Linear-Decoupling Enables Accurate Speed and Accuracy Predictions for Copolymerization Processes.

Area of Science:

• Biophysics
• Biochemistry
• Polymer Science

Background:

• Biological processes require high accuracy and speed.
• Markov-chain copolymerization theory offers exact solutions but is nonlinear and difficult to solve.
• Enzyme-kinetics approaches simplify processes but can lack accuracy.

Purpose of the Study:

• To address the inaccuracies of the enzyme-kinetics approach in modeling biological polymerization.
• To develop a simplified, accurate approximation for steady-state probabilities in copolymer chains.
• To accurately predict the trade-offs between speed and accuracy in high-fidelity biological processes.

Main Methods:

• Proposed a simplified linear-decoupling approximation for steady-state probabilities.
• Applied the method to higher-order copolymer chains under biologically relevant conditions.
• Extended the technique to processes with proofreading and internal states, including DNA replication and transcription.

Main Results:

• The linear-decoupling approximation yields stationary speed and error rates closely matching exact Markov-chain (nonlinear) values.
• The method accurately describes the speed-accuracy trade-offs in DNA replication and transcription elongation.
• Demonstrated that the enzyme-kinetic approach can produce inaccurate fluxes even for simple polymerization.

Conclusions:

• The linear-decoupling approximation effectively overcomes the limitations of the enzyme-kinetic approach and the nonlinear complexity of the Markov-chain approach.
• This approximation ensures accurate predictions for high-fidelity biological processes.
• The findings are crucial for understanding and modeling complex biological systems like DNA replication and transcription.