Bursting and calcium oscillations in pancreatic beta-cells: specific pacemakers for specific mechanisms.

Oscillatory phenomenon in electrical activity and cytoplasmic calcium concentration in response to glucose are intimately connected to multiple key aspects of pancreatic ß-cell physiology. However, there is no single model for oscillatory mechanisms in these cells. We set out to identify possible pacemaker candidates for burst activity and cytoplasmic Ca(2+) oscillations in these cells by analyzing published hypotheses, their corresponding mathematical models, and relevant experimental data. We found that although no single pacemaker can account for the variety of oscillatory phenomena in ß-cells, at least several separate mechanisms can underlie specific kinds of oscillations. According to our analysis, slowly activating Ca(2+)-sensitive K(+) channels can be responsible for very fast Ca(2+) oscillations; changes in the ATP/ADP ratio and in the endoplasmic reticulum calcium concentration can be pacemakers for both fast bursts and cytoplasmic calcium oscillations, and cyclical cytoplasmic Na(+) changes may underlie patterning of slow calcium oscillations. However, these mechanisms still lack direct confirmation, and their potential interactions raises new issues. Further studies supported by improved mathematical models are necessary to understand oscillatory phenomena in ß-cell physiology.

A model of action potentials and fast Ca2+ dynamics in pancreatic beta-cells.

We examined the ionic mechanisms mediating depolarization-induced spike activity in pancreatic beta-cells. We formulated a Hodgkin-Huxley-type ionic model for the action potential (AP) in these cells based on voltage- and current-clamp results together with measurements of Ca(2+) dynamics in wild-type and Kv2.1 null mouse islets. The model contains an L-type Ca(2+) current, a "rapid" delayed-rectifier K(+) current, a small slowly-activated K(+) current, a Ca(2+)-activated K(+) current, an ATP-sensitive K(+) current, a plasma membrane calcium-pump current and a Na(+) background current. This model, coupled with an equation describing intracellular Ca(2+) homeostasis, replicates beta-cell AP and Ca(2+) changes during one glucose-induced spontaneous spike, the effects of blocking K(+) currents with different inhibitors, and specific complex spike in mouse islets lacking Kv2.1 channels. The currents with voltage-independent gating variables can also be responsible for burst behavior. Original features of this model include new equations for L-type Ca(2+) current, assessment of the role of rapid delayed-rectifier K(+) current, and Ca(2+)-activated K(+) currents, demonstrating the important roles of the Ca(2+)-pump and background currents in the APs and bursts. This model provides acceptable fits to voltage-clamp, AP, and Ca(2+) concentration data based on in silico analysis.

Reactive species and early manifestation of insulin resistance in type 2 diabetes.

The early stages of type 2 diabetes mellitus are characterized by the development of insulin resistance (IRe) in muscle cells and adipocytes with the concomitant loss of beta-cell compensation. We have extensively reviewed the literature related to metabolic and signalling pathways of reactive oxygen species (ROS) in regard to the coordinated development of oxidative stress and IRe. We considered the hypothesis that oxidative stress leads to IRe in muscle cells and adipocytes, but found that the data are more consistent with the hypothesis that the cellular mechanisms that protect against oxidative stress per se are capable of creating an ROS-dependent insulin-resistant state. Furthermore, ROS-induced mitochondrial dysfunction can lead to disruptions of lipid metabolism, increasing the intracellular lipid content, and, in addition, contribute to lipid-dependent IRe in myocytes. Together, these two ROS-activated pathways to IRe can contribute to a global state of profound resistance to insulin action. Therapeutic strategies should, therefore, be directed towards reducing insulin resistance without an increase in ROS production or concentration. Pharmacological or other approaches to IRe that result in the activation of mitochondrial biogenesis in particular could be highly beneficial in the prevention or treatment of both insulin resistance and type 2 diabetes.

Regulation in metabolic systems under homeostatic flux control.

The general properties of metabolic systems under homeostatic flux control are analyzed. It is shown that the main characteristic point for an enzyme in such a system is a sharp transition from limitation outside the system to limitation by some enzyme inside the system. A method for the quantitative treatment of the experimental dependence of metabolic flux on enzyme content is presented. The conception of "nonlimiting," "near-limiting," and "limiting" enzymes is developed for these systems. It is pointed out that reactions close to a thermodynamic equilibrium under normal conditions can considerably limit the homeostatic fluxes. The rules for regulation of fluxes in such systems are illustrated by the data obtained for transgenic plants with reduced activities of some Calvin-cycle enzymes and further examples. A comparison is made between the developed quantitative description of metabolic fluxes under homeostatic flux control and the methods of metabolic control analysis.

Regulation of the Calvin cycle for CO2 fixation as an example for general control mechanisms in metabolic cycles.

The theory of a metabolic cycle with the main portion of its intermediates remaining inside the cycle during one turnover has been developed. On this basis, the regulation of the Calvin cycle is analyzed. It is demonstrated that not only the reactions of non-equilibrium enzymes, as the carboxylation of ribulose 1,5-bisphosphate, but reactions that operate close to a thermodynamic equilibrium, especially the reduction of 3-phosphoglycerate and the transketolase reaction can significantly influence the total turnover period in the Calvin cycle. The role of compensating mechanisms in the maintenance of the photosynthesis rate upon changes of environmental conditions and of enzyme contents is analyzed for the Calvin cycle. It is shown that the change of the total quantity of the metabolites is one of the main self-regulated mechanisms in the Calvin cycle. A change of the ATP/ADP ratio can be used by the cell to maintain the CO2 assimilation rate, when the total quantity of the metabolites is changed. The developed analysis permits to explain some experimental data obtained with transgenic plants with restricted efflux of carbon from the chloroplasts.

Flux control of the malate valve in leaf cells.

The coupled processes of the chloroplast trans-envelope transport of malate and oxaloacetate and their interconversion as catalyzed by the stromal NADP-linked malate dehydrogenase are quantitatively analyzed by means of a steady-state model. The equation for the NADP-malate dehydrogenase reaction is developed. The empirical dependence of enzyme activity on NADPH and NADP+ is used to determine its actual activity. The trans-envelope counter exchange of malate and oxaloacetate is described by a kinetic model of the translocator. Kinetic parameters are derived from known data, except for the Km value and the maximum rate for oxaloacetate transport, which are estimated from oxaloacetate-dependent malate formation in isolated intact chloroplasts. Using the kinetic properties of the system and the known metabolite concentrations, the model demonstrates that photosynthetically generated NADPH can be exported efficiently from the chloroplasts to the cytosol by the malate-valve system. The transfer capacity of the malate valve is estimated not to exceed 20 mumol (mg Chl)-1 h-1 (or 5% of the electron transport) under normal physiological conditions. The possible role of the malate valve in leaf cells under normal conditions and during stress is discussed.

Models of CO2 concentrating mechanisms in microalgae taking into account cell and chloroplast structure.

Detailed mathematical models have been developed for the functioning of CO2 concentration mechanisms in microalgae. The models treat a microalgal cell as several compartments: pyrenoid, chloroplast stroma, cytoplasm and periplasmic space. Cases for both the active bicarbonate transport through the plasmalemma and the passive CO2 diffusion through it with the subsequent concentrating of CO2 inside the chloroplast are analyzed. CO2 evolution from bicarbonate inside the pyrenoid is modeled. The great diffusion resistance for CO2 flux from the pyrenoid is caused by a starch envelope and the concentric thylakoid membranes surrounding it. The role of carbonic anhydrase in the periplasmic space, cytoplasm and inside the chloroplast is evaluated numerically. The models also offer an explanation for the absence of 'short-circuited' inorganic carbon fluxes between the external medium and the cytoplasm under active bicarbonate transport through the plasmalemma and in the presence of carbonic anhydrase in the cytoplasm. If the cytoplasm is driven from the space between a chloroplast envelope and plasmalemma upon the microalgae adaptation to low concentration of the dissolved inorganic carbon, the inorganic carbon leak might be avoided. The models reproduce accurately the majority of known experimental data. The high efficiency of CO2 concentrating mechanisms in microalgae can be explained by a considerable diffusion resistance for CO2 flux from the pyrenoid and by the effective scavenging of CO2 leaking outward from the chloroplast to cytoplasm and from cell to periplasmic space.

Possible CO2 concentrating mechanism in chloroplasts of C3 plants. Role of carbonic anhydrase.

The possibility of a specific CO2 concentrating mechanism present in chloroplasts of C3 plants is analyzed. Proton gradient between thylakoids and the stroma is assumed to be the driving force for this process. The possible CO2 concentrating mechanisms are: 1. HCO3- permeation into thylakoids, its dehydration there and diffusion of CO2 formed into the stroma; 2. Dehydration of HCO3- present in the stroma at the thylakoid surface in a reaction with H+ leaving the thylakoids through: a) channels of membrane-bound carbonic anhydrase; b) channels of the ATPase complex. A system of equations describing CO3- and CO2 diffusion as well as CO2 assimilation and formation was used. The increase in photosynthesis rate, upon CO2 diffusion being facilitated in the presence of carbonic anhydrase, and due to the action of CO2 concentrating mechanisms, was numerically estimated. The CO2 concentrating mechanism was shown to function effectively only with the entire chloroplast being the CO2 concentrating zone. This is the case when the bulk of stromal carbonic anhydrase is localized near the inner chloroplast envelope. The existence of CO2 concentrating mechanisms around a single granum or around thylakoids is hardly possible. Approaches enabling the detection of similar concentrating mechanisms are discussed.