The short-term effect of prolactin on the active Na transport system of the tadpole skin during metamorphosis

Prolactin (PRL) induced a transient increase in active Na transport measured as the short circuit current (SCC) of the tadpole skin. Increase in SCC by PRL accelerated as the stage advanced between stages XXII and XXV. Prolactin caused two types of effect on the electric parameters of the active Na transport. In type I, it increased both the electromotive force of the active Na current (ENa) and the resistance to the active Na current (RNa). In type II, it decreased both ENa and RNa. A second application of PRL had no effect on SCC; that is, desensitization to PRL was observed.     

The effect of Na+ and K+ on the thermal denaturation of Na+ and + K+-dependent ATPase.

To increase our understanding of the physical nature of the Na+ and K+ forms of the Na+ + K+-dependent ATPase, thermal-denaturation studies were conducted in different types of ionic media. Thermal-denaturation measurements were performed by measuring the regeneration of ATPase activity after slow pulse exposure to elevated temperatures. Two types of experiments were performed. First, the dependence of the thermal-denaturation rate on Na+ and K+ concentrations was examined. It was found that both cations stabilized the pump protein. Also, K+ was a more effective stabilizer of the native state than was Na+. Secondly, a set of thermodynamic parameters was obtained by measuring the temperature-dependence of the thermal-denaturation rate under three ionic conditions: 60 mM-K+, 150 mM-Na+ and no Na+ or K+. It was found that ion-mediated stabilization of the pump protein was accompanied by substantial increases in activation enthalpy and entropy, the net effect being a less-pronounced increase in activation free energy.     

A model of neurovascular coupling and the BOLD response: PART I

The mechanisms with which neurons communicate with the vasculature to increase blood flow, termed neurovascular coupling is still unclear primarily due to the complex interactions between many parameters and the difficulty in accessing, monitoring and measuring them in the highly heterogeneous brain. Hence a solid theoretical framework based on existing experimental knowledge is necessary to study the relation between neural activity, the associated vasoactive factors released and their effects on the vasculature. Such a framework should also be related to experimental data so that it can be validated against repetitive experiments and generate verifiable hypothesis. We have developed a mathematical model which describes a signaling mechanism of neurovascular coupling with a model of pyramidal neuron and its corresponding fMRI BOLD response. In the first part of two papers we describe the integration of the neurovascular coupling unit extended to include a complex neuron model, which includes the important Na/K ATPase pump, with a model that provides a BOLD signal taking its input from the cerebral blood flow and the metabolic rate of oxygen consumption. We show that this produces a viable signal in terms of initial dip, positive and negative BOLD signals.     

Computer simulation of synchronization of Na/K pump molecules

The behavior of Na/K pump currents when exposed to an oscillating electric field is studied by computer simulation. The pump current from a single pump molecule was sketched based on previous experimental results. The oscillating electric field is designed as a symmetric, dichotomous waveform varying the membrane potential from −30 to −150 mV around the membrane resting potential of −90 mV. Based on experimental results from skeletal muscle fibers, the energy needed to overcome the electrochemical potentials for the Na and K-transports are calculated in response to the field’s two half-cycles. We found that a specially designed oscillating electric field can eventually synchronize the pump molecules so that all the individual pumps run at the same pumping rate and phase as the field oscillation. They extrude Na ions during the positive half-cycle and pump in K ions during the negative half-cycle. The field can force the two ion-transports into the corresponding half-cycles, respectively, but cannot determine their detailed positions. In other words, the oscillating electric field can synchronize pumps in terms of their pumping loops but not at a specific step in the loop. These results are consistent with our experimental results in measurement of the pump currents.     

The rapid adjustment of renal sodium excretion to changes in dietary sodium intake in sheep

The rapidity with which the kidney alters sodium excretion (ENa) in response to changes in dietary Na was studied in Merino sheep by analyzing hourly ENa for three control days, and then for three days after a change in Na intake. On a control diet of 117 mmol Na, sheep had a pre-feeding ENa of 3.5 mmol/hr., a striking post-feeding natriuresis that began 2 hours after feeding (less than 0.01), peaked at 4 hrs. and then declined to pre-feeding levels 7 hrs. after feeding. When in balance on a high Na diet the feeding of a low Na meal resulted in marked depression of ENa within 4 hours after feeding. On a low Na diet, a 100 mmol Na meal resulted in an increase in ENa within 4 hours but a 50 mmol Na meal did not. Thus, the sensitivity of post-feeding natriuresis is between 50 and 100 mmols Na. As post feeding natriuresis is a naturally occurring physiological event it should provide a useful paradigm for the investigation of mechanisms controlling Na balance.     

Analysis of sodium and potassium redistribution during sustained permeability increases at the innervated face of Electrophorus electroplaques

Cholinergic agonists cause an increase in the membrane permeability of Na and K at the innervated face of Electrophorus electroplaques. Therefore, sustained exposure to agonist reduces Na and K concentration gradients. There gradients are monitored with voltage-clamp sequences and pharmacological treatments that selectively measure the Nernst potentials for individual ions. EK is normally near--90 mV but moves toward zero during bath application of agonist. Depolarizations by bath- applied agonist measure primarily this shift of EK, not short- circuiting of EK by the agonist-induced conductance. After a rapid jump of agonist concentration, there is a fast (millisecond) depolarization due to the conductance increase, followed by a much slower additional "creep" due to the shift in EK. Sodium replaces the lost intracellular potassium: ENa, normally very positive, also moves toward zero. The shifts in EK and ENa are normally reversible but become permanent after blockade of the Na-K pump. In the presence of agonist, the shifts can be driven further by passing current of the appropriate polarity. Similar ion redistribution occurs with other drugs, such as batrachotoxin and nystatin, which induce prolonged increases in Na permeability. The redistributions cause little net change in the reversal potential of the neurally evoked postsynaptic current.     

Large signal,low frequency characteristics of the systemic arterial system

A 4-parameter model to represent the relationship between slowly changing arterial inflow and the resulting pressure change was proposed. In order to determine values for the parameters and test the model in a wide range of pressure and flow, two experimental procedures were used. Firstly, slow oscillations in aortic pressure (period, 4 sec) were produced by means of an external pump connected to the aorta, and secondly, cardiac arrest was induced for about 2–3 sec by stimulating the right vagus. It was shown mathematically that the pressure and pump displacement information obtained in these experiments could be related to the model parameters. Values for the model parameters were obtained in 6 anesthetized dogs using a least squares adjustment procedure. Using aX ²-test, it was concluded that the model represented the arterial system for each animal well.     

An analytical model of ionic movements in airway epithelial cells.

A new mathematical model of ion movements in airway epithelia is presented, which allows predictions of ion fluxes, membrane potentials and ion concentrations. The model includes sodium and chloride channels in the apical membrane, a Na/K pump and a cotransport system for Cl- with stoichiometry Na+:K+:2Cl- in the basolateral membrane. Potassium channels in the basolateral membrane are used to regulate cell volume. Membrane potentials, ion fluxes and intracellular ion concentration are calculated as functions of apical ion permeabilities, the maximum pump current and the cotransport parameters. The major predictions of the model are: (1) Cl- concentration in the cell is determined entirely by the intracellular concentration of negatively charged impermeable ions and the osmotic conditions; (2) changes in intracellular Na+ and K+ concentrations are inversely related; (3) cotransport provides the major driving force for Cl- flux, increases intracellular Na+ concentration, decreases intracellular K+ concentration and hyperpolarizes the cell interior; (4) the maximum rate of the Na/K pump, by contrast, has little effect on Na+ or Cl- transepithelial fluxes and a much less pronounced effect on cell membrane polarization; (5) an increase in apical Na+ permeability causes an increase in intracellular Na+ concentration and a significant increase in Na+ flux; (6) an increase in apical Cl- permeability decreases intracellular Na+ concentration and Na+ flux; (7) assuming Na+ and Cl- permeabilities equal to those measured in human nasal epithelia, the model predicts that under short circuit conditions, Na+ absorption is much higher than Cl- secretion, in agreement with experimental measurements.     

Regulation of Cell Volume by Active Cation Transport in High and Low Potassium Sheep Red Cells

A model cell which controls its cation composition and volume by the action of a K-Na exchange pump and leaks for both ions working in parallel is presented. Equations are formulated which describe the behavior of this model in terms of three membrane parameters. From these equations and the steady state concentrations of Na, K, and Cl, values for these parameters in high potassium (HK) and low potassium (LK) sheep red cells are calculated. Kinetic experiments designed to measure the membrane parameters directly in the two types of sheep red cells are also reported. The values of the parameters obtained in these experiments agreed well with those calculated from the steady state concentrations of ions and the theoretical equations. It is concluded that both HK and LK sheep red cells control their cation composition and volume in a manner consistent with the model cell. Both have a cation pump which exchanges one sodium ion from inside the cell with one potassium ion from outside the cell but the pump is working approximately four times faster in the HK cell. The characteristics of the cation leak in the two cell types are also very different since the HK cells are relatively more leaky to sodium as compared with potassium than is the case in the LK cells. Both cell types show appreciable sodium exchange diffusion but this process is more rapid in the LK than in the HK cells.     

A model study of the contribution of active Na-K transport to membrane repolarization in cardiac cells

A biochemical model of active Na-K transport in cardiac cells was studied in conjunction with a representation of the passive membrane currents and ion concentration changes. The active transport model is based on the thermodynamic and kinetic properties of a six-step reaction scheme for the Na,K-ATPase. It has a fixed Na:K stoechiometry of 3:2, and its activation is governed by three parameters: membrane potential intracellular Na+ concentration, and interstitial K+ concentration. The Na-K pump current is directly proportional to the density of Na,K-ATPase molecules. The passive membrane currents and ion concentration changes involve only Na+ and K+ ions, and no attempt was made to provide a precise representation of Ca2+ currents or Ca2+ concentration changes. The surface-to-volume ratio of the interstitial compartment is 55 times larger than that of the intracellular compartment. The flux balance conditions are such that the original equilibrium concentration values are re-established at each stimulation cycle. The underlying assumptions of the model were checked against experimental measurements on Na-K pump activity in a variety of preparations. In addition, the qualitative validation of the model was carried out by comparing its behavior following sudden frequency shifts to corresponding experimental observations. The overall behavior of the model is quite satisfactory and it is used to provide the following indications: (1) when the intracellular and interstitial volumes are relatively large, the ion concentration transients are small and the pumping rate depends essentially on average concentration levels. (2) An increase in internal Na+ concentration potentiates the response of the Na-K pump to rapid membrane depolarizations. (3) When the internal Na+ concentration is large enough, the Na-K pump current transient plays an important role in shaping the plateau and repolarization phase of the action potential. (4) A rapid increase in external K+ concentration during voltage clamp in multicellular preparations could saturate the Na-K pump response and lead to a fairly linear dependence of the pump activity on the internal Na+ concentration.     

Access channel model for the voltage dependence of the forward-running Na+/K+ pump

The voltage dependence of steady state current produced by the forward mode of operation of the endogenous electrogenic Na+/K+ pump in Na(+)- loaded Xenopus oocytes has been examined using a two-microelectrode voltage clamp technique. Four experimental cases (in a total of 18 different experimental conditions) were explored: variation of external [Na+] ([Na]o) at saturating (10 mM) external [K+] ([K]o), and activation of pump current by various [K]o at 0, 15, and 120 mM [Na]o (tetramethylammonium replacement). Ionic current through K+ channels was blocked by Ba2+ (5 mM) and tetraethylammonium (20 mM), thereby allowing pump-mediated current to be measured by addition or removal of external K+. Control measurements and corrections were made for pump current run-down and holding current drift. Additional controls were done to estimate the magnitude of the inwardly directed pump-mediated current that was present in K(+)-free solution and the residual K(+)- channel current. A pseudo two-state access channel model is described in the Appendix in which only the pseudo first-order rate coefficients for binding of external Na+ and K+ are assumed to be voltage dependent and all transitions between states in the Na+/K+ pump cycle are assumed to be voltage independent. Any three-state or higher order model with only two oppositely directed voltage-dependent rate coefficients can be reduced to an equivalent pseudo two-state model. The steady state current-voltage (I-V) equations derived from the model for each case were simultaneously fit to the I-V data for all four experimental cases and yielded least-squares estimates of the model parameters. The apparent fractional depth of the external access channel for Na+ is 0.486 +/- 0.010; for K+ it is 0.256 +/- 0.009. The Hill coefficient for Na+ is 2.18 +/- 0.06, and the Hill coefficient for K+ (which is dependent on [Na]o) ranges from 0.581 +/- 0.019 to 1.35 +/- 0.034 for 0 and 120 mM [Na]o, respectively. The model provides a reasonable fit to the data and supports the hypothesis that under conditions of saturating internal [Na+], the principal voltage dependence of the Na+/K+ pump cycle is a consequence of the existence of an external high- field access channel in the pump molecule through which Na+ and K+ ions must pass in order to reach their binding sites.     

Effects of magnesium and ATP on pre-steady-state phosphorylation kinetics of the Na+,K(+)-ATPase.

The aim of the present work was to elucidate the role played by ATP and Mg2+ ions in the early steps of the Na+,K(+)-ATPase cycle. The approach was to follow pre-steady-state phosphorylation kinetics in Na(+)-containing K(+)-free solutions under variable ATP and MgCl2 concentrations. The experiments were performed with a rapid mixing apparatus at 20 +/- 2 degrees C. The concentrations of free and complexes species of Mg2+ and ATP were calculated on the basis of a dissociation constant of 0.091 +/- 0.004 mM, estimated with Arsenazo III under identical conditions. A simplified scheme were ATP binds to the ENa enzyme, which is phosphorylated to MgEPNa and consequently dephosphorylated returning to the ENa form, was used. In the absence of ADP and phosphate four rate constants are relevant: k1 and k-1, the on and off rate constants for ATP binding; k2, the transphosphorylation rate constant and k3, the constant that governs the dephosphorylation rate. The values obtained were: k1 = 0.025 +/- 0.003 microM-1 ms-1 for both free ATP and ATPMg; k-1 = 0.038 +/- 0.004 ms-1 for free ATP and 0.009 +/- 0.002 ms-1 for ATPMg; k2 = 0.199 +/- 0.005 ms-1; k3 = 0.0019 +/- 0.0002 ms-1. The model that seems best to explain the data is one where (i) the role of true substrate can be played equally well by free ATP or ATPMg, and (ii) free Mg2+, an essential activator, acts by binding to a specific Mg2+ site on the enzyme molecule.     

Differential effects of aldosterone and ADH on intracellular electrolytes in the toad urinary bladder epithelium

Summary Quantitative electron microprobe analysis was employed to compare the effects of aldosterone and ADH on the intracellular electrolyte concentrations in the toad urinary bladder epithelium. The measurements were performed on thin freeze-dried cryosections utilizing energy dispersive x-ray microanalysis. After aldosterone, a statistically significant increase in the intracellular Na concentration was detectable in 8 out of 9 experiments. The mean Na concentration of granular cells increased from 8.9±1.3 to 13.2±2.2 mmol/kg wet wt. A significantly larger Na increase was observed after an equivalent stimulation of transepithelial Na transport by ADH. On average, the Na concentration in granular cells increased from 12.0±2.3 to 31.4±9.3 mmol/kg wet wt (5 experiments). We conclude from these results that aldosterone, in addition to its stimulatory effect on the apical Na influx, also exerts a stimulatory effect on the Na pump. Based on a significant reduction in the Cl concentration of granular cells, we discuss the possibility that the stimulation of the pump is mediated by an aldosterone-induced alkalinization.Similar though less pronounced concentration changes were observed in basal cells, suggesting that this cell type also participates in transepithelial Na transport. Measurements in mitochondria-rich cells provided no consistent results.     

Effect of experimental error on the efficiency of different optimization methods for bioprocess media optimization

Four optimization methods (Simplex, Rosenbrock, iterative factorial experimental design (IFED) and genetic algorithms) for the optimization of the biotechnological media composition under conditions where the measured quantities are subjected to the experimental error were compared. The computer simulations were performed on some of the selected two- to six- parameter biotechnological models. The optimization process was modified in such a way that the experimental error was considered. The results show that the optimization efficiency increases when this new termination criteria is implemented. In addition, the method efficiency becomes independent of the experimental error. In general, Simplex and Rosenbrock methods need fewer experiments and their distribution of necessary experiments is narrower than for IFED and genetic algorithms. The increase of model parameters that need to be optimized results in a decrease in the method efficiency and in an increase of the average number of required experiments. The results were further verified on the cultivation of Saccharomyces cerevisiae and were found to be in good agreement with the results obtained from the computer simulations.     

Models of the Na-K pump in cardiac muscle predict the wrong intracellular Na+ activity

The Na-K pump in cardiac Purkinje strands has been carefully studied with voltage clamp and Na+-selective microelectrodes. In three of these studies both the rate of change of intracellular Na+ activity, a(Nai), after pump blockade, and the time constant of reduction of a(Nai) after an Na+ load were measured. These two parameters can be employed with a formalism relating pump activity to a(Nai) in order to predict the a(Nai) in the steady state. Several formalisms were tested: (a) a first-order dependence on a(Nai); (b) a model based on the assumption of a single, saturable, Na+-binding site that must be occupied for transport to occur; (c) a model based on n equivalent, saturable, Na+ binding sites per pump molecule all of which must be occupied for transport to occur. The first two models predicted an a(Nai) that is far below the value of about 6 mM that is experimentally obtained. The third model would work for n greater than or equal to 4. These results suggest that either the cardiac Na-K pump is not well described by available Na-K pump models for n less than 4 or that the measured Na+ influx rate, extrusion rate or a(Nai) are in error.     

Computational binding assays of antigenic peptides

Summary Computer models can be combined with laboratory experiments for the efficient determination of (i) peptides that bind MHC molecules and (ii) T-cell epitopes. For maximum benefit, the use of computer models must be treated as experiments analogous to standard laboratory procedures. This requires the definition of standards and experimental protocols for model application. We describe the requirements for validation and assessment of computer models. The utility of combining accurate predictions with a limited number of laboratory experiments is illustrated by practical examples. These include the identification of T-cell epitopes from IDDM-, melanoma-and malaria-related antigens by combining computational and conventional laboratory assays. The success rate in determining antigenic peptides, each in the context of a specific HLA molecule, ranged from 27 to 71%, while the natural prevalence of MHC-binding peptides is 0.1–5%.     

Computational binding assays of antigenic peptides

Computer models can be combined with laboratory experiments for the efficient determination of (i) peptides that bind MHC molecules and (ii) T-cell epitopes. For maximum benefit, the use of computer models must be treated as experiments analogous to standard laboratory procedures. This requires the definition of standards and experimental protocols for model application. We describe the requirements for validation and assessment of computer models. The utility of combining accurate predictions with a limited number of laboratory experiments is illustrated by practical examples. These include the identification of T-cell epitopes from IDDM-, melanoma- and malaria-related antigens by combining computational and conventional laboratory assays. The success rate in determining antigenic peptides, each in the context of a specific HLA molecule, ranged from 27 to 71%, while the natural prevalence of MHC-binding peptides is 0.1–5%.     

A mathematical treatment of integrated Ca dynamics within the ventricular myocyte

We have developed a detailed mathematical model for Ca2+ handling and ionic currents in the rabbit ventricular myocyte. The objective was to develop a model that: 1), accurately reflects Ca-dependent Ca release; 2), uses realistic parameters, particularly those that concern Ca transport from the cytosol; 3), comes to steady state; 4), simulates basic excitation-contraction coupling phenomena; and 5), runs on a normal desktop computer. The model includes the following novel features: 1), the addition of a subsarcolemmal compartment to the other two commonly formulated cytosolic compartments (junctional and bulk) because ion channels in the membrane sense ion concentrations that differ from bulk; 2), the use of realistic cytosolic Ca buffering parameters; 3), a reversible sarcoplasmic reticulum (SR) Ca pump; 4), a scheme for Na-Ca exchange transport that is [Na]i dependent and allosterically regulated by [Ca]i; and 5), a practical model of SR Ca release including both inactivation/adaptation and SR Ca load dependence. The data describe normal electrical activity and Ca handling characteristics of the cardiac myocyte and the SR Ca load dependence of these processes. The model includes a realistic balance of Ca removal mechanisms (e.g., SR Ca pump versus Na-Ca exchange), and the phenomena of rest decay and frequency-dependent inotropy. A particular emphasis is placed upon reproducing the nonlinear dependence of gain and fractional SR Ca release upon SR Ca load. We conclude that this model is more robust than many previously existing models and reproduces many experimental results using parameters based largely on experimental measurements in myocytes.     

A computer simulation of the effect of heart rate on ion concentrations in the heart

At steady-state the passive fluxes of Na+ and K+ across the cell membrane of a heart cell are exactly matched by active fluxes of the two ions in the opposite direction via the Na-K pump, and the concentrations of Na+ and K+ both within the cell and in the clefts between cells are steady. An alteration of the heart rate (or the rate of stimulation) disrupts this balance because the passive fluxes are affected, and there are changes in pump activity as well as the Na+ and K+ concentrations. A computer model incorporating a cell separated from the bathing medium by a restricted extracellular cleft was devised to investigate these changes further. The model was able to simulate the changes observed with a variety of stimulation protocols as well as the effect of block of the Na-K pump. It is concluded that the changes in Na+ and K+ balance with heart rate can be explained in terms of the known properties of cardiac tissue incorporated into the model.