Multistate Kinetic Model of the Sodium-Potassium ATPase

The Na,K-ATPase is a complex membrane protein that exploits the hydrolysis of ATP as a source of chemical energy to actively transport K⁺ and Na⁺ ions against their electrochemical potential gradient across the cellular membrane. The function of this ATP-driven ion pump is broadly explained by the schematic Post-Albers alternating-access mechanism. Accordingly, the free energy gained from the phosphorylation/dephosphorylation processes, where the γ-phosphate of ATP is transferred to a conserved Asp located on a cytoplasmic domain of the protein, is used by the enzyme to interconvert between two main conformational states. As a result of experimentally determined structures at atomic resolution, a detailed Post-Albers transport cycle of Na,K-ATPase can comprise more than 20 conformational states of the system. This presents a great opportunity to formulate a detailed multistate kinetic framework model of the transport cycle of the Na,K-ATPase, displaying the thermodynamic and biophysical constraints under which it must operate. Particular attention is given to the effect of coupling to the membrane potential via incremental displacement charges for the microscopic steps of the transport cycle. On the multistate kinetic framework, a simplified continuous model of the transport cycle based on the Smoluchowski equation is formulated, and its consequences on the kinetic efficiency of the turnover rate are explored. These considerations lead to the conjecture that the free energy of the microstates of Na,K-ATPase is optimized for achieving a fast turnover rate when the membrane is depolarized.