In this article one of the possible mathematical models of potassium ion channel with mobile structure is discussed. The basic conception of the model was developed earlier. This conception postulates the conformational changes in the channel molecule caused by the strong local electric field of the permeating ions inside the channel. Charged groups, moved by this field, slowly relax to the initial position after the ion passing and affect the energy profile for subsequent permeating ions. The system shows the self-organization, which leads to the appearance of the discrete open and closed conductivity states. This conception is applied to the potassium channel The model correctly describes the activation-deactivation processes. A special attention is paid to the concentration dependencies of the channel's kinetic constants and states occupancy probabilities, which are qualitatively explained. It is shown that Hodgkin-Huxley parameters α and β are [K_out]-dependent and the channel conductance in the closed state is much more sensitive to [K_out] than in the open one. The existence of the non-monotonous concentration dependencies, obtained in some experiments, is investigated. It is shown that the model proposed gives essentially monotonous dependencies. Some unusual features of volt-ampere characteristics are explained. The results obtained are compared with the experimental data earlier reported.