The code provided models the sodium-potassium (Na⁺/K⁺) pump, a vital membrane protein known as Na⁺/K⁺-ATPase. The Na⁺/K⁺ pump is crucial for maintaining the electrochemical gradients of sodium and potassium ions across the cell membrane, which are essential for numerous cellular processes, including electrical excitability, nutrient transport, and osmotic pressure regulation. ### Key Biological Concepts: 1. **Ion Gradients**: The Na⁺/K⁺ pump actively transports sodium and potassium ions against their concentration gradients, using energy from ATP hydrolysis. For each cycle, the pump typically exports three Na⁺ ions out of the cell and imports two K⁺ ions into the cell. This activity helps maintain the higher concentration of K⁺ ions inside the cell compared to outside, and a higher concentration of Na⁺ ions outside the cell compared to inside, creating and preserving the membrane potential. 2. **Energy Consumption and Electrical Contribution**: The code reflects these ionic movements by assigning the currents `ik` and `ina` based on the flux function. The usage of `imax` as a maximal current density represents the active transport capacity of the pump. The coefficients `-2` and `-3/2` in `ik` and `ina` equations capture the stoichiometry of the pump (two K⁺ ions imported for three Na⁺ ions exported per cycle), reflecting the consumption of energy and contribution to the cell's current balance. 3. **Kinetic and Affinity Constants**: Parameters `km_k` and `km_na` represent the Michaelis-Menten constants for potassium and sodium, respectively. These constants are critical in depicting the affinity of the Na⁺/K⁺ ATPase for its substrates, influencing how the rate of pumping adapts to changes in intracellular and extracellular ion concentrations. 4. **Ion Homeostasis and Cellular Function**: This model highlights the pump's role in maintaining ion homeostasis and cellular functioning. Dysfunctional Na⁺/K⁺ pumps can lead to cell depolarization and have been implicated in various medical conditions, including heart failure and certain neurological disorders. In summary, the code models the Na⁺/K⁺ pump's essential role in maintaining the electrochemical gradients necessary for proper cellular and neuronal function by simulating the ionic currents through mathematical representations. This model captures several crucial biological aspects such as stoichiometry, ion affinity, and effects on membrane potential, which are imperative for understanding electrophysiological behavior in excitable cells.