This work discusses the problem of forecasting the tertiary structure of a protein, based on its primary sequence. The problem is that science, with all its computing power and a set of experimental data, has not learned to build models that describe the process of protein molecule coagulation and predict the tertiary structure of a protein, based on its primary structure. However, it is wrong to assume that nothing is happening in this field of science. The regularities of folding (convolution) of the protein are known, methods for its modelling have been developed. Analysis of the current state of research in the field of these problems indicates the presence of shortcomings associated with the accuracy of forecasting and the time necessary to obtain the optimal solution. Consequently, the development of new computational methods, deprived of these shortcomings, seems relevant. In this work, the authors focused on the lattice model, which is a special case of the known hydrophobic-polar dill. protein conformation according to the chosen model, hybrid algorithms of cloning selection, differential are proposed. Since the processes of protein coagulation have not been fully understood, the researchers proposed several simplified models based on the physical properties of molecules and which leads to problems of combinatorial optimization. A hydrophobic-polar simplified model on the planar triangular lattice is chosen as a protein model. From the point of view of the optimization problem, the problem of protein folding comes down to finding a conformation with minimal energy. In lattice models, the conformation is represented as a non-self-cutting pathway. A hybrid artificial immune system in the form of a combination of clonal selection and differential evolution algorithms is proposed to solve this problem. The paper proposes a hybrid method and algorithm to solve the protein folding problem using the HP model on a planar triangular lattice. In this paper, a hybrid method and algorithm for solving the protein folding problem using the HP model on a planar triangular lattice are proposed. The developed hybrid algorithm uses special methods for encoding and decoding individuals, as well as the affinity function, which allows reducing the number of incorrect conformations (self-cutting solutions). Experimental studies on test hp-sequences were conducted to verify the effectiveness of the algorithm. The results of these experiments showed some advantages of the developed algorithm over other known methods. Experiments have been taught to verify the effectiveness of the proposed approach. The results labelled "Best" show the minimum energy values achieved over 30 runs, while the results labelled "Medium" show the robustness of the algorithm to achieve minima. Regarding robustness, the hybrid algorithm also offers an advantage, showing higher results. A comparative analysis of the performance results of the proposed algorithm on test sequences with similar results of other published methods allows us to conclude the high efficiency of the developed method. In particular, the result is more stable, and, in some cases, conformations with lower energy are obtained. Keywords: protein folding; hydrophobic-polar model; clonal selection; differential evolution; artificial immune systems; hydrophobic-polar model.
Some Nondegenerate Limit Laws for the Selection Differential
