A simple geometrical model of the electrostatic environment around the catalytic center of the ribosome and its significance for the elongation cycle kinetics

The central function of the large subunit of the ribosome is to catalyze peptide bond formation. This biochemical reaction is conducted at the peptidyl transferase center (PTC). Experimental evidence shows that the catalytic activity is affected by the electrostatic environment around the peptidyl transferase center. Here, we set up a minimal geometrical model fitting the available x-ray solved structures of the ribonucleic cavity around the catalytic center of the large subunit of the ribosome. The purpose of this phenomenological model is to estimate quantitatively the electrostatic potential and electric field that are experienced during the peptidyl transfer reaction. At least two reasons motivate the need for developing this quantification. First, we inquire whether the electric field in this particular catalytic environment, made only of nucleic acids, is of the same order of magnitude as the one prevailing in catalytic centers of the proteic enzymes counterparts. Second, the protein synthesis rate is dependent on the nature of the amino acid sequentially incorporated in the nascent chain. The activation energy of the catalytic reaction and its detailed kinetics are shown to be dependent on the mechanical work exerted on the amino acids by the electric field, especially when one of the four charged amino acid residues (R, K, E, D) has previously been incorporated at the carboxy-terminal end of the peptidyl-tRNA. Physical values of the electric field provide quantitative knowledge of mechanical work, activation energy and rate of the peptide bond formation catalyzed by the ribosome. We show that our theoretical calculations are consistent with two independent sets of previously published experimental results. Experimental results for E.coli in the minimal case of the dipeptide bond formation when puromycin is used as the final amino acid acceptor strongly support our theoretically derived reaction time courses. Experimental Ribo-Seq results on E. coli and S. cerevisiae comparing the residence time distribution of ribosomes upon specific codons are also well accounted for by our theoretical calculations. The statistical queueing time theory was used to model the ribosome residence time per codon during nascent protein elongation and applied for the interpretation of the Ribo-Seq data. The hypo-exponential distribution fits the residence time observed distribution of the ribosome on a codon. An educated deconvolution of this distribution is used to estimate the rates of each elongation step in a codon specific manner. Our interpretation of all these results sheds light on the functional role of the electrostatic profile around the PTC and its impact on the ribosome elongation cycle.