Energy-based bond graph models of glucose transport with SLC transporters

Abstract

The SLC (solute carrier) superfamily mediates the passive transport of small molecules across apical and basolateral cell membranes in nearly all tissues. In this paper we employ bond graph approaches to develop models of SLC transporters that conserve mass, charge and energy, respectively, and which can be parameterised for a specific cell and tissue type for which the experimental kinetic data is available. We show how analytic expressions that preserve thermodynamic consistency can be derived for a representative four- or six-state model, given reasonable assumptions associated with steady-state flux conditions. We present details on fitting parameters for SLC2A2 (a GLUT transporter) and SLC5A1 (an SGLT transporter) to experimental data and show how well the steady-state flux expressions match the full kinetic analysis. Since the bond graph approach will not be familiar to many readers, we provide a detailed description of the approach and illustrate its application to a number of familiar biophysical processes. SIGNIFICANCEPhysiological systems typically involve coupled mechanical, electrical and chemical processes, with energy acting as a universal currency across these domains. We propose a new visual representation for all components of these processes using bond graphs. Bringing all physical processes under one consistent framework greatly simplifies the task of understanding multiscale physiological processes. This energy-based framework, which is the 0D version of a more general 3D port-Hamiltonian theory, can be used to model all lumped parameter physiological processes. A small number of bond graph templates can be used to model all members of the large SLC transporter family, and reduced thermodynamically consistent steady-state flux models provide a useful simplification for many situations. Glucose transport is chosen here to illustrate the bond graph approach because it represents the first step in cell metabolic processes, where energy conservation needs to be a fundamental characteristic of quantitative models. Our future work on cell metabolism will build on the foundation established here.