The purpose of this study is to contribute to understanding the role of Na+-K+-ATPase and of ionic cotransporters in the regulation of cell volume, by employing a model that describes the rates of change of the intracellular concentrations of Na+, K+, and Cl−, of the cell volume, and of the membrane potential. In most previous models of dynamic cellular phenomena, Na+-K+-ATPase is incorporated via phenomenological formulations; the enzyme is incorporated here via an explicit kinetic scheme. Another feature of the present model is the capability to perform short-term cell volume regulation mediated by cotransporters of KCl and NaCl. The model is employed to perform numerical simulations for a “typical” nonpolarized animal cell. Basically, the results are consistent with the view that the Na+ pump mainly plays a long-term role in the maintenance of the electrochemical gradients of Na+ and K+ and that short-term cell volume regulation is achieved via passive transport, exemplified in this case by the cotransport of KCl and NaCl.

The purpose of this work is to contribute to the understanding of the fundamental kinetic properties of the processes of energy coupling in biological membranes. For this, we consider a model of a microorganism that, in its plasma membrane, expresses two electrogenic enzymes (E(1) and E(2)) transporting the same monovalent cation C and electrodiffusive paths for C and for a monovalent anion A. E(1) (E(2)) couples transport C to the reaction S(1)<-->P(1) (S(2)<-->P(2)). We developed a mathematical model that describes the rate of change of the electrical potential difference across the membrane, of the internal concentrations of C and A, and of the concentrations of S(2) and P(2). The enzymes are incorporated via two-state kinetic models; the passive ionic fluxes are represented by classical formulations of electrodiffusion. The microorganism volume is maintained constant by accessory regulatory devices. The model is utilized for stationary and dynamic studies for the case of bacteria employing the electrochemical gradient of Na(+) as energetic intermediate. Among other conclusions, the results show that the membrane potential represents the relevant kinetic intermediate for the overall coupling between the energy donor reaction S(1)<-->P(1) and the synthesis of S(2).

Bacterial physiological responses integrate energy-coupling processes at the membrane level with metabolic energy demand. The regulatory design behind these responses remains largely unexplored. Propionigenium modestum is an adequate organism to study these responses because it presents the simplest scheme known integrating membrane potential generation and metabolic ATP consumption. A hypothetical sodium leak is added to the scheme as the sole regulatory site. Allosteric regulation is assumed to be absent. Information of the rate equations is not available. However, relevant features of the patterns of responses may be obtained using Metabolic Control Analysis (MCA) and Metabolic Control Design (MCD). With these tools, we show that membrane potential disturbances can be compensated by adjusting the leak flux, without significant perturbations of ATP consumption. Perturbations of membrane potential by ATP demand are inevitable and also require compensatory changes in the leak. Numerical simulations were performed with a kinetic model exhibiting the responses for small changes obtained with MCA and MCD. A modest leak (10% of input) was assumed for the reference state. We found that disturbances in membrane potential and ATP consumption, produced by environmental perturbations of the cation concentration, may be reverted to the reference state adjusting the leak. Leak changes can also compensate for undesirable effects on membrane potential produced by changes in nutrient availability or ATP demand, in a wide range of values. The system is highly robust to parameter fluctuations. The regulatory role of energy dissipating processes and the trade-off between energetic efficiency and regulatory capacity are discussed.