Cooperativity has been a fundamental concept in our understanding of biological systems for over a century. Here, we describe the observation of cooperative binding that exhibits long-lived hysteresis and cannot be described by a standard Hill model. Inspired by the Ising model of ferromagnetism, we describe this hysteresis as a consequence of cooperative binding in the limit of large complexes. We provide a method to relate the amount of hysteresis to the strength of the neighboring interactions between bound proteins and DNA. This novel kinetic feature of macromolecular complexes allows cells to create a binary response to small changes in external conditions and causes complexes to retain a memory of past conditions over long timescales.

Abstract

In all organisms, DNA molecules are tightly compacted into a dynamic 3D nucleoprotein complex. In bacteria, this compaction is governed by the family of nucleoid-associated proteins (NAPs). Under conditions of stress and starvation, an NAP called Dps (DNA-binding protein from starved cells) becomes highly up-regulated and can massively reorganize the bacterial chromosome. Although static structures of Dps–DNA complexes have been documented, little is known about the dynamics of their assembly. Here, we use fluorescence microscopy and magnetic-tweezers measurements to resolve the process of DNA compaction by Dps. Real-time in vitro studies demonstrated a highly cooperative process of Dps binding characterized by an abrupt collapse of the DNA extension, even under applied tension. Surprisingly, we also discovered a reproducible hysteresis in the process of compaction and decompaction of the Dps–DNA complex. This hysteresis is extremely stable over hour-long timescales despite the rapid binding and dissociation rates of Dps. A modified Ising model is successfully applied to fit these kinetic features. We find that long-lived hysteresis arises naturally as a consequence of protein cooperativity in large complexes and provides a useful mechanism for cells to adopt unique epigenetic states.