Transmembrane K+ and Cl− Activity Gradients for the Muscle Fiber of the Giant Barnacle

1971 ◽  
Vol 49 (4) ◽  
pp. 312-322 ◽  
Author(s):  
J. A. M. Hinke ◽  
D. C. Gayton
Keyword(s):  
Steady State ◽  
Membrane Potential ◽  
Muscle Fiber ◽  
Steady States ◽  
Intracellular Water ◽  
Significant Fraction ◽  
Ionic Activity ◽  
Single Fibers ◽  
Final Experiment ◽  
Water Heterogeneity

The activities of K+ and Cl− in the myoplasm of single fibers from the giant barnacle were measured at differing steady states by means of ion-selective microelectrodes. In one experiment, the fiber was equilibrated in a series of solutions in which [K]o and [Cl]o varied but [K]o × [Cl]o and [K]o + [Na]o were constant. In a second experiment, the fiber was equilibrated in solutions in which [K]o varied but [Cl]o and [K]o + [Na]o were constant. In a final experiment, the fiber was equilibrated in solutions in which [K]o, [Cl]o, and osmolarity were increased. The results support the view that the free K+ and Cl− activities in the myoplasm of the muscle fiber in the steady state can be defined by the equation (aK)o/(aK)i = (aCl)i/(aCl)o = exp (EF/RT), where a refers to ionic activity and E to the membrane potential. (Subscripts o and i refer to 'outside' and 'inside' the fiber, respectively.) The results are consistent with the results presented in the following paper which indicate that a significant fraction of the intracellular Cl− is not free in the myoplasm and that free myoplasmic Cl− is excluded from about 45% of the intracellular water. Free myoplasmic K+ appears to be excluded from only 15% of the intracellular water. The results also demonstrate that, because of the ion and water heterogeneity in the fiber, fiber concentrations of K+ and Cl− cannot be used in place of activities in the above equation.

scholarly journals Solvent Water for Electrolytes in the Muscle Fiber of the Giant Barnacle

1970 ◽  
Vol 56 (4) ◽  
pp. 521-541 ◽  
Author(s):  
J. A. M. Hinke
Keyword(s):  
Membrane Potential ◽  
Muscle Fiber ◽  
Extracellular Space ◽  
Fiber Volume ◽  
Single Fibers ◽  
Solvent Water ◽  
Free Ion ◽  
Ion Activity

Seven experiments are described which permit estimation of the "solvent water" or the "osmotically active water" of the dissected fiber from the giant barnacle, Balanus nubilus. Each of the first four experiments includes the measurement of a free ion activity in the myoplasm by means of a Na+, K+, or Cl- ion-specific microelectrode. The fifth experiment makes use of a membrane potential vs. [K]o curve. The last two experiments measured fiber water and fiber volume as bath osmolarity was changed. The seven independent estimations of solvent water ranged from 0.64 to 0.72 of fiber water with a mean of 0.68. Since the extracellular space of single fibers was about 7% of fiber water, it was concluded that 25% of analyzable water was not acting as solvent for the osmotically active solutes in the myoplasm.

Acidification of rat liver lysosomes: quantitation and comparison with endosomes

1993 ◽  
Vol 265 (4) ◽  
pp. C901-C917 ◽  
Author(s):  
R. W. Van Dyke
Keyword(s):  
Steady State ◽  
Membrane Potential ◽  
Rat Liver ◽  
Proton Pumps ◽  
Intact Cells ◽  
Early Endosomes ◽  
Medium Permeability ◽  
Electrogenic Proton Pump ◽  
Secondary Lysosomes ◽  
Permeability Studies

Both lysosomes and endosomes are acidified by an electrogenic proton pump, although studies in intact cells indicate that the steady-state internal pH (pHi) of lysosomes is more acid than that of endosomes. We undertook the present study to examine in detail the acidification mechanism of purified rat liver secondary lysosomes and to compare it with that of a population of early endosomes. Both endosomes and lysosomes exhibited ATP-dependent acidification, but proton influx rates were 2.4- to 2.7-fold greater for endosomes than for lysosomes because of differences in both buffering capacity and acidification rates, suggesting that endosomes exhibited greater numbers or rates of proton pumps. Lysosomes, however, exhibited a more acidic steady-state pHi due in part to a slower proton leak rate. Changes in medium Cl- increased acidification rates of endosomes more than lysosomes, and the lysosome ATP-dependent interior-positive membrane potential was only partially eliminated by high-Cl- medium. Permeability studies suggested that lysosomes were less permeable to Na+, Li+, and Cl- and more permeable to K+ and PO4(2-) than endosomes. Na-K-adenosine-triphosphatase did not appear to regulate acidification of either vesicle type. Endosome and lysosome acidification displayed similar inhibition profiles to N-ethylmaleimide, dicyclohexyl-carbodiimide, and vanadate, although lysosomes were somewhat more sensitive [concentration producing 50% maximal inhibition (IC50) 1 nM] to bafilomycin A1 than endosomes (IC50 7.6 nM). Oligomycin (1.5-3 microM) stimulated lysosome acidification due to shunting of membrane potential. Overall, acidification of endosomes and lysosomes was qualitatively similar but quantitatively somewhat different, possibly related to differences in the density or rate of proton pumps as well as vesicle permeability to protons, anions, and other cations.

POVERTY TRAPS AND INFERIOR GOODS IN A DYNAMIC HECKSCHER–OHLIN MODEL

2012 ◽  
Vol 17 (6) ◽  
pp. 1227-1251 ◽  
Author(s):  
Eric W. Bond ◽  
Kazumichi Iwasa ◽  
Kazuo Nishimura
Keyword(s):  
Economic Theory ◽  
Steady State ◽  
World Economy ◽  
Steady States ◽  
The Other ◽  
Poverty Traps ◽  
Poverty Trap ◽  
Multiple Steady States ◽  
The World ◽  
State Capital

We extend the dynamic Heckscher–Ohlin model in Bond et al. [Economic Theory(48, 171–204, 2011)] and show that if the labor-intensive good is inferior, then there may exist multiple steady states in autarky and poverty traps can arise. Poverty traps for the world economy, in the form of Pareto-dominated steady states, are also shown to exist. We show that the opening of trade can have the effect of pulling the initially poorer country out of a poverty trap, with both countries having steady state capital stocks exceeding the autarky level. However, trade can also pull an initially richer country into a poverty trap. These possibilities are a sharp contrast with dynamic Heckscher–Ohlin models with normality in consumption, where the country with the larger (smaller) capital stock than the other will reach a steady state where the level of welfare is higher (lower) than in the autarkic steady state.

Electrogenic Na+ Transport in a Crustacean Coxal Receptor

1979 ◽  
Vol 78 (1) ◽  
pp. 29-45
Author(s):  
MAURIZIO MIROLLI
Keyword(s):  
Steady State ◽  
Membrane Potential ◽  
Input Resistance ◽  
Scylla Serrata ◽  
Partial Action ◽  
State Response ◽  
Electrogenic Na Pump ◽  
K Concentration ◽  
Low K ◽  
In Cells

1. The response of the coxal receptors of the crab Scylla serrata to step stretches consisted of a partial action potential, Vα, followed by a steady-state depolarization, V8. The input resistance of the fibre was reduced during V8. 2. In the absence of stimulation, the dendrites of the receptors depolarized when external Na+ was substituted with choline or Li+, and when the external K+ concentration was increased or decreased. The dendrites also depolarized when ouabain was added to the saline. 3. The amplitude of both Vα and V8 was dependent on external Na+. In cells which were depolarized by ouabain, the amplitude of V8 increased when the K+ concentration of the saline was reduced. 4. V8 was followed by a small, but long-lasting, after-potential which was depolarizing when the membrane potential was between −70 and −60 mV. In cells depolarized by ouabain or by low K+ saline, the after-potential became hyperpolarizing. 5. When trains of brief stretches (each 5 ms in duration) were used as stimuli, the cells responded with trains of Vα responses. During this tetanic stimulation the cells hyperpolarized; cessation of the stimulus train was followed by a long-lasting hyperpolarization (PTH). 6. PTH was abolished in Li+ saline, in low K+ saline, and in the presence of ouabain. In control or in low K+ saline, PTH was not accompanied by a decrease in the input resistance of the fibres. 7. It is concluded that an electrogenic Na+ pump (or equivalent process) contributes a substantial fraction of the membrane potential of the unstimulated coxal receptors. Pump activity could be increased by Na+-loading the distal part of the cells with trains of Vα responses. By contrast, during the steady-state response to stretch, the pump was not activated.

scholarly journals Zero Eigenvalue Analysis for the Determination of Multiple Steady States in Reaction Networks

1998 ◽  
Vol 53 (3-4) ◽  
pp. 171-177
Author(s):  
Hsing-Ya Li
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Reaction Network ◽  
Steady States ◽  
Eigenvalue Analysis ◽  
Zero Eigenvalue ◽  
Positive Steady State ◽  
Positive Steady States ◽  
Positive Rate ◽  
System Of Inequalities

Abstract A chemical reaction network can admit multiple positive steady states if and only if there exists a positive steady state having a zero eigenvalue with its eigenvector in the stoichiometric subspace. A zero eigenvalue analysis is proposed which provides a necessary and sufficient condition to determine the possibility of the existence of such a steady state. The condition forms a system of inequalities and equations. If a set of solutions for the system is found, then the network under study is able to admit multiple positive steady states for some positive rate constants. Otherwise, the network can exhibit at most one steady state, no matter what positive rate constants the system might have. The construction of a zero-eigenvalue positive steady state and a set of positive rate constants is also presented. The analysis is demonstrated by two examples.

Voltage dependence of chloride current through Xenopus muscle membrane in alkaline solutions

1980 ◽  
Vol 58 (9) ◽  
pp. 999-1010 ◽  
Author(s):  
Peter C. Vaughan ◽  
James G. McLarnon ◽  
Donald D. F. Loo
Keyword(s):  
Steady State ◽  
Membrane Potential ◽  
Chloride Conductance ◽  
Resting Potential ◽  
Muscle Membrane ◽  
Alkaline Solutions ◽  
Constant Field ◽  
Confined Space ◽  
Initial Current ◽  
Test Current

Three-microelectrode voltage-clamp experiments have been conducted on surface fibres of Xenopus laevis sartorius muscles. When potassium and chloride were substituted by rubidium and sulphate, negligibly small currents were observed. In solutions containing rubidium and chloride at pH 8.4–8.8 normally polarized fibres exhibited instantaneous current–voltage relations that were linear over a wide voltage range. Chloride conductance varied widely from fibre to fibre; the mean resting conductance at −80 mV was 7.4 × 10−4 ± 2.6 × 10−4 S/cm2 (mean ± SE). When hyperpolarizing voltage steps were made, conductance declined from the initial to the steady state; inward currents saturated near 14 μA/cm2. In experiments performed on fibres depolarized by immersion in K+-and Rb+-rich solutions it was found that resting conductance did not increase by as much as would be expected from constant field – constant permeability precepts, by comparison with normally polarized fibres. Despite the low chloride transmembrane concentration ratio, rectification in the steady state was similar in depolarized and normally polarized fibres.When a two-pulse protocol was employed to test the availability of chloride conductance after conditioning of the system at some voltage, it was found that the test current, the initial current at the onset of the test voltage step, depended sigmoidally on the conditioning voltage. The sigmoid relationships had asymptotic limits: after hyperpolarizing conditioning the test current was minimal, after depolarizing conditioning, maximal. Normalized sigmoid relations were superimposable, whether from normally polarized or chronically depolarized cells.When the protocol was repeated using different test potentials and initial currents following a particular conditioning voltage were plotted against the test potential, families of straight lines were obtained. The slopes of the members of these families were dependent on the conditioning voltage: the more negative the conditioning step the lower the slope. The lines projected through a mutual intersection at a voltage slightly more positive than the resting potential. This is interpreted as indicating that there is some voltage, slightly positive with respect to the membrane potential, at which the initial current is independent of the conditioning voltage.It is concluded that the state of the chloride conductance mechanism is a function of the deviation of the membrane from the resting potential rather than of the absolute membrane potential and that relaxations from initial to steady states reflect properties of the permeation mechanism rather than accumulation or depletion of chloride in a confined space, although some contribution by a mechanism such as the latter cannot be completely ruled out.

Influence of acclimation temperature on mitochondrial DNA, RNA, and enzymes in skeletal muscle

1998 ◽  
Vol 275 (3) ◽  
pp. R905-R912 ◽  
Author(s):  
Brendan James Battersby ◽  
Christopher D. Moyes
Keyword(s):  
Skeletal Muscle ◽  
Mitochondrial Dna ◽  
Steady State ◽  
Muscle Fiber ◽  
Copy Number ◽  
White Muscle ◽  
Fiber Types ◽  
Mitochondrial Enzymes ◽  
Dna Copy Number ◽  
Mitochondrial Content

Skeletal muscle fibers typically undergo modifications in their mitochondrial content, concomitant with alterations in oxidative metabolism that occur during the development of muscle fiber and in response to physiological stimuli. We examined how cold acclimation affects the mitochondrial properties of two fish skeletal muscle fiber types and how the regulators of mitochondrial content differed between tissues. After 2 mo of acclimation to either 4 or 18°C, mitochondrial enzyme activities in both red and white muscle were higher in cold-acclimated fish. No significant differences were detected between acclimation temperatures in the abundance of steady-state mitochondrial mRNA (cytochrome- c oxidase 1, subunit 6 of F0F1-ATPase), rRNA (16S), or DNA copy number. Steady-state mRNA for nuclear-encoded respiratory (adenine nucleotide translocase 1) and glycolytic genes showed high interindividual variability, particularly in the cold-acclimated fish. Although mitochondrial enzymes were 10-fold different between the two muscle types, mitochondrial DNA copy number differed only 4-fold. The relative abundance of mitochondrial mRNA and nuclear mRNA in red and white muscle reflected the differences in copy number of their respective genes. These data suggest that the response to physiological stimuli and determination of tissue-specific mitochondrial properties likely result from the regulation of nuclear-encoded genes.

scholarly journals Thermal Robustness of Entanglement in a Dissipative Two-Dimensional Spin System in an Inhomogeneous Magnetic Field

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1066
Author(s):  
Gehad Sadiek ◽  
Samaher Almalki
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Nearest Neighbor ◽  
Quantum Phase Transitions ◽  
Inhomogeneous Magnetic Field ◽  
Steady States ◽  
Inhomogeneous Field ◽  
Spin States ◽  
Two Dimensional ◽  
Spin Lattice

Recently new novel magnetic phases were shown to exist in the asymptotic steady states of spin systems coupled to dissipative environments at zero temperature. Tuning the different system parameters led to quantum phase transitions among those states. We study, here, a finite two-dimensional Heisenberg triangular spin lattice coupled to a dissipative Markovian Lindblad environment at finite temperature. We show how applying an inhomogeneous magnetic field to the system at different degrees of anisotropy may significantly affect the spin states, and the entanglement properties and distribution among the spins in the asymptotic steady state of the system. In particular, applying an inhomogeneous field with an inward (growing) gradient toward the central spin is found to considerably enhance the nearest neighbor entanglement and its robustness against the thermal dissipative decay effect in the completely anisotropic (Ising) system, whereas the beyond nearest neighbor ones vanish entirely. The spins of the system in this case reach different steady states depending on their positions in the lattice. However, the inhomogeneity of the field shows no effect on the entanglement in the completely isotropic (XXX) system, which vanishes asymptotically under any system configuration and the spins relax to a separable (disentangled) steady state with all the spins reaching a common spin state. Interestingly, applying the same field to a partially anisotropic (XYZ) system does not just enhance the nearest neighbor entanglements and their thermal robustness but all the long-range ones as well, while the spins relax asymptotically to very distinguished spin states, which is a sign of a critical behavior taking place at this combination of system anisotropy and field inhomogeneity.

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