Epitopes of T-cells (tregitopes) are linear sequences of amino acids present in many animal and human proteins. Tregitopes suppress the immunological response and could play a significant regulatory role in the pathogenesis of autoimmune diseases. They modulate T-cell response activated by the antigens of the major histocompatibility complex class I (MHC-I).The aim of this study was an attempt to determine the correlation between physicochemical properties and structures of tregitopes and their binding strength with MHC-I. 21 amino acid sequences of immunoglobulin G with verified or similar to tregitopes function were selected. The analysis of the binding strength with MHC-I was carried out on 41 various alleles since MHC-I can be coded by numerous alleles. The first phase of study attempted to find a correlation between the half minimal inhibitory concentration (LogIC50) calculated for MHC-I and physicochemical properties. From formulated arithmetic statements, only one allowed to determine significant correlation with LogIC50 with reference to alleles A*02:01 and A*02:06. The correlations for the alleles were linear and sigmoid, respectively (p<0.001). The presence of the repeated amino acids was confirmed in the sequences of the studied compounds. These amino acids are connected with stronger binding or lack of the binding with MHC-I expressed by LogIC50. The study shows the translation from the classification (cloud) model to the linear one. The significant linear dependence between chemical structure of tregitopes and their LogIC50 calculated for MHC-I was displayed. The presented method can be used in screening of new sequences that have regulatory properties for regulatory T-cells.