Работа посвящена численному исследованию известной математической модели динамики системы p53-Mdm2-Wip1 при различных воздействиях, приводящих к повреждениям ДНК. Главное внимание уделено ранее не рассматривавшимся методическим аспектам - оценке чувствительности модели, качественному анализу свойств решения в биологически адекватном диапазоне значений параметров, анализу применимости модели к описанию критических состояний системы, связанных с известными дегенеративными заболеваниями. Показано, что простейшая модификация исходной модели делает ее существенно более эффективным инструментом для численного анализа широкого диапазона состояний системы p53-Mdm2-Wip1
In the context of the survival and death of cells with DNA damage, a special role is assigned to the p53 protein. The management of p53 and its inhibitors can provide a protective effect in a wide range of degenerative diseases, such as cancer, infarctions, and dementia. Therefore, there are increased requirements for mathematical models designed to study the mechanism of functioning of the p53 signaling pathway. Our work is devoted to the study of the properties of the well-known mathematical model of the dynamics of the p53-Mdm2-Wip1 system under various influences leading to DNA damage. A simple modification of the model is proposed. The main attention is paid to the analysis of the sensitivity and qualitative properties of solutions, as well as the validation of the model before and after its modification. In numerical experiments, it was found that within the framework of the accepted models, the stationary state of the p53-Mdm2-Wip1 system can be unstable to negligible changes in the initial conditions, so that the system can function under the same parameter values according to the bifurcation scenario with a doubling of the period. The mathematical conditions under which the multiplicity of solutions and complex dynamic modes were detected allow for a biological interpretation as a reflection of the variability in the response of the p53 protein pathway to the damage signal. The range of applicability of the models was compared using the example of a wellknown laboratory experiment, in which the most complete set of observed in vitro and in vivo states of the p53-Wip1 system was demonstrated when irradiating cancer cells with wild-type p53. It is shown that the simplest modification of the original model significantly expands the scope of its applicability, allows describing the transition from normal to critical states of the system associated with known degenerative diseases. Thus, the modified model is a more effective tool for numerical analysis of a wide range of states of the p53-Mdm2-Wip1 system