Velocity field of pulsatile flow in a porous tube

This paper describes velocity fields for fully developed periodic laminar flow in a rigid tube with a porous wall. We obtained an analytical solution of the flow by the linear approximation of the Navier-Stokes equation. Unlike the previous works with a constant seepage rate along the axis, we used a wall velocity which contained hydraulic permeation constant Lp. The axial velocity profile shows a local maximum velocity near the wall at a large Womersley number alpha. This suggests that concentration polarization in porous tubular membrane may be reduced at high frequencies if a membrane device is operated under pulsatile flow conditions. The magnitude of wall permeation velocity decreases linearly along the tube axis because the damping of the pressure difference between the inside and the outside of the tube is very small.     

Dependence of ion flux across a membrane on ionic concentration

A graph of ion flux across a membrane against the ionic concentration on one side of the membrane which has a shape similar to that given by the Michaelis-Menten equation has often been considered to indicate that ion movement is carrier-mediated rather than diffusional.The dependence of unidirectional and net ion fluxes upon the concentration ratio across the membrane has been investigated here for purely diffusional processes, on the basis of several models. The graph sometimes has a Michaelis-Menten shape, and it is concluded that in some systems at least, such a shape can be explained without postulating the presence of a carrier. A test which can help in elucidating the nature of ion permeation is described.     

Importance of the Difference in Surface Pressures of the Cell Membrane in Doxorubicin Resistant Cells That do not Express Pgp and ABCG2

P-glycoprotein (Pgp) represents the archetypal mechanism of drug resistance. But Pgp alone cannot expel drugs. A small but growing body of works has demonstrated that the membrane biophysical properties are central to Pgp-mediated drug resistance. For example, a change in the membrane surface pressure is expected to support drug–Pgp interaction. An interesting aspect from these models is that under specific conditions, the membrane is predicted to take over Pgp concerning the mechanism of drug resistance especially when the surface pressure is high enough, at which point drugs remain physically blocked at the membrane level. However it remains to be determined experimentally whether the membrane itself could, on its own, affect drug entry into cells that have been selected by a low concentration of drug and that do not express transporters. We demonstrate here that in the case of the drug doxorubicin, alteration of the surface pressure of membrane leaflets drive drug resistance.     

Theoretical Analysis of Net Tracer Flux Due to Volume Circulation in a Membrane with Pores of Different Sizes : Relation to solute drag model

When osmotic pressure across an artificial membrane, produced by a permeable electrically neutral solute on one side of it, is balanced by an external pressure difference so that there is no net volume flow across the membrane, it has been found that there will be a net flux of a second electrically neutral tracer solute, present at equal concentrations on either side of the membrane, in the direction that the "osmotic" solute diffuses. This has been ascribed to solute-solute interaction or drag between the tracer and the osmotic solutes. An alternative model, presented here, considers the membrane to have pores of different sizes. Under general assumptions, this "heteroporous" model will account for both the direction of net tracer flux and the observed linear dependence of unidirectional tracer fluxes on the concentration of the osmotic solute. The expressions for the fluxes of solutes and solvent are mathematically identical under the two models. An inequality is derived which must be valid if the solute interaction model and/or the heteroporous model can account for the data. If the inequality does not hold, then the heteroporous model alone cannot explain the data. It was found that the inequality holds for most published observations except when dextran is the osmotic solute.     

Cation permeability and cation-anion interactions in a mutant GABA-gated chloride channel from Drosophila.

To investigate the structural basis of anion selectivity of Drosophila GABA-gated Cl(-) channels, the permeation properties of wild-type and mutant channels were studied in Xenopus oocytes. This work focused on asparagine 319, which by homology is one amino acid away from a putative extracellular ring of charge that regulates cation permeation in nicotinic receptors. Mutation of this residue to aspartate reduced channel conductance, and mutation to lysine or arginine increased channel conductance. These results are consistent with an electrostatic interaction between this site and permeating anions. The lysine mutant, but not the arginine mutant, formed a channel that is permeable to cations, and this cannot be explained in terms of electrostatics. The lysine mutant had a 25-mV reversal potential in solutions with symmetrical Cl(-) and asymmetrical cations. The permeability ratio of K(+) to Cl(-) was determined as 0. 33 from reversal potential measurements in KCl gradients. Experiments with large organic cations and anions showed that cation permeation can only be seen in the presence of Cl(-), but Cl(-) permeation can be seen in the absence of permeant cations. Measurements of permeability ratios of organic anions indicated that the lysine mutant has an increased pore size. The cation permeability of the lysine-containing mutant channel cannot be accounted for by a simple electrostatic interaction with permeating ions. It is likely that lysine substitution causes a structural change that extends beyond this one residue to influence the positions of other channel-forming residues. Thus protein conformation plays an important role in enabling ion channels to distinguish between anions and cations.     

Optimized recovery of monoclonal antibodies from transgenic goat milk by microfiltration

The Predictive Aggregate Transport Model for microfiltration is used in combination with optimum fluid mechanics and electrostatics to maximize recovery of a heterologous immunoglobulin (IgG) from transgenic goat milk. The optimization algorithm involved varying pH (6.8-9), transmembrane pressure (2-4.5 psi), milk feed concentration (1-2X), membrane module type (linear vs. helical design), and axial velocity (Reynolds number: 830-1170). Operation in the pressure-dependent regime at low uniform transmembrane pressures (approximately 2 psi) using permeate circulation in co-flow, at the pI of the protein (9 in this case) was used to increase IgG recovery from less than 1% to over 95%. Sodium dodecyl sulfate polyacrylamide gel electrophoresis and attenuated total reflection Fourier transform infrared spectroscopy of the microfiltration permeate samples confirmed that all the fat globules and most of the casein micelles were retained in the MF membrane whereas a large amount of the target IgG was transported through the membrane. Transmembrane pressure and hence permeation flux was kept low (approximately 15 lmh) to maximize IgG membrane transport and thus recovery, due to a sparse deposit on the membrane which facilitated high solute transport. Next, an analytical method was used to optimize the diafiltration process using the aggregate transport model, experimental target protein sieving coefficients and permeation flux (Baruah and Belfort, 2003). The methodology reported here should be generalizable to the recovery of target proteins found in other complex suspensions of biological origin using the microfiltration process.     

Passive Membrane Potentials: A Generalization of the Theory of Electrotonus

The theory of electrotonus, which has been well developed for small cylinders, is extended: the fundamental potential equations for a membrane of arbitrary shape are derived, and solutions are found for cylindrical and spherical geometries. If two purely conductive media are separated by a resistance-capacitance membrane, then Laplace's equation describes the potential in either medium, and two boundary equations relate the transmembrane potential to applied currents and to currents flowing into the membrane from each medium. The core conductor model, on which most previous work on cylindrical electrotonus has been based, gives rise to a one dimensional diffusion equation, the cable equation, for the transmembrane potential in a small cylinder. Under the assumptions of the core conductor model the more general equations developed here are shown to reduce to the cable equation. The two theories agree well in predicting the transmembrane potential in a small cylinder owing to an applied current step, and the extracellular potential for this cylinder is estimated numerically from the general theory. A detailed proof is given for the isopotentiality of a spherical soma membrane.     

The antennapedia peptide penetratin translocates across lipid bilayers - the first direct observation

The potential use of polypeptides and oligonucleotides for therapeutical purposes has been questioned because of their inherently poor cellular uptake. However, the 16-mer oligopeptide penetratin, derived from the homeodomain of Antennapedia, has been reported to enter cells readily via a non-endocytotic and receptor- and transporter-independent pathway, even when conjugated to large hydrophilic molecules. We here present the first study where penetratin is shown to traverse a pure lipid bilayer. The results support the idea that the uptake mechanism involves only the interaction of the peptide with the membrane lipids. Furthermore, we conclude that the translocation does not involve pore formation.     

Computer modelling of glycolipids at membrane surfaces.

Interactions of membrane anchored molecules such as glycolipids with a membrane surface are important in determining headgroup conformation. It is therefore essential to represent these membrane surface interactions in molecular modeling studies of glycolipids and other membrane bound molecules. We introduce here an energy term that represents the interaction of molecules with a membrane bilayer. This membrane interaction energy term has been added to the potential energy function of a molecular dynamics and mechanics program and has been parameterized using partition coefficients between an aqueous solution and a vesicular membrane for two model glycolipids.     

Cooperative interaction among surface beta- and gamma-carboxyl groups mediating the permeation of ions into frog muscle cells

A new equation for the ion permeation into living cells is described. This equation, differs from earlier ones, in that cooperative interaction among the fixed surface beta- and gamma-carboxyl groups mediating ion entry via the adsorption-desorption route is taken into account. Results of a single set of experiments describing labeled Cs+ into frog sartorius muscles at 0 degree C affirms the existence of the predicted cooperative interaction which endows the cell membrane and other organelles with a mechanism for coherence and control.     

A theory for the effects of neutral carriers such as the macrotetralide actin antibiotics on the electric properties of bilayer membranes

Summary To develop a quantitiative theoretical treatment for the effects of neutral macrocyclic antibiotics on the electrical properties of phospholipid bilayer membranes, this paper proceeds from the known ability of such molecules to form stoichiometric, lipid-soluble complexes with cations and deduces the electrical properties that a simple organic solvent phase would have if it were made into a membrane of the thinness of the phospholipid bilayer. In effect, we postulate that the essential barrier to ion movement across a bilayer membrane is its liquid-like hydrocarbon interior and that the neutral macrocyclic antibiotics bind monovalent cations and solubilize them in the membrane as mobile positively charged complexes. Using the Poisson-Boltzmann equation to describe the equilibrium profile of the electrical potential, it is shown that an excess of the positive complexes over all the other ions is expected in the membrane as a net space charge for appropriate conditions of membrane thickness and values of the partition coefficients of the various ionic species and without requiring the presence of fixed charges. Describing the fluxes of these complexes by the Nernst-Planck equation and neglecting the contribution to the electric current of uncomplexed ions, theoretical expressions are derived for the membrane potential in ionic mixtures, as well as for the limiting value of the membrane conductance at zero current when the membrane is interposed between identical solutions. The expressions are given in terms of the ionic activities and antibiotic concentrations in the aqueous solutions so as to be accessible to direct experimental test. Under suitable experimental conditions, the membrane potential is described by an equation recognizible as the Goldman-Hodgkin-Katz equation, in which the permeability ratios are combinations of parameters predicted from the present theory to be independently determinable from the ratio of membrane conductances in single salt solutions. Since this identity between permeability and conductance ratios is expected also for systems obeying the Independence Principle of Hodgkin and Huxley, the applicability of this principle to membranes exposed to antibiotics is discussed, and it is shown that this principle is compatible with the permeation mechanism proposed here.     

Membrane reactor coupled with electrophoresis for enzymatic production of aspartic acid

Aspartic acid production by aspartase reaction on ammonium fumarate was carried out in a membrane reactor coupled with electrophoresis. A pressurized, stirred vessel attached with an ultrafiltration membrane was used as a membrane reactor. An electric field was applied across the membrane to preferentially remove the product aspartate from the reactor into the permeate stream. The charged molecule, aspartate, is much smaller than the molecular-weight cutoff of the membrane (10(4)) so that the ions would move freely through pores of the membrane. The concentration of aspartate in the permeate stream is determined by the electromigration velocity of the ions and the permeation rate of solvent (water) through the membrane. The permeation rate of solvent could be controlled by the applied pressure, and the migration velocity of the ions could be controlled by the electric field strength applied. The equilibrium conversion of ammonium fumarate to the aspartate was 70%. In the presence of electric field, the aspartase activity was not disturbed. Also, it is shown that the aspartate concentration in the permeate stream was 20% higher than that in the reaction solution with the permeate flow rate of 0.7 mL/min. The steady-state conversion was 60%. Instead of aspartate, aspartic acid can be recovered directly from the permeate stream by controlling the circulation of buffer electrolyte in the anode compartment.     

Theoretical evaluation of a possible nature of the outer membrane potential of mitochondria

A possibility of generation of the outer membrane potential in mitochondria has been suggested earlier in the literature, but the potential has not been directly measured yet. Even its nature, metabolic impact and a possible range of magnitudes are not clear, and require further theoretical and experimental analysis. Here, using simple mathematical model, we evaluated a possible contribution of the Donnan and metabolically derived potentials to the outer membrane potential, concluding that the superposition of both is most probable; exclusively Donnan origin of the potential is doubtful because unrealistically high concentrations of charged macromolecules are needed for maintaining its relatively high levels. Regardless of the mechanism(s) of generation, the maximal possible potential seems to be less than 30 mV because significant osmotic gradients, created at higher values, increase the probability of the outer membrane rupture. New experimental approaches for direct or indirect determination of true value of the outer membrane potential are suggested here to avoid a possible interference of the surface electrical potential of the inner membrane, which may change as a result of the extrusion of matrix protons under energization of mitochondria.     

Mixtures of tight-binding enzyme inhibitors. Kinetic analysis by a recursive rate equation.

When two or more tight-binding inhibitors are present in an enzyme assay, the equation that relates the initial velocity v to the concentration of reactants cannot be written in an algebraically explicit form. Rather, for n inhibitors it is an implicit polynomial equation of degree n + 1 with respect to v. The complexity of the polynomial coefficients dramatically increases with each added inhibitor. Solving the transcendental rate equation by traditional methods of numerical mathematics has proven tedious because of the sensitivity of these methods to initial estimates and because of the existence of multiple roots. However, the equation can be rearranged into a convenient recursive form, one in which the velocity appears on both sides and the solution is found iteratively. The algebraic form of the recursive rate equation is remarkably simple and differs from the rate equation for classical rather than tight-binding inhibition only by an added term. The numerical stability and the speed of convergence were tested on the case of two competitive inhibitors. Initial estimates of velocity that spanned 12 orders of magnitude converged within five iterations. The velocities computed with the recursive method for a single tight-binding inhibitor were identical with the values predicted by the Morrison equation. The method is used to analyze experimental data for the inhibition of rat liver dihydrofolate reductase by mixtures of the anticancer drug methotrexate and its metabolic precursor form, methotrexate-alpha-aspartate (a prodrug).     

Tether extrusion from red blood cells: integral proteins unbinding from cytoskeleton

We investigate the mechanical strength of adhesion and the dynamics of detachment of the membrane from the cytoskeleton of red blood cells (RBCs). Using hydrodynamical flows, we extract membrane tethers from RBCs locally attached to the tip of a microneedle. We monitor their extrusion and retraction dynamics versus flow velocity (i.e., extrusion force) over successive extrusion-retraction cycles. Membrane tether extrusion is carried out on healthy RBCs and ATP-depleted or -inhibited RBCs. For healthy RBCs, extrusion is slow, constant in velocity, and reproducible through several extrusion-retraction cycles. For ATP-depleted or -inhibited cells, extrusion dynamics exhibit an aging phenomenon through extrusion-retraction cycles: because the extruded membrane is not able to retract properly onto the cell body, each subsequent extrusion exhibits a loss of resistance to tether growth over the tether length extruded at the previous cycle. In contrast, the additionally extruded tether length follows healthy dynamics. The extrusion velocity L depends on the extrusion force f according to a nonlinear fashion. We interpret this result with a model that includes the dynamical feature of membrane-cytoskeleton association. Tether extrusion leads to a radial membrane flow from the cell body toward the tether. In a distal permeation regime, the flow passes through the integral proteins bound to the cytoskeleton without affecting their binding dynamics. In a proximal sliding regime, where membrane radial velocity is higher, integral proteins can be torn out, leading to the sliding of the membrane over the cytoskeleton. Extrusion dynamics are governed by the more dissipative permeation regime: this leads to an increase of the membrane tension and a narrowing of the tether, which explains the power law behavior of L(f). Our main result is that ATP is necessary for the extruded membrane to retract onto the cell body. Under ATP depletion or inhibition conditions, the aging of the RBC after extrusion is interpreted as a perturbation of membrane-cytoskeleton linkage dynamics.     

Discerning perturbed assembly of lipids in a model membrane in presence of violacein

Violacein is a naturally found pigment that is used by some gram negative bacteria to defend themselves from various gram positive bacteria. As a result, this molecule has caught attention for its potential biomedical applications and has already shown promising outcomes as an antiviral, an antibacterial, and an anti-tumor agent. Understanding the interaction of this molecule with a cellular membrane is an essential step to extend its use in the pharmaceutical paradigm. Here, the interaction of violacein with a lipid monolayer formed at the air–water interface is found to depend on electrostatic nature of lipids. In presence of violacein, the two dimensional (2D) pressure–area isotherms of lipids have exhibited changes in their phase transition pressure and in-plane elasticity. To gain insights into the out-of-plane structural organization of lipids in a membrane, X-ray reflectivity (XRR) study on a solid supported lipid monolayer on a hydrophilic substrate has been performed. It has revealed that the increase in membrane thickness is more pronounced in the zwitterionic and positively charged lipids compared to the negatively charged one. Further, the lipid molecules are observed to decrease their tilt angle made with the normal of lipid membrane along with an alteration in their in-plane ordering. This has been quantified by grazing incidence X-ray diffraction (GIXD) experiments on the multilayer membrane formed in an environment with controlled humidity. The structural reorganization of lipid molecules in presence of violacein can be utilized to provide a detailed mechanism of the interaction of this molecule with cellular membrane.     

Ovotransferrin antimicrobial peptide (OTAP-92) kills bacteria through a membrane damage mechanism

Ovotransferrin antimicrobial peptide (OTAP-92) is a cationic fragment of hen ovotransferrin (OTf). OTAP-92 consists of 92 amino acid residues located within the 109-200 sequence of the N-lobe of OTf. This study was aimed to delineate the antimicrobial mechanism of OTAP-92 and to identify its interaction with bacterial membranes. OTAP-92 caused permeation of Escherichia coli outer membrane (OM) to 1-N-phenylnaphthylamine fluorescent probe in a dose-dependent manner. These results suggested that OTAP-92 crossed the bacterial OM by a self-promoted uptake. Cytoplasmic membrane of E. coli was found to be the target for OTAP-92 bactericidal activity, as assayed by the unmasking of cytoplasmic beta-galactosidase due to membrane permeabilization in a kinetic manner. Pretreatment of bacteria with uncoupler, carbonyl cyanide m-chlorophenylhydrazone, markedly enhanced permeation of cytoplasmic membrane, suggesting that the membrane permeation due to OTAP-92 is independent of the transmembrane potential. In an E. coli phospholipid liposome model, it was demonstrated that OTAP-92 has the ability to dissipate the transmembrane electrochemical potential. Intrinsic fluorescence spectra of the two tryptophan residues in OTAP-92, using liposomal membrane, have identified the lipid-binding region as a helix-sheet motif, and suggested an adjacent Ca(2+)-sensitive site within OTAP-92. These data indicated that OTAP-92 possesses a unique structural motif similar to the insect defensins. Further, this cationic antimicrobial peptide is capable of killing Gram-negative bacteria by crossing the OM by a self-promoted uptake and cause damage to the biological function of cytoplasmic membrane.