Kinetics of self-assembly via facilitated diffusion: formation of the transcription complex

TL;DR

This paper introduces an analytically solvable model for the self-assembly of molecular complexes on filaments driven by facilitated diffusion, comparing sequential and random binding mechanisms, with implications for transcription factor dynamics.

Contribution

The study provides a new analytical framework for understanding self-assembly via facilitated diffusion, including probability and timing of complex formation, and predictions for experimental observables.

Findings

Random binding increases the probability of complete assembly.

Completion time scales exponentially with complex size for random binding.

Sequential binding results in slower, power-law scaling of completion time.

Abstract

We present an analytically solvable model for self-assembly of a molecular complex on a filament. The process is driven by a seed molecule that undergoes facilitated diffusion, which is a search strategy that combines diffusion in three-dimensions and one-dimension. Our study is motivated by single molecule level observations revealing the dynamics of transcription factors that bind to the DNA at early stages of transcription. We calculate the probability that a complex made up of a given number of molecules is completely formed, as well as the distribution of completion times, upon the binding of a seed molecule at a target site on the filament (without explicitly modeling the three-dimensional diffusion that precedes binding). We compare two different mechanisms of assembly where molecules bind in sequential and random order. Our results indicate that while the probability of completion is greater for random binding, the completion time scales exponentially with the size of the complex; in contrast, it scales as a power-law or slower for sequential binding, asymptotically. Furthermore, we provide model predictions for the dissociation and residence times of the seed molecule, which are observables accessible in single molecule tracking experiments.