The diagram methods for the evaluation of exchange fluxes in membrane transport systems

In this paper theoretical methods for the evaluation of fluxes of ligand exchange processes in a transporter-mediated membrane transport system are studied. The exchange process of a transport system is defined as a set of reactions of the transporters in the membrane that do not result in a complete turnover and must include the following consecutive sequence of steps: the binding of ligands from bath 1 and a subsequent release of bound ligands to bath 2 followed immediately by a binding of ligands from bath 2 and a subsequent release of bound ligands to bath 1. Thus, unlike the ordinary one-way cycles, the completion of an exchange process does not result in a net transport of ligands across the membrane. However, since it exchanges the ligands between the two baths, the exchange process of a transport system is closely related to the operational tracer flux of labelled ligands in the system. In this paper, both the numerical and the analytical procedures for the evaluation of exchange fluxes in any given biochemical diagram are discussed. In particular, we show that the exchange fluxes of a given kinetic diagram, like one-way cycle fluxes, can be expressed analytically in terms of the rate constants of the diagram with the use of either the original diagram or an expanded diagram. The diagram methods presented in this paper should be very useful in analyzing the mechanisms of transporter-mediated transport systems when tracer flux data are available.     

Mitochondrial Ca<Superscript>2+</Superscript> and regulation of the permeability transition pore

The mitochondrial permeability transition pore was originally described in the 1970’s as a Ca²⁺ activated pore and has since been attributed to the pathogenesis of many diseases. Here we evaluate how each of the current models of the pore complex fit to what is known about how Ca²⁺ regulates the pore, and any insight that provides into the molecular identity of the pore complex. We also discuss the central role of Ca²⁺ in modulating the pore’s open probability by directly regulating processes, such as ATP/ADP balance through the tricarboxylic acid cycle, electron transport chain, and mitochondrial membrane potential. We review how Ca²⁺ influences second messengers such as reactive oxygen/nitrogen species production and polyphosphate formation. We discuss the evidence for how Ca²⁺ regulates post-translational modification of cyclophilin D including phosphorylation by glycogen synthase kinase 3 beta, deacetylation by sirtuins, and oxidation/ nitrosylation of key residues. Lastly we introduce a novel view into how Ca²⁺ activated proteolysis through calpains in the mitochondria may be a driver of sustained pore opening during pathologies such as ischemia reperfusion injury.     

Comparative study on central metabolic fluxes of <Emphasis Type="Italic">Bacillus megaterium</Emphasis> strains in continuous culture using <Superscript>13</Superscript>C labelled substrates

Fluxes of central carbon metabolism [glycolysis, pentose phosphate pathway (PPP), tricarboxylic acid cycle (TCA cycle), biomass formation] were determined for several Bacillus megaterium strains (DSM319, WH320, WH323, MS941) in C- and N-limited chemostat cultures by ¹³C labelling experiments. The labelling patterns of proteinogenic amino acids were analysed by GC/MS and therefrom flux ratios at important nodes within the metabolic network could be calculated. On the basis of a stoichiometric metabolic model flux distributions were estimated for the different B. megaterium strains used at various cultivation conditions. Generally all strains exhibited similar metabolic flux distributions, however, several significant changes were found in (1) the glucose flux entering the PPP via the oxidative branch, (2) the reversibilities within the PPP, (3) the relative fluxes of pyruvate and acetyl-CoA fed to the TCA cycle, (4) the fluxes around the pyruvate node involving a futile cycle.     

Influence of Ca<Superscript>2+</Superscript> Oscillatory Influx on Membrane Ca<Superscript>2+</Superscript>-ATPase Activity: a Kinetic Model

A kinetic model for the membrane Ca²⁺-ATPase is considered. The catalytic cycle in the model is extended by enzyme auto-inhibition and by oscillatory calcium influx. It is shown that the conductive enzyme activity can be registered as damped or sustained Ca²⁺ pulses similar to observed experimentally. It is shown that frequency variations in Ca²⁺ oscillatory influx induce changes of pulsating enzyme activity. Encoding is observed for the signal frequency into a number of fixed levels of sustained pulses in the enzyme activity. At certain calcium signal frequencies, the calculated Ca²⁺-ATPase conductivity demonstrates chaotic multi-level pulses, similar to those observed experimentally.__________Translated from Biokhimiya, Vol. 70, No. 4, 2005, pp. 539–544.Original Russian Text Copyright © 2005 by Goldstein, Mayevsky, Zakrjevskaya.     

Cell physiological aspects of the plasma membrane electrogenic H<Superscript>+</Superscript> pump

This article deals with cell physiological aspects of the plasma membrane electrogenic proton (H⁺) pump and emphasizes the contribution of the giant algal cells of the Characeae in elucidating the mechanism of the pump. First, a history of the development of intracellular perfusion techniques in characean internodal cells is described, including preparation of tonoplast-free cells. Then, an outline of the hypothesis of the electrogenic H⁺ pump proposed by Kitasato is introduced, who prophesied the existence of an electric potential generated by an active H⁺ efflux. Subsequently, a history of finding ATP as the direct energy source of the electrogenic ion pump is presented. Quantitative agreement between the pump current and the ATP-dependent H⁺ efflux supports the notion that the ion carried by the electrogenic ion pump is H⁺. The role of the H⁺ pump in regulation of the cytosolic pH is discussed. Mechanisms of light-induced potential change through photosynthesis-controlled activation of the H⁺ pump are discussed in terms of changes in the levels of adenine nucleotides and in modulation of the K_m value for the ATP of H⁺-ATPase. Recent progress in the molecular mechanism of the blue-light-induced activation of the H⁺-ATPase in guard cells is presented. However, there are cases where H⁺-ATPase activity is inhibited by blue light, indicating the flexibility of the control mechanisms of H⁺-ATPase activity. Finally, modulation of H⁺-pumping or H⁺-ATPase activities in response to environmental factors, such as anoxia, membrane excitation, osmotic and salt stresses, nutrient deficiencies and aluminum toxicity are described. Discussions are presented on the regulation of the electrogenic H⁺ pump.     

Density functional calculations of chemical shielding of backbone <Superscript>15</Superscript>N in helical residues of protein G

We performed density functional calculations of backbone ¹⁵N chemical shielding tensors in selected helical residues of protein G. Here we describe a computationally efficient methodology to include most of the important effects in the calculation of chemical shieldings of backbone ¹⁵N. We analyzed the role of long-range intra-protein electrostatic interactions by comparing models with different complexity in vacuum and in charge field. Our results show that the dipole moment of the α-helix can cause significant deshielding of ¹⁵N; therefore, it needs to be considered when calculating ¹⁵N chemical shielding. We found that it is important to include interactions with the side chains that are close in space when the charged form for ionizable side chains is adopted in the calculation. We also illustrate how the ionization state of these side chains can affect the chemical shielding tensor elements. Chemical shielding calculations using a 8-residue fragment model in vacuum and adopting the charged form of ionizable side chains yield a generally good agreement with experimental data.     

The role of cytoplasmic nanospaces in smooth muscle cell Ca<Superscript>2+</Superscript> signalling

We address the importance of cytoplasmic nanospaces in Ca^2?+? transport and signalling in smooth muscle cells and how quantitative modelling can shed significant light on the understanding of signalling mechanisms. Increasingly more convincing evidence supports the view that these nanospaces—nanometre-scale spaces between organellar membranes, hosting cell signalling machinery—are key to Ca^2?+? signalling as much as Ca^2?+? transporters and Ca^2?+? storing organelles. Our research suggests that the origin of certain diseases is to be sought in the disruption of the proper functioning of cytoplasmic nanospaces. We begin with a historical perspective on the study of smooth muscle cell plasma membrane–sarcoplasmic reticulum nanospaces, including experimental evidence of their role in the generation of asynchronous Ca^2?+? waves. We then summarize how stochastic modelling approaches have aided and guided our understanding of two basic functional steps leading to healthy smooth muscle cell contraction. We furthermore outline how more sophisticated and realistic quantitative stochastic modelling is now being employed not only to deepen our understanding but also to aid in the hypothesis generation for further experimental investigation.     

Fast loading ester fluorescent Ca<Superscript>2+</Superscript> and pH indicators into pollen of <Emphasis Type="Italic">Pyrus pyrifolia</Emphasis>

Loading of Ca²⁺-sensitive fluorescent probes into plant cells is an essential step to measure activities of free Ca²⁺ ions in cytoplasm with a fluorescent imaging technique. Fluo-3 is one of the most suitable Ca²⁺ indicators for CLSM. We loaded pollen with fluo-3/AM at three different temperatures. Fluo-3/AM was successfully loaded into pollen at both low (4°C) and high (37°C) temperatures. However, high loading temperature was best suited for pollen, because germination rate of pollen and growth of pollen tubes were relatively little impaired and loading time was shortened. Moreover, Ca²⁺ distribution increased in the three apertures of pollen after hydration and showed a Ca²⁺ gradient, similar to the tip of growing pollen tubes. The same protocol can be used with the AM-forms of other fluorescent dyes for effective labeling. When loading BCECF-AM into pollen at high temperature, the pollen did not show a pH gradient after hydration. Ca²⁺ activities and fluxes had the same periodicity as pollen germination, but pH did not show the same phase and mostly lagged behind. However, the clear zone was alkaline when pollen tube growth was slowed or stopped and turned acidic when growth recovered. It is likely that apical pH_i regulated pollen tube growth.     

Calmodulin can induce and control damped oscillations in plasma membrane Ca<Superscript>2+</Superscript>-ATPase activity: A kinetic model

Plasma membrane Ca²⁺-ATPase is the pump that extrudes calcium ions from cells using ATP hydrolysis to maintain low Ca²⁺ concentrations in the cell. Calmodulin stimulates Ca²⁺-ATPase by binding to the autoinhibitory enzyme domain, which allows the access of cytoplasmic ATP and Ca²⁺ to the catalytic and transport sites. Our kinetic model predicts damped oscillations of the enzyme activity and interprets the known nonmonotonic kinetic behavior of the enzyme in the presence of calmodulin. For parameters close to experimental data, the kinetic model explains the dependence of the frequency and damping factor of the oscillatory enzyme activity on the calmodulin concentration. The calculated pre-steady-state curves fit well to known experimental data. Kinetic analysis allows us to assign Ca²⁺-ATPase to hysteretic enzymes exhibiting activity oscillations in open systems.     

Role of Energized States of (Na<Superscript>+</Superscript> + K<Superscript>+</Superscript>-ATPase in the Sodium Pump

IN an earlier paper¹ we have presented a model for a sodium pump based on the operation of the adenosine triphosphatase component of membranes which is sensitive to ouabain and is activated by sodium and potassium; that is (Na⁺+K⁺)-ATPase. We attempted to correlate the biochemical properties of this enzyme system as they were then known with the essential properties of Na⁺ transport systems. The model suggested further experiments which could clarify the role of (Na⁺ + K ⁺)-ATPase in ion transport and some experimental evidence is now available for the stoichiometry of ouabain binding to isolated enzyme preparations^2,3 although differences in the experimental techniques which have been used make the data equivocal.     

Classical versus stochastic kinetics modeling of biochemical reaction systems

We study fundamental relationships between classical and stochastic chemical kinetics for general biochemical systems with elementary reactions. Analytical and numerical investigations show that intrinsic fluctuations may qualitatively and quantitatively affect both transient and stationary system behavior. Thus, we provide a theoretical understanding of the role that intrinsic fluctuations may play in inducing biochemical function. The mean concentration dynamics are governed by differential equations that are similar to the ones of classical chemical kinetics, expressed in terms of the stoichiometry matrix and time-dependent fluxes. However, each flux is decomposed into a macroscopic term, which accounts for the effect of mean reactant concentrations on the rate of product synthesis, and a mesoscopic term, which accounts for the effect of statistical correlations among interacting reactions. We demonstrate that the ability of a model to account for phenomena induced by intrinsic fluctuations may be seriously compromised if we do not include the mesoscopic fluxes. Unfortunately, computation of fluxes and mean concentration dynamics requires intensive Monte Carlo simulation. To circumvent the computational expense, we employ a moment closure scheme, which leads to differential equations that can be solved by standard numerical techniques to obtain more accurate approximations of fluxes and mean concentration dynamics than the ones obtained with the classical approach.     

Involvement of protons in the ion transport cycle of Na<Superscript>+</Superscript>,K<Superscript>+</Superscript>-ATPase

The effect of pH on electrogenic sodium transport by the Na⁺,K⁺-ATPase has been studied. Experiments were carried out by admittance recording in a model system consisting of a bilayer lipid membrane with adsorbed membrane fragments containing purified Na⁺,K⁺-ATPase. Changes in the membrane admittance (capacitance and conductance increments in response to photo-induced release of ATP from caged ATP) were measured as function of AC voltage frequency, sodium ion concentration, and pH. In solutions containing 150 mM Na⁺, the frequency dependence of capacitance increments was not significantly dependent on pH in the range between 6 and 8. At a low NaCl concentration (3 mM), the capacitance increments at low frequencies decreased with the increasing pH. In the absence of NaCl, the frequency-dependent capacitance increment at low frequencies was similar to that measured in the presence of 3 mM NaCl. These results may be explained by involvement of protons in the Na⁺,K⁺-ATPase pump cycle, i.e., electroneutral exchange of sodium ions for protons under physiological conditions, electrogenic transport of sodium ions at high pH, and electrogenic transport of protons at low concentrations (and in the absence) of sodium ions.     

<Superscript>13</Superscript>C metabolite profiling to compare the central metabolic flux in two yeast strains

¹³C metabolite profiling to quantify the dynamic changes of central carbon metabolites was attempted using mass isotopomer distribution analysis in two yeast strains, Saccharomyces cerevisiae and Kluyveromyces marxianus. Mass and isotopomer balances of the intermediates were examined and calculated in both yeast species and central carbon metabolic fluxes were successfully determined. Metabolic fluxes of pentose phosphate pathway in K. marxianus were 1.66 times higher than S. cerevisiae. The flux difference was also supported by relatively high abundance of partially labeled fructose 6-phosphate and 3-phosphoglycerate as well as an increased concentration of labeled L-valine in K. marxianus. Metabolic flux analysis combined with dynamic metabolite profiling has provided better understanding in the central carbon metabolic pathways of two model organisms and can be applied as a method to analyze more complicated metabolic networks in other organisms.     

H<Superscript>+</Superscript> translocation by weak acid uncouplers is independent of H<Superscript>+</Superscript> electrochemical gradient

According to the common view, weak acid uncouplers increase proton conductance of biological (and phospholipid bilayer) membranes, thus effecting H⁺ fluxes driven by their electrochemical gradients. Under certain conditions, however, uncouplers can induce unexpected effects opposite to the dissipation of H⁺ gradients. Results are presented here demonstrating CCCP-induced proton influx into Saccharomyces cerevisiae cytosol driven by the electrochemical potentials of CCCP and its CCCP^? anions, independent of electrochemical H⁺-gradient. Another view of week acid uncouplers’ action is proposed that is logically consistent with these observations.     

Metabolism of [U-<Superscript>13</Superscript>C]Leucine in Cultured Astroglial Cells

Leucine is rapidly metabolized in astroglial primary cultures. Therefore, it is considered as valuable fuel in brain energy metabolism. Only few of the leucine metabolites generated and released by astroglial cells have been identified. Therefore, a more detailed study was performed analyzing by NMR techniques the ¹³C-labeled metabolites, which were released by astroglial primary cultures during the degradation of [U-¹³C]leucine. Confirming a former radioactive study this analysis revealed ¹³C-labeled 2-oxoisocaproate and ketone bodies. Additionally, ¹³C-labeled alanine, citrate, glutamine, lactate and succinate were identified. Their detailed isotopomer analysis proves that ¹³C-labeled acetyl-CoA enters the tricarboxylic acid cycle, that intermediates with a characteristic ¹³C-labeling pattern can be withdrawn at several positions of the cycle, and that in the case of lactate and alanine there appears to be a participation of an active phosphoenolpyruvate carboxykinase and/or malic enzyme pathway. Thus, astroglial cells generate and release into the extracellular fluid not only the leucine catabolites 2-oxoisocaproate and ketone bodies, but also several tricarboxylic acid cycle dependent metabolites.Special issue dedicated to Dr. Lawrence F. Eng.M. Gabriele Bixel and Jörn Engelmann contributed equally to this work.     

<Superscript>1</Superscript>H, <Superscript>13</Superscript>C and <Superscript>15</Superscript>N chemical shift assignments of Saccharomyces cerevisiae type 1 thioredoxin in the oxidized state by solution NMR spectroscopy

Thioredoxins (Trx) are ubiquitous proteins that regulate several biochemical processes inside the cell. Trx is an important player, displaying oxidoreductase activity and helping to keep and regulate the oxidative state of the cellular environment. Trx also participates in the regulation of many cellular functions, such as DNA synthesis, protection against oxidative stress, cell cycle and signal transduction. The oxidized Trx is the target for another set of proteins, such as thioredoxin reductase (TrR), which used the reductive potential of NADPH. The oxidized state of Trx also plays important role in regulation of redox state in the cells. In this regard, the oxidized form of Trx is a putative conformer that contributes to the cellular redox environment. Here we report the chemical shift assignments (¹H, ¹³C and ¹⁵N) in solution at 15 °C. We also showed the secondary structure analysis of the oxidized form of yeast thioredoxin (yTrx1) as basis for future NMR studies of protein–target interactions and dynamics. The assignment was done at low concentration (200 µM) because it is important to keep intact the water cavity.     

Ca<Superscript>2+</Superscript>-Dependent Phosphorylation of RyR2 Can Uncouple Channel Gating from Direct Cytosolic Ca<Superscript>2+</Superscript> Regulation

Phosphorylation of the cardiac ryanodine receptor (RyR2) is thought to be important not only for normal cardiac excitation-contraction coupling but also in exacerbating abnormalities in Ca²⁺ homeostasis in heart failure. Linking phosphorylation to specific changes in the single-channel function of RyR2 has proved very difficult, yielding much controversy within the field. We therefore investigated the mechanistic changes that take place at the single-channel level after phosphorylating RyR2 and, in particular, the idea that PKA-dependent phosphorylation increases RyR2 sensitivity to cytosolic Ca²⁺. We show that hyperphosphorylation by exogenous PKA increases open probability (P _o) but, crucially, RyR2 becomes uncoupled from the influence of cytosolic Ca²⁺; lowering [Ca²⁺] to subactivating levels no longer closes the channels. Phosphatase (PP1) treatment reverses these gating changes, returning the channels to a Ca²⁺-sensitive mode of gating. We additionally found that cytosolic incubation with Mg²⁺/ATP in the absence of exogenously added kinase could phosphorylate RyR2 in approximately 50% of channels, thereby indicating that an endogenous kinase incorporates into the bilayer together with RyR2. Channels activated by the endogenous kinase exhibited identical changes in gating behavior to those activated by exogenous PKA, including uncoupling from the influence of cytosolic Ca²⁺. We show that the endogenous kinase is both Ca²⁺-dependent and sensitive to inhibitors of PKC. Moreover, the Ca²⁺-dependent, endogenous kinase–induced changes in RyR2 gating do not appear to be related to phosphorylation of serine-2809. Further work is required to investigate the identity and physiological role of this Ca²⁺-dependent endogenous kinase that can uncouple RyR2 gating from direct cytosolic Ca²⁺ regulation.