Random-walk model of diffusion in three dimensions in brain extracellular space: comparison with microfiberoptic photobleaching measurements

Diffusion through the extracellular space (ECS) in brain is important in drug delivery, intercellular communication, and extracellular ionic buffering. The ECS comprises ∼20% of brain parenchymal volume and contains cell-cell gaps ∼50 nm. We developed a random-walk model to simulate macromolecule diffusion in brain ECS in three dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction (α), cell size, cell-cell gap geometry, intercellular lake (expanded regions of brain ECS) dimensions, and molecular size of the diffusing solute. Model output was relative solute diffusion in water versus brain ECS (D_o/D). Experimental D_o/D for comparison with model predictions was measured using a microfiberoptic fluorescence photobleaching method involving stereotaxic insertion of a micron-size optical fiber into mouse brain. D_o/D for the small solute calcein in different regions of brain was in the range 3.0-4.1, and increased with brain cell swelling after water intoxication. D_o/D also increased with increasing size of the diffusing solute, particularly in deep brain nuclei. Simulations of measured D_o/D using realistic α, cell size and cell-cell gap required the presence of intercellular lakes at multicell contact points, and the contact length of cell-cell gaps to be least 50-fold smaller than cell size. The model accurately predicted D_o/D for different solute sizes. Also, the modeling showed unanticipated effects on D_o/D of changing ECS and cell dimensions that implicated solute trapping by lakes. Our model establishes the geometric constraints to account quantitatively for the relatively modest slowing of solute and macromolecule diffusion in brain ECS.     

Cation binding to beta-casein. A comparison of electrostatic models

The binding of cations of β-casein at pH 6.6 was considered previously. Available for three sodium concentiations, I = 0.04, 0.08, or 0.16 M are: [1] proton releases between I and [2] for each I, as calcium activity is increased, correlated sequences of monomer net charge, proton release, site bound calcium and protein Solvation- Models for ion binding are examined. Critical considerations are the intrinsic binding constants between hydrogen[H], calcium[Ca] and sodium[Na] ions and phosphate[P] and caiboxyIate[C] sites, and the effects of electrostatic interaction between sites as influenced by spatial fixed charge distribution, ionic strength and dielectric constant [D]. Anticipated intrinsic binding constants are k_H,P^o = 3 × 10⁶, k_Ca,P^o = 120, k_Na,P^o = 1, k_H,C^o = 7 × 10⁴ and k_Ca,C^o = 5.6Distributed charge models, either surface or volume, are inadequate since any reasonable monomer size yields fixed charge densities requiring k_H,P^o and k_Ca,C^o which are too low when the maximum in D is 75. Also, with increasing calcium binding, calculated proton release is only 0.4 to 0.5 of that observed.Discrete charge models accept anticipated k^o and yield calculated sequences of calcium binding and proton release which are in good agreement with those observed provided that: (1) using the known amino acid sequence of the phosphate-containing acidic peptide portion of the molecule, pep tide fixed charge is distributed at the lowest I so as to minimize electrostatic free energy; (2) in the region of fixed charge, D is approximately 5; (3) the distances between peptide fixed charges decrease with increasing ionic strength or calcium binding and (4) while protein is in solution, the acidic peptide and the remainder of the molecule are essentially electrostatically independent.     

Dendrite‐Free Flexible Fiber‐Shaped Zn Battery with Long Cycle Life in Water and Air

Fiber‐shaped aqueous rechargeable Zn batteries (FARZBs) show flexibility, good reliability, cost‐effectiveness, high energy/power densities, and high safety that have attracted increasing attention as promising energy storage devices for future wearable applications. However, the development of FARZB is limited by its poor cycling life and inferior charge–discharge performance, mainly suffering from zinc dendrite growth and increasing electrode irreversibility. In this work, dendrite‐free fiber‐shaped Zn//Co₃O₄ rechargeable batteries with a long cycle life tested in water and air, are obtained via tuning the surface binding energy of Zn on the anode using the zincophilic N,O‐functional carbon fiber, as well as engineering the Co₃O₄ cathode with a nanowire array structure. The fiber‐shaped Zn//Co₃O₄ full battery demonstrates remarkable long cycle life in water and air with high energy density, impressive flexibility, and excellent waterproof ability (fully immersed and charged/discharged under water for more than 33 h for 3000 cycles with capacity retention of ≈80%). The reversible electrochemical mechanisms of the FARZBs, without obvious zinc dendrite deposits and structural change of Co₃O₄ nanowires, are confirmed by a series of characterizations. These results demonstrate that the FARZBs are promising power sources for emerging wearable electronics.     

Configurational effect on the reflection coefficient for rigid solutes in capillary pores

Osmosis-driven flow through a leaky porous membrane is analyzed by combining the relevant equations describing spatial and orientational distributions of rigid non-spherical solute particles with the equations of fluid flow in a single capillary which is very narrow compared to its length. The capillary cross-section is either circular or rectangular and connects two bulk solution reservoirs having equal pressures but unequal concentrations of solute (osmotic pressure). The objective of this analysis is to study the effect of particle and pore shape on the reflection coefficient (σ₀). The most significant result is that for solute particles of any eccentricity from one (sphere) to infinity (needle) in either the circular or rectangular pores, σ₀ ≈ (1?K)², where K is the pore-bulk equilibrium partition coefficient. A corollary of this result is that, comparing solute particles of equal volume, the more elongated a solute is the higher is its reflection coefficient; furthermore, for a given solute, the reflection coefficient is higher for pores that are more eccentric compared to a circle of equal area.     

Water Transfer and Cell Structure in Isolated Crayfish Muscle Fibers

Changes in volume of crayfish single muscle fibers in response to changes in ionic or electrical conditions have been studied in conjunction with electrophysiological measurements and electron microscopic examinations. The occurrence of at least three mechanisms of water movements is revealed, two being processes which are superimposed on the normal osmotic water movement that results from a change in the concentration of solute in the medium. Differences between the time courses of the changes in volume and potential on changing K_i/K_o indicate that water may be distributed unequally for a time within compartments of the fiber. Electron micrographs reveal a selective accumulation of water at the periphery of the fiber under certain conditions. A correlation of H₂O transfer with a change in membrane potential is apparent in crayfish muscle fibers and is probably due to electroosmotic effects. Electrokinetic water movements are produced whenever the membrane potential is changed to a considerable degree by changing the level of K and/or Cl in the medium, or by applying currents with an intracellular microelectrode. Depolarizations cause shrinkage. Hyperpolarizations or repolarizations cause swelling. The volume changes are independent of the occurrence or absence of swelling in the anion-permselective transverse tubular system. They indicate that the fiber membrane along the surface is heterogeneous, not only with respect to the signs of its fixed charge sites, but also with respect to the sizes and relative permselectivities of these charged channels.     

Effects of caffeine on crayfish muscle fibers. II. Refractoriness and factors influencing recovery (repriming) of contractile responses

When caffeine evokes a contraction, and only then, crayfish muscle fibers become refractory to a second challenge with caffeine for up to 20 min in the standard saline (5 mM K_o). However, the fibers still respond with contraction to an increase in K_o, though with diminished tension. Addition of Mn slows recovery, but the latter is greatly accelerated during exposure of the fiber to high K_o, or after a brief challenge with high K_o. Neither the depolarization induced by the K, nor the repolarization after its removal accounts for the acceleration, which occurs only if the challenge with K had itself activated the contractile system; acceleration is blocked when contractile responses to K are blocked by reducing the Ca in the bath or by adding Mn. Recovery is accelerated by redistribution of intracellular Cl and by trains of intracellularly applied depolarizing pulses, but not by hyperpolarization. The findings indicate that two sources of Ca can be mobilized to activate the contractile system. Caffeine mobilizes principally the Ca store of the SR. Depolarizations that are induced by high K_o, by transient efflux of Cl, or by intracellularly applied currents mobilize another source of Ca which is strongly dependent upon the entry of Ca from the bathing medium. The sequestering mechanism of the SR apparently can utilize this second source of Ca to replenish its own store so as to accelerate recovery of responsiveness to a new challenge with caffeine.     

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

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.     

Calcium Efflux from Barnacle Muscle Fibers : Dependence on External Cations

Calcium-45 was injected into single giant barnacle muscle fibers, and the rate of efflux was measured under a variety of conditions. The rate constant (k) for ⁴⁵Ca efflux into standard seawater averaged 17 x 10^–4 min^–1 which corresponds to an efflux of about 1–2 pmol/cm²·s. Removal of external Ca (Ca_o) reduced the efflux by 50%. In most fibers about 40% of the ⁴⁵Ca efflux into Ca-free seawater was dependent on external Na (Na_o); treatment with 3.5 mM caffeine increased the magnitude of the Na_o-dependent efflux. In a few fibers removal of Na_o, in the absence of Ca_o, either had no effect or increased k; caffeine (2–3.5 mM) unmasked an Na_o-dependent efflux in these fibers. The Na_o-dependent Ca efflux had a Q₁₀ of about 3.7. The data are consistent with the idea that a large fraction of the Ca efflux may be carrier-mediated, and may involve both Ca-Ca and Na-Ca counterflow. The relation between the Na_o-dependent Ca efflux and the external Na concentration is sigmoid, and suggests that two, or more likely three, external Na⁺ ions may activate the efflux of one Ca⁺². With a three-for-one Na-Ca exchange, the Na electrochemical gradient may be able to supply sufficient energy to maintain the Ca gradient in these fibers. Other, more complex models are not excluded, however, and may be required to explain some puzzling features of the Ca efflux such as the variable Na_o-dependence.     

The passive properties of muscle fibers are velocity dependent

The passive properties of skeletal muscle play an important role in muscle function. While the passive quasi-static elastic properties of muscle fibers have been well characterized, the dynamic visco-elastic passive behavior of fibers has garnered less attention. In particular, it is unclear how the visco-elastic properties are influenced by lengthening velocity, in particular for the range of physiologically relevant velocities. The goals of this work were to: (i) measure the effects of lengthening velocity on the peak stresses within single muscle fibers to determine how passive behavior changes over a range of physiologically relevant lengthening rates (0.1–10L_o/s), and (ii) develop a mathematical model of fiber viscoelasticity based on these measurements. We found that passive properties depend on strain rate, in particular at the low loading rates (0.1–3L_o/s), and that the measured behavior can be predicted across a range of loading rates and time histories with a quasi-linear viscoelastic model. In the future, these results can be used to determine the impact of viscoelastic behavior on intramuscular stresses and forces during a variety of dynamic movements.     

Differential Effects of RGK Proteins on L-Type Channel Function in Adult Mouse Skeletal Muscle

Work in heterologous systems has revealed that members of the Rad, Rem, Rem2, Gem/Kir (RGK) family of small GTP-binding proteins profoundly inhibit L-type Ca²⁺ channels via three mechanisms: 1), reduction of membrane expression; 2), immobilization of the voltage-sensors; and 3), reduction of P_o without impaired voltage-sensor movement. However, the question of which mode is the critical one for inhibition of L-type channels in their native environments persists. To address this conundrum in skeletal muscle, we overexpressed Rad and Rem in flexor digitorum brevis (FDB) fibers via in vivo electroporation and examined the abilities of these two RGK isoforms to modulate the L-type Ca²⁺ channel (Ca_V1.1). We found that Rad and Rem both potently inhibit L-type current in FDB fibers. However, intramembrane charge movement was only reduced in fibers transfected with Rad; charge movement for Rem-expressing fibers was virtually identical to charge movement observed in naïve fibers. This result indicated that Rem supports inhibition solely through a mechanism that allows for translocation of Ca_V1.1’s voltage-sensors, whereas Rad utilizes at least one mode that limits voltage-sensor movement. Because Rad and Rem differ significantly only in their amino-termini, we constructed Rad-Rem chimeras to probe the structural basis for the distinct specificities of Rad- and Rem-mediated inhibition. Using this approach, a chimera composed of the amino-terminus of Rem and the core/carboxyl-terminus of Rad inhibited L-type current without reducing charge movement. Conversely, a chimera having the amino-terminus of Rad fused to the core/carboxyl-terminus of Rem inhibited L-type current with a concurrent reduction in charge movement. Thus, we have identified the amino-termini of Rad and Rem as the structural elements dictating the specific modes of inhibition of Ca_V1.1.     

Differential Effects of RGK Proteins on L-Type Channel Function in Adult Mouse Skeletal Muscle

Work in heterologous systems has revealed that members of the Rad, Rem, Rem2, Gem/Kir (RGK) family of small GTP-binding proteins profoundly inhibit L-type Ca²⁺ channels via three mechanisms: 1), reduction of membrane expression; 2), immobilization of the voltage-sensors; and 3), reduction of P_o without impaired voltage-sensor movement. However, the question of which mode is the critical one for inhibition of L-type channels in their native environments persists. To address this conundrum in skeletal muscle, we overexpressed Rad and Rem in flexor digitorum brevis (FDB) fibers via in vivo electroporation and examined the abilities of these two RGK isoforms to modulate the L-type Ca²⁺ channel (Ca_V1.1). We found that Rad and Rem both potently inhibit L-type current in FDB fibers. However, intramembrane charge movement was only reduced in fibers transfected with Rad; charge movement for Rem-expressing fibers was virtually identical to charge movement observed in naïve fibers. This result indicated that Rem supports inhibition solely through a mechanism that allows for translocation of Ca_V1.1’s voltage-sensors, whereas Rad utilizes at least one mode that limits voltage-sensor movement. Because Rad and Rem differ significantly only in their amino-termini, we constructed Rad-Rem chimeras to probe the structural basis for the distinct specificities of Rad- and Rem-mediated inhibition. Using this approach, a chimera composed of the amino-terminus of Rem and the core/carboxyl-terminus of Rad inhibited L-type current without reducing charge movement. Conversely, a chimera having the amino-terminus of Rad fused to the core/carboxyl-terminus of Rem inhibited L-type current with a concurrent reduction in charge movement. Thus, we have identified the amino-termini of Rad and Rem as the structural elements dictating the specific modes of inhibition of Ca_V1.1.     

A physics-based approach of coarse-graining the cytoplasm of Escherichia coli (CGCYTO)

We have investigated protein stability in an environment of Escherichia coli cytoplasm using coarse-grained computer simulations. To coarse-grain a small slide of E. coli's cytoplasm consisting of over 16 million atoms, we have developed a self-assembled clustering algorithm (CGCYTO). CGCYTO uses the shape parameter and asphericity as well as a parameter λ (ranging from 0 to 1) that measures the covolume of a test protein and a macromolecule against the covolume of a test protein and a sphere of equal volume as that of a macromolecule for the criteria of coarse-graining a cytoplasmic model. A cutoff λ_c = 0.8 was chosen based on the size of a test protein and computational resources and it determined the resolution of a coarse-grained cytoplasm. We compared the results from a polydisperse cytoplasmic model (PD model) produced by CGCYTO with two other coarse-grained hard-sphere cytoplasmic models: 1), F70 model, macromolecules in the cytoplasm were modeled by homogeneous hard spheres with a radius of 55 Å, the size of Ficoll70 and 2), HS model, each macromolecule in the cytoplasm was modeled by a hard sphere of equal volume. It was found that the folding temperature T_f of a test protein (apoazurin) in a PD model is ～5° greater than that in a F70 model. In addition, the deviation of T_f in a PD model is twice as much as that in a HS model when an apoazurin is randomly placed at different voids formed by particle fluctuations in PD models.     

Development of diagnostics in the search for an explanation of aerotoxic syndrome

Aerotoxic syndrome is assumed to be caused by exposure to tricresyl phosphate, an additive in engine lubricants and hydraulic fluids that is activated to the toxic 2-(ortho-cresyl)-4H-1,3,2-benzodioxaphosphoran-2-one (CBDP). Currently, there is no laboratory evidence to support intoxication of airline crew members by CBDP. Our goal was to develop methods for testing in vivo exposure by identifying and characterizing biomarkers. Mass spectrometry was used to study the reaction of CBDP with human albumin, free tyrosine, and human butyrylcholinesterase. Human albumin made a covalent bond with CBDP, adding a mass of 170 amu to Tyr411 to yield the o-cresyl phosphotyrosine derivative. Human butyrylcholinesterase made a covalent bond with CBDP on Ser198 to yield five adducts with added masses of 80, 108, 156, 170, and 186 amu. The most abundant adduct had an added mass of 80 amu from phosphate (HPO₃), a surprising result given that no pesticide or nerve agent is known to yield phosphorylated serine with an added mass of 80 amu. The next most abundant adduct had an added mass of 170 amu to form o-cresyl phosphoserine. It is concluded that toxic gases or oil mists in cabin air may form adducts on plasma butyrylcholinesterase and albumin, detectable by mass spectrometry.     

Study of Plasma Flow Modes in Imploding Nested Arrays

Results from experimental studies of implosion of nested wire and fiber arrays at currents of up to 4 МА at the Angara-5-1 facility are presented. Depending on the ratio between the radii of the inner and outer arrays, different modes of the plasma flow in the space between the inner and outer arrays were implemented: the sub-Alfvénic (V _r < V _А ) and super-Alfvénic (V _r > V _А ) modes and a mode with the formation of the transition shock wave (SW) region between the cascades. By varying the material of the outer array (tungsten wires or kapron fibers), it is shown that the plasma flow mode between the inner and outer arrays depends on the ratio between the plasma production rates ?_in /?_out in the inner and outer arrays. The obtained experimental results are compared with the results of one-dimensional MHD simulation of the plasma flow between the arrays. Stable implosion of the inner array plasma was observed in experiments with combined nested arrays consisting of a fiber outer array and a tungsten inner array. The growth rates of magnetic Rayleigh?Taylor (MRT) instability in the inner array plasma at different numbers of fibers in the outer array and different ratios between the radii of the inner and outer arrays are compared. Suppression of MRT instability during the implosion of the inner array plasma results in the formation of a stable compact Z-pinch and generation of a soft X-ray pulse. A possible scenario of interaction between the plasmas of the inner and outer arrays is offered. The stability of the inner array plasma in the stage of final compression depends on the character of interaction of plasma jets from the outer array with the magnetic field of the inner array.     

Experimental determination of sarcomere force–length relationship in type-I human skeletal muscle fibers

The objectives of this study were to measure the active and passive force–length (F–L) relationships in type-I human single muscle fibers and to compare the results to predictions from the sliding filament model (the “standard model”). We measured isometric forces in chemically skinned fibers at different sarcomere lengths (SLs) in separate maximal activations. The experimental tolerance interval for optimal SL was calculated to be (2.37, 2.95 μm), which included the prediction by the standard model (2.64, 2.81 μm). Average passive slack length was 2.22±0.08 μm, and the passive F–L relationship was well described by an exponential function. Best fit lines were used to estimate the ascending and descending limbs from the active F–L data using the average SL obtained from a digital image of the fiber. The experimental descending limb was also estimated using the shortest SL to address the possible effects of sarcomere inhomogeneity (SI). The experimental slopes of the ascending and descending limbs, 0.42 F_o/μm and ?0.52 F_o/μm (vs. ?0.55 F_o/μm with the shortest SL) respectively, F_o being the maximal isometric force, were significantly less in magnitude than those from the standard model. These results suggested that the difference between experimental and standard models was not fully explained by SI and other factors could be important. The broader experimental F–L curve compared to the standard model implies that human muscle has functionally a wider operating length range where its force-generating capacity is not compromised.     

Osmotic responses of maize roots

Water and solute relations of excised seminal roots of young maize (Zea mays L) plants, have been measured using the root pressure probe. Upon addition of osmotic solutes to the root medium, biphasic root pressure relaxations were obtained as theoretically expected. The relaxations yielded the hydraulic conductivity Lp _r) the permeability coefficient (P _sr), and the reflection coefficient (σ _sr) of the root. Values of Lp _r in these experiments were by nearly an order of magnitude smaller than Lp _r values obtained from experiments where hydrostatic pressure gradients were used to induce water flows. The value of P _sr was determined for nine different osmotica (electrolytes and nonelectrolytes) which resulted in rather variable values (0.1·10^-8–1.7·10^-8m·s^-1). The reflection coefficient σ _sr of the same solutes ranged between 0.3 and 0.6, i.e. σ _sr was low even for solutes for which cell membranes exhibit a σ _s≈1. Deviations from the theoretically expected biphasic responses occured which may have reflected changes of either P _sr or of active pumping induced by the osmotic change. The absolute values of Lp _r, P _sr, and σ _sr have been critically examined for an underestimation by unstirred layer effecs. The data indicate a considerable apoplasmic component for radial movement of water in the presence of hydrostatic gradients and also some solute flow byppassing root protoplasts. In the presence of osmotic gradients, however, there was a substantial cell-to-cell transport of water. Cutting experiments demonstrated that the hydraulic resistance for the longitudinal movement of water was much smaller than for radial transport except for the apical ends of the segments (length=5 to 20 mm). The differences in Lp _r as well as the low σ _sr values suggest that the simple osmometer model of the root with a single osmotic barrier exhibiting nearly semipermeable properties should be extended for a composite membrane model with hydraulic and osmotic barriers arranged in series and in parallel.     

Bis{2-[(3-aminopropyl)amino]ethanolato}nickel(II) chloride and bromide: Crystal structure and magnetic characterization

The title compounds, Ni(C₅H₁₄N₂O)₂Cl₂ and Ni(C₅H₁₄N₂O)₂Br₂, are isomorphous and crystallize in the orthorhombic space group Pnna with unit cell dimensions a = 13.182(3), b = 14.860(4), c = 8.742(2) Å, and a = 13.637(5), b = 15.009(4), c = 8.815(3) Å, respectively. The densities D_c and D_m are 1.42 and 1.425(4) g cm⁻³ for the chloride compound and 1.67 and 1.65(1) g cm^-3 for the bromide; Z = 4. The data of both compounds were collected with an automatic four-circle diffractometer using ω-scan mode. The crystal structures were solved by direct methods, and the refinements, based upon 1388 and 1285 reflections with F_o > 6.0σ(F_o), yielded conventional R factors of 4.0 and 7.5%, respectively.The compounds are monomeric bischelates, where four nitrogen atoms and two oxygen atoms are coordinated octahedrally to a nickel(II) ion. The oxygen atoms are in cis-position to each other. The exact symmetries of the cations are C₂. The ligand molecules are not deprotonated and are coordinated tridentately to the central atom. The six-membered ring of the chelate is in chair conformation and the five-membered ring in antisymmetric skew conformation. The chloride and bromide ions are weakly bonded to the structure with hydrogen bridges.The magnetic susceptibilities of the compounds were determined in the temperature range 93–303 K, and in both cases the magnetic data indicated octahedral nickel(II) coordination sphere with no interaction between the metal atoms.     

Cation binding to β-casein. a comparison of electrostatic models

The binding of cations of β-casein at pH 6.6 was considered previously. Available for three sodium concentiations, I = 0.04, 0.08, or 0.16 M are: [1] proton releases between I and [2] for each I, as calcium activity is increased, correlated sequences of monomer net charge, proton release, site bound calcium and protein Solvation- Models for ion binding are examined. Critical considerations are the intrinsic binding constants between hydrogen[H], calcium[Ca] and sodium[Na] ions and phosphate[P] and caiboxyIate[C] sites, and the effects of electrostatic interaction between sites as influenced by spatial fixed charge distribution, ionic strength and dielectric constant [D]. Anticipated intrinsic binding constants are k_H,P^o = 3 × 10⁶, k_Ca,P^o = 120, k_Na,P^o = 1, k_H,C^o = 7 × 10⁴ and k_Ca,C^o = 5.6Distributed charge models, either surface or volume, are inadequate since any reasonable monomer size yields fixed charge densities requiring k_H,P^o and k_Ca,C^o which are too low when the maximum in D is 75. Also, with increasing calcium binding, calculated proton release is only 0.4 to 0.5 of that observed.Discrete charge models accept anticipated k^o and yield calculated sequences of calcium binding and proton release which are in good agreement with those observed provided that: (1) using the known amino acid sequence of the phosphate-containing acidic peptide portion of the molecule, pep tide fixed charge is distributed at the lowest I so as to minimize electrostatic free energy; (2) in the region of fixed charge, D is approximately 5; (3) the distances between peptide fixed charges decrease with increasing ionic strength or calcium binding and (4) while protein is in solution, the acidic peptide and the remainder of the molecule are essentially electrostatically independent.     

Interrelation of ethylene glycol,urea and water transport in the red cell

The reflection coefficient, σ_j, which measures the coupling between the jth solute and water transport across a semipermeable membrane, varies between 0 and 1.0. Values of σ_j significantly less than 1.0 provide irreversible thermodynamic proof that there is coupling between the transport of solute and solvent and thus that they share a common pathway. We have developed an improved method for measuring σ and have used it to determine that σ_{ethylene glycol} = 0.71 ± 0.03 and σ_urea = 0.65 ± 0.03, in agreement with many, but not all, previous determinations. Since both of these values are significantly lower than 1.0, they show that there is a common ethylene glycol/water pathway and a common urea/water pathway. Addition of first one and then two methyl groups to urea increases σ to 0.89 ± 0.04 for methylurea and 0.98 ± 0.4 for 1,3-dimethylurea, consistent with passage through an aqueous pore with a sharp cutoff in the 6–7 Å region.