A Mathematical Model for Elongation of a Peptide Chain

Model Status

This is the original unchecked version of the model imported from the previous CellML model repository, 24-Jan-2006.

Model Structure

Protein expression is an essential feature of cellular development and operation. The process involves the transcription of genes (DNA) into messenger RNA (mRNA) molecules, which are then translated into polypeptide chains, and finally folded and chemically modified to become functioning protein molecules. Transcription and translation are highly regulated processes, with activator, inhibitor and catalyst molecules controlling the rates of the reactions.

In 2001 Donald Drew published a mathematical model consisting of differential equations representing the rate of change in the concentration of each protein involved in polypeptide synthesis. The model also has the ability to account for the activating or inhibiting effects of transcription factors on the rate of gene transcription. This model describes each reaction in terms of kinetic rate constants for sub-parts of the overall reaction. One sub-process is peptide chain elongation which occurs during the translation of mRNA into a polypeptide. The process of elongation occurs as amino acids are added to the growing chain, one by one, facilitated by the ribosome which holds the mRNA molecule in the correct position, and the transfer RNA (tRNA) molecules which bring in the complementary amino acids. The binding of an aminoacyl-tRNA (amino acid bound tRNA complex - aa-tRNA) to the complementary site on a ribosome is catalysed by the elongation factor Tu complex (EF-Tu). EF-Tu, aa-tRNA and GTP bind together in a multi step process to form a stable ternary complex which then binds to the ribosome.

In the 2003 publication described here in CellML (see below), Heyd and Drew developed a mathematical model of the operation of the ribosome during peptide elongation. In addition, the reset sb-process for the elongation process is modelled (see the figure below). They found that the rate of peptide elongation is a function of the concentration of the amino acid to be bound and the concentration of all the other amino acids. In addition, the overall elongation rate depends on the concentration of elongation factors.

The complete original paper reference is cited below:

A Mathematical Model for Elongation of a Peptide Chain, Andrew Heyd and Donald A. Drew, 2003, Bulletin of Mathematical Biology , 65, 1095-1109. (Full text (HTML) and PDF versions of the article are available on the Bulletin of Mathematical Biology website.) PubMed ID: 14607290

The following variables are the various states that were accounted for in the multi-step model: A - EF-Tu:aa-tRNA complex. A1 refers to the correct complex, A2 is the wrong complex. B - open A-site on ribosome (ribosome is able to any amino acid). C - initial binding. D - codon recognition. E - GTPase activation and GTP hydrolysis. F - EF_tu released after EF-Tu conformation change. G - accommodation and peptide transfer. The sub-states in the sub-process of G resetting are: G' - ribosome after peptide transfer. H - EF-G. I - binding of EF-G. J - GTP hydrolysed. K - conformation change inducing transition state. L - tRNA and mRNA movement. M - ribosome returns to ground state. B - EF-G (GDP) and tRNA dissociate, ribosome is completely reset with an open A-site.