APPROACH TO EVALUATE THE RISK OF CANCER FOR DIFFERENT NUMBER OF TUMOR SUPPRESSOR GENES IN THE INDIVIDUAL

Significant progress in understanding the mechanisms of carcinogenesis is associated with the discovery of tumor suppressor genes (or antioncogenes). It is known that in the human population, the number of normally functioning suppressor genes varies in different individuals at birth. The aim of the study was to assess the probability of cancer development in an individual with a different initial number of undamaged normally functioning antioncogenes. On the basis of the probabilistic mathematical model of carcinogenesis, the most probable age of cancer development depending on the number of intact antioncogenes was assessed. As a result of the studies, the probability of cancer development depending on the age of the patient is estimated. The dependence of the probability of cancer development in an individual on the number of undamaged antioncogenes is also investigated. The analysis of the significance of the number of tumor suppressor genes, the damage of which may be the cause of initiation of cell malignancy, has been carried out.

The purpose of this study was the development of a methodology for assessing the probability of cancer development in an individual with a different initial number of undamaged normally functioning tumor suppressor genes.

RESULTS AND DISCUSSION
Proceeding from the fact that tumor formation is a probabilistic process, we will use for its description laws and concepts of probability theory.Let's introduce some assumptions and parameters.
Let N be the maximum number of oncopotent cells in an individual; k is the initial number of TSGs in an arbitrarily chosen individual.
The values of the parameters N and k are unknown a priori, and their estimation is the main problem in constructing the model.In further calculations, we will assume that the duration of the cell cycle is one day (this is typical for the HeLa cell line), and the probability of mutational damage of one tumor suppressor gene in one act of division is 5 10 − [20].At given values of N and k, the values of the most probable age, as well as the average age of the individual in which cancer can develop, can be calculated and thereby an acceptable correct estimate of these ages can be obtained.But since the numerical values of the parameters N and k are unknown, in this paper we discuss only the methodology of estimating the probability of cancer developing at a certain age at a different number of undamaged normally functioning TSGs.
In our previous studies [21], a probabilistic mathematical model was constructed that makes it possible to calculate the most probable age (τ) of the individual, in which the cancer develops, depending on the number (k) of TSGs present in the cells.Equation for calculation this age was solved in numerical terms and has the form where T is duration of one cycle of cell division; Then the dependence of the values of the most probable age of the individual, in which the cancer develops, on the values of the parameter k has the form shown in Figure 1.
As can be seen from the graph, the greater the number of undamaged TSGs present in an individual, the greater the probability that he/she will develop cancer at a later age.Cases in which k = 1 and 2 are too unlikely for oncological disease to occur.Cases in which k = 7 and 8 correspond to an age of more than 100 years, which is not taken into account in the statistical data on the cancer incidence.
Figure 2 shows the dependence of the probability of cancer development on the age of the individual.Data on the number of n = 8288 cancer patients were obtained in the archive of the S.P. Grigoryev Kharkov Institute of Medical Radiology.
We compared the results of the study presented in Figures 1 and 2. Knowing the most probable age (t) for the cancer development in individuals for various numbers of intact TSGs (k), using data on the probability (p) of oncological disease development depending on the age of the patient, the probability of cancer development in the individual at the corresponding value of TSGs number (k) can be determined.It can be seen from the graph that the probability of cancer development at 3 k ≤ and 7 k ≥ are practically equal to zero.Thus, the contributions of these numbers of undamaged TSGs to the general distribution can be neglected.
Suppose that for the values of the number of undamaged TSGs equal to k = 4; 5 and 6, the quantities 4 .Thus the following numbers of undamaged TSGs are the significant quantities for cancer developing: k = 4; 5 and 6.
Of course, further studies may require a significant correction of the values of both the parameter N and the parameter k.In addition, the accuracy of the method for assessing the probability of cancer development at a different number of intact TSGs based on the calculation of the most probable age of oncology development depends on the volume of statistical data.

CONCLUSIONS
1.The estimation of the most probable age of the individual in which the oncological disease occurs is performed, depending on the number of intact TSGs present in individual.
2. On the basis of experimental data, the probability of cancer development depending on the patient's age is analyzed.
3. The dependence of the probability of cancer development in an individual on the number of intact TSGs present in individual is studied.
4. The analysis of the significance of the number of TSGs, the damage of which may cause initiation of cell malignancy, has been carried out.
5. A methodology for estimation of probability of cancer development in an individual at a different number of intact TSGs has been developed.

1 ,
α -the probability of damaging one TSG in one division cycle.Let, for example, the maximum value of number

Fig. 1 .Fig. 2 .
Fig. 1.Dependence of the most probable age of the individual in which the cancer develops on the number (k) of undamaged TSGs .

Fig. 3 .
Fig. 3. Dependence of the probability (p) of cancer development in an individual on the number (k) of intact TSGs.