Kinetic modelling of 70S ribosome and F1-ATPase - Le, Quang Luan (Nanyang Technological University, 2021)
Theoretical models have been developed to understand kinetics of ribosomes and F1- ATPase which are important enzymes responsible for protein synthesis and ATP production in cells respectively. One important aspects of protein synthesis is accuracy - translation speed relation and how it is related to overall cell growth. For F1-ATPase , it is important to understand how F1-ATPase hydrolyzes ATP molecules based on which the mechanism of ATP synthesis is deduced due to the assumption that synthesis is just the reverse of hydrolysis. A novel pseudo-GTPase activated state, which was discovered recently, may play a role in selection of cognate during initial selection phase of protein synthesis. By assuming the state to exist after codon recognition and prior GTPase activation, kinetic analysis shows that rates between codon recognition and pseudo-GTPase activation are comparable for cognates (7 s−1) and near cognates (3 s−1). However, cognate in pseudo-GTPase activated state can proceed at significantly faster rate (138 s−1) to GTPase activated compared to near cognate (0.3 s−1). The effective rate from codon recognition to GTPase activated is slowed down, thus requiring less intrinsic selectivity between two states for selection while maintain good accuracy and fast speed. The effect of free [Mg2+] on translation kinetics and accuracy has been investigated based on a coarse-grained model of detailed translation scheme. Ribosomes can be broady categorized into three states: free, initial selection and proofreading. Increasing [Mg2+] will accelerate association speed between ternary complexes (both cognates and near cognates) and free ribosomes, resulting in decrease in accuracy. Increasing [Mg2+] from 1 mM to 3 mM results in faster translation speed due to increasing association speed of cognates with sufficient free ribosomes. Despite the drop in accuracy, it is still sufficient for selection and with faster speed, ribosomes seem to operate in ”effizienter” regime. Further increase of [Mg2+] to 7 mM leads to plummet of translation speed. This is attributed to more sluggish ribosomes occupied with near cognates, causing less ribosomes for cognates. The regime is termed ”competition” highlighting the effect of near cognates on translation. The translation model is incorporated into a growth model in an attempt to study the effect of accuracy on cellular proteome and growth during exponential phase. The proteome consists of free amino acids, metabolic proteins and ribosomes. The assumption iis that accuracy affects the number of ribosomes capable of producing proteins. The remaining fraction is ribosomes with high mutations which waste amino acid. This suggests that increasing [Mg2+] leads to lower growth rate due to decreasing accuracy. Besides, free amino acid and metabolic proteins follow similar trend of translation speed due to the assumption that net peptide rate follows Michaelis-Menten kinetics. Due to assumption of constant mass, at high [Mg2+] , ribosomes show opposite trend with growth rate, suggesting second growth law. F1-ATPase kinetics during fast transition of 120 µs is revealed by analysis of bead rotation. The analysis shows the angular jump exhibits bimodal distributions. Besides, the angular jump profile varies at different angles, suggesting F1-ATPase rotates with varying speed during 120◦ rotation. The reason for bimodal distribution can be attributed to slow visco-elastic response of the bead compared to fast transition rates between states of F1-ATPase . The angular jump profile also reveals a newly postulated short-lived chemical state of F1-ATPase where all three β pockets are occupied with nucleotides. It is the state just after ATP binding and before ADP release.