Ulf-Peter Hansen

Interpretation of current-voltage relationships for "active" ion transport systems: I. Steady-state reaction-kinetic analysis of class-I mechanisms.

SummaryThis paper develops a simple reaction-kinetic model to describe electrogenic pumping and co- (or counter-) transport of ions. It uses the standard steady-state approach for cyclic enzyme- or carrier-mediated transport, but does not assume rate-limitation by any particular reaction step. Voltage-dependence is introduced, after the suggestion of Läuger and Stark (Biochim. Biophys. Acta211:458–466, 1970), via a symmetric Eyring barrier, in which the charge-transit reaction constants are written ask12=k120exp(zFΔΨ/2RT) andk21=k210exp(−zFΔΨ/2RT). For interpretation of current-voltage relationships, all voltage-independent reaction steps are lumped together, so the model in its simplest form can be described as a pseudo-2-state model. It is characterized by the two voltage-dependent reaction constants, two lumped voltage-independent reaction constants (K12,K21), and two reserve factors (ri,r0) which formally take account of carrier states that are indistinguishable in the current-voltage (I–V) analysis. The model generates a wide range ofI–V relationships, depending on the relative magnitudes of the four reaction constants, sufficient to describe essentially allI–V data now available on “active” ion-transport systems. Algebraic and numerical analysis of the reserve factors, by means of expanded pseudo-3-, 4-, and 5-state models, shows them to be bounded and not large for most combinations of reaction constants in the lumped pathway. The most important exception to this rule occurs when carrier decharging immediately follows charge transit of the membrane and is very fast relative to other constituent voltage-independent reactions. Such a circumstance generates kinetic equivalence of chemical and electrical gradients, thus providing a consistent definition of ion-motive forces (e.g., proton-motive force, PMF). With appropriate restrictions, it also yields both linear and log-linear relationships between net transport velocity and either membrane potential or PMF. The model thus accommodates many known properties of proton-transport systems, particularly as observed in “chemiosmotic” or energy-coupling membranes.

Current-voltage relationships for the plasma membrane and its principal electrogenic pump inNeurospora crassa: I. Steady-state conditions

SummaryThe nonlinear membrane current-voltage relationship (I–V curve) for intact hyphae ofNeurospora crassa has been determined by means of a 3-electrode voltage-clamp technique, plus “quasi-linear” cable theory. Under normal conditions of growth and respiration, the membraneI–V curve is best described as a parabolic segement convex in the direction of depolarizing current. At the average resting potential of −174 mV, the membrane conductance is ≈190 μmhos/cm2; conductance increases to ≈240 μmhos/cm2 at −300 mV, and decreases to ≈130 μmhos/cm2 at 0 mV. Irreversible membrane breakdown occurs at potentials beyond this range.Inhibition of the primary electrogenic pump inNeurospora by ATP withdrawal (with 1mm KCN) depolarizes the membrane to the range of −40 to −70 mV and reduces the slope of theI–V curve by a fixed scaling factor of approximately 0.8. For wild-typeNeurospora, compared under control conditions and during steady-state inhibition by cyanide, theI–V difference curve — presumed to define the current-voltage curve for the electrogenic pump — is a saturation function with maximal current of ≈20 μA/cm2, a half-saturation potential near −300 mV, and a projected reversal potential of ca. −400 mV. This value is close to the maximal free energy available to the pump from ATP hydrolysis, so that pump stoichiometry must be close to 1 H+ extruded:1 ATP split.The time-courses of change in membrane potential and resistance with cyanide are compatible with the steady-stateI–V curves, under the assumption that cyanide has no major effects other than ATP withdrawal. Other inhibitors, uncouplers, and lowered temperature all have more complicated effects.The detailed temporal analysis of voltage-clamp data showed three time-constants in the clamping currents: one of 10 msec, for charging the membrane capacitance (0.9 μF/cm2) a second of 50–75 msec; and a third of 20–30 sec, perhaps representing changes of intracellular composition.

Generalized kinetic analysis of ion-driven cotransport systems: a unified interpretation of selective ionic effects on Michaelis parameters

SummaryA major obstacle to the understanding of gradient-driven transport systems has been their apparently wide kinetic diversity, which has seemed to require a variety of ad hoc mechanisms. Ordinary kinetic analysis, however, has been hampered by one mathematically powerful but physically dubious assumption: that rate limitation occurs in transmembrane transit, so that ligand-binding reactions are at equilibrium. Simple models lacking that assumption turn out to be highly flexible and are able to describe most of the observed kinetic diversity in co- and counter-transport systems.Our “minimal” model of cotransport consists of a single transport loop linking six discrete states of a carrier-type molecule. The state transitions include one transmembrane charge-transport step, and one step each for binding of substrate and cosubstrate (driver ion) at each side of the membrane. The properties of this model are developed by sequential use of realisticexperimental simplifications and generalized numerical computations, focussed to create known effects of substrate, driver ion, and membrane potential upon the apparent Michaelis parameters (Jmax,Km) of isotopic substrate influx.Specific behavior of the minimal model depends upon the arrangement of magnitudes of individual reaction constants among the whole set (12) in the loop. Well defined arrangements have been found which permit either increasing membrane potential or increasing external driverion selectively to reduce the substrateKm, elevateJmax, jointly raise bothKm andJmax, or lowerKm while raisingJmax. Other arrangements allow rising internal driver ion to act like either a competitive or a noncompetitive inhibitor of entry, or allow internal substrate to shut down (“transinhibit”) influx despite large inward driving forces.These findings obviate most postulates of special mechanisms in cotransport: e.g., stoichiometry changes, ion wells, carrier-mediated leakage, and gating —at least as explanations for existing transport kinetic data. They also provide a simple interpretation of certain kinds of homeostatic regulation, and lead to speculation that the observed diversity in cotransport kinetics reflects control-related selection of reaction rate constants, rather than fundamental differences of mechanism.

Determination of DPPH Radical Oxidation Caused by Methanolic Extracts of Some Microalgal Species by Linear Regression Analysis of Spectrophotometric Measurements

The demonstrated modified spectrophotometric method makes use of the 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical and its specific absorbance properties. The absorbance decreases when the radical is reduced by antioxidants. In contrast to other investigations, the absorbance was measured at a wavelength of 550 nm. This wavelength enabled the measurements of the stable free DPPH radical without interference from microalgal pigments. This approach was applied to methanolic microalgae extracts for two different DPPH concentrations. The changes in absorbance measured vs. the concentration of the methanolic extract resulted in curves with a linear decrease ending in a saturation region. Linear regression analysis of the linear part of DPPH reduction versus extract concentration enabled the determination of the microalgaes methanolic extracts antioxidative potentials which was independent to the employed DPPH concentrations. The resulting slopes showed significant differences (6 - 34 μmol DPPH g−1 extract concentration) between the single different species of microalgae (Anabaena sp., Isochrysis galbana, Phaeodactylum tricornutum, Porphyridium purpureum, Synechocystis sp. PCC6803) in their ability to reduce the DPPH radical. The independency of the signal on the DPPH concentration is a valuable advantage over the determination of the EC50 value.

Mechanism of Cl− transport at the plasma membrane ofChara corallina: II. Transinhibition and the determination of H+/Cl− binding order from a reaction kinetic model

SummaryInternal Cl− and low internal pH are strong inhibitors of Cl− influx at the plasma membrane ofChara. The present investigation seeks to understand the mechanism by which this is achieved. Since both Cl− and H+ are transported by the same system, one possible mechanism is simply through a change in the electrochemical gradients of these ions. However, it is found that transport is more sensitive to theinternal concentrations of the two ions than to their respective gradients. It is demonstrated that Cl− influx, which shows Michaelis-Menten kinetics with respect to external concentration, is affected only in itsVmax by internal Cl− and pH; the apparentKm of the transport system for external Cl− is unchanged. In addition, it is found that there is an apparent interaction between internal Cl− and pH in their effects on Cl− influx, both in intact cells and those that have been perfused internally. A kinetic model is proposed which can account quantitatively for all these observations simply through the effects of substrate concentration on the apparent rate constants of a recycling carrier. The model predicts (i) strictly ordered binding of Cl− and H+ to the carrier at both internal and external surfaces, with Cl− first on and first off (ii) movement of charge through the membrane on the loaded, rather than the unloaded, carrier. The present model is expected to account for similar kinetic observations from a variety of other cotransport systems.

Cytoplasmic Ca2+-H+-exchange buffers in green algae

SummaryFluorescence ratio imaging was used for simultaneous measurement of cytosolic pHc and pCac inChara corallina, Nitella flexilis, andEremosphaera viridis. In some experiments the electrical membrane potential was also recorded. The first hint of coupling between changes in pHc and pCac was found in characean cells when the influence of butyrate on cytosolic streaming was studied by laser-Doppler-anemometry (LDA). The observed butyrate-induced cessation of cytosolic streaming supports the assumption that changes in pHc cause changes in pCac. This hypothesis was tested by simultaneously loading cells with Fura-2-dextran and BCECF-dextran. The addition of butyrate revealed strong coupling between pCac and pHc although this only occurred when the difference between pHc and pCac was less than 0.4 units (± 0.24, n=7). The measured relationship between the changes in pCac and pHc could be fitted by a cytoplasmic buffer exchange process. Protons imported by butyrate into the cytoplasm are able to displace Ca++ ions from cytoplasmic buffer sites. Three dissociation constants of the cytoplasmic buffer were pK1=6.2, pK2=7.1 for proton buffering, and pKca=6.7 for Ca++ ion buffering. Other possible mechanisms, such as butyrate-induced Ca++ influx through the plasmalemma and Ca++ release from internal stores are discussed. They are not necessary to explain the observed coupling but cannot be excluded from the process. Using the butyrate technique, the cytosolic in vivo proton buffer capacities ofN. flexilis, C. corallina, andE. viridis were determined as βi=30 mM · H+/pH-unit, βi=46 mM · H+/pH-unit, and βi=90 mM · H+/pH-unit, respectively. The values obtained in vivo are greater than those found previously using extraction methods. This can be explained in terms of pump activity and exchange with cell organelles, i.e., the vacuole. The high value of βi found inEremosphaera reflects adaptation to its habitat.

A reduced model of the fluorescence from the cyanobacterial photosynthetic apparatus designed for the in situ detection of cyanobacteria

Fluorometric determination of the chlorophyll (Chl) content of cyanobacteria is impeded by the unique structure of their photosynthetic apparatus, i.e., the phycobilisomes (PBSs) in the light-harvesting antennae. The problems are caused by the variations in the ratio of the pigment PC to Chl a resulting from adaptation to varying environmental conditions. In order to include cyanobacteria in fluorometric analysis of algae, a simplified energy distribution model describing energy pathways in the cyanobacterial photosynthetic apparatus was conceptualized. Two sets of mathematical equations were derived from this model and tested. Fluorescence of cyanobacteria was measured with a new fluorometer at seven excitation wavelength ranges and at three detection channels (650, 685 and 720 nm) in vivo. By employing a new fit procedure, we were able to correct for variations in the cyanobacterial fluorescence excitation spectra and to account for other phytoplankton signals. The effect of energy-state transitions on the PC fluorescence emission of PBSs was documented. The additional use of the PC fluorescence signal in combination with our recently developed mathematical approach for phytoplankton analysis based on Chl fluorescence spectroscopy allows a more detailed study of cyanobacteria and other phytoplankton in vivo and in situ.

Do light-induced changes in the membrane potential ofNitella reflect the feed-back regulation of a cytoplasmic parameter?

SummaryKinetic studies of the linearized response of membrane potential inNitella to light have revealed the existence of a feedback loop in the pathway of light action. Its existence can hardly be seen in the time course of the responses to dark/light transitions. However, making use of sine waves as input signals and employing a computeraided evaluation has resulted in finding complex time constants in the transfer function of the light effect which point out the existence of a feedback loop. Besides, sometimes spontaneous oscillations with periods of about 1 hr have been observed. It is shown that this system is different from that one reported in literature to be related to cytoplasmic streaming. By measuring the electrical low-frequency impedance, it has been demonstrated that it is not the purpose of the system to control membrane potential, even though secondary effects of the injected current have been found. It seems to be reasonable to assume that this system is involved in the control of a biochemically relevant parameter like the cytoplasmic pH by means of adjusting the balance of counteracting transmembrane transport processes.

Fast and slow gating are inherent properties of the pore module of the K+ channel Kcv.

Kcv from the chlorella virus PBCV-1 is a viral protein that forms a tetrameric, functional K+ channel in heterologous systems. Kcv can serve as a model system to study and manipulate basic properties of the K+ channel pore because its minimalistic structure (94 amino acids) produces basic features of ion channels, such as selectivity, gating, and sensitivity to blockers. We present a characterization of Kcv properties at the single-channel level. In symmetric 100 mM K+, single-channel conductance is 114 ± 11 pS. Two different voltage-dependent mechanisms are responsible for the gating of Kcv. “Fast” gating, analyzed by β distributions, is responsible for the negative slope conductance in the single-channel current–voltage curve at extreme potentials, like in MaxiK potassium channels, and can be explained by depletion-aggravated instability of the filter region. The presence of a “slow” gating is revealed by the very low (in the order of 1–4%) mean open probability that is voltage dependent and underlies the time-dependent component of the macroscopic current.

Repetitive Ca2+ spikes in a unicellular green alga

Cytosolic Ca2+ activity ([Ca2+]cy) and membrane potential were measured simultaneously in the unicellular green alga Eremosphaera viridis. Steady state [Ca2+]cy was about 160 nM. A ‘light‐off’ stimulus induced a transient elevation of [Ca2+]cy ([Ca2+]cy spike) in parallel with a transient hyperpolarization of the plasma membrane. Caffeine and Sr2+, known to release Ca2+ from intracellular stores in animal cells, induced repetitive [Ca2+]cy spikes in Eremosphaera which were always accompanied by parallel repetitive transient hyperpolarizations. These transient hyperpolarizations could be used as an indicator for [Ca2+]cy spikes. Repetitive [Ca2+]cy spikes in Eremosphaera were similar to repetitive [Ca2+]cy spikes in excitable animal cells. The mechanisms underlying these [Ca2+]cy oscillations seem to be comparable in animal and plant cells.