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This paper develops a stochastic kinetic model of loop extrusion by condensin, incorporating a "scrunching mechanism" to explain both forward and backward steps observed in magnetic tweezer experiments. The model quantitatively reproduces force-dependent step size and dwell time distributions in both directions. A key finding is the prediction of an intermediate state with a lifetime that initially increases with force, characteristic of catch bonds, before decreasing at higher forces.
Condensin's loop extrusion mechanism relies on catch bonds, meaning that, counterintuitively, applying a small amount of force actually *increases* the lifetime of a key intermediate state.
Structural Maintenance Complexes (SMC) are energy consuming motors that are important in folding the genome by loop extrusion (LE) in all stages of the cell cycle. Single molecule magnetic tweezer pulling experiments have revealed that condensin, a member of the SMC family involved in mitosis, takes occasional backward steps, thus coughing up the gains in the length of the extruded loop. To reveal the mechanism of the forward and backward steps simultaneously, we developed a theory using the stochastic kinetic model and the scrunching mechanism for LE. The calculations quantitatively account for the measured force-dependent step size and dwell time distributions in both the directions. By postulating the existence of an intermediate state in the ATP-driven cycle that is poised to take a forward or a backward step, we predict that its lifetime increases as the external mechanical force increases till a critical value and subsequently decreases at higher forces. The surprising finding of lifetime increase in an active motor, at sub-piconewton forces, is the characteristic of catch bonds, known in force-induced rupture of several passive protein complexes. The identification of catch bond-like states in condensin not only expands our understanding of LE but also highlights the significance of mechanical forces in regulating genome organization.
