Molecular diffusion and binding kinetics are sufficient to explain condensate-like nuclear clustering

Abstract

Many key transcriptional regulators form clusters in cell nuclei that are proposed to promote transcription by concentrating reactants. These clusters exhibit emergent biophysical properties consistent with biomolecular condensates such as high local densities, spherical morphologies, fusion, and rapid molecular exchange kinetics. Whether these properties are specific hallmarks of condensation or can arise from simpler mechanisms is unclear. Here we developed SPARK (Simulation of Protein Accumulation from Reaction Kinetics), a computational framework parameterized by genomic, and molecular diffusion and binding kinetics data, to simulate the spatial distributions of chromatin-binding proteins as they would appear under an optical microscope. These simulations recapitulate key reported features of Brd4, Nanog, Sox2, and Bicoid clusters, without including any higher-order protein-protein interactions or phase separation. We demonstrate that commonly used signatures of condensates instead emerge directly from molecular scale binding and diffusion kinetics. Through systematic variation of nuclear concentrations and enhancer binding-site composition, we show that distinct combinations of molecular kinetics can result in similar spatial distributions of transcription factors. These analyses establish that imaging-based features of protein clusters cannot uniquely define the underlying physical mechanism of their formation. We therefore conclude that condensation is not required to drive transcription factor occupancy and that protein-protein interactions off chromatin are not required to explain cluster formation. Our results instead imply that mechanisms other than clustering are sufficient for target-search acceleration and robust occupancy. SPARK thus provides a quantitative null model for identifying which molecular mechanisms are necessary to explain experimental observations of nuclear protein clustering.