The principles and methods of cell sychronization in cancer chemotherapy

The principles and methods of cell sychronization in cancer chemotherapy

Biochimica et Biophysica Acta, 458 (1976) 243-282 © Elsevier Scientific Publishing C o m p a n y , A m s t e r d a m - Printed in The Netherlands BBA ...

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Biochimica et Biophysica Acta, 458 (1976) 243-282 © Elsevier Scientific Publishing C o m p a n y , A m s t e r d a m - Printed in The Netherlands BBA 87027

THE

PRINCIPLES

CANCER

AND

METHODS

OF

CELL

SYNCHRONIZATION

IN

CHEMOTHERAPY

CLAUDIO NICOLINI

Division of Biophysics, Department of Biophysics and Physiology and Department of Pathology, Temple University Health Science Center Philadelphia, Pa. 19140 (U.S.A.) (Received January 14th, 1976)

CONTENTS 1.

Introduction

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II.

The rationale for cell synchronization in vivo

II1.

Index of synchrony

IV.

Methods of cell synchronization in vivo . . A. N o r m a l tissues . . . . . . . . . . . . B. T u m o r s . . . . . . . . . . . . . . . C. Metastases . . . . . . . . . . . . . .

V.

Characterization of intact cell and cell cycle phases A. A u t o r a d i o g r a p h y . . . . . . . . . . . . . B. Laser flow microfluorimetry . . . . . . . . C. Geometric and densitometric texture analysis

. . . .

VI.

Cell cycle-specific agents A. Radiations . . . . B. Antimetabolites . . C. Antimitotic drugs . D. Alkylating agents . E. Antibiotics . . . .

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VII.

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247 247 254 256

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257 257 257 261

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262 263 264 265 266 266

Mathematical modeling in cell kinetics . . . . . . . . . . . . . . . . . . . . . A. G r o w t h fraction and cell loss . . . . . . . . . . . . . . . . . . . . . . .

267 268

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VIII. C o m p u t e r optimization of drug schedule for cell synchrony in animal and for chemotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . B. Control system analysis and various algorithms . . . . . . . . . . . . .

cancer . . . . . .

269 269 275

IX.

Pharmaco-enzyme kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . A. Ara-C metabolism . . . . . . . . . . . . . . . . . . . . . . . . . . . B. D r u g combination . . . . . . . . . . . . . . . . . . . . . . . . . . .

276 276 277

X.

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

277

Acknowledgements References

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Abbreviations: Ara-A, 1-flD-arabinofuranosyladenine; Ara-C, 1-flD-arabinofuranosylcytosine; F d U r d , fluorodeoxyuridine; I d U r d , iododeoxyuridine; PLM, percentage labelled mitoses.

244 1. 1NTRODUCYION In the broadest contest, cancer research aims to discover: (1) the cause of cancer; (2) means of preventing cancer; and (3) means for successful treatment of cancer (in this sense, ~cancer" is intended as several kinds of diseases). Over the past years, scientists from several diciptines (physics, chemistry, mathematics and biology) and physicians have worked together in a theoretical-pragmatic marriage (which frequently ends up in divorce based on incompatibility) for developing chemotherapy as a utile means (or adjunct) for the cure or long term control of disseminated cancer. The first phase has been characterized by the production of a variety of drugs with different mechanism of action and quite different degrees of effectiveness against cancer. A second phase has been characterized by an attempt to analyze the kinetics of cell proliferation: (1) to learn about the normal process of cell division, growth, and growth control; (2) to understand the dynamics of disease process: and (3) to use kinetics for therapetic purpose [1,2,3]. In this respect the finding of a methodology for synchronizing cells in the intact animal could be of considerable interest in planning cancer chemotherapy. Up to now, synchronization has been achieved in cells growing in culture [6,4,5], but large difficulties are encountered in synchronizing cell population in vivo. The methods that have been thus far developed for synchronizing cells in culture can be divided in three main groups: (1) selective harvesting of mitotic cells; (2) selective blocking; and (3) selective killing. The physical method of selective harvesting is by far the most physiological and efficient, but it appears quite obvious that this technique cannot be used in vivo. Selective blocking and selective killing both rely on chemical methods. As pointed out by Nias and Fox [5] in their review of the various chemical methods for synchronization in vivo, "in each case only a cohort of the population is triggered to proliferate and the degree of synchrony is relatively low in proportion to the total population". This review will deal with several chemical methods which have been described recently (and in which varying degrees of synchrony in vivo have been achieved). Several factors are determinant in establishing the degree of synchronization, by defining the point of arrest in the cell cycle, and by determining the speed of release of the block. Recently Verbin and Farber [7] discussed in their review the difficulty encountered in trying to synchronize cells in vivo, and showed how only a partial synchronization was achieved in intestinal crypt cells by a combined administration of Ara-C and colcemide. The same authors, however, indicate that "this synchronization is dissipated once the cells originally arrested in mitosis pass into subsequent stages of the cell cycle". More recently [8,9] a good synchronization in the lining epithelium of the intestinal tract was maintained up to a second wave of labeled cells by proper combination of Ara-A and Ara-C or by fasting and Ara-C (or FdUrd). However, despite all recent and previous efforts, a reproducible true synchronization of cells in the intact animal has not yet been reported, perhaps with the only exception of the basal cells of the esophagus [8,9].

245 It must be stressed that an idealized synchronized cell population, to be really utilized in an efficient cancer chemotherapy, should show no perturbation in any of the metabolic pathways of the cell, and the short term and long term effects of each chemical in cell metabolism should be minimized and quantitized. This will require that the old marriage between basic science and empiric trial be rephrased in new terms. Specifically, cell characterization during the cycle and during various extents of proliferation, the molecular and cellular mechanism of drug action and interaction in the intact animal, and the mathematically aided optimization procedure for cell synchrony and chemotherapy treatment should be further exploited, not as independent channels, but in combination and coordination with parallel clinical efforts made by physicians. Several excellent reviews [3,10] have been already recently published on the clinical aspects of cancer chemotherapy in solid tumor and leukemia. This review will particularly stress the new development of our knowledge of the molecular and cellular mechanisms of various drugs frequently utilized in cancer chemotherapy, of the new technique for physical, chemical characterization of intact cells, and on the consequent fundamental principles (based both on theoretical and experimental grounds) of cell synchronization in vivo.

!I. THE RATIONALE FOR CELL SYNCHRONIZATION IN VIVO Surgery or ionizing radiation, or both, have long been, and still are, the methods of choice for treatment of cancer that is not widespread at the time of diagnosis. Localized cancer, even of large size, slowly growing tumor cell masses, are often curable by these procedures. However, surgery and irradiation fail when viable cancer cells are not extirpated or are greatly exposed, for instance, when metastases did already occur. It is well known that the effective antimetabolites are all antagonistic of enzymes involved in DNA replication at various levels of its metabolic pathway, as specified later on. Furthermore, the alkylating agents and various DNA binders react or bind to D N A regardless of cycle phase during exposure; however, even they apparently kill only those neoplastic or normal cells that attempt replication prior to repair [3]. In general, we may say that most drugs employed are cell cycle specific, i.e., it will be possible to kill tumor or normal cells, with a given drug, in the phase of the cycle in which they are most sensitive. Making use of cell cycle differences, one could markedly increase the effectiveness of the chemotherapeutic approach by a discriminate killing of tumor cells, without adversely affecting normal cells. For instance, the G2 phase of the lining epithelium of the small intestine lasts only one hour, while the G2 phase of most tumors lasts longer, between 4-6 h [11]. Thus, if one could synchronize both normal and tumor cells at the S-G2 boundary, within 2 h, all normal cells of the crypt of the small intestine will undergo mitosis, whereas few tumor cells will have reached metaphase. If a specific mitotic poison, for instance,

246 vincristine, is now administered between 2 and 6 h, tumor cells can be selectively killed in mitosis. A similar program can be applied to the chemotherapy of several cancers (especially their metastases) in which tumor cells could be selectively killed, while rapidly proliferating normal cells (small intestine, bone marrow) are spared. Alternatively, one could instead attempt to synchronize the tumor (either the primary one or its metastasis), regardless of the effect on normal populations, such to enhance the killing effect on the tumor cells themselves. Both approaches require the achievement of a true cell synchronization in the intact animal (and in man), maintained for two or more cell cycles of the given tumor or normal tissue, with a minimum alteration in the metabolic pathways of the normal cells. We must, however, emphasize, at this point, that the need for synchronizing cells in vivo is also given by other considerations, specifically: (1) study of the molecular mechanisms involved in the control of DNA synthesis and the cell division; correlation of the biochemical and biophysical events occuring in G1, S, G2, and mitosis under the environmental conditions in which a given population of cells actually exist. (2) Study of the mechanism of carcinogenesis under environmental conditions. It has been recently reported that the susceptibility of cells to chemical carcinogens (as well as to oncongenic viruses) depends on the phase of the cell cycle in which they are at the time the carcinogen comes in contact.

Ill. INDEX OF SYNCHRONY Let us consider a parasynchronous culture in which there are N cells at time T. We may then describe [12] the growth of the culture without referring to the actual size of the cell population by defining a normalized rate of cell division, R where R = d N / d T / N where R is the fractional increase in cell number per unit time. The integral of R with a respect to time in an arbitrary time interval between TI and 7"2, namely, the area under R versus T plot between T1 and T2, is f R d T = f ( d N / N d T ) d T = f ( d N / N ) = In ( N J N , )

where NI and N2 are respectively the number of cells of time T1 and T2 and in represents the natural logarithm. It then follows that the area under R, during any period of time in which any culture doubles its number of cells, is ln2. This result is obviously independent of the specific growth pattern of the culture [12], which can then make use of this property of the R dependence on time T in defining the degree of synchronization of the cell culture. If we now define asynchronous culture as one in which the rate of cell division R is a constant, which is independent of time, we then have Ra = (ln2)/Tg where T, is generation doubling time of the culture. We are now in position to provide a quantitive definition of the index of synchronization of the cell population, in accordance with Engelberg [12]

247

IS .

Overlap area . . . . x 100 Total area under R between T1 and Ta

Under this definition of synchronization [12] any growth pattern which differs from the pattern obtained in logarithmic growth indicates some degree of synchronization. Specifically when the culture is completely asynchronous, R coincides with R a. Thus, there is no overlap and I S ~ 0 %. When the culture is completely synchronized, the R essentially falls into the overlap region, hence, I S -- 100 ~/o. The most commonly used definition of degree of synchronization is empirically given by I S = LIm~x/GF where Llmax is the maximum labeling index and G F is the growth fraction of the given population. As an indication of the degree of synchrony, some authors used the method of Sinclair and Morton [13], while others [14] utilized the difference between the peak and the subsequent minimum value of the labeling index curve. In our own opinion, a more flexible and comprehensive definition of index of synchrony can be obtained by comparing the percentage of labeled cells, obtained experimentally during the first cycle after the block release, with a percentage of cells in the S phase as expected by computer simulation, with the hypothesis of 100~/o synchrony, i.e., all cells are released as a step function, and by knowing the means and standard deviations of each phase duration for the given population [15].

IV. METHODS OF CELL SYNCHRONIZATION IN VIVO I VA. N o r m a l tissues

While numerous methods are available for synchronizing cell in culture, few methods have been described for synchronizing cells in vivo i.e., in experimental animals. One reason for the difficulty encountered in vivo can be attributed, to a large extent, to the inherent diversity in the proliferative capacity of mammalian cells. In fact, all tissues of the body can be divided at least in three major categories, with respect to their growth kinetics: (a) permanent non-proliferating cells like those that have lost the ability to proliferate under any circumstance, i.e., neurons; (b) resting "GO" cells, which can be brought back into the cycle by an appropriate stimulus; (c) cells programmed for continuous replication. Two typical examples of the "GO resting" cell population are represented by: (1) the population of the hepatocytes which are stimulated to enter the cell cycle following partial hepatectomy. Between 22 and 24 h after surgery 55-60 ~o of the liver cells are stimulated to engage in DNA synthesis [16] while the peak of mitotic activity, approximately 4.0 percent, is reached 28 h post-operation [17]; (2) in the mouse salivary gland, cells can be stimulated to proliferate by isoproterenol, up to 80 ~ [18], or up to 50 ~o in the basal layer of the epidermis after wounding. However, as pointed out by Nias and Fox [6], "in each case, only a cohort of the population is triggered to proliferate and the degree of synchrony is relatively low in proportion to total population". In contrast, there are a variety of tissues in

248 the body that demonstrate a high and sustained rate of replication, like the hematopoietic and lymphoid elements, as well as the intestinal crypts. This feature, together with the accessability, quite naturally have made them attractive model systems in which to test the variety of drugs and manipulations which might induce a state of synchronous division. In vivo. Partial synchronization by X-ray exposure is a well known phenomenon [19,20,21]. The induction of self-synchronization in intact animals through the introduction of chemicals has, for the most part, been hindered by several factors, like the ability to collect a sufficiently large number of cells in any given phase of the cell cycle, and the induction of the irreversible damage in those cells exposed to the inhibitor. Gillette, and co-workers [22], studied the synchronization of epithelial cells of mouse small intestine after intraperitoneal application of hydroxyurea. The authors [22] observed two waves of cells in S phase at eight hours interval, each corresponding to about 50 ~o~ of the total cell number. Other investigators [23] have demonstrated that the exposure of bone marrow cells to hydroxyurea leads to an accumulation of up to 52~/o of colony forming unit in S phase, 12 h after the administration of a 0.5 milligram per gram dose of the inhibitor. A somewhat higher concentration, 57 ~ of DNA synthesizing colony forming unit, was noted at 16 h, in animals treated with 2.5 mg/g of hydroxyurea. In control mice 20~/o of colony forming units were in the S phase. In a subsequent study [24], Dethlefsen and Riley measured the radio-activity in mouse duodenal crypts following the administration of [125I]IdUrd at various times after a single injection of 3 mg/g body weight of hydroxyurea. Their results showed that there was no incorporation of the isotope until the sixth hour. However, by 8 h the radio-activity increased sharply to a peak of 55 ~o of control value. This value, when compared to a mean labeling index of 0.26 in control animals, reflected a two-fold increase in the number of cells engaged in the DNA synthesis. The same two-fold increase has been obtained in our laboratory [8,9] with the same dose of hydroxyurea of the crypt of the small intestine, with the exception of a quite lower release of the chemical block. Partial synchronization has also been achieved in the intestinal crypt epithilal ceils via the administration of Ara-C followed, at an appropriate time, by the injection of colcemide [7]. The same authors [7] however, indicate "that this synchronization is dissipated when cells originally arrested in mitosis passed into subsequent stages of the cell cycle". Recently most of the known antimetabolites were subjected to screening in our laboratory in order to determine their effectiveness with respect to producing synchrony of the proliferating cell population of the large and small bowels (crypts) and the esophagus (basal cells) of mice [8,9]. The most surprising result was the effect of fasting and refeeding on the cell populations described above. The fasting of mice for 54 h causes by itself some degree of synchronization by blocking the crypt cells of the small intestine at the G1-S interphase and the basal cells of the esophagus at early G1 (see Fig. 1). The synchronizing effect of fasting is readily apparent when the data from the fasted mice are compared with similar data from non-fasted mice. The differential

249 9C

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Fig. 1. Fasting: The mice were fasted for 54 h; then, every 4 h, 0.25 #Ci/g body weight of [3H]thymidine was injected subcutaneously into the same mice which were then sequentially killed (3 mice every 2 h). The figure shows the labeling index as a function of time after feeding ( O - - © ) , in the crypt cells of the small intestine and large intestine, and in the basal cells of the esophagus. As control, the same progressive labeling index carried out irt mice normally fed ( 1 - - - 1), is also shown. The growth fractions were 0.9 in the crypt cells of the small intestine, 0.68 in the crypt cells of the large intestine, and 0.70 in the basal cells of the esophagus [8,9].

response of the three tissues to the same caloric deficiency appears evident by analyzing the labeling index o f the esophagus (see Fig. 2) and the small intestine (Fig. 3), on the same mice, seven hours after refeeding and two successive injections o f 0.25 #Ci/g b o d y weight o f [3H]thymidine. The effect o f fasting on the large intestine seems to be compatible with the existence o f at least two distinct populations in the crypt o f the large intestine as suggested by P L M analysis [8,9] and by m o r p h o logical evidence [25]. This speculative conclusion seems to be compatible with the low degree of synchrony achieved under various chemical treatments o f the large intestine crypt cells o f mice [8,9]. Independently, other investigators [26] have demonstrated an increase in total cell cycle time during starvation, and a subsequent decrease after refeeding, o f the small bowel mucosa o f the rat. The labeling index distribution curve at 96 h after starvation of the rat shows a decrease in the m a x i m u m labeling index and immediate increase after refeeding. The same authors [26] coneluded that "a block in the flow of cells f r o m G1 to S is possible" at the proper calori¢

250

Fig. 2. Autoradiographic section of esophagus cells of a fasted mouse [8,9], 7 h after refeeding and two successive injections of 0.25/~Ci/g body weight of 3H]thymidine, (see Fig. 1, middle panel). No label appears evident even in the basal cells.

deficiency, in complete agreement with our findings on the crypt of the small intestine of mice [8,9]. The degree of synchrony has been shown in our laboratory to be substantially enhanced by a combination of fasting with the proper inhibitor of D N A systhesis such as Ara-C or FdUrd. Fig. 4 shows the labeling index versus time, for the basal cells of the esophagus, after feeding, when mice were fasted in the metabolic

Fig. 3. Autoradiographic section of small intestinal crypt cells of the same fasted mouse as Fig. 2, 7 h after refeeding and two successive injections of 0.25 pCi/g body weight of [3H]thymidine (see Fig. 1, top panel). More than 92 ~ of the crypt cells are labeled, i.e. have more than 6 grains.

251

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Fig. 4. Ara-C with fasting: The mice were fasted in metabolic cages for 54 h, thert three successive injections of Ara-C were given at T~ = 3.5, 7'2 ~ 7.5 and 7"3 = 11,5 h after the beginning of feeding. Each injection (D) consisted of 80 mg/kg weight of Ara-C. The labeling index and mitotic rate are plotted as functions of time after feeding in the basal cells of the esophagus (upper panel). (Middle panel): Mice were fasted for 54 h, then three successive injections were given at T1 = 8 h, 7"2 = 12 h and T3 = 16 h after feeding. Each injection consisted of 250 mg/kg body weight (3D) of Ara-C. The labeling index as function of time is shown, in the basal cells of the esophagus, calculated over three mice per point [8,9]. (Lower panel): As middle, but in the crypt cells of the large intestine. The arrow indicates in all three panels the labeling index in the mice normally fed, and untreated, for the given tissue [8,9].

cages for 54 h, then three successive injections o f A r a - C were given at T1 ---- 3.5 h, T2 = 7.5 h a n d Ta = l l.5 h after the beginning o f feeding. Each injection (D) consisted o f 80 mg o f A r a - C / k g b o d y weight. This dosage a n d t i m i n g o f injection causes necrosis in the c r y p t cells o f the small intestine, little effect o n the c r y p t cells o f the large intestine, a n d an excellent degree o f s y n c h r o n y in the b a s a l cells o f the lining epithelium o f the e s o p h a g u s (Fig. 4). The synchronizing effect a p p e a r s striking if we observe the a u t o r a d i o g r a p h i c sections o f the e s o p h a g u s in the 54 h fasted mice where the labeling index goes f r o m 0 ~ at 1 4 h after feeding a n d A r a - C t r e a t m e n t (Fig. 5), to a b o u t 70 % 4 h later (Fig. 6): the average labeling index in the n o r m a l , fed, u n t r e a t e d mice is ~ 6 ~ . The high yield o f necrosis, with l y m p h o c y t e infiltration, o b t a i n e d in the c r y p t o f the small intestine, when the mice are fasted a n d then the first injection o f A r a - C is given 3.5 h after feeding, is c o m p a t i b l e with an S-phase wave after 54 h fasting. O n the c o n t r a r y , a

252

Fig. 5. Autoradiographic section of the esophagus of a 54 h fasted mouse, 14 h after refeeding and Ara-C treatment (as described in Fig. 4). Even the basal section of the esophagus shows no labelled cells, i.e., no cells with 6 or more grains.

high degree of synchrony is obtained in the same crypts of the small intestine if the same injection is given before the mice are fed again after the 54 h fasting [8,9]. This high degree of synchrony obtained on Fels A mice was reproduced on the basal cells of the esophagus, by the same treatment of the black C57 mice bearing a melanoma B16 tumor [27]: instead blood infiltration appears in the small intestine, after the same duration of fasting, of these mice [27]. Evidently, the same concentration of a given drug (e.g., FdUrd or Ara-C) can be lethal, or of varying degree of effectiveness as an inhibitory agent, in accordance with the phase of the cell cycle in which the cell is found. Timing and proper manipulation of conditions, such as fasting prove to be extremely critical. For this reason the utilization of a protocol involving continuous feedback between experiment and computer simulation ([28], see also page 269) could become useful if cell synchrony in vivo can be further improved, and maintained for several waves, with the minimum alteration of the metabolic pathways of the given cell. The use of the proper drug combination could be also~ profitably exploited. Fig. 7 shows the results obtained by the combined utilization of Ara-C and Ara-A, which were suggested to be mildly synergistic by a mathematical model, which simulates the effect of a combination of an inhibitor of D N A biosynthesis on cells in vivo, by an open steady state system regulated by a network of feedback controls [29,30,15]. Two waves of labeled cells are evident in the crypt cells of the small

253

Fig. 6. Autoradiographic section of the esophagus of a fasted mouse, 18 h after refe~ding and the same Ara-C treatment (as described in Figs. 4 and 5). About 70% of the basal cells of the esophagus are labeled, i.e., have 6 or more grains per cell.

intestine, indicating a high degree of synchronization, maintained even after one cell cycle. The index of synchrony obtained from the basal cells of the esophagus is also reasonable, considering that the block has been extended for only 20 h, i.e. about half

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Fig. 7. Ara-A with Ara-C: A combination of Ara-A and Ara-C is given successively by two subcutaneous injections, the first consisting of 300 mg/kg of Ara-A combined with 130 mg/kg body weight of Ara-C, the second one, given 15 h later, consisting of 100 mg/kg of Ara-A combined with 130 mg/kg of Ara-C. The labeling index is shown as function of time after the last injection, for the crypt cells of the small intestine and for the basal cells of the esophagus. In a separate experiment, a single injection of vincristine (V) (3 mg/kg) was given subcutaneously, 17 h after the last injection of the Ara-A and Ara-C combination [8,9]. The dotted line in the panel represents the mitotic rate of the basal cells of the esophagus after the administration of vincristine. This data could not be obtained for the small intestinal crypts because most of the cells were necrotic [8,9]. The arrows indicate the values of the parameters which are usually observed in untreated populations [8,9].

254 of the esophagus cell cycle. The results obtained with the large intestine were still modest [8,9]. It must be pointed out, however, that several necrotic cells are found in the crypt of the small intestine during the first 6 h after the last injection of the drug combination. Fig. 7 shows also the effect of vincristine, a specific antimitotic poison, given 17 h after the last injection of drug combination. As a consequence of this mitotic poison given at the proper time, a large number of mitotic cells are found in the crypt cells of the small intestine [8,9]. IVB. Tumor tissues

For several years, human tumor therapy has tried to use the differential sensitivity of the phase of a cycle for better regimens [31,32,33]. For these new methods of therapy a synchrony passage of tumor cells through the cycle is a prerequisitie. Promising results on solid rat carcinoma has been obtained by Rajewsky [14] by a temporary inhibition of DNA synthesis by hydroxyurea. As an indication of the degree of synchrony achieved in this system, Rajewsky used the difference between the peak and the subsequent minimum value of the labeling index curve and obtained for the DICR-MIR rat carcinoma a value of 5 0 ~ . In a more recent investigation G6hde [34] achieved a reversible accumulation of about 70 ~,/, of Ehrilich Ascites cells in the G2 phase by irradiation of 300 rads of neutrons. Radiation-induced partial synchronization was also shown in the Walker carcinoma in vivo by Linden et al. [35]. By utilizing pulse-cytophotometry they have shown that irradiation of the Walker carcinoma with a dose of 900 rads caused a reversible accumulation of about 50~o of cells in the G2 phase. These results are consistent with those of Raju, et al. [36] who irradiated K H T tumor cells in mice, and with those of Frindel et al. [37], in Ascites tumor cells. These last authors [37] reported that after a continued irradiation of 40 h, the total dose being 2000 rads of CO-y-rays, 61 ~ of the cells were in G2-phase versus 5 O//oin the controls. It should be pointed out that the cells accumulating in G2 after X-ray or neutron irradiation will contain a fraction of ~'doomed" cells having a limited proliferation capacity; "'doomed cells" [35] which are incapable of forming viable clones may well continue cell division for 2 or 3 cycles. These cells, as reported by the same authors [35], are included in the analysis. Thus, for therapeutic application, pulse-cytophotometric study should be supported by the determination of clonogenecity of the tumor cell. An apparent increase of synchrony has also been accomplished in murine melanoma, as well as ehrlich ascites tumors, by utilization of Ara-C [38]. The best result, with respect to synchronization, obtained by the authors [39] in their transplantable B-16 mouse melanoma was achieved in animals receiving several injections of Ara-C, each 12.5 mg/kg body weight, spaced at 2 h intervals. This synchronization index, as determined by the method of Sinclair and Morton [13] was 40.7, with a peak of labeling index only little above normal control value. The studies with human and experimental cancers are interesting, but difficult to interpret. It is now widely appreciated that many solid neoplasms have only a minority of cells that are proliferating and that it is possible to change the growth

255 fraction by e x p e r i m e n t a l m a n i p u l a t i o n . Therefore, an effect o f any p r o p o s e d sync h r o n i z a t i o n regimen on the triggering o f n o n - p r o l i f e r a t i n g cells into the cell cycle m u s t be ruled o u t before a b o n e fide increase in the degree o f s y n c h r o n i z a t i o n can be c o n s i d e r e d as possible. A n internal r e p o r t to the A m e r i c a n Joint C o m m i t t e e o f the T a s k F o r c e on Colon, Rectum, a n d A n u s (January, 1975) shows the survival curve based on past surgical e v a l u a t i o n for the cancer o f anus (Fig. 8). F r o m these d a t a it a p p e a r s evident

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Fig. 8. Survival curve of patients operated surgically for cancer of the anus, as reported by the American Joint Committee of the Task force on Colon, Rectum and Anus (January 1975). The percentage of men surviving post-surgery is plotted versus the number of years after surgery for different groups of diagnosis: Carcinoma in situ, no distant metastasis ( O - - - O ) ; tumor penetration confined to mucosa, no distant metastasis ( © - - © ) ; tumor infiltration of adjacent organs and musculature, no evidence of distant metastasis (& ---A ); tumor penetration, regional and intra-pelvic lymph node involvement, and distant metastasis ( , - - I ) .

that the p r i m a r y t u m o r , when localized, can be easily r e m o v e d by surgery (or alternatively by irradiation), a n d that the m a j o r cause o f d e a t h are the metastases, either detectable o r undetectable at the time o f the early diagnosis. U n d e r these circumstances the e m p h a s i s on cancer c h e m o t h e r a p y , a n d the achievement o f cell s y n c h r o n y in this respect, should b e a r on the metastases instead o f the p r i m a r y t u m o r , because o f their quite smaller size, high g r o w t h fraction a n d high proliferating rate. Consequently, in the selection o f an a n i m a l t u m o r system as a screening m o d e l

256 for potential anti-cancer agent, heavy emphasis should be given to the capability of inducing distant matastasis. Two more pertinent questions must also obviously be asked [40]: (1) is the model predictive for some part of the human problem? (2) can the model be manipulated relatively easily to provide reliable, reproducible, quantitive data? Among the various screening tumor models available, we think that Melanoma B-16 more adequately represents the need of human cancer chemotherapy, because of (1) the capability to metastasize, not only in the lungs but also in other organs such as spleen, kidney, and liver (like many tumors of man); (2) the closest correspondence to the spectrum of solid tumors in man, where in fact the greatest part of cancer chemotherapy lies, considering its relatively long volume doubling time, the moderately small growth fraction and some morphological similarity [27,40,40a]. On the other hand, for what concerns human leukemia, the LI210 ascites (Ll21 leukemia in BDFI mice) has proved to be quite a good screening model for cancer chemotherapy both from morphological and behavioral standpoints [41]. IVC. Metastases

At present the major advantage of chemotherapy, alone or in combination with other modalities, stems from its capacity to affect widely metastatic diseases of undeterminable extents with varying degrees of selectivity. This selectivity often appears to depend on the proliferative states of the neoplastic cells (versus certain host cells) and it is influenced by dose levels and intervals between doses [42]. Considering that, as previously shown, it is very unlikely to obtain simultaneously, by the same treatment, a high degree of synchrony in different tissues (either normal or tumor), it will be highly desirable to achieve a cell synchrony in the metastatic population such as to enhance the killing or, alternatively, to synchronize the fast proliferating tissue, like bone marrow and small intestine, to a degree such that the exposure of the metastatic tumor to a given drug or irradiation (cell cycle specific) occurs only when the very fast proliferating cell populations are out of the sensitive phase. For this reason we are presently conducting experiments on C57 black mice, carrying a B-16 Melanoma capable of inducing metastases as early as 7 or 8 days after the primary tumor induction in the foot pad. Preliminary data seems to indicate a correlation between the size of the occurring metastases and the cell cycle generation times [27]. These experiments, aimed at a specific killing of the metastases induced by the primary tumor (Melanona B-16), are at a very preliminary stage. To our knowledge no experiment has been yet carried out to achieve synchrony in the metastases; only few experiments [43], have been carried out to characterize the effect of surgery on the kinetics of the distant metastases. Presently, because of the enormous amount of time required to reduce the autoradiographic data and the empirical nature of most experiments, no "reproducible", generalizable and positive results on "effective" selective killing of cancer cells, while sparing normal tissues, are available. It is then evident that there is a need for

257 acquiring new cell observables, with higher speed and accuracy, and also for a quantitative evaluation of drug action and interaction in vivo.

v. CHARACTERIZATION OF INTACT CELL AND CELL CYCLE PHASES The concept of the discrete phases, through which the cells proceed stochastically with certain log-normal (or normal) distributions, beside being supported originally by PLM analysis [44,45] is supported by physical and chemical evidence obtained by utilizing the most various and sophisticated techniques [46].

VA. Autoradiography The method of percentage labeled mitosis (PLM) has been up to now the cornerstone of any kinetic analysis. The PLM method is cumbersome, biased toward short cycle, occasionally ambiguous, and prohibitive in most clinical situations; but it still is the one most common method to give the transit time and coefficient of variation of transit time for all four phases in the cell cycle. The cell cycle includes in fact a series of metabolic events which progress through four distinct phases, operationally defined as G1, S, G2, and M. Since the mitotic phase is the only one visually distinguishable in the cycle, until recently most of our knowledge about the cycle was obtained by indirect means such as autoradiography. Many of the approaches to extract parameters by hand from PLM curves can suffer from serious drawbacks, particularly the general one, that the PLM curves are seldom as simple as they seem. Several examples have been indicated in the literature of the potential misleading character of PLM curves [1,47,48]. The pitfalls of autoradiography and the impossibility of equating grain counts over cells labeled with [aH]thymidine with rate of DNA synthesis have been extensively reviewed in a separate article [46]. Many biologists seem to have difficulty accepting the concept that the grain count after the proper background subtraction measures only [3H]thymidine incorporation into DNA, in the most ideal situation. To determine the rate of DNA synthesis, one needs to know the specific activity of the precursors pool, the size of the endogenous thymidine pool, activity of thymidine kinase, the route of injection, (when an animal is used), the activity of catabolic enzymes, the competition from other cell populations and activities of other synthetic pathways. Regardless of all these inconveniences, autoradiographic studies may be of practical usefulness in clinical areas [48a]. VB. Laser flow microfluorimetry The recent introduction of laser flow microfluorimetry (more frequently called as pulse-cytophotometry) considerably speeds the determination of cell cycle parameters, representing a strong improvement over autoradiography [49,50]. Various configurations of this instrument, mainly if on line with a digital computer, like the PDP-I 1/40, will allow us to automatically evaluate the fluorescence and size of each cell under study. The cells in suspension are transported through the beam of a high

258 power laser. Optical interactions, which include scatter a n d fluorescence, can be simultaneously acquired in separate electronic channels a n d plotted as a two d i m e n sion scatter diagram. Use o f a pulse-height analyser permits construction o f a histog r a m o f any one p a r a m e t e r and the configuration with a digital c o m p u t e r permits

GO GI

W I - 3 8 UNST I MULATF~)

W I - 3 8 STIMULATED 30 MI NUTF~

W I - 3 8 STIMULATED 60 r',,llNUTES

Fig. 9. G0-GI transition in vitro by laser flow microfluorimetry. The frequency distributions of fluorescence intensity per cell, taken directly from the cathode ray tube, are shown for quiescent (GO) Wl-38 human diploid fibroblasts 0.5 and 1 h after simulation to proliferate (G1) by addition of 10% fresh calf serum [60,61].

259 recording of simultaneously digitized events on magnetic media for subsequent analysis. The ability of the pulse-cytophotometer to sort cells according to given criteria enables fractionation of cell populations which can then be further analysed by this instrument and/or used for the preparation of samples for morphological examination by means of shape analysis and densitometric texture analysis, as described later on. Until recently the DNA content distribution observed by pulsecytophotometry yields considerable overlap between the various phases. The resulting cell kinetic parameters are then heavily model-dependent [50,5t,52]. No identification of GO cells and no objective classification of the component of each phase (G2 and G1 are still treated as "black boxes") are possible by the simple measurements of DNA content. Differences in the chromosome cycle, which are visualized by light microscopy only during mitosis, are resolved during interphase and also during the transition G0-G1, as well as by various physical-chemical techniques [53-57]. A recent review [58] indicates that significant correlation exists between the structure of chromatin and extent of cell proliferation (aging, serum stimulation, virus transformations, cell cycle phases, etc.). Chromatin of course refers to the diffuse interphase form of chromosomes isolated from eukaryotic cells [59], and the question remains open as to whether observed chromatin changes are reflecting the intact cell. A new method has been recently introduced [60] for the physical-chemical characterization of the intact cell, by obtaining distribution of fluorescence intensity per cell as function of ethidum bromide concentration. By progressively increasing the amount of ethidium bromide added to the suspension of living cells, it is possible to discriminate between the various binding processes occurring in the intact cell (primary and secondary, with DNA and with RNA). Fig. 9 shows how it is possible to distinguish between GO and G1 phases by our method [61]: WI-38 cells, seven days after plating in Falcon flasks containing 100 ml of Basal Medium Eagle, were either left untouched or were stimulated to proliferate by addition of 10~o fetal calf serum. The medium was then discarded and the cells were removed by means of a rubber policeman and then immediately suspended in 10 ml. Hanks balanced solution. The three distributions shown in Fig. 10 were taken directly from the face of the pulse-height analyser cathode ray tube; they show the frequency of distribution of fluorescence intensity per cell at fixed ratio R -- 0.75 (/~M EB/#M DNA). The frequency distribution of light scattering for the same three cell populations are indistinguishable [61]. These results indicate that resting GO and proliferating G1 phase, which do not differ in DNA content, are drastically different (maybe due to alteration of chromatin conformation and RNA contribution) as indicated by the quantum jump in the fluorescence intensity after serum stimulation of WI-38 human diploid fibroblasts. Analagous results [63] in terms of characterization of G0-G1 transition in intact cells were found recently by laser flow microfluorimetry. The authors, studying acridine orange-stained lymphocytes stimulated to proliferate by phytohemagglutinin detected, after stimulation, an increase in acridine orange binding sites with DNA

260

Fig. 10. Video display of HeLa Feulgen stained cell image [70], projected from the microscope into the face plate of a television scanner [66,67]. The white portions of each cell indicate the picture points of the chromatin with absorbance greater than the given absorbance threshold: respectively 0.04 (upper left), 0.12 (upper right), 0.24 (lower left) and 0.40 (lower right).

and in the amount of double-stranded R N A [62]. These results [61,62] obtained in vitro, need, however, to be confirmed in vivo, i.e., in normal or tumor cell suspensions extracted from animals. The recent availability of suspensions of intact and viable intestinal cells from rats, specifically of the crypts of the small intestine [63], or of pure viable parenchymal cells from rat m a m m a r y glands [64], may offer the opportunity for substantial improvement in cell characterization, by laser flow microftuorimetry. However, in our and other laboratories several difficulties have often been encountered in extending these procedures, obtained with rats, to the isolation of tissues from other experimental animals, like mice. In our laboratory isolation of small intestinal crypt cells from mice has been achieved [65] with a good degree of reproducibility, after long experimentation and extensive modification of a previous method [63]. Our impression is that, regardless of some success, the preparation of viable homogeneous cell suspensions of different specific tissues, from animals, still represents the major obstacle in cell characterization by laser flow microfluoremetry. For this reason, we think that different physical techniques like geometric and densitometric analysis

261 should be further explored with the aim of studying the intact cell in situ (i.e., in a tissue section). VC. Geometric and densitometric texture analysis Objective analysis, by means of computer digitizing of the image projected from the microscope into the face plate of a television scanner [66,67] allows determination of the absorbance of each picture point, the area (at the selected absorbance threshold), the Ferret diameter, the horizontal and vertical lagging edge projection, and the integrated absorbance of a given cell component. A recent report [68] has shown that the total nuclear area, the area of chromatin at different absorbance thresholds and the mean absorbance of chromatin significantly vary between G1, middle S and G2 nuclei of WI-38 human fibroblasts stained with a Feulgen method. It is interesting that morphological changes of interphase nuclei during the cell cycle are the reflection of structural changes in the chromatin [53]. A more detailed texture analysis of first and second order statistics is presently carried out by the combined utilization of the Quantimet 720-D and the Digital Equipment Corporation PDP-11/40 computer [69,70]. Hela cells were synchronized by selective mitotic detachment and cells were harvested at 1, 3, 5, 8, 12, 15, and 18 h following detachment. Slides containing Feulgen stained cells from each collection, at 3 different hydrolysis times, were subjected to a major analysis by means of the Quantimet 720-D image analyser. Each nucleus examined was defined as having a minimum absorbance of 0.04; at this base threshold the integrated absorbance, area, perimeter and horizontal projection were computed from nuclear images. The latter three parameters were also computed for each nucleus as the absorbance threshold was raised successively to the value of 0.08, 0.12, 0.16, 0.20, 0.24, 0.32 and 0.40 (Fig. 10). Images from each field on a slide were viewed by an observer who provided a go or skip command, depending on whether the field contained cells, artifacts, or was blank. The data obtained were recorded on magnetic tape cassettes and later transferred to disk for analysis. Fortran programs [69] were written to extract the data, compute means, standard deviations and ranges, and print histograms. Four derived parameters were computed from the original data; they were average absorbance (A) per unit area (U) (U. A I A i / U i ) , form factor (FFi = Ui/Pj), mean free path (MFPi : U~/Hi) and area ratio (Ri : UJU~), for all thresholds except the first. Analysis has only been conducted presently for the first threshold data and showed that, while area, perimeter and projection have different mean values for each cell cycle phase, their distributions have substantial overlap between the phases. In contrast, the derived parameters, form factor and mean free path, changed more sharply between cells in early S and mid-late S, between late G1 and early S and between late S and early G2 [70]. For the nature of these quantities it appears that the combination of two or more parameters, derived from three or more direct measurements, allows determination of cell cycle phases and their segments on the basis of chromatin geometry and to an extent which is not possible by simply mea=

262 suring a single parameter such as DNA content. A single directly measured parameter (including the geometric ones) has been never observed by us to be other than distributed and is only interpretable by a model in the absence of any other observable. Finally, texture analysis of first and second order, combined with the laser flow microfluorimetry, seems to be in condition to shed new light on the cell cycle phase characterization and cell kinetics. The direct determination of GO cells, consequently of growth fraction, and the direct determination of cell cycle phases and their segments, with special references to the G1-S and S-G2 boundary, are a few points which are extremely important in planning chemotherapy, especially with regard to the action of given antimetabolites or antimitotics (with consequent effect on progression through the cycle). A better knowledge of the cell and its kinetics can allow us to further define any perturbation occurring under various treatments. It appears that even the most physiological treatment adopted in synchronizing cells in culture, as mitotic selection, yielded a cell sub-population of about 5.5 )/o of the total cells, with G1 DNA content, which remains viable but not cycling for 5 days. Tobey [71] proposed the introduction of a new term, as "traverse perturbation index", which is defined as the fraction of cells converted to a non-cycle traversing state as the result of the experimental manipulation. A knowledge of the perturbation index will allow direct comparisons of the effect on cell cycle traverse of various synchrony-induction protocols. The combined utilization of autoradiography, laser flow microfluorimetry, geometric and densitometric texture analyses will allow us to further characterize the cell cycle specificity of various drugs and their effect on cell progression after the synchronizing agent is applied. We must stress that image analysis techniques which show the capability to distinguish also between resting "GO" and proliferating " G I " WI-38 cells (see Fig. 11), may help to overcome the problems associated with the preparation of viable cell suspensions from animals (major obstacle to laser flow microfluorimetry). Even if the examples quoted here are relative to tissue culture (the most obvious system to test a new technique and to search for new "observables"), image analysis has already been successfully applied to the study of intact tissues. The extension of geometric and densitometric analysis to cell characterization in the section of any intact tissue can be considered feasible even if it will constitute a difficult task and will require considerable skill during the preparation of the specimen and subsequent imaging prior to making measurements.

V|. CELL CYCLE-SPECIFIC A G E N T S

A necessary step toward the achievement of cell synchrony and proper cancer chemotherapy is the determination of the site of action (and its eventual uniqueness during the cell cycle) of the various agents. The brief review, contained in this section,

263

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1625O IA [au)

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Fig. 11. Frequency distribution of integrated absorbance (1A, left panel), area (middle panel) and perimeter (right panel) for Feulgen stained WI-38 human diploid fibroblast confluent cells (GO, - - ) and W1-38 3 h after stimulation to proliferate (G1, ----). These measurements were performed with an image analyser Quantimet 720-D (Cambridge-Imanco) and reduced with a PDP-I 1/40 (Giarretti, W., Eisen, M., Desaive, C., Kendall, F., Macri, N. and Nicolini, C., manuscript in preparation) [103]. The frequency distributions of area (and perimeter) show the appearence of two distinct peaks ("GO" and "GI") after the nutritional stimulus ( . . . . ), similar to the frequency distributions of fluorescence per cell (see Fig. 9). The data shows that while no difference could be detected between the integrated absorbance (DNA content) of unstimulated (GO) and stimulated (G1) WI-38 cells, a striking difference was found both in area and perimeter, compatible with a chromatin dispersion during G0-GI transition. These data are consistent with DNA conformational change and increase in binding sites in both isolated chromatin [54,55,58] and intact cell [60,61,62] during G0-GI transition. The mean of these two geometric parameters were found significantly different (P < 0.001) using a two-tailed Student "T" test.

is i n t e n d e d to recall a t t e n t i o n to the uncertainties still existing on the m e c h a n i s m a n d m e t a b o l i s m o f m o s t "cell cycle specific" agents, which m a y be o v e r c o m e by m a t h e matical modeling. Obviously, further studies a t the m o l e c u l a r level for the agent-cell interaction are necessary, b u t enzyme kinetics a n d cell kinetics m a y help to elucidate the c o m p l e x f e e d b a c k m e c h a n i s m regulating the a c t i o n a n d i n t e r a c t i o n o f the v a r i o u s " a g e n t s " in intact animals [15].

VIA. Radiations V a r i a t i o n s in radiosensitivity have been observed d u r i n g different phases o f the cell cycle o f plants [72], b a c t e r i a [73] a n d m o u s e s p e r m a t o c y t e s [74]. W h i l e in all these cell lines (plants, b a c t e r i a a n d the spermatocytes), the c h r o m o s o m e s a p p e a r to be m o r e radiosensitive d u r i n g p r o p h a s e a n d m e t a p h a s e , studies c o n d u c t e d with v a r i o u s a n i m a l cell lines like intestinal e p i t h e l i u m [75], L-P59 m o u s e fibroblasts g r o w i n g in vitro, a n d m o u s e ascites t u m o r cells g r o w i n g b o t h in vivo a n d in vitro [76], seem to indicate t h a t cells in S phase are a b o u t twice as radiosensitive as those in G1, a n d those in G 2 are only slightly m o r e radiosensitive t h a n those in G1. Similar findings have been r e p o r t e d frequently in the literature, like the case o f the spleen a n d b o n e m a r r o w [77], a n d it generally seems t h a t m a m m a l i a n cells in the S p e r i o d

264 at the time of irradiation not only suffered more chromosomal damage than the rest of the population, but also did not proliferate as readily. V1B. Antimetabolites

During the last 15 years our knowledge of the biosynthesis of the nucleic acids has expanded greatly, due largely to the discovery and use of various inhibitors of R N A and DNA synthesis [78]. Among these inhibitors some are known to act by binding to template or primer DNA, whereas others exert their effects directly on the enzyme polymerases. While there is considerable knowledge of the biochemical modes of action of several cytotoxic drugs frequently used in cancer chemotherapy, in more recent times the knowledge of the mechanisms by which these drugs exert their lethal effects is improving. The determination of a response of mammalian cells in vitro to various drugs has been shown [79] to have a clear "phase specificity": i.e., inhibitors of D N A synthesis appear to be most effective in killing cells in S phase, inhibitors of protein synthesis at the GI-S transition, whereas inhibitors of RNA synthesis elicit an X-ray-like age response and show greatest activity on cells in M and at the GI-S transition. These lethal effects of various drugs are not necessarily related to the chemical effects on the various metabolic pathways of DNA (or RNA), which may or may not be unique for a specific site, mainly due to different feedback mechanisms. Controversy and doubt still exist about the molecular mechanism of most of the used drugs, including the various inhibitors of DNA biosynthesis (methotrexate, FdUrd, Ara-C, Ara-A, hydroxyurea, and isoquinoline. The most extensively studied drug is Ara-C and its mechanism of action at molecular level, its metabolism, chemistry and pharamacology have been recently reviewed [80]. Ara-C is a nucleoside analog with a configuration similar to those of cytidine and deoxycytidine [81]. Ara-C (1-fl-D-arabinofuranosylcytosine) is generally believed to inhibit DNA synthesis through the action of its 5'-triphosphate, AraCTP, on the polymerization of deoxyribonucleotides [83,84]. This inhibition of DNA polymerase [85] has also been shown to interfere, maybe through a complex feedback mechanism, with the reduction of cytidine diphosphate [86] and with the incorporation of small amounts of Ara-C into DNA and RNA [87]. While the Sphase specificity of Ara-C is not in discussion, recent studies of the kinetics of chromosome breakage [88] and on the cell cycle passage time [89] seem to indicate that Ara-C affects the passage rate of cells from S to G2 phase to a greater extent than from G 1 to S, stopping this cell in the S phase. Hydroxyurea has been shown to be a potent inhibitor of deoxyribonucleic acid synthesis, by interfering with ribonucleoside diphosphate reductase, which converts the ribonucleosides to deoxyribonucleosides [90,91]. However, experiments designed to reverse the inhibition by addition of deoxyribonucleosides have had limited success [92,93], and this casts doubt on a single site of action. Furthermore, some others [94,95], indicate that nucleotide reductase is not the enzyme affected by hydroxyurea. The question seems to be not quite settled yet because at the same time, other authors [96] showed that hydroxyurea inhibits DNA synthesis in mouse fibroblast (L) cells by inhibiting ribonucleotide reductase,

265 and no other site of action could be found; in addition, inhibition of D N A synthesis could be reversed either by removal of the drug or by addition of deoxyribonucleoside [96]. As such the authors [96] strongly suggest that hydroxyurea can be a very useful agent to induce synchronized replication of DNA. For most of the other inhibitors of DNA biosynthesis, the mechanism is even less clear and more controversial: for instance, flurodeoxyuridine (FdUrd), seems to inhibit thymidylate synthetase [97,98] but, through complex and obscure feedback mechanisms, other sites of action in the DNA metabolic pathway are affected. Similarly, methotrexate, which presumably inhibits thymidylate synthetase, and Ara-A which inhibits D N A polymerase, in competition with the adenine pool, may have more than one site of action in the metabolic pathway of D N A biosynthesis, and they can only be generally considered as S-phase specific agents, maybe at the GI-S interphase. It must be stressed that among the various antimetabolites, methotrexate is the only one which does not release spontaneously, i.e., requires the presence of an antagonist such as folinic acid to release the block of DNA synthesis. As a general comment we must point out that most of these inhibitors of DNA synthesis in mammalian cells have been shown to cause "unbalanced growth" [99]. By preventing the synthesis of DNA, while allowing RNA and proteins to accumulate, the observation that the exposure to hydroxyurea produces a threefold increase in thymidine kinase activity may indeed be a general phenomenon resulting from the unbalanced growth induced by the inhibition of DNA synthesis [100]. Unbalanced growth has been shown to take place in cultured mammalian cells treated with FdUrd [101] Ara-C [102] and hydroxyurea [91]. Several groups of investigators have noted that an accumulation of RNA and proteins in an "unbalanced growth" of mammalian cells is accompanied by cell enlargement; but the most complex study in this respect in our opinion was the one which compared and contrasted the effects, on HeLa cells, of a number of inhibitors of DNA synthesis with differing modes of action, paying particular attention to the correlation of cell RNA and protein content with the cell volume [104]. It was found that treatment with cytostatic concentrations of inhibitors of DNA synthesis led to approximately equivalent increases in cell RNA, cell protein and cell size. It seems that these changes did not depend on the mode of action of the agent used to treat the cell and they were considered to represent some of the basic characteristics of unbalanced growth [105].

VIC. Antimitotic drugs It has been known for many years that colchicine in certain doses acts to stop cells passing through metaphase without detectable influence during other periods of the cell cycle [106]. Eigstei and Dustin summarized the properties that the "mitotic arrest" drugs should possess and found that colchicine often failed to meet these requirements. They observed that [107] the arrest in metaphase rapidly degenerated even after a high dose of the drug was administered: anaphases and telophases could still be seen, showing the metaphase block to be incomplete. Colcemide, a closely related drug, has been found to show a toxicity more than 3 times lower than that of

266 colchicine in an experimental animal [108]. Other authors [109] claimed that all metaphases were arrested, when colcemide was utilized in their work on skin carcinogenesis. More recently the vinca alkaloids, vincristine and vinblastine have become available as stathmokinetic drugs. Several authors [110,111] have investigated their metabolism and have found an approximately linear correlation of metaphases for the first 6 h after the injection of either vinblastine or vincristine. Furthermore, some authors [112] have shown in L cells that only those cells in or near mitosis were irreversibly damaged in their reproductive capacity whereas cells in the remaining stages were intact and the rate of progression was normal. Kane and Stanbuk [113] have employed vinblastine as a synchronizing agent in a mammalian cell culture; exposure of HeLa cells to vinblastine-sulfate for approximately one cell-cycle time and subsequent complete removal of metaphase-arrested cells left behind a partially synchronized population [113]. Surprisingly and confusingly enough some authors, utilizing a partially synchronized population of murine lymphoma cells in vivo by means of hydroxyurea, claim a major S-phase sensitivity of the two vinca alkaloid agents (vincristine and vinblastine), with only a minor killing effect during Mphase [114].

VID. Alkylating agents The alkylating agents, like cyclophosphamide, melbhalan, busulfan, dibromomannitol, nitrogen mustard, react with or bind to D N A regardless of cell cycle phase during exposure; however they apparently kill only those neoplastic or normal cells that attempt DNA replication prior to repair. The age response of cells to aikylating agents appears to be characterized by a relative sensitivity at or around mitotis [3,79] and, in the case of nitrogen and uracil mustard, an additional sensitivity at the G1-S transition. However, the interaction of the various alkylating agents with chromosomes during the cycle is somewhat undefined, because evidence exists of major vulnerability to alkylating agents both during the condensed state or at, and just prior to, DNA replication [115]; evidence also exists that they may interact with DNA precursor molecules such as thymidylic acid [116]. VIE. Antibiotics A large number of antibiotics are inhibitors of RNA and/or DNA synthesis [117,118]. Some of these antibiotics have been shown to inhibit DNA-dependent RNA polymerase by binding specifically either to DNA, to the enzyme or to one of the enzyme sub-units, but no antibiotic has yet been shown to inhibit specifically the activity of DNA-dependent DNA polymerase [78]. Actinomycin-D, the most studied and commonly used antibiotic, has various biological effects, but its principal action is the inhibition of transcription, due to its ability to bind specifically to guanine residues in DNA and alter its structure, and its role in DNA-dependent RNA biosynthesis. Hamilton et al. [119] have proposed a

267 model for the actinomycin-D DNA interaction, in which the antibiotic is bound in a minor groove of the D N A helix and the purine 2-amino group of the deoxyguanosine is required for actynomycin binding to native DNA. The minor groove is believed to be the specific template site for RNA polymerase. The age response of HeLa cells to Actinomycin has been proved to have a marked relative sensitivity during the G1/S transition [79]. The reason for this is not completely clear but it is interesting to know that at this point of the cycle the rate of R N A synthesis sharply increases by a factor 2 in HeLa cells [120]. Daunomycin and adriamycin, at low dosage level, prove to have only a slight effect upon entry of cells into S, but they were more or almost totally effective in preventing cells from reaching mitosis [121]. Similarly, mithramycin very mildly affects the entry into S phase of mammalian cells, while completion of G2 phase was partially inhibited; the antibiotic camptothecin which has a sizeable antitumor and antileukemic activity [122], by affecting the synthesis of both RNA and DNA in the mammalian cell [123], had little or no effect on initiation of genome replication, but instead had a pronounced effect at the completion of interphase, i.e., seems to block the cell in the G2 phase of the cell cycle [ 120,124]. As shown in a different paper [125], by utilizing the new technique of flow microfluorimetry, although most cells in the population have initiated DNA synthesis (i.e., are labeled) at the time of preparation of the autoradiographs, few cells have completed synthesis of a full complement of DNA. These results are in contrast to those obtained with another antibiotic compound, bleomycin, which allows initiation and synthesis of a full complement of DNA at the normal rate [126].

vii. MATHEMATICAL MODELING IN CELL KINETICS Mathematical models have been used for many years to study the cell kinetics. Most of the time, models have been devised to help with the interpretation of specific experimental data; for instance many mathematical models have been developed to obtain optimal information from the percentage labeled mitoses experiment [127-131]. This method generally assumes a basic trapezoid foundation for the average progression of the cohort of labeled cells, and then they convolute the trapezoid with one or another dispersion function. For instance, the Barrett model is based on a lognormal dispersion, Hartmann early model on a Gaussian dispersion and Takahashi model on a gamma distribution. Bimodal distributions, heterogeneous mixture, and correlated behavior from one phase to the next (like the question of heredity by which is meant correlation between parent and daughter cell cycle times) has been recently modeled with varying degrees of sophistication [132]. Even if such sophisticated mathematical extensions of the analysis may find some justification on biological grounds, their impact on actual practice is not yet clear, considering the limited amount of information contained in PLM curves. The method of frequency of labeled mitosis is cumbersome, biased to short cycle, occasion-

268 ally ambiguous, and prohibitive in most usual situations; but it was up to now the only method that could give transit time and coefficient of variation of transit time for all four phases and for the total cell cycle. Mathematical modeling undoubtedly represents a substantial improvement with respect to the extraction of the cell cycle by hand, which suffers from serious drawbacks as frequently pointed out in previous papers [133,134]. However, new observerables are necessary in order to take further advantage of the higher degree of sophistication achieved in the recent times in mathematical modeling of cell kinetics, already valuable in cancer treatment [48a, 132]. A technique for one-day quantitive determination of the kinetic parameters of a randomly growing cell population has been recently developed [135]. The technique makes use of an electronic cell sorter to select cells in a narrow window of the cell cycle, in mid-S phase, using the DNA content as the basis for sorting. A pulse of radioactively labeled DNA precursor is administered to the population and the time sequence of samples is taken subsequently. By counting the sequence of samples utilizing a liquid scintillation counter, a curve reminiscent of the PLM curve is obtained [135]. VIIA. Growth fraction and cell loss A population may grow because of increase of rate of proliferation, increased fraction of dividing cells (growth fraction), and by decreasing the rate of cell loss. Such a statement is true both for normal and tumor cell populations, and under the steady-state condition (like for adult tissue) the number of new cells is equal to the number of cells lost. Several mathematical models have been developed to formulize hypotheses about growing populations of cells: for instance, the model of Mendelsohn [136], or, alternatively, that one presented by Burns and Tannock [137], and the ones estimating cell loss [138-140]. Few papers deal with a mathematical representation of populations of cells without specifying, a priori, a particular application. Some general procedures have been presented by Hahn [141] by Valleron and Frindel [142], and by Jansson [143,144], in which a compartmental model including cell differential and stability problem was developed in a matrix notation. To summarize briefly, the growth of a cell population can be formulated in terms of the number proliferating cells (P), non-proliferating cells (Q), and cells that are being lost (L). The growth fraction GF ~ P~ (P -k Q) is measured by the disparity between the labeling index predicted from the cell cycle and the observed labeling index either after pulse labeling [145] or after multiple or continuous labeling [146]. The combination of both growth fraction and the cell cycle parameters may give us the cell production rate, that is, the virtual cellular volume. Actual cellular volume or actual growth rate is based on sequential growth measurements of a cell population, and the difference between virtual and actual cell volume is ascribed to cell loss. Cell loss can occur either from any one of the proliferating compartments P (GI, S, G2, and M) or from the non-proliferating pool, specifically from the Q compartment, which recently one author [140] divides in two sub-compartments with an influx of cells with G1 and G2 DNA content respectively. In tumors [147] cell loss can take a

269 variety of forms, including that of P cells during the mitotic process, destruction as a result of differentation, and tissue necrosis. It is clear that cell loss is a major activity in most tumors and therefore tumor kinetics involve both net growth and turnover of cells, mainly from the relatively inaccessable Q cell compartment [1].

VIll. COMPUTER OPTIMIZATION OF DRUG SCHEDULE FOR CELL SYNCHRONY IN ANIMAL AND CANCER CHEMOTHERAPY The difficulty encountered in obtaining a cell synchronization in vivo may be due to two factors: (1) the rapidity with which an inhibitor reaches its maximum effect, and (2) the rapidity with which it is catabolized. Both factors are determinant in establishing a degree of synchronization by specifying the point of arrest in the cell cycle, and by determining the speed of release from the block. Furthermore, the ideally synchronized cell population should show no perturbation in any of the metabolic pathways of the cells, and the short-term and long-term effect of each chemical on cell metabolism should be minimized. Under these circumstances, the hope to find by empirical means the best combination of drugs (among the numerous inhibitors of DNA, RNA, and protein synthesis, and the various antibiotic and alkylating agents), doses and timing, that will stop all proliferating cells simultaneously in a given point of the cycle, with a minimum alteration of metabolic pathways, seems rather forlorn. One way of optimizing the synchronization regimens would involve a programmed attempt to test a wide variety of combination of drugs, dosage, and time schedule in order to select the best one. However, in view of the fact that a very large number of possible combinations exist, and that the analysis of each experiment is time consuming, (particularly if autoradiography has to be used), it is doubtful whether the best solution will evolve from such strategy in our lifetime. Accordingly, several computer-aided techniques have been recently developed in a few laboratories in order to evolve a protocol which will optimize drug dosage regimens for the experimental synchronization of cells in intact animals, and for cancer chemotherapy in general. VillA. Monte Carlo simulation

A number of computer simulation models have been developed and reported [148-153] in the field of cell biology; and recently a generalized simulation language [154] for stochastic modeling has been directed specifically toward cell cycle kinetics, with a number of built-in-collection algorithms that automatically regroup and reassign cells when the population approaches the memory limit of the computer system. None of these systems, however, can be conveniently adapted to study the effect of drugs on the cell cycle and to find a combination of drugs, timing, and manipulations (such as fasting) which gives the best synchronization of the cell population in vivo; only through an iterative fitting procedure between the experimental data and the theoretical prediction of the specific model used, it is possible to evaluate the

270

PROGRAM

DRGFIT

Input : N=I Y = Cycle phase of drug sensitivity T, ± ~ = Optimized cell cycle parameters ( L - f ) = F r a c t i o n of GO cells (INB, ~, T2, T3 ) = I m t i a l values for d r u g

metabolism parameters

I I

I n p u t of each dose - same d r u g E x p lab cells N# and observation times Exp

i

mit. cells

NE M and observation times

FREFLD Check input data in i n t e r a c t i v e mode

NVERTX At T = O, t h e percentage of ceils ~n phase " X " correspond to Tx/Tcycle Then follow each ceil in the cycle

t

G I ~ S ~ G 2 ~

1

M~GO

( log - n o r m a l residence times )

N LE 4

TO BLOCK

F i g . ] 2 . F l o w chart of the p r o g r a m D R G F I T , computer as described in the text [ 1 5 , 2 8 ] .

written in F O R T R A N

language for a C D C - 6 4 0 0

parameters (slope and maximum of inhibitory effect, rate of block release, cell-kill, etc.) of each separate drug in different cell populations (See Figs. 12, 13 and 14), in order to decide which drug is the most effective in achieving cell synchronization and the minimum alteration of metabolic pathways [28]. The model, contained in the overall program "DRGFIT" [28]; (see also Figs. 12, 13 and 14) consists of 1265 Fortran IV statements, is divided into a main routine and 14 sub-routines and has two main assumptions: (a) the cell proceeds stochastically through four discrete phases (G1, S, G2, and M) with log-normal distribution of residence times in each phase; an absorptive phase (GO) is also introducted to simulate the effect of a non-proliferate compartment. (b) the inhibitory effect of a given drug is assumed to be a trapezoidal function of time: the drug is metabolized linearly in time T1, maintains its maximum inhibitory effect for time T2 and is linerally catabolized during time T3. Cells which are in the drug sensitive phase are assumed to be stopped, randomly with the fraction stopped

271 depending on the current values of the drug metabolism parameters. In accordance with the slope of their release, each cell goes back randomly in the cycle, between (T, + T2) and (T, + T2 q- T3) h. The values of the drug metabolism parameters are changed three times for each parameter, and the chi-square value is determined each time such that the value of each parameter which corresponds to a minimim chisquare value Y, can be computed from a quadratic relationship. The next parameter is then considered. The whole process is then repeated using the most recently computed parameters until the resulting chi-square either converges or fails to converge within 20 iterations (Figs. 12, 13 and 14). Being aware of the difficulty associated with optimizing one parameter at the time, we recently introduced a minimizing routine which utilizes the method of steepest descendent, which considers

FROM

NVERTX

L

BLOCK cells in " Y "

Block at T = t only phase Trapezoidal i n h i b i t o r y effect reaches m a x i m u m (INB) L i n e a r l y in t i m e ?'1, remains for t i m e T2, and l i n e a r l y catabolizes by t i m e T3 Cells progressively go back in t h e cycle f r o m " Y " phase b e t w e e n t=(T1 * T2) and t = ( T1 * T2 * T 3)

S N T and

PHASE M N T using c u r r e n t

inhibitory values

By means of the

Evaluate

W 3" w

trapezoidal S/. S

N~.//NT

r a t i o , e v a l u a t e cells suspended ( C S ) d u r i n g t h e e a r l y h o u r s and cells killed (CK) (late h o u r s ) f o l l o w i n g block release.

U z

CHI

SQUARE

MINFUN Given t h r e e values of ZNB ( o r T~, T2, T3, CS, CK) and corresponding values of Chl-Square, make successive quadratic i n t e r p o l a t i o n s t o find values w h i c h m i n i m i z e chi-square

NO

2

2

XIQst - XIQSt. 1

< E

,

YES

TO OUTPUT

Fig. 13. Continuation of the flow chart of the program DRGFIT (see Fig. 12).

272 TO INPUT

YES

l

OUTPUT C h i - s q u a r e , d e g r e e s of f r e e d o m , confidence level M histograms of optimized NTS and N T v e r s u s t i m e

optimized drug metabolism parameters: (!NB, 1"1, T2, 1-3)

(CK, CS)

Index of s y n c h r o n y Proportional response values stored in M (Z, L) where r = index of dose level L : index of metabolism parameters

N:N*I

No

YES

Using response data m and C L in the form: ( M ( / , L ) ) -1 =

KL*

DOSE M (I, L), evaluate K L

ALOG

by a maximum likelihood

(Ol) *CL,

(L=1,5,

(I:1,4)i

method

Fig. 14. Continuation of the flow chart of the program DRGFIT (see Figs. 12 and 13).

a response surface function of the six metabolic parameters. The computed metabolism parameters for each of the four doses of the same drug are then stored in a matrix and used to predict the response of any given dosage in accordance with the linear least square (or maximum likelihood) method of the general form: F -1 --- C +

KD

where D is the dosage level and F is the functional relationship which we have found to be most appropriate for fitting a given parameter. In the case of proportional responses (INB, CK, CS) the function is assumed to be log-normal and the inverse is the corresponding normally equivalent N.E.D. [28]. In the cases of the times for drug metabolism, the function corresponds to TI -- K1/D ÷ C1 T2 = Cz * D x2 T 3 - - C 3 * D K3

Program output (see Fig. 14) consists of the pairs of constants ( C,K) which specify the optimized dose-response relationship of each of the six parameters of the model

273

as well as the value of the optimized parameters at each dose level, the value of minimum chi-square, the number of degrees of freedom, and the relative confidence level. In the intact animal complicated enzymatic reactions occur, regulated by a network of unknown feedback mechanisms. This computer simulation program allows a quantitive estimation of metabolism and catabolism of the given drugs in vivo, useful in measuring drug toxicity as a function of dosage, its short and long term effect, and in planning chemotherapy treatment. The optimized values of drug metabolism parameters, as functions of dosage, together with cell cycle parameters [8,9,156], are finally utilized as input to a Monte Carlo program, SIVF|T, (see Fig. 15 and 16), which predicts timing, dosage, and drug combination necessary to achieve the best degree of synchrony in the intact animal. This second Monte Carlo simulation system, implemented on a CDC-6400 computer, also in Fortran IV language, is intended to help the investigator to: (1) decide which combination of drug and manipulations can be most effectively attempted in order to achieve the best synchronization, (2) plan the proper scheduling of timing and dose of injection, as

PROGRAM

SIVFIT

Purpose: given the optimized residence times for the given cell population, and the two d o s e - response constants (to evaluate t h e L optimized metabolism parameters) for each of I different drugs (and manipulations), predict the values of dose level and timing which will optimize synchrony Input :

optimized cell cycle p a r a m e t e r s from "FTLiVl" K ([, L) a n d C ( I , L ) = optimized dose - response constants f r o m " D R G F I T " Y ( [ ) = cell cycle phase sensitive to d r u g [ T~ ( [ ) = initial injection time for each d r u g O i ( I ) = initial dosage value for each d r u g a t TL ( r ) I = index of drug designation L = index of metabolism

Check

input~ta in

parameters

interactive mode

At T=O,the percentage N V E R T X of ceils in phase "X"I correspond to Tx/Tcycl e Thenfolloweach cell in the cycle: = G1 ~

S ~G2

( log - n o r m e l

I ~

iv1 ~ G O

residence times )

TO

BLOCK

2

Fig. 15. Flow chart of the program S1VFIT, written in F O R T R A N computer, as described in the text [15].

IV language for a C D C - 6 4 0 0

274 FROM

NVERTX

BLOCK 2 Simulate the e f f e c t of manipulation ( I ) a n d / o r drug ( I ) in accordance w i t h the model specified by the input parameters. D ( [ ) and T~(r), given initially as first guess, are teratively mproved The r o u t i n e evaluates the percentage of cells in S phase ( N s) as a f u n c t i o n of t i m e following block release Evaluate N1OO, the expected f r a c t i o n of cells ~n S please f o r 1OO% synchrony (step f u n c t i o n )

CHI SQUARE X 2 = ~ ( Ns - Nloo)2/(z~Ns) 2

MINFUN Given three values of D,(I) (or TI (Z)) and correspondmg chi-square, make successive quadratic i n t e r p o l a t i o n s to find values which m i n i m i z e chi- square.

-

-

NO ~

X

2 st - X l a s t - 1

YES

OUTPUT Time schedule T~ (2") and dose Di (Z) which best fit 1OO % synchrony. M a x i m u m d r e g r e e of s y n c h r o n y expected

Fig. 16. Continuation of the flow chart of the program SIVFIT (see Fig. 15).

close as possible to optimal conditions, (3) evaluate the degree of synchrony in the given combination of drugs, dosage and timing, by comparing the percentage of labeled cells obtained experimentally during the first 15 h after the block release, with a percentage of cell in S phase expected by computer simulation, with the hypothesis of 100% synchrony (step function release) and by knowing the mean and standard deviation of each phase for a given population. All this mathematical simulation is based on the Monte Carlo techniques, i.e., methods of solving problems by subjecting random numbers to the numerical process [157]. We must, however, emphasize that a magic answer and solution to the problems of cell synchrony in vivo cannot be expected by the utilization of such computer simulation programs; neither the computer simulation nor the blind experimental approach can by themselves solve such complex problems. We wish to stress that only a continuous feedback between computer simulation and experiments conducted in vivo will eventually achieve the

275 goal of obtaining the best synchrony of cells in experimental animals, with a minimum alteration of the metabolic pathway and with minimum effort. To achieve the same results, with the usual empirical approach, the investigator will be forced to carry on blindly an interminable series of experiments which could include only a portion of all possible combinations of timing, dose, drugs, and manipulations. The computer can be used instead to explore all possible combinations and to quantitate the drug effect on the cell kinetics in a very short time, without actually carrying out the experiment and suggesting only the most promising ones, with time and dose schedules and with the predicted value for the index of synchrony and the labeling index versus time. It must be stressed that since each tissue responds differently to the same treatment [8,9], the computer program is aimed at specifying the best drug regimen to apply in a specific situation. As such, no general "magic" protocol is available, as "input" information will differ in each case. From each case it would be necessary, thererefore, to obtain information on the cell cycle parameters (including growth fraction) and tissue response to four concentrations of the given drug. We have conducted, in mice, a screening of six antimetabolites, 2 antimitotics, 3 antibiotics, in order to obtain the optimized metabolism parameters of each drug for four different normal tissues (large and small bowels, esophagus, bone marrow), Melanoma B16 tumor and its metastases. We are presently reducing the data, hoping to find a response pattern that can be extrapolated to humans. The approach is undoubtedly long, and would be prohibitive without the introduction of the new "cell technology". However, the present empirical approach, regardless of some occasional successful protocol, has already proved its limitations and new, more quantitative answers to human cancer chemotherapy are being offered in the literature [15,48a,80,143,163, 166].

VIIIB. Control systems analysis and various algorithms The cell cycle kinetic state of a tumor cell population system can be determined by assigning a cell age factor and by utilizing system theory [160] in order to design an optimized antitumor drug schedule. The optimized schedule is found by solving the problem of finding a sequence of drug control functions U (K) which minimize the performance index, subject to the dynamics of the system [158]. This problem can be solved by optimization techniques utilized in control theory [161]. In a separate article Jansson [143] has stressed the importance of taking into account, when one describes the growth of cell populations, those changes that are due to changes in the environment of the ceil. The environmental factor, that is of the most growth-controlling importance, was the number of individuals in the population. This, however, did not imply that it must be primarily this number that has a decisive influence; any factor proportional to the number of individuals has the same effect. The feasibility of making growth description dynamics by very simple methods has been demonstrated with an example from an ascites tumor [143]. Comparison between theoretical and experimental results has shown good and promising agree-

276 ments. However, the demand is a new one and there remains a great deal of research to be done before we reach the final goal of being able to plan and control strategy for chemotherapy treatment with the aid of such quantitives models. Recently, a computer simulation method [162] has been proposed for studying the non-lethal and lethal effects of treatment from experimental data, and for setting theoretical treatment protocols. This computer model is essentially based on the utilization of a Monte Carlo method previously described by Valleron and Fringel [163]; at the present time the program may be used to study the effect of a sequence of up to 10 treatments on a one-type cell population, during up to 10 generations.

1X. PHARMACO-ENZYME KINETICS IXA. Ara-C metabolism Pharmaco-kinetic simulation seeks to put the effort of discriminate killing of neoplastic cells, without undue damage to the host, on a firm rational basis based on the physiology, molecular biology and biochemistry of drug distribution and metabolism. As a result of such simulation, we should be able to compute tissue-specific drug exposure which will make available to the chemotherapist the same kind of dosimetry which is already available to the radiologist. Some pioneering work has been already conducted on the pharmaco-kinetics of anticancer agents such as methotrexate [164] and Ara-C [165]. This work has been recently extended with Ara-C [166] to include the simulation and prediction of intra-cellular metabolites and enzyme kinetics within those target cells which are the sites of the ultimate cytotoxic and cytostatic effects. This new approach of mathematical modeling of the pharmacokinetics (drug deposition and metabolism), intracellular enzyme kinetics and cell kinetics, has been applied to the treatment of L-1210 leukemia by Ara-C. The active metabolite of Ara-C is the triphosphate, Ara-CTP, which kills cells (primarily in S-phase) at high concentrations, and inhibits the synthesis of D N A at lower concentrations. Even the most simple set of pharmaco-kinetics and enzymatic relations, used to describe analytically the intracellular concentration for Ara-C is of such complexity as to be beyond the purpose of this review. Nevertheless, we would like to point out, that by relating intracellular concentration to cell death and inhibition of D N A synthesis, in this analytical way, a more realistic approach to the prediction and interpretation of optimal schedule can be developed. Several mathematical models on the use of Ara-C in cancer chemotherapy have been recently published [167-169]. The choice of Ara-C, as a model, relies essentially on its theoretical interest, the amount of experimental data available, and the drug's demonstrated clinical usefulness. The pharmacology of Ara-C has been recently reviewed, and integrated with data on the cell kinetics of normal hematopoietic and leukemic stem cells, to form a model for the chemical therapy of acute leukemia [80]. This last paper represents a clear example of an improvement in the chemotherapy of a cancer (acute leukemia), which in the past has been relying only on the utilization of therapeutic regimens

277 designed by semi-empirical methods. Such an approach was unavoidable in the past, because of the inadequacy of the biological and pharmacological data. The recent accumulation, however, of fundamental knowledge in the field of pharmacology, chemistry, molecular biology and mathematical modeling, suggests that maybe other approaches to chemotherapy should also be explored. IXB. Drug combination A mathematical model has been published recently which simulates the effect of a combination of inhibitors of DNA biosynthesis on cell growth in vitro, by an open steady-state system regulated by a network of feedback controls [30]. This model gives the intensity of interaction of drug in combination, whether antagonistic, synergistic or additive. This model has been recently extended to analyze the effect of combining various antimetabolites, like hydroxyurea, FdUrd, Ara-A, Ara-C, methotrexate and isoquinoline, on the metabolic pathway and cell growth in intact animal [15,29]. These last two papers represent an improvement with respect to the original work by Werkheiser et al. [30]. in that they introduced a general method for simultaneously solving a system of N non-linear equations for N unknowns which arise from analytically describing the enzyme kinetics of the various drugs on the DNA metabolism. These models predict [15,29,30] the combination of hydroxyurea with Ara-C or with Ara-A to be most synergistic, the combination of Ara-C with Ara-A to be additive or mildly synergistic in contrast to all the other combinations of the antimetabolites most frequently utilized (like hydroxyurea, methotrexate, Ara-C, Ara-A and FdUrd) which are predicted to be antagonistic. By utilizing this model, [15,29,30] which predicts also the time courses of various nucleotide pools in approaching their inhibited steady-state condition, it would then be possible to reduce the total amount of drugs injected in the animal, with a minimum alteration of metabolic pathways, by choosing the most synergistic combination of drugs in blocking a given cell population at a specific point of the cell cycle.

x. CONCLUSION An unfortunate corollary to the use of drugs and/or radiation for the treatment of cancer is that these agents are toxic to normal tissue as well, particularly those tissues whose functional integrity requires a high rate of proliferation. The most sensitive tissues which come to mind are the intestinal epithelium and bone marrow. Simply stated, the rationale for achieving cell synchronization in vivo is the attempt to spread the range between the effective dose and the toxic dose of any drug. This can be accomplished in two ways: (1) to decrease the sensitivity of the non-target cells to the agent, and/or (2) to increase the sensitivity of the target cells to the agent. In view of current knowledge, reviewed in this paper, synchronization of cell populations can be utilized because it is known that various drugs, or radiations, are specific in their toxic effects for a certain portion of the cell cycle. On the other hand,

278 the synchronizing agents must be therapeutically tractable: i.e., they should not produce permanent functional or genetic damage in the healthy cell before or after they are metabolically degraded in vivo. Thus, the problem of cell synchronization is reducible to the standard therapeutic question: how to achieve a treatment regimen that will optimize the synchronization of a given cell population, in the intact animal and in human, with a minimum of toxic side effects. The encouraging results [8,9, 14,39] obtained so far, mainly in normal tissue (80-90 ~,/, degree of synchrony in the esophagus) mostly by the utilization of semi-empirical methods, might be further improved, mainly with respect to the maintenance of cell synchrony for one or more cell cycles, by a continuous feedback between computer simulation, at the cellular and molecular levels, and experiments conducted in vivo, towards the goal of achieving the best synchrony of cells in experimental animals (and later on in humans) with minimum alteration of metabolic pathways and with minimum effort. To achieve the same results, with the usual empirical approach (the only one possible until recently, because of the inadequacy of biological, pharmacological, physico-chemical data and mathematical simulation), the investigator will be forced to carry on blindly, assisted only by his luck and intuition, an interminable series of experiments which could only include a portion of all possible combinations of timing, dose, drugs, and manipulation. To enhance any potential application to cancer chemotherapy, the short and long term toxic effects of each regimen should be quantitatively characterized and reduced, and the affected physico-chemical parameters systematically specified, and the search for new "observables" should be further carried out in order to uniquely characterize the intact cell during the cycle, in the presence or absence of a given treatment. The recent introduction of various new techniques, like pattern, geometric and densitometric texture analysis and laser flow microfluorimetry, allow the objective assignment of the intact celll, with high speed and accuracy, during various phases (and sub-phases) of the cell cycle, including the "GO" non-cycling compartment. These techniques, combined with the new pharmaco-enzyme kinetics and the sophistication reached in the mathematical modeling of cell kinetics, have and will shed new light and speed in the efforts for improving cell synchronization and cancer chemotherapy.

ACKNOWLEDGEMENTS The author wishes to thank Prof. F. Kendall, colleague and friend, and all other members of the Division of Biophysics, Drs. C. DeSaive, J. Drees, M. Eisen, S. Wu, J. Schiller, J. Tarka, W. Giarretti and Messrs. S. Toton, J. Loffredo, P. Miller, J. Murphy and Ms. L. Varani, V. Kremski and Mrs. C. Singleton. The author is particularly grateful to Miss Kathleen Betz, for the efficiency shown in typing and proof-reading the text. The recent work conducted on "cell synchrony in vivo", both in normal tissue (intestines) and tumors, was supported by the National Cancer

279 Institute, grant number CA-18258.

O t h e r e x p e r i m e n t s o u t l i n e d in this r e v i e w w e r e

s u p p o r t e d also by g r a n t n u m b e r C A - 1 2 9 2 3 f r o m N . I . H . thank

T h e a u t h o r also wishes to

Dr. R. B a s e r g a , P r o f e s s o r o f P a t h o l o g y , for f r e q u e n t a n d s t i m u l a t i n g dis-

cussions.

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