Theoretical Biology and Medical Modelling Redox-mediated Bypass of Restriction Point via Skipping of G1pm

Background: It is well known that cancer cells bypass the restriction point, R, and undergo uncontrolled cell proliferation.


Background
The normal cell cycle consists of four main phases; G 1 , S, G 2 and M. G 1 is further subdivided into two parts, G 1pm and G 1ps [1]. In G 1pm , a series of mitogenic events prepares the cell to enter G 1ps and to continue to S and M [1,2]. At the end of G 1pm , there is a restriction point, R, which monitors the cell and checks its qualifications for entry into G 1ps . If the accumulation of mitogenic events is inadequate, or if the cell is confluent with neighboring cells fully around its perimeter, the cell cannot pass from G 1pm through R into G 1ps and proliferate. Instead, the cell leaves the cell cycle and enters G 0 , the quiescent phase [1][2][3][4][5]. Cancer cells, on the other hand, bypass R with consequent uncontrolled proliferation [2].
Zetterberg and Larsson demonstrate that the transformed 3T3 cells, SV-3T3, behave in a similar way [3,4]. Further-more, they demonstrate that these transformed cells do not enter G 0 . They conclude from this that tumor cells do not enter G 0 [4].
Zetterberg and Larsson [1] have measured the duration of both G 1pm and the complete cell cycle. Larsson and Zetterberg [3] have determined the cycle period of SV-3T3 cells. From the data in [1] and [3], we calculate that the difference between the cycle periods of the 3T3 and SV-3T3 cells is 23%; i.e. the cycle period of SV-3T3 cells is 23% shorter than that of 3T3 cells and matches the duration of G 1pm .
We hypothesize here that the 23% decrease in cycle period of SV-3T3 is observed because these cells skip G 1pm and enter G 1ps directly from the exit from M. In skipping G 1pm the SV-3T3 cells bypass R. This hypothesis is supported by the following: (1) it readily accounts for the qualitative differences between non-transformed and transformed cells as noted above; and (2) it accounts for the quantitative difference between the non-transformed and transformed cell-cycle periods.
The relationship between Rb brake and other aspects of cell cycle is depicted in figure 1. The mechanism we suggest for the cancer cell skipping G 1pm follows from our model of redox modulation of cellular proliferation [6]. Beyond the restriction point, R, the cell is committed to duplicating its DNA and proceeding to mitosis. For a cell to pass R, special proliferation-promoting proteins must be phosphorylated to promote the activation of the genes necessary for the cell to traverse R, enter G 1ps , and proliferate. These include the retinoblastoma protein (pRb) [2,5], regulatory enzymes such casein kinase [7], and transcription factors such as jun [7] and NF-κB [8]. When the intracellular redox potential, E, is high, these proteins are dephosphorylated; when E is low they are phosphorylated [7][8][9][10].
An example of a critical phosphorylation-dependent pathway regulating passage through G 1pm is the cyclin D-cdk4 complex. This complex phosphorylates pRb, thereby deactivating its repressor activity and allowing for transcription of S-phase genes. For this reason, the hypothesis is limited to transformed and malignant cells in which pRb is functional. According to the redox model, the dephosphorylation of pRb can occur only if the intracellular redox potential, E, is above a threshold value, θ, which we have estimated to be between -218 and 196 mV [6]. The cell normally sets E below θ when the activating proteins are to be phosphorylated, and sets E above θ when they are to be dephosphorylated [6] (see figure 1).
During normal proliferation, when the cell is in M, a phosphatase dephosphorylates pRb [5], and the transcription factors no longer become available for activating the proliferation-promoting genes. The cell then exits M and enters G 1pm and again begins to accumulate mitogenic events necessary for the cell once more to pass R and enter G 1ps [2].
Relationship between Rb brake and other aspects of cell cycle Figure 1 Relationship between Rb brake and other aspects of cell cycle. The Rb protein acts as a brake on several of the phases of the cell cycle, dependent upon its state of phosphorylation. In the hyperphosphorylated state, the Rb brake is inactive, permitting the transcription factors to become activated and cellular proliferation to proceed. During this period the ratio [GSSG]/[GSH] is low and E falls below θ. The cell passes through the restriction point R to the later stage of G 1 , termed G 1ps , on to S, from which it passes through G 2 to the early M phase. After mid-M, the Rb protein becomes hypophosphylated and the brake is active. The transcription factors are inactivated and cell proliferation is stopped. During this period the ratio [GSSG]/[GSH] is high and E rises above θ. The cell passes through M to the early stage of G 1 , termed G 1pm , from which it may either return to the cell cycle via R or it passes into a resting stage, G 0 . In cancer, a portion of the cycle can be short-circuited, via the M to G 1ps bypass. R = site of restriction point. Arrow with interrupted line represents short-circuit in cancer. θ = -207 ± 11 mV.
Although multiple, often overlapping, pathways impinge on cell-cycle regulatory points, pRb is one of the key downstream elements known to play a critical regulatory role [2,5]. Since the proper functioning of the unmutated pRb is dependent on cycling between its phosphorylated and unphosphorylated states, the redox state may contribute to altering the cell cycle by affecting pRb directly or at an upstream point. According to this redox model, if E were to be below θ for the duration of the complete cell cycle, pRb would remain phosphorylated through the cycle thereby resulting in loss of its normal regulatory properties. Indeed, several workers have noted that the level of phosphorylated pRb is higher in cancer than in normal cells [11,12]. Our hypothesis is that some transformed and malignant cells are characterized by an E that is constantly below θ, regardless of external conditions such as confluence or growth factors. A low E keeps pRb from becoming dephosphorylated, preventing the passage from M into G 1pm , but allowing their entry from M directly into G 1ps [5], resulting in these cells skipping G 1pm . Hutter et al. have reported that, in contrast to normal cells, the average E of fibrosarcoma cells is below the value we have estimated as θ, independent of the degree of confluence [13]. These cells can be thought of as internally redox-biased.
The redox model predicts that even normal cells, in which E is artificially maintained below θ for a complete cell cycle, will also skip, or short-circuit, G 1pm . In other words, the cycle period of an artificially redox-biased normal cell will, according to the model, be shortened like the cycle period of a cancer cell. As a result of the shorter cycle period, the cell density of the redox-biased cells should be higher than that of the non-redox-biased cells. Hutter et al. [13] did exactly that experiment. They lowered E for 24 hours by adding GSH precursors. They did two experiments, adding 0.05 mM N-acetylcysteine (NAC) in the first and 0.002 mM oxothiazolidine-4-carboxylate in the second. These additions each resulted in a lowering of E, by 10 mV in the first and by 8 mV in the second. In both cases, the resulting E was below our estimated value of θ and in both cases the cell density increased by 26%, com-pared to the controls, during the 24-hour experiment. These data may be interpreted as the results of a combination of increased growth rate along with decreased sensitivity to contact inhibition. To the extent that the cells are not contact-inhibited, we can infer that they bypass R.

Results and discussion
The doubling time, τ n , of various fibroblasts was measured, as was the doubling time of fibrosarcoma cells, τ c (see Table 1). Whereas doubling times can be dependent on the passage level in the case of non-immortal cell lines, as well as the culture medium, doubling times of normal cells were determined only at low passage and represent the lowest doubling times observed. Under these conditions it is reasonable to suppose that the observed doubling times of the fibroblasts were indeed representative of the true doubling times and did not reflect the trapping of some cells in G 0 .  For exponentially growing cells, it can be shown that the ratio, r, of the cell densities of the redox-biased fibroblasts compared to the non-redox-biased fibroblast controls is given by In the experiment of Hutter et al., the cell density of the Ebiased fibroblasts was 26% greater than that of the unbiased cells, so we set r = 1.26 in (1). The duration of their experiment was T = 24 h. As noted above, τ n for CUA-4 cells = 24.1 h. We then deduce from (1) that τ e = 18.  Moreover, using the data from (1), we have computed the doubling time of the 3T3 cells to be 15.40 h and that of the cells if they had skipped G 1pm to be 11.82 h. The ratio of these is The close correspondence of all three of these ratios supports our hypothesis that cells in which E is continually below θ skip G 1pm .
Although these numbers do not necessarily prove that Ebiased normal cells skip G 1pm , they do show that their doubling time is the same as that of fibrosarcoma cells. This result may be consistent with these cells bypassing R by skipping G 1pm . Yet it is possible that the doubling time is shorter only because none of the cells can now enter G 0 , whereas without the E bias, some of the cells can enter G 0 . This possibility seems unlikely, however, because of the way the doubling times were measured. In any case, these data do demonstrate a redox-mediated bypass of R that reduces the doubling time of the normal cells to about 75% of its former value. Data of the sort obtained by Zetterberg & Larsson [1] for these CUA-4 cells and for the fibrosarcoma cells would help determine how closely the cycle period of normal cells corresponds to what would be the period if the normal cell would have skipped G 1pm .
Nevertheless, there are other types of transformed cells that apparently behave differently. For example, Irani et al. note that 3T3 cells transformed with H-ras V12 produce superoxide constitutively, and such production is required for their uncontrolled proliferation [14]. Exposure of these cells to a reductant such as NAC inhibits their growth. In contrast, these authors report in an earlier paper that there is little if any response of Raf-transformed 3T3 cells to NAC [15]. Finkel reconciles these results [16] by suggesting that in some cells, ROS may mediate growth regulatory pathways, whereas in other cells, the data suggest that ROS play a role in apoptotic pathways. Furthermore, other data may appear to be inconsistent with our proposal of how E affects cell proliferation. For example, Szatrowski and Nathan report that ROS production is increased in cancer cells [17]. Radisky et al. report that experimental evidence indicates a direct link between abnormal signal transduction by oxygen species, that is redox signaling, and malignant invasive cell growth [18]. In addition, Chiarugi and Cirri point out that transduction by ROS, through reversible phosphotyrosine phosphate, is triggered by growth-factor receptors [19]. Nevertheless, none of these results show that the increase in ROS levels is sufficient to affect E significantly, nor do they contradict the hypothesis of bypassing G 1pm . Indeed, attempts to measure the effect of increased physiological concentrations of ROS have been shown to be inadequate to alter cellular E [20] as defined here, and as seen by the molecules in the cell. The addition of NAC to a cell does not always alter the [GSSG]/[GSH] ratio (21). Martindale and Holbrook [22] conclude that at the cellular level, the response of cells to oxidants can range from proliferation, to growth arrest, to senescence, and to cell death. The particular response varies from one type of cell to the next, the agent, its dosage and duration of treatment [23].

Conclusion
In summary, we have presented two independent sets of experimental data that are consistent with the difference between the cell-cycle period of fibroblasts and transformed SV-3T3 cells approximating the G 1pm fraction of the cycle period of the fibroblast controls, as measured by Zetterberg and Larsson [1]. Moreover, the data demonstrate that by imposing an external E bias on the fibroblasts, they can be made to mimic the fibrosarcoma cellcycle period and its bypassing of R. These data support our hypothesis that a low E can cause the fibrosarcoma cells to skip G 1pm . This hypothesis has therapeutic ramifications. Larsson et al. have suggested that further insight into the differences between normal and transformed cells could be useful in the search for anti-tumor agents [3]. Our hypothesis leads to the conclusion that increasing the E of the some tumor cells will not only prevent their skipping G 1pm , but may result in these cells being arrested in G 1pm , and selectively undergoing apoptosis [6]. An experiment that would partially test our theory would be to raise the E of proliferating fibroblasts gradually by adding a GSH-decreasing agent, such as diamide plus BCNU [23]. We predict that cell proliferation would be unaffected as E rises, but when E exceeds the value we have identified as the threshold, proliferation will come to a stop. Such a response could be exploited to provide a new treatment modality for some forms of cancer.

Methods
The doubling times of tumor cells were measured and compared to those of proliferating normal cells. Doubling times were determined for cultures grown in Delbecco's modified minimal essential medium supplemented with 10% fetal bovine serum. This formulation was determined to provide the shortest doubling times for the cells studied. Although doubling times of these cell strains are dependent upon passage level (for fibroblasts) and the growth media used, including the brand and lot of serum, this formulation provided fairly consistent results across experiments and passage levels while retaining the relative difference between the normal cell strains and the fibrosarcoma cells. Cell counts were measured in duplicate in a hemocytometer every 24 h for 96 h. The counts were plotted on a log scale and were fitted to a straight line by linear regression. The standard error in the counts with respect to the line of regression was less than 2.5% for all curves. The correlation coefficients of all the growth lines were in the range 0.91-0.93.