells were then fixed in 3:1 v/v  acetic in ice and washed threefold in the same solvent. Fixed cells were dropped onto glass slides to spread chromosomes, and air dried. Slides were stained with Giemsa before scoring.

Immunofluorescence
------------------

For immunofluorescence characterization, cells were grown on 20 × 20 mm coverslips in medium containing 10% foetal calf serum for 3- to 6-days with or without RPR-130401. At that time, the coverslips were irradiated to 3.5 Gy (HCT-116), 5 Gy (A-549) or 5.5 Gy (MiAPaCa-2) and allowed to rest in the incubator for 24-h prior to fixation.

To visualize polymerized actin and tubulin, cells were processed according to Mies *et al.*\[[@B79]\]. Briefly, cells were fixed in 0.25% glutaraldehyde, 0.5% Triton X-100 for 1-min, followed by 10-min in freshly prepared 4% formaldehyde and extensive washing. The coverslips were then incubated (30-min, 37°C) with 0.2 μg/ml TRITC-labeled phalloidin, or with a 1:200 working dilution of monoclonal anti-α tubulin antibody followed by a 30-min incubation with a 1:1,000 dilution of FITC-conjugated sheep anti-mouse IgG at 37°C.

To visualize lamin, cells were fixed in acetone/methanol (1:1, v/v) for 20-min at -20°C, allowed to air dry, then washed 3 times with PBS and treated with 0.5% Triton X-100 for 5-min at 4°C to permeabilize cells. The coverslips were incubated (30-min, 37°C) with 5 μg/ml of monoclonal anti-lamin B antibody followed by a 30-min incubation with 1:500 Alexa^®^ 488 goat anti-mouse IgG conjugate.

To visualize nuclei, the cells were counter-stained with bisbenzimide (0.2 μg/ml) or DAPI (0.12 μg/ml). Cells were viewed on a Zeiss microscope and photographed with Ilford HP-5 film.

Western blots
-------------

For determination of lamin B cleavage, HCT-116, A-549 and MiAPaCa-2 cells were exposed for 5-days at 10 × IC~50~ each of RPR-130401. At the end of treatment, cells were harvested in PBS with 2 mM EDTA and lysed for 20-min on ice with gentle agitation in PHEM buffer (80 mM PIPES, 80 mM HEPES, 10 mM EDTA, 5 mM MgCl~2~, 1% Triton X-100, pH 7.4) supplemented with 1 mM PMSF, 10 μg/ml aprotinin and 1 μg/ml each of leupeptin and pepstatin. The insoluble fraction, containing lamin B, was recovered by centrifugation, solubilized in Laemmli buffer (3% lauryl sulfate, 10% glycerol, 5% 2-mercaptoethanol, 62.5 mM Tris-HCl, pH 6.8) and titrated.

An aliquot (20 μg total protein) of each extract was loaded onto 7.5% polyacrylamide gel, electrophoresed, and blotted onto nitrocellulose (Schleicher & Schuell, Dassel, Germany). The membrane was saturated with bovine serum albumine and incubated with a mouse monoclonal antibody directed against lamin B. Protein detection was carried out using a peroxidase-conjugated goat anti-mouse secondary antibody and an ECL kit (Amersham Pharmacia Biotech, Orsay, France). Quantification was performed by densitometry with the aid of QuantityOne^®^ software (Bio-Rad, Hercules, California).

Curve fittings and correction for cellular multiplicity
-------------------------------------------------------

Care was taken to avoid contamination of seed cell suspensions by clusters, as their presence introduces large, systematic errors in viability measurements with clonogenic assays \[[@B80]\]. For this reason, the cellular multiplicity, *i.e*., the number of cells per potential colony-forming unit was carefully checked by microscope observation at the time of irradiation throughout the whole study. When the average multiplicity was less than 1.1 (for 1- and 2-h drug exposure), no correction was applied. Corrections were necessary for longer lengths of drug exposure (≥ 3-h), because viable colony-forming units contained a substantial amount of doublets and quadruplets at these times. In that case, the equation:

![](1471-2210-2-2-i1.gif)

(where S~exp~ is the experimental cell survival determined from bulk colony scoring and a~n~ the fraction of colony-forming units with n viable cells) was used in order to calculate the single-cell surviving fraction (SCSF).

Radiation survival curves with or without co-treatment with RPR-130401 were drawn for best fit to a linear-quadratic equation, as usual \[[@B81]\]:

![](1471-2210-2-2-i2.gif)

where S~0~ is the clonogenic efficiency, S the residual survival, D the radiation dose, and α and β numerical parameters characterizing the radiosensitivity of the cell line.

Equation (1) was solved with the aid of a home-made program. Least-squares regressions were performed on a Macintosh microcomputer using Kaleidagraph software (Synergy Software, Reading, Pennsylvania).

List of abbreviations
=====================

FTase, farnesyltransferase;

FPP, farnesyl pyrophosphate;

FTI, farnesyltransferase inhibitor;

GGTase, geranylgeranyl transferase; HBSS, Hank\'s balanced salt solution;

BrdUrd, 5-Bromo-2\'-deoxyuridine;

PMSF, phenylmethylsulfonyl fluoride;

FISH, Fluorescence In Situ Hybridation; IC~50~, amount of drug that reduces the growth of treated cells to 50% of that of controls.

Acknowledgments
===============

The authors wish to thank Drs. Patrick Mailliet and Jean-François Riou (Aventis Pharma) for the generous gift of RPR-130401. Grafetul thanks are also due to Hervé Tourbez for creating the program used for the correction of cell multiplicity and to Dany Rouillard for flow cytometric analysis. This work was supported by grants from the Association pour la Recherche sur le Cancer (ARC-9746) and the Institut Curie (Radiobiology and Genotoxicology program), and by financial aid from the Institut National de la Santé et de la Recherche Médicale.