On the kinetics and thermodynamics of templated polymerisation: graphs, paths, and proofreading motifs
File(s)
Author(s)
Qureshi, Benjamin Javed
Type
Thesis
Abstract
Biological systems use template molecules, such as DNA or mRNA, to catalyse the production of specific, sequence dependent polymers, such as proteins. Templated polymerisation is a powerful mechanism for the production of complex molecules, which can store information. As such, templated polymerisation is both widely utilised in biology, and promises to be useful for synthetic systems.
Templated polymerisation is used to create daughter polymers with specific sequences. The newly created daughter polymer needs to be separated from the template, meaning no long-term interactions with the template may bias the distribution of daughter polymers. This observation makes templating a highly non-trivial process, with interesting thermodynamic consequences. Templated polymerisation processes can have complex reaction steps leading to monomer incorporation, such as kinetic proofreading, to improve their accuracy. These complex sub-steps often involve coupling to fuel reservoirs, leading to trade-off between free-energy costs, speed and accuracy. Further, these sub-steps can lead to correlations between monomers within the daughter copolymer.
In this thesis, I first introduce a framework for solving a broad class of detailed polymerisation models. This framework allows, for the first time, for the solving of thermodynamically consistent, complex polymerisation models with dependence on monomer incorporation rates on previous monomers in the growing polymer. After having studied detailed polymerisation models with this framework, I zoom out to study a class of enzymatic templating systems, focusing on the effects of multiple pathways leading to creation/degradation of polymers. Here, I derive fundamental bounds on the accuracy of these multi-pathway polymerisation systems as a function of the free-energies changes along the pathways.
Templated polymerisation is used to create daughter polymers with specific sequences. The newly created daughter polymer needs to be separated from the template, meaning no long-term interactions with the template may bias the distribution of daughter polymers. This observation makes templating a highly non-trivial process, with interesting thermodynamic consequences. Templated polymerisation processes can have complex reaction steps leading to monomer incorporation, such as kinetic proofreading, to improve their accuracy. These complex sub-steps often involve coupling to fuel reservoirs, leading to trade-off between free-energy costs, speed and accuracy. Further, these sub-steps can lead to correlations between monomers within the daughter copolymer.
In this thesis, I first introduce a framework for solving a broad class of detailed polymerisation models. This framework allows, for the first time, for the solving of thermodynamically consistent, complex polymerisation models with dependence on monomer incorporation rates on previous monomers in the growing polymer. After having studied detailed polymerisation models with this framework, I zoom out to study a class of enzymatic templating systems, focusing on the effects of multiple pathways leading to creation/degradation of polymers. Here, I derive fundamental bounds on the accuracy of these multi-pathway polymerisation systems as a function of the free-energies changes along the pathways.
Version
Open Access
Date Issued
2024-09-23
Date Awarded
01/05/2025
License URL
Advisor
Ouldridge, Thomas
Publisher Department
Department of Bioengineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)