Speed-Energy-Efficiency Trade-off in Hsp70 Chaperone System.

Proteins must fold into their native structure to carry out cellular functions. However, they can sometimes misfold into non-native structures, leading to reduced efficiency or malfunction. Chaperones help prevent misfolding by guiding proteins to their active state using energy from ATP hydrolysis. Experiments have revealed numerous kinetic and structural aspects of how various chaperones facilitate the folding of proteins into their native structure. However, what remains missing is a fundamental theoretical understanding of their operational mechanisms, especially the limits and constraints imposed on their efficiency by energy flow and dissipation. To address this, we built a kinetic model of the Hsp70 chaperone system by incorporating all key structural and kinetic details. Then, using the chemical kinetic equations, we investigate how energy expenditure shapes the efficiency of Hsp70 chaperones in the proper folding of misfolded proteins. We show that ATP consumption by chaperones significantly enhances the folding of proteins into their native states. Our investigations reveal that a chaperone achieves optimal efficiency when its binding to misfolded proteins is much faster than the misfolding kinetics of that protein. We also demonstrate the presence of an upper bound on a chaperone's efficiency of protein folding and its overall rescue rate. This upper bound increases with energy dissipation until it reaches a saturation point. Furthermore, we show a speed-energy-efficiency trade-off in chaperone action, demonstrating that it is impossible to simultaneously optimize the efficiency of chaperone-assisted protein folding and the energy efficiency of the process.