An elementary kinetic model of energy coupling in biological membranes

Regulatory design in a simple system integrating membrane potential generation and metabolic ATP consumption. Robustness and the role of energy dissipating processes

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.

Minimal models of electric potential oscillations in non-excitable membranes

Sustained oscillations in the membrane potential have been observed in a variety of cellular and subcellular systems, including several types of non-excitable cells and mitochondria. For the plasma membrane, these electrical oscillations have frequently been related to oscillations in intracellular calcium. For the inner mitochondrial membrane, in several cases the electrical oscillations have been attributed to modifications in calcium dynamics. As an alternative, some authors have suggested that the sustained oscillations in the mitochondrial membrane potential induced by some metabolic intermediates depends on the direct effect of internal protons on proton conductance. Most theoretical models developed to interpret oscillations in the membrane potential integrate several transport and biochemical processes. Here we evaluate whether three simple dynamic models may constitute plausible representations of electric oscillations in non-excitable membranes. The basic mechanism considered in the derivation of the models is based upon evidence obtained by Hattori et al. for mitochondria and assumes that an ionic species (i.e., the proton) is transported via passive and active transport systems between an external and an internal compartment and that the ion affects the kinetic properties of transport by feedback regulation. The membrane potential is incorporated via its effects on kinetic properties. The dynamic properties of two of the models enable us to conclude that they may represent alternatives enabling description of the generation of electrical oscillations in membranes that depend on the transport of a single ionic species.

Hazardous to your health: kinetic foundations of risk stratification and therapeutic triage

BACKGROUND

Risk stratification is widely used in the prognostic assessment of patients with a variety of clinical disorders on the unquestioned assumption that the intensity of treatment should be proportionate to the threat of an adverse event over some finite period of time (risk). However, just as the physical trajectory of an object depends on its current magnitude of displacement (velocity) and the concurrent rate of change of that displacement (acceleration), the prognostic trajectory of a patient depends on the current magnitude of risk and the concurrent rate of change of that risk (hazard). Clinical risk stratification nevertheless relies only on the former.

METHODS

We therefore integrated the quantitative assessment of risk and hazard by way of a kinetic model that characterizes the development of an adverse event as a series of exponential state-to-state transitions-from stable to unstable to event. This model serves to shift the clinical emphasis from prognosis (the assessment of risk) to treatment (the improvement in outcome). In this context, treatment is well advised (even in low-risk individuals) when the hazard is large (risk is rising), and is less well advised (even in high-risk individuals) when the hazard is small (risk is stable).

RESULTS

The kinetic model outlined here thereby promises to supersede the superficial practice of risk stratification with a more sophisticated strategy of therapeutic triage that allows one to predict the incremental clinical benefit of alternative treatment strategies.

Kinetics of electron transfer through the respiratory chain

We show that the rate at which electrons pass through the respiratory chain in mitochondria and respiring prokaryotic cells is described by the product of three terms, one describing electron donation, one acceptance, and a third, the thermodynamic drive. We apply the theory of nonequilibrium thermodynamics in the context of the chemiosmotic model of proton translocation and energy conservation. This approach leads to a closed-form expression that predicts steady-state electron flux as a function of chemical conditions and the proton motive force across the mitochondrial inner membrane or prokaryotic cytoplasmic membrane. The rate expression, derived considering reverse and forward electron flow, is the first to account for both thermodynamic and kinetic controls on the respiration rate. The expression can be simplified under specific conditions to give rate laws of various forms familiar in cellular physiology and microbial ecology. The expression explains the nonlinear dependence of flux on electrical potential gradient, its hyperbolic dependence on substrate concentration, and the inhibiting effects of reaction products. It provides a theoretical basis for investigating life under unusual conditions, such as microbial respiration in alkaline waters.