Electrocoupling of Ion Transporters in Plants: Interaction with Internal Ion Concentrations

There are five major electroenzymes in the plasmalemma of plant cells: a driving electrogenic pump, inward and outward rectifying K⁺ channels, a Cl⁻-2H⁺ symporter, and Cl⁻-channels. It has been demonstrated previously (Gradmann, Blatt & Thiel 1993, J. Membrane Biol. 136:327–332) how voltage-gating of these electroenzymes causes oscillations of the transmembrane voltage (V) at constant substrate concentrations. The purpose of this study is to examine the interaction of the same transporter ensemble with cytoplasmic concentrations of K⁺ and Cl⁻. The former model system has been extended to account for changing internal concentrations. Constant-field theory has been applied to describe the influence of ion concentrations on current-voltage relationships of the active channels. The extended model is investigated using a reference set of model parameters. In this configuration, the system converges to stable slow oscillations with intrinsic changes in cytoplasmic K⁺ and Cl⁻ concentrations. These slow oscillations reflect alternation between a state of salt uptake at steady negative values of V and a state of net salt loss at rapidly oscillating V, the latter being analogous to the previously reported oscillations. By switching off either concentration changes or gating, it is demonstrated that the fast oscillations are mostly due to the gating properties of the Cl⁻ channel, whereas the slow oscillations are controlled by the effect of the Cl⁻ concentration on the current. The sensitivity of output results y (e.g., frequency of oscillations) to changes of the model parameters x (e.g., maximum Cl⁻ conductance) has been investigated for the reference system. Further examples are presented where some larger changes of specific model parameters cause fundamentally different behavior, e.g., convergence towards a stable state of only the fast oscillations without intrinsic concentration changes, or to a steady-state without any oscillations. The main and general result of this study is that the osmotic status of a plant cell is stabilized by the ensemble of familiar electroenzymes through oscillatory interactions with the internal concentrations of the most abundant ions. This convergent behavior of the stand-alone system is an important prerequisite for osmotic regulation by means of other physiological mechanisms, like second messengers and gating modifiers. Received: 23 February/Revised: 16 July 1998     

Correlation Networks from Flows. The Case of Forced and Time-Dependent Advection-Diffusion Dynamics

Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system. Network links in climate networks typically imply information, mass or energy exchange. However, the specific connection between oceanic or atmospheric flows and the climate network’s structure is still unclear. We propose a theoretical approach for verifying relations between the correlation matrix and the climate network measures, generalizing previous studies and overcoming the restriction to stationary flows. Our methods are developed for correlations of a scalar quantity (temperature, for example) which satisfies an advection-diffusion dynamics in the presence of forcing and dissipation. Our approach reveals that correlation networks are not sensitive to steady sources and sinks and the profound impact of the signal decay rate on the network topology. We illustrate our results with calculations of degree and clustering for a meandering flow resembling a geophysical ocean jet.     

Ion and Glycerol Concentrations in 12 Isolates of Dunaliella

Ginzburg, M., and Ginzburg, B. Z., 1985. Ion and glycerol concentrationsin 12 isolates of Dunaliella.—J. exp. Bot. 36: 1064–1074. Twelve isolates of Dunaliella with average cell volumes rangingfrom 50 to 1400x10^–18 m³ were grown in batch culture at0.5 M or 2.0 M NaCl. Glycerol and ions (Na⁺, K⁺, Mg²⁺, CI^–,phosphate) were measured in log-phase cultures. The contentsof Mg²⁺, K⁺ and phosphate per cell were found to be a functionof cell-volume. Cell glycerol, Na⁺ and Cl^– were functionsof cell-volume and of the NaCl concentration in the medium.Solute concentrations were calculated from the measured cell-volumesand from the ³H₂O content of pellets corrected for intercellularspace using Blue Dextran. Cell glycerol was found to accountfor about one-half of the expected osmolarity, the remainderbeing largely accounted for by Na⁺ and CI^–. Key words: —Dunaliella, isolates, glycerol, ion concentrations     

Measurements of Ion Concentrations and Fluxes in Dunaliella parva

Measurements of K⁺, Na⁺, and Cl^– were made on a halotolerantstrain of Dunaliella growing at 500 mM NaCl, 25 ?C, and a relativelylow light intensity (6000 Lx). Much effort was spent in searchingfor a means of measuring the extracellular volume of fluid trappedbetween the cells of centrifuged pellets. All of the sugarstried as markers were rejected because they were found to bedigested in the cell suspension. The most suitable marker wasfound to be [¹⁴C]polyethylene glycol² (mol. wt. 4000); althoughthis substance was apparently adsorbed to the cell exterior,it was found possible to correct for adsorption and then obtaina reasonable figure for the trapped fluid. The final concentrationsof cell K⁺ and Na⁺ were 128 ? 53 mM and 131 ? 117 mM respectively.Cl^– balanced the sum of K⁺ Na⁺. Influxes of ²²Na⁺, ⁴²K⁺,and ³⁶C1^– were measured in cells in which the ions werein the steady state. Averages of 610 and 6.6 nmol m^–2s^–1 were obtained for Na⁺ and K⁺ respectively. Cl^–influx was divided into 2 phases with values of 1540 and 178mmol m^–2 s^–1. The faster influx was considered tobe across the outer cell membrane. The membrane responsiblefor the slower influx has not been identified. By comparingvalues of the potential difference calculated from the Nernstand Goldman equations, it was concluded that Na⁺ and K⁺ areprobably controlled by active mechanisms, whereas cell Cl^–is likely to be at thermodynamic equilibrium with the medium.     

Non-Equilibrium Dynamics Contribute to Ion Selectivity in the KcsA Channel

The ability of biological ion channels to conduct selected ions across cell membranes is critical for the survival of both animal and bacterial cells. Numerous investigations of ion selectivity have been conducted over more than 50 years, yet the mechanisms whereby the channels select certain ions and reject others are not well understood. Here we report a new application of Jarzynski’s Equality to investigate the mechanism of ion selectivity using non-equilibrium molecular dynamics simulations of Na⁺ and K⁺ ions moving through the KcsA channel. The simulations show that the selectivity filter of KcsA adapts and responds to the presence of the ions with structural rearrangements that are different for Na⁺ and K⁺. These structural rearrangements facilitate entry of K⁺ ions into the selectivity filter and permeation through the channel, and rejection of Na⁺ ions. A mechanistic model of ion selectivity by this channel based on the results of the simulations relates the structural rearrangement of the selectivity filter to the differential dehydration of ions and multiple-ion occupancy and describes a mechanism to efficiently select and conduct K⁺. Estimates of the K⁺/Na⁺ selectivity ratio and steady state ion conductance for KcsA from the simulations are in good quantitative agreement with experimental measurements. This model also accurately describes experimental observations of channel block by cytoplasmic Na⁺ ions, the “punch through” relief of channel block by cytoplasmic positive voltages, and is consistent with the knock-on mechanism of ion permeation.     

Modelling spatiotemporal olfactory data in two steps: from binary to Hodgkin-Huxley neurones

Network models of synchronously updated McCulloch-Pitts neurones exhibit complex spatiotemporal patterns that are similar to activities of biological neurones in phase with a periodic local field potential, such as those observed experimentally by Wehr and Laurent (1996, Nature 384, 162-166) in the locust olfactory pathway. Modelling biological neural nets with networks of simple formal units makes the dynamics of the model analytically tractable. It is thus possible to determine the constraints that must be satisfied by its connection matrix in order to make its neurones exhibit a given sequence of activity (see, for instance, Quenet et al., 2001, Neurocomputing 38-40, 831-836). In the present paper, we address the following question: how can one construct a formal network of Hodgkin-Huxley (HH) type neurones that reproduces experimentally observed neuronal codes? A two-step strategy is suggested in the present paper: first, a simple network of binary units is designed, whose activity reproduces the binary experimental codes; second, this model is used as a guide to design a network of more realistic formal HH neurones. We show that such a strategy is indeed fruitful: it allowed us to design a model that reproduces the Wehr-Laurent olfactory codes, and to investigate the robustness of these codes to synaptic noise.     

A Mathematical Model of Valveless Pumping: A Lumped Model with Time-Dependent Compliance,Resistance, and Inertia

A new lumped model of flow driven by pumping without valves is presented, motivated by biomedical applications: the circulation of the human fetus before the development of the heart valves and mechanism of blood flow during the external cardiopulmonary resuscitation (CPR). The phenomenon of existence of a unidirectional net flow around a loop of tubing that consists of two different compliances is called valveless pumping. The lumped parameter model of valveless pumping in this paper is governed by the ordinary differential equations for pressure and flow, with time-dependent compliance, resistance, and inertia. This simple model can represent the essential features of valveless pumping we observed in earlier mathematical models and physical experiments of valveless pumping. We demonstrate that not only parameters of the driving function, such as frequency or amplitude, but also physical parameters, such as wall thickness and tube stiffness, are important in determining the direction and magnitude of a net flow. In this system, we report two new and interesting phenomena of valveless pumping: One is that the shifted peak frequency can be predicted by the pulsewave speed and the other is that time-dependent resistance is a crucial factor in generating valveless pumping. We also demonstrate that this lumped model can be extended to a one-dimensional flow model of valveless pumping and explain why a linear case, the case of the constant compliance, resistance, and inertia, generates almost zero net flow. This emphasizes that the nonlinearity of valveless pumping is also an important factor to generate a net flow in a closed loop model of valveless pumping.     

A Comparison of the Methods of X-ray Microanalysis, Compartmental Analysis and Longitudional Ion Profiles to Estimate Cytoplasmic Ion Concentrations in Two Maize Varieties

Hajibagheri, M. A., Flowers, T. J., Collins, J. C. and Yeo,A. R. 1988. A comparison of the methods of X-ray microanalysis,compartmental analysis and longitudinal ion profiles to estimatecytoplasnuc ion concentrations in two maize varieties.—J.exp. Bot. 39: 279-290. The ion content of compartments within plant root cells hasbeen studied by three different methods; flux analysis usingradioactive isotopes, longitudinal ion profiles and X-ray microanalysis.The data provide estimates of the concentrations of K⁺ and CI^–in the cytoplasm of roots of culture solution and salt grownmaize by three independent methods. In the cultivar LG₁₁ grown in 50 mol m^–3 NaCl X-ray microanalysis,compartmental analysis and longitudinal profiles yielded approximatelyagreeing values for cytoplasmic K⁺ of 90, 70 and 62 mol m^–33of tissue volume respectively. However, the methods disagreedon cytoplasmic Cl^– where the value obtained by compartmentalanalysis was about four times that from X-ray microanalysisand longitudinal profiles. Possible reasons for this are discussed. Key words: X-ray microanalysis, longitudinal ion profiles, compartmental analysis, salt-tolerance.     

Conformational Dynamics in the Selectivity Filter of KcsA in Response to Potassium Ion Concentration

Conformational change in the selectivity filter of KcsA as a function of ambient potassium concentration is studied with solid-state NMR. This highly conserved region of the protein is known to chelate potassium ions selectively. We report solid-state NMR chemical shift fingerprints of two distinct conformations of the selectivity filter; significant changes are observed in the chemical shifts of key residues in the filter as the potassium ion concentration is changed from 50 mM to 1 μM. Potassium ion titration studies reveal that the site-specific K_d for K⁺ binding at the key pore residue Val76 is on the order of ∼ 7 μM and that a relatively high sample hydration is necessary to observe the low-K⁺ conformer. Simultaneous detection of both conformers at low ambient potassium concentration suggests that the high-K⁺ and low-K⁺ states are in slow exchange on the NMR timescale (k_ex < 500 s^− 1). The slow rate and tight binding for evacuating both inner sites simultaneously differ from prior observations in detergent in solution, but agree well with measurements by electrophysiology and appear to result from our use of a hydrated bilayer environment. These observations strongly support a common assumption that the low-K⁺ state is not involved in ion transmission, and that during transmission one of the two inner sites is always occupied. On the other hand, these kinetic and thermodynamic characteristics of the evacuation of the inner sites certainly could be compatible with participation in a control mechanism at low ion concentration such as C-type inactivation, a process that is coupled to activation and involves closing of the outer mouth of the channel.     

Calcium and Hydrogen Ion Concentrations in the Parasitophorous Vacuoles of Epithelial Cells Infected with the Microsporidian Encephalitozoon hellem

ABSTRACT. Microsporidia of the genus Encephalitozoon undergo merogony and sporogony in a parasitophorous vacuole within the host cell. Cultured green monkey kidney cells infected with Encephalitozoon hellem were loaded with the fluorescent dyes fura-2 or BCECF in order to measure intracellular concentrations of calcium and hydrogen ions respectively. Both the parasitophorous vacuole calcium concentration and pH values resembled those of the host cell cytoplasm in infected cells. Calcein entered the parasitophorous vacuole but not other host cell vacuoles or parasite stages within the parasitophorous vacuole. The lack of a pH or calcium concentration gradient across the parasitophorous vacuole membrane and the permeability of this membrane to a large anion such as calcein suggest that the vacuole membrane surrounding E. hellem resembles that surrounding some other intracellular parasites such as Toxoplasma gondii. A potential role is discussed for the parasitophorous vacuole calcium concentration in germination in situ.     

Using the QICAR Model to Correlate Metal Ion Characteristics with Toxicity Order Numbers

The quantitative ion character–activity relationship (QICAR) was used to correlate nine ion characteristics with ion toxicity order numbers (TON) in 19 metals. A multi-parameter regression model was used to simulate the metals toxicity order numbers after minimization of the multicollinearity among the ion characteristics using principal component analysis (PCA). The toxicity order numbers of the metals increased with the positively correlated variables AN, X_m ²r, AN/ΔIP, AW, and X_m , and decreased with the negatively correlated variables ΔE ₀, |logK _OH|, AR/AW, and σ _P . The regression model provided high prediction ability, with Nash-Suttcliffe simulation efficiency coefficients (NSC) of 0.93 for the modeling phase and 0.87 for the testing phases. The model may be successfully employed to predict the stability constants and metal toxicity and used as a first step in the further risk assessment modeling.     

Self-Calibrated Line-Scan STED-FCS to Quantify Lipid Dynamics in Model and Cell Membranes

Only a limited number of noninvasive techniques are available to directly measure the dynamic behavior of lipids in model and cell membranes. Here, we explored whether a commercial instrument could be used for fluorescence correlation spectroscopy (FCS) under pulsed stimulated emission depletion (STED). To overcome issues with photobleaching and poor distinction between confocal and STED signals, we implemented resonant line-scan STED with filtered FCS, which has the additional benefit of autocalibrating the dimensions of the point-spread function and obtaining spatially resolved molecular mobility at subdiffraction resolution. With supported lipid bilayers, we achieved a detection spot radius of 40 nm, although at the expense of decreased molecular brightness. We also used this approach to map the dynamics of Atto646N-labeled sphingomyelin and phosphatidylethanolamine in the plasma membrane. Despite the reliability of the method and the demonstration that photobleaching and the photophysical properties of the dye did not influence diffusion measurements, we found great heterogeneities even within one cell. For both lipids, regions of high local density correlated with slow molecular diffusion, indicating trapping of Atto646N-labeled lipids. Future studies with new dyes are needed to reveal the origin of the trapping.     

Membrane Dynamics at the Nuclear Exchange Junction during Early Mating (One to Four Hours) in the Ciliate Tetrahymena thermophila

Using serial-section transmission electron microscopy and three-dimensional (3D) electron tomography, we characterized membrane dynamics that accompany the construction of a nuclear exchange junction between mating cells in the ciliate Tetrahymena thermophila. Our methods revealed a number of previously unknown features. (i) Membrane fusion is initiated by the extension of hundreds of 50-nm-diameter protrusions from the plasma membrane. These protrusions extend from both mating cells across the intercellular space to fuse with membrane of the mating partner. (ii) During this process, small membrane-bound vesicles or tubules are shed from the plasma membrane and into the extracellular space within the junction. The resultant vesicle-filled pockets within the extracellular space are referred to as junction lumens. (iii) As junction lumens fill with extracellular microvesicles and swell, the plasma membrane limiting these swellings undergoes another deformation, pinching off vesicle-filled vacuoles into the cytoplasm (reclamation). (iv) These structures (resembling multivesicular bodies) seem to associate with autophagosomes abundant near the exchange junction. We propose a model characterizing the membrane-remodeling events that establish cytoplasmic continuity between mating Tetrahymena cells. We also discuss the possible role of nonvesicular lipid transport in conditioning the exchange junction lipid environment. Finally, we raise the possibility of an intercellular signaling mechanism involving microvesicle shedding and uptake.