Protein-DNA Clusters Explain the Non-ExponentialDNA Residence Time Distributions of TranscriptionFactors

The transcription process is regulated by temporal interactions of transcription factors with DNA. In the last decade, computational and experimental studies revealed the residence times of transcription factors on DNA correlate with transcriptional output. Biochemical studies suggest that transcription factor bindings exhibit bi-exponential dynamics, often explained by the binary affinity model composed of nonspecific and specific protein-DNA interactions. Recently, transcription factor residence times were shown to display a power law in vivo implicating effective protein-DNA interactions controlling the dissociation kinetics are rather more complex than suggested. One contribution that can cause such continuous residence-time distributions could be higher-order protein-DNA complexes or protein coacervates. Here, by using molecular dynamics simulations of a coarse-grained polymer model for bacterial chromosomes interacting with homodimeric transcription factors at physiologically relevant concentrations, we demonstrate that residence time distributions of dimeric proteins follow a multi-exponential pattern even when a single interaction describes the affinity between DNA and protein. Our simulations reveal that this emergent behavior is due to the formation of DNA-protein clusters of various sizes at a wide range of protein concentrations and affinities. These findings add another layer to transcriptional regulation and, consequently, to gene expression by connecting transcription factor concentrations and affinities, DNA-protein clusters, and DNA residence times of transcription factors.