Speed–Energy–Efficiency Trade-offs in the Hsp70 Folding Cycle

Protein molecules must reach their native conformation to perform their biological functions, yet they frequently misfold into alternative structures that impair functionality. The Hsp70 family of molecular chaperones assists folding through ATP-dependent cycles of binding and release. While numerous studies have mapped structural intermediates and kinetic transitions, a quantitative theoretical framework clarifying how energy consumption restricts or enhances chaperone performance remains limited. Here, we develop a detailed kinetic model of the Hsp70 cycle that incorporates both experimentally determined structural states and rate parameters. By solving the chemical master equations, we characterize how ATP hydrolysis influences folding yields. Our results show that nucleotide-driven cycles substantially improve the probability of reaching the native state compared to spontaneous folding. We identify a regime of optimal performance in which substrate recognition occurs on a timescale much faster than spontaneous misfolding. Importantly, the analysis predicts a strict ceiling on achievable efficiency and folding rescue rates. This limit increases with dissipation but eventually saturates. Finally, the framework uncovers a fundamental trade-off: accelerating folding and maximizing rescue efficiency requires greater energy expenditure, implying that speed, energy cost, and efficiency cannot be simultaneously optimized in Hsp70-assisted folding.