Cellular physiology operates at the theoretical limits set by physical laws – for example, ion channels are sensitive to the passage of a single elementary charge, and retinae can detect one photon. Eukaryotic cells also exploit every form of energy storage mechanism available – biochemical (e.g., solute concentrations and chemical bonds), electrical (e.g., capacitive charge storage in the cell membrane), mechanical (e.g., the elastic compliance of cellular membranes), and thermal (the heat storage essential for maintaining body temperature). Since cells appear to have evolved to maximally exploit the laws of physics within their particular environmental niche, we should try to explain cell behaviour in the light of those laws.

This talk will present an analysis of cell homeostasis using a ‘bond graph’ modelling approach that ensures that the conservation laws of physics (i.e., conservation of mass, charge, and energy, respectively) are satisfied for the interdependent biochemical, electrical, mechanical, and thermal energy storage mechanisms operating within the cell. The bond graph approach is applied to several cell membrane transport mechanisms and then used to consider how physics constrains intracellular electrolyte homeostasis for enterocytes (the epithelial absorptive cells in the lining of the intestinal mucosa). The model includes the electrogenic sodium-potassium ATPase pump (NKA) and an inwardly rectifying potassium channel (Kir) in the basolateral membrane, the electrogenic sodium-driven glucose transporter (SGLT1) in the apical membrane, and the glucose transporter (GLUT2) expressed in both membranes.

Glycolysis converts the imported glucose to ATP to drive NKA. For specified levels of sodium (Na⁺), potassium (K⁺), and glucose in the blood, the model demonstrates how enterocytes absorb Na⁺ and glucose from the lumen and transfer glucose to the blood while maintaining the membrane potential and homeostasis of intracellular Na⁺ and K⁺. The Gibbs free energy available from the ATP hydrolysis ensures that the cell operates as a ‘sodium battery’ with a high external to internal ratio of Na⁺ concentration in order to provide the energy for many other cellular transport processes. We show balanced homeostasis of Na⁺, K⁺, glucose, ATP, and membrane potential under varying levels of glucose in the lumen. We demonstrate that this balance is due to the 3:2 stoichiometry of Na⁺/K⁺ exchange in NKA, the 2:1 Na⁺/glucose cotransport in SGLT1, the 1:2:2 ratio between glucose consumption, ATP, and water production in glycolysis, the K⁺ efflux through Kir, and the glucose transport via GLUT2. We analyse the energy costs of varying the ratio of GLUT2 to SGLT1 in the apical membrane of the enterocyte. We also show how the flux for SLC transporters, ATPase pumps and ion channels can be expressed in a consistent and thermodynamically valid expression.  

A bond graph approach captures the laws of physics at the appropriate scale for understanding physiological mechanisms. In the example presented here, a biophysical analysis of enterocyte homeostasis provides a quantitative explanation for the variable and transient expression of GLUT2 transporters, against the background of SGLT1 expression, under varying post-prandial levels of glucose and sodium in the intestinal lumen.