Cheek cell membrane fluidity measured by fluorescence recovery after photobleaching and steady-state fluorescence anisotropy

Membrane fluidity of human cheek cells was determined using fluorescence recovery after photobleaching (FRAP) and steady-state fluorescence anisotropy. The FRAP data showed that the lateral diffusion coefficient (D) and mobile fraction (%R) of lipid in the plasma membrane of control cells were 2.01×10^–9 cm²/ sec and 54.25%, respectively. Trypsin treatment increased D and %R to 6.4×10^–9 cm²/sec and 72.15%. In contrast, the anisotropy (r) for control cells was 0.270 which remained unchanged by trypsin treatment. The results show that diffusion of lipids in the plane of the membrane is restricted by trypsin-sensitive barriers.     

Chain length and pressure dependence of lipid translational diffusion

The translational diffusion of pyrene, pyrene butyric acid and pyrene decanoic acid has been determined in phosphatidylcholine bilayers of different chain length and under pressure up to 200 bars. In the liquid crystalline phase and at a given temperature the diffusion decreases with increasing chain length. At a constant reduced temperature, T _red (about 10 K above the transition temperature), long chain lipids exhibit the fastest diffusion which is in disagreement with hydrodynamic models but favours free volume models for diffusion in lipid bilayers. The volume of activation, V _act, calculated from the decrease of the diffusion coefficient with pressure, ln D/P, depends on lipid chain length. V _act decreases with decreasing lipid chain length at a given temperature, T=65°C, and increases at the reduced temperature. These results are again in agreement with the dependence of the diffusion on lipid chain length and therefore with the free volume model.Abbreviations DLPC Dilauroylphosphatidylcholine - DMPC Dimyristoylphosphatidylcholine - DPPC Dipalmitoylphosphatidylcholine - DSPC Distearoylphosphatidylcholine - LUV Large unilamellar vesicles - SUV Small unilamellar vesicles - Tris Tris(hydroxymethyl)aminomethan     

Separation process of binary protein solution by ultracentrifuge

Separation process of a binary protein solution by ultracentrifuge with an angle rotor was discussed by considering the calculated distribution of concentration in an ultracentrifugal tube. The weight fraction of the desired protein and the recovery index after the ultracentrifugation were calculated from the distribution of the concentration. When the weight fraction after the ultracentrifugation is given, the optimal ultracentrifugal time was determined so as to maximize the recovery index.List of Symbols c _B kg/cm³ concentration of Bovine serum albumin - c _L kg/cm³ concentration of Lysozyme - D cm²/s diffusion coefficient - d cm diameter of ultracentrifugal tube - R dimensionless collecting range - r ^* dimensionless radial coordinate - r ₁ cm minimum radius of ultracentrifugal tube - r ₂ cm maximum radius of ultracentrifugal tube - s s sedimentation constant - t s ultracentrifugal time - X _L weight fraction of Lysozyme - X _LO initial weight fraction of Lysozyme - Y _L recovery index of Lysozyme - inclination of ultracentrifugal tube - s^–1 angular velocity of rotation     

Lateral diffusion of proteins and lipids in the plasma membrane of rose protoplast

Summary Lateral diffusion measurements have been made on lipids and proteins in the plasma membrane of live protoplasts derived from rose (Rosa sp. Paul's Scarlet) suspension-cultured cells. Two different fluorescent lipid probes exhibited markedly different diffusion rates, indicating possible heterogeneity in the lipid domain of the membrane. Membrane proteins were labeled directly with covalently-reactive fluorophores, and factors that might perturb the lateral diffusion of these labeled proteins were investigated. Treatment of the protoplasts with various cytoskeleton-disrupting drugs generally had little effect on protein diffusion, although treatment with oryzalin, a microtubule-disrupting drug, did slightly reduce the mobile fraction of membrane proteins. Elevation of the CaCl₂ concentration in the medium from 1 mM to 10 mM significantly reduced the mobile fraction of membrane proteins and also increased the fraction of protoplasts that were able to regenerate cell walls and divide in culture. These results are discussed in relation to reported evidence of lipid domains in the plasma membranes of other cells and protoplasts. The relative importance of lipid domains and membrane-cytoskeleton interaction in governing protein diffusion is considered.Abbreviations D lateral diffusion coefficient - RCA Ricinus communis agglutinin - BPA Bauhinia purpurea agglutinin - DTAF dichlorotriazinylaminofluorescein - FTSC fluorescein-5-thiosemicarbazide - C₁₈-Fl 5-(N-octadecanoyl)aminofluorescein - LY-Chol Lucifer yellow conjugate of cholesterol, i.e., dilithium 4-amino-N-[(-(carbo(5-cho-lesten-3-yl)oxy)hydrazinocarbonyl)amino]-1,8-naphthalimide-3,6-disulfonate - APM amiprophosmethyl - DMSO dimethylsulfoxide - FPR fluorescence photobleaching recovery - sd standard deviation - FRAF fluorescence redistribution after fusion - M mobile fraction     

A comparison of the translational diffusion of a normal and a membrane-spanning lipid in Lα phase 1-palmitoyl-2-oleoylphosphatidylcholine bilayers

We have used the fluorescence recovery after photobleaching technique to study the translational diffusion, in L phase multibilayers of 1-palmitoyl-2-oleoylphosphatidylcholine (POPC), of fluorescent derivatives of 1-palmitoyl-2-oleoylphosphatidylethanolamine (NBD-POPE) and a membrane-spanning phosphatidylethanolamine (NBD-MSPE). The latter derivative was prepared from a membrane-spanning glycerol-dialkyl-glycerol tetraether lipid isolated from the thermophilic and acidophilic archaebacterium Sulfolobus solfataricus. The translational diffusion was examined between about 15° and 45°C. It is shown that over this temperature range the translational diffusion coefficient for NBD-MSPE is 2/3 that for NBD-POPE which spans only one monolayer of the bilayer. The result is interpreted in terms of existing models for translational diffusion in lipid membranes.Abbreviations D _t translational diffusion coefficient - FRAP fluorescence recovery after photobleaching - MSPE a membrane-spanning phosphatidylethanolamine derived from a glycerol-dialkyl-glycerol tetraether lipid isolated from Sulfolobus solfataricus - NBD 4-nitrobenz-2-oxa-1,3-diazolyl - PE phosphatidylethanolamine - POPC 1-palmitoyl-2-oleoylphosphatidylcholine - POPE 1-palmitoyl-2-oleoylphosphatidylethanolamine     

A novel computational framework for D(t) from Fluorescence Recovery after Photobleaching data reveals various anomalous diffusion types in live cell membranes

Diffusion of proteins and lipids in lipid membranes plays a pivotal role in almost all aspects of cellular biology, including motility, exo?/endocytosis and signal transduction. For this reason, gaining a detailed understanding of membrane structure and function has long been a major area of cell biology research. To better elucidate this structure‐function relationship, various tools have been developed for diffusion measurements, including Fluorescence Recovery After Photobleaching (FRAP). Because of the complexity of cellular microenvironments, biological diffusion is often correlated over time and described by a time‐dependent diffusion coefficient, D(t) , although the underlying mechanisms are not fully understood. Since D(t) provides important information regarding cellular structures, such as the existence of subresolution barriers to diffusion, many efforts have been made to quantify D(t) by FRAP assuming a single power law, D(t) = Γt ^{α ? 1} where Γ and α are transport coefficient and anomalous exponent. However, straightforward approaches to quantify a general form of D(t) are lacking. In this study, we develop a novel mathematical and computational framework to compute the mean square displacement of diffusing molecules and diffusion coefficient D(t) from each individual time point of confocal FRAP data without the single power law assumption. Additionally, we developed an auxiliary equation for D(t) which can readily distinguish normal diffusion or single power law anomalous diffusion from other types of anomalous diffusion directly from FRAP data. Importantly, by applying this approach to FRAP data from a variety of membrane markers, we demonstrate the single power law anomalous diffusion assumption is not sufficient to describe various types of D(t) of membrane proteins. Lastly, we discuss how our new approaches can be applied to other fluorescence microscopy tools such as Fluorescence Correlation Spectroscopy (FCS) and Single Particle Tracking (SPT).     

Potassium movement during hyperpolarization of cardiac muscle

Summary When a bundle of cardiac muscle cells is hyperpolarized, membrane current declines with time. Voltage clamp experiments on sheep and cat ventricular bundles showed that the magnitude of inward current depended on the external K⁺ concentration. Following prolonged hyperpolarization, membrane current near the resting potential was generally outward. The half-time of decay of this outward current was approximately 2.5 sec at –60 mV. The potential measured in the absence of externally supplied current was generally more negative than it would have been without conditioning hyperpolarization.The half-time of recovery of the current response following hyperpolarization was also approximately 2.5 sec at –60 mV, a factor of approximately 3.7 slower than the preceding decline of inward current. The rate of recovery has only a slight temperature dependence (Q ₁₀1.2).The experimental results are consistent with the idea that during hyperpolarization K⁺ is depleted from approximately 3% of the total muscle volume, and that the replenishment of K⁺ occurs primarily by K⁺ diffusion from a much larger fraction of the extracellular space.     

Estimation of oxygen penetration depth in immobilized cells

Summary A simple method is proposed for calculating oxygen pentration depth in immobilized cells by assuming zero order kinetics in the presence of several external oxygen transport resistances. Calculations indicate that typical penetration depths of oxygen for immobilized microbial cells are in the range of 50–200 and those for immobilized or encapsulated animal and plant tissue culture are about 500–1000 . Based on calculations, oxygen transport in microencapsulation and microcarriers for tissue cultures are not transport-limited, but a slight limitation is expected for those in a hollow fiber reactor.Nomenclature a_s specific area of a support (cm) - Bi Biot number - dimensionless - C_b oxygen concentration in the bulk liquid (mM) - C _b C _b ^* -C_cr (mM) - C _b ^* bulk oxygen concentration in equilibrium with air (mM) - C_cr critical oxygen concentration (mM) - C_s oxygen concentration in the solid phase (mM) - d_p diameter or thickness of a support (cm) - D_eff effective diffusivity of oxygen in the solid phase (cm²/s) - k_m membrane permeability of oxygen (cm/s) - k _m ^* D_eff/_m - k_La_L liquid phase mass transfer rate coefficient (1/s) - k_sa_s solid phase mass transfer rate coefficient (1/s) - (OUR)_v volumetric oxygen uptake rate (mmol O₂/l) - p geometry parameter, p=0 for slab, p=1 for cylinder, p=2 for sphere - P_d oxygen penetration depth (cm) - P _d oxygen penetration depth in the absence of external diffusion limitation (cm) - Q volumetric oxygen uptake rate, (mmol O₂/l·h) - specific oxygen uptake rate (mmol O₂gm biomass (dry)·h) - r length coordinate (cm) - r_c oxygen penetration depth for sphere (cm) - r _c r_c in the absence of external diffusion limitation (cm) - r _c ^* oxygen penetration depth for cylinder (cm) - r _c ^* r _c ^* in the absence of external diffusion limitation (cm) - r_com combined mass transfer rate resistance (s) - r_d location where C_s becomes zero or C_cr (cm) - r_i radius of cylinder or sphere, half thickness of slab (cm) - U_sg superficial gas velocity (cm/s) - X cell concentration (g/l) Greek letters Thiele modulus, dimensionless - _L, _s liquid and solid phase volume fraction, respectively, dimensionless - effectiveness factor On sabbatical leave from KAIST, Seoul, Korea     

Precipitation of protein by ultracentrifuge with angle rotor

Precipitation of a protein by ultracentrifuge with an angle rotor was simulated by a model for sedimentation process. Assuming that the concentration of solute in an inclined ultracentrifugal tube is given by averaging the concentration in the imaginary horizontal tube, the governing equation describing the concentration in the rectangular-shaped tube with a uniform field of ultracentrifugal force for an inclined tube in an angle rotor was derived. The exact solution to this governing equation was obtained under the condition that the diffusion is absent or present. The dimensionless concentration which is reduced by the initial concentration can be expressed as the function of a dimensionless ultracentrifugal times ² t in case that the diffusion is absent, and as the function of dimensionless parameters andt ^*in case that the diffusion is present. From our first approximated model it is found that the precipitation of a protein by ultracentrifuge with an angle rotor proceeds more rapidly than that with a swing rotor whether diffusion is absent or present.List of Symbols c kg/m³ concentration of solute - c ⁰ kg/m³ initial concentration of solute - c ^A kg/m³ concentration of solute for angle rotor - c ^s kg/m³ concentration of solute for swing rotor - D cm²/s diffusion coefficient - d cm diameter of ultracentrifugal tube - k ₁ dimensionless constant - k ² dimensionless constant - r cm radial coordinate - r ₁ cm minimum radius of ultracentrifugal tube - r ₂ cm maximum radius of ultracentrifugal tube - r _m cm mean radius of ultracentrifugal tube - r _s cm radius from which sedimentation starts - s s sedimentation constant - t s time - z cm vertical coordinate - dimensionless parameter - ^m dimensionless parameter - deg inclination of ultracentrifugal tube - s^–1 angular velocity of rotation     

The fidelity of response by 1-[4-(trimethylammonio)phenyl]-6-phenyl-1,3,5-hexatriene in time-resolved fluorescence anisotropy measurements on lipid vesicles

Time-resolved fluorescence anisotropy measurements on 1⁰-[4-(tri-methylammonio)phenyl]-6-phenyl-1,3,5-hexatriene (TMA-DPH) molecules in lipid vesicles of palmitoyloleoylphosphatidylcholine (POPC), PC extracted from egg yolk (EggPC), dioleoyl-PC (DOPC), dilinoleoyl-PC (DLPC), phosphatidylglycerol extracted from egg yolk (EggPG), dioleoyl-PG (DOPG), sulfoquinovosyldiacylglycerol (SQDG) and digalactosyl-DG (DGDG) with and without cholesterol are presented. The observed intensity decay curves are analyzed simultaneously in terms of the Brownian rotational diffusion model. The analysis thus yields the isotropic fluorescence decay, the initial anisotropy r (0), the order parameters P ₂ and P ₂ as well as the diffusion coefficient of the long molecular axis. It is shown that increasing unsaturation in the acyl chains of the PC lipids results in an increase in the rotational diffusion rates of the probes and a decrease in the order parameter P ₂. However, the value of P ₂ remains unchanged. The corresponding orientational distribution function of the probes is bimodal, with fractions lying preferentially parallel and perpendicular to the local vesicle surface. Surprisingly, the fraction of probe molecules lying with their long axes parallel to the bilayer surface increases with increasing unsaturation with a concomitant narrowing in the width of the distribution of the fraction lying perpendicular to it. As expected, cholesterol is found to increase the order parameters in all the systems and to suppress the tendency of the molecules to lie parallel to the bilayer surface. Furthermore, the rotational diffusion coefficients of the probes is found to increase in all the systems except for DLPC. Interestingly, the effects of unsaturation on the reorientational dynamics of TMA-DPH molecules in the vesicle systems are opposite to those found in the corresponding planar multibilayers (Deinum et al. 1988), whereas the same cholesterol effect is observed for the two systems. Nevertheless, the TMA-DPH molecules exhibit higher diffusion coefficients in the vesicle than in the planar multibilayer systems. In addition, a unimodal distribution of the probe molecules is found in the multibilayer systems. The differences between the two systems are ascribed to the differences in the radius of curvature and the hydration of the bilayers. Lastly we rationalize the bimodal distribution of the TMA-DPH molecules in the vesicles in terms of their observed partition between the lipid and aqueous phases.Abbreviations DPH 1,6-diphenyl-1,3,5-hexatriene - TMA-DPH 1-[4-(trimethylammonio)-phenyl]-6-phenyl-1,3,5-hexatriene - POPC palmitoyloleoylphosphatidylcholine - EggPC PC extracted from egg yolk - DOPC dioleoyl-PC - DLPC dilinoleoyl-PC - EggPG phosphatidylglycerol extracted from egg yolk - DOPG dioleoyl-PG - SQDG sulfoquinovosyldiacylglycerol - DGDG di-galactosyl-DG - HPTLC high performance thin layer chromatography     

Conformation of mucous glycoproteins in aqueous solvents

Light-scattering techniques have been used to measure the z-average radius of gyration R_g z-average translational diffusion coefficient D_t and weight–average molecular weight M_w of porcine submaxillary mucin (PSM) in solution. PSM isolated at low shear in the presence of protease inhibitors has a M_w about twice as large as a sample prepared without these precautions. The former sample has a M_w of 17 × 10⁶ in 0.1M NaCl, which decreases to 8 × 10⁶ in 6M guanidine hydrochloride (GdnHCl) and then to 2 × 10⁶ on addition of 0.1M mercaptoethanol to the 6M GdnHCl solution. The R_g or D values obtained for PSM in this work superimpose with those of other authors for different mucin glycoproteins, leading to linear log–log relationships to the molecular weight of the protein core. Comparison of these results with those in the literature for denatured proteins suggest that mucins are linear random coils in which the protein core is stiffened by the presence of the oligosaccharide side chains. The length of the oligosaccharides and the nature of the solvent have little effect on the extension of the protein core. This suggests that the stiffness of the protein core is maintained by steric repulsion of the residues at the beginning of the oligosaccharide chains.     

Dependence of laser light scattering of DNA on NaCl concentration

We show that the persistence length a of DNA, derived from total intensity laser light scattering of linear Col E₁ DNA and corrected for excluded-volume effects, varies from about 68 nm in 0.005M NaCl to about 40 nm in 0.2M NaCl, leveling off to a constant value (about 27 nm) at high NaCl (1–4M) concentration. These observations do not agree with current views on the effect of electrostatic charge and ionic conditions on DNA dimensions. The apparent diffusion constant D_app, determined from laser light scattering autocorrelation as a function of scattering vector q, at NaCl concentrations 0.005–4M, correctly yields the translational diffusion coefficient D_t at low values of q and scales with molecular dimensions rather than segment length at high values of q; thus, D_app/D_t yields a universal curve when plotted against q²R, where R_g is the radius of the gyration. The sedimentation coefficients s at 0.1 and 0.2M NaCl concentration closely agree with the well-tested empirical relations, and a combination of s, D_t, and the appropriate density increments yield correct molar masses over the whole salt concentration range. Approximate constancy of D_tR_g indicates limited draining in translational flow. We present some observations and thoughts on the regimes in which a dependence of the correlation decay times on q³ rather than q² applies. We conclude that quasielastic laser light scattering discloses little information about dynamics of internal motion of DNA chains.     

One-dimensional model of the acid hydrolysis of cellulosic substrates in a solid-liquid cyclone reactor

The use of rotating flow in an annulus is investigated as a means of enhancing the yield of glucose and xylose in the acid hydrolysis of cellulosic slurries. A one-dimensional model of such a cyclone reactor is developed for flow cases, co-current and counter-current flow. For the case of 250°C, 1% w/w acid, the one-dimensional model indicates an increase in the maximum glucose yield from 48.1% in a plug flow reactor to 69.3% in a co-current cyclone reactor, and up to 81.0% in a countercurrent cyclone reactor. The corresponding xylose yields are 91.6% for co-current operation and 97.7% for countercurrent operation. In the co-current case the maximum glucose and xylose yields do not occur at the same location in the reactor; however, in the countercurrent case they do. Although product yields are dramatically improved over those obtained in a plug flow reactor, the product concentrations are lower than would typically be obtained in a plug flow reactor.List of Symbols A cm² cross sectional area perpendicular to radial flow - A _c cm² cross sectional area of slurry inlet - A _c cm² cross sectional area of steam inlet - A _w cm² cross sectional area of water inlet - C _c concentration of cellulose as potential glucose (grams of potential glucose/cm³ of total stream) - C _c ^* grams cellulose/cm³ of solids concentration of cellulose as potential glucose - C _ginitial ^* grams glulose/cm³ of solids concentration of cellulose entering reactor - C _g grams glucose/cm³ of total stream concentration of glucose - C _g ^* grams glucose/cm³ of liquid stream concentration of glucose - C _cinitial ^* grams cellulose/cm³ of liquid concentration of glucose entering reactor - C _xn concentration of xylan as potential xylose (grams of potential xylose/cm³ of total stream) - C _xs grams xyclose/cm³ of total stream concentration of nylose - d _f dilution factor - dr cm radial increment - g cm/s² gravitational acceleration - g ^* centrifugal acceleration proportionality constant - h cm height of cyclone reactor - j cm/s flux - K constant in general equation for vortex flow, Eq. (4.9) - k ₁ 1/s kinetic rate constant of cellulose hydrolysis - k _a 1/s kinetic rate constant of xylan hydrolysis - k ₂ 1/s kinetic rate constant of glucose decomposition - k _2a 1/s kinetic rate constant of xylose decomposition - m vortex exponent - M _steam g/s mass rate of steam addition at outer radius - M _water g/s mass rate of cold water addition at outer radius - n cm³/s empirically determined settling parameter - Q cm³/s net volumetric flow in outward radial direction - Q _tot cm³/s total volumetric flow through reactor - q _c cm³/s volumetric flow of slurry feed - q _s cm³/s volumetric flow of stream feed - q _water cm³/s volumetric flow of cold water feed - r cm radial position - r _c 1/s rate of cellulose hydrolysis - r _g 1/s rate of glucose decomposition - r _i cm inner radius - r _o cm outer radius - r _xn 1/s rate of xylan hydrolysis - r _xs 1/s rate of xylose decomposition - s _mom cm g/s² inlet steam momentum - T _bulk s bulk residence time in reactor - T °C reactor temperature - v _c cm³/g specific volume of slurry feed - v _s cm³/g specific volume of steam - v _w cm³/g specific volume of water - V _f cm/s velocity of liquid as a function of radius - V _i cm/s inlet velocity - V _s cm/s velocity of solids as a function of radius - V _steam cm/s inlet steam velocity to cyclone - V cm/s terminal settling velocity - V _q cm/s tangential velocity - w _mom cm g/s² water inlet momentum - Y grams product out/grams reactant in yield of product - solids volumetric fraction - _f solids volumetric fraction in slurry feed - _i initial solids volumetric fraction of slurry - Pi     

A mechanism for isotonic fluid flow through the tight junctions of Necturus gallbladder epithelium

During isotonic fluid flow, Necturus gallbladder epithelium mediates net fluxes of paracellular probes by a convective process. We show here that the paracellular system is modeled by permeation through three populations of channels: (i) convective parallel-sided ones of width 7.7 nm (ii) small diffusive ones of radius 0.6 nm, and (ii) large diffusive ones of radius exceeding 50 nm. The reflexion coefficient of the convective channels is very low and the calculated osmotic flow rate is close to zero when compared with the observed fluid absorptive rate of 2 x 10^–6 cm/sec. Analysis reveals that the convective channels behave as though closed to back-diffusion of probes; if this is due to solvent drag then very high fluid velocities are required, acting through minute areas. There are no transjunctional gradients that could drive the flow, and so the fluid must be propelled through the channel by components of the junction.We propose a mechanism based upon an active junctional peristalsis which allows discrimination on the basis of molecular size, in which the channels are always occluded at some point and so back-diffusion cannot occur. There is no local gradient of salt distal to the junctions and therefore the osmotic permeability of the membranes is irrelevant. High fluid velocities are not required, and the flow can occur over a substantial fraction of the junction. The mechanism must involve motile and contractile elements associated with the junction for which there is already considerable evidence.Symbols A _i filtration area of channel i;i=b (big), s (small) and c (convectional) - B constant for streamline flow - C _i concentration of probe at i - D diffusion coefficient - D ^o diffusion coefficient in free solution - d width of junction - F _i diffusive drag factor in channel i - g ionic conductivity - G _i convective drag factor in channel i - J _ij probe flux from i to j - J _net net probe flux - J _v volume flow per cm² of epithelium - l linear extent of junction per cm² epithelial plane - L length of junctional channel - L _p hydraulic conductivity - N Avogadro's number - q available filtration area fraction of channel - r _s probe molecular radius - r _c channel radius or half-width - S _i steric factor in channel i - V _w,s partial molar volume of water or salt - v _i fluid velocity in channel i - _w dynamic viscosity of water - specific conductivity - ratio of solute radius to channel radius or half-width - diffusive/pressure-driven flow ratio - reflexion coefficient     

Preliminary investigations on somatic embryogenesis from leaf discs of red oak (Quercus rubra L.)

Somatic embryos were obtained from leaf discs of juvenile red oak plants. Basal inductive nutrient medium was a modified Murashige and Skoog solution enriched with 500 mg L^–1 casein hydrolysate, 100 mg L^–1 polyvinylpyrrolidone, 5.4 M naphthaleneacetic acid and 0.09 M benzyladenine. Embryogenesis was obtained only from leaf discs in the presence of light and increased when the adaxial surface of the explants (with midrib or main veins present) was in contact with the medium. Large variation was observed in all experiments. Recurrent embryogenesis was observed at the base of embryo clusters with callus present; conversely, embryogenic potential was rapidly lost by subculturing full calli. Maturation, germination and development of isolated somatic embryos were obtained. However, the vast majority of embryos did not have viable apical bud meristems and on only a few occasions were shoots produced.Abbreviations BA N⁶-benzyladenine - CH casein hydrolysate - 2iP isopentenyladenine - NAA naphthaleneacetic acid - 2.4-D 2.4-dichlorophenoxyacetic acid - GA gibberellic acid - PVP polyvinylpyrrolidone     

Modelling of enzyme hydrolysis of maltose in a single pellet of immobilized biocatalyst

The reversible hydrolysis of maltose to glucose by immobilized glucoamylase entrapped in spherical solid particles is studied theoretically. For this purpose a known kinetic model taking into account these reversible reactions and the competitive synthesis of iso-maltose was adopted. The mass transfer limitations in the bulk liquid and in the pores of the particles containing the enzyme are considered, using Fick's law. On the basis of mathematical modelling the optimum conditions for biocatalyst performance are established. An appropriate combination of particle size and initial substrate concentration may lead to reduction of undesirable mass transfer resistance and therefore product inhibition and to an improved selectivity of the biocatalyst with respect of glucose formation.List of Symbols C _i kmoles/m³ current concentration ofi-th component along the radius - C _oi kmoles/m³ bulk concentration ofi-th component - C _i ^* kmoles/m³ concentrations ofi-th component on the pellet surface - D _si ,D _i m²/s internal and molecular diffusion coefficient ofi-th component - W _M kmoles/m³·s reaction rate of maltose hydrolysis - W _IM kmoles/m³·s reaction rate of iso-maltose formation - W _G kmoles/m³·s reaction rate of glucose production - R ₀ m pellet radius - r m current radius of the pellet - t s time coordinate - r ₀ ratio of the time step to the square of the radial coordinate - Re Reynolds number =w·R/v - Sc Schmidt number =v/D - Bi Biot number = R/D - A _j ,B, C _j coefficients in the system of linear equations, Eq. (8) - X _i dimensionless degree of transformation - NR number of independent reactions - N number of division sections of the pellet radius - G kmoles/m³ concentration of glucose - M kmoles/m³ concentration of maltose - IM kmoles/m³ concentration of isomaltose - K _m kmoles/m³ Michaelis constant - V _max kmoles/m³·s maximum reaction rate in Eq. (6) - K _i kmoles/m³ inhibition constant - K _1eq ,K _2eq equilibrium constants in Eq. (6) - , h steps along the time and radial coordinate in the pellet - m/s mass transfer coefficient - dimensionless radius of the pellet - computation accuracy Indices i number of reaction component - j index along the radius of the pellet - k index along the time coordinate This work was accomplished with thanks to the financial support of the Bulgarian National Fund for Scientific Investigations —Grant No. MU-1-BE/93.     

Diffusion of sucrose in xanthan gum solutions

Molecular diffusion of solutes, like sucrose in the xanthan gum fermentation, is important in order to understand the complex behavior of mass transfer mechanisms during the process. This work was focused to determine the diffusion coefficient of sucrose, a carbon source for xanthan production, using similar sucrose and xanthan concentrations to those occurring in a typical fermentation. The diaphragm cell method was used in experimental determinations. The data showed that diffusion coefficient of sucrose significantly decreases when xanthan gum concentration increases. Theoretical and semiempirical models were used to predict sucrose diffusivity in xanthan solutions. Molecular properties and rheological behavior of the system were considered in the modeling. The models tested fitted well the behavior of experimental data and that reported for oxygen in the same system.List of Symbols A constant in eq. (5) - C _pg cm^–3 polymer concentration - D cm² s^–1 diffusivity - D _ABcm² s^–1 diffusivity of A through liquid solvent - D _APcm² s^–1 diffusivity of A in polymer solution - D _AWcm² s^–1 diffusivity of A in water - D _Pcm² s^–1 diffusivity of polymer in liquid solvent - E _D gradient of the activation energy for diffusion - H _P hydratation factor of the polymer in water (g of bound water/g of polymer) - K dyn sⁿ cm^–2 consistency index - K ₁ constant in eq. (5) - K _P overall binding coefficient [g of bound solute/cm³ of solution]/[g of free solute/cm³ of polymer free solution] - n flow behavior index - M _Bg g mol^–1 molucular weight of liquid solvent - M _Pg g mol^–1 molecular weight of the polymer - M _Sg g mol^–1 Molecular weight of polymer solution (= M _BX_B+M_PX_P) - R cm³ atm g mol^–1 K^–1 ideal gas law constant - T K absolute temperature - V _Bcm³ g mol^–1 molar volume of liquid solvent - V _Pcm³ g mol^–1 molar volume of polymer - V _Scm³ g mol^–1 molar volume of polymer solution - X _B solvent molar fraction - X _P polymer molar fraction - polymer blockage shape factor - _P volume fraction of polymer in polymer solution - g cm^–1 s^–1 viscosity - _ag cm^–1 s^–1 apparent viscosity of the polymer solution - _icm³ g^–1 intrinsic viscosity - ₀ g cm^–1 s^–1 solvent viscosity - _Pg cm^–1 s^–1 polymer solution viscosity - _R relative viscosity (= / ₀) - ₌₀ g cm^–1 s^–1 viscosity of polymer solution obtained at zero shear rate - ₀ g cm^–3 water density     

Characterization of membrane domains by frap experiments at variable observation areas

In this paper we show that FRAP experiments at variable beam radii provide an experimental approach for investigating membrane organization and dynamics, with great potential for identifying micrometer-sized domains and determining their size and the diffusion coefficient of the lipid and protein molecules they contain. Monte Carlo simulations of FRAP experiments at variable beam radii R on models of compartmentalized membranes have allowed us to establish the relationships (i) between the mobile fraction M of a diffusing particle and the size r of the domains, and (ii) between the apparent diffusion coefficient D_app and the real diffusion coefficient D₀ of this particle inside the domains. Furthermore, in its present stage of development, this approach allows us to specify whether these domains are strictly closed or not. This approach was first validated on an experimental model of a strictly compartmentalized membrane consisting of a monolayer of apposed spherical phospholipid bilayers supported by silica beads of known radius (0.83 μm). To prevent fusion between the spherical bilayers 5 mol% of a polymer-grafted phospholipid was added to the lipids. Analysis of the M versus R data yielded a radius r of 0.92±0.09 μm for the spherical bilayers, close to that of the supporting silica beads. When applied to the experimental data available for lipids and proteins in the plasma membrane of living cells, this approach suggests the existence of domains within these membranes with a radius of about 0.4 – 0.7 μm for the lipids and 0.25 μm for the proteins. These domains are not strictly closed and they are believed to be delineated by fluctuating barriers which are more or less permeable to lipid and protein molecules. Received: 4 September 1997 / Revised version: 19 January 1998 / Accepted: 19 January 1998     

Determination of effective diffusivity of substrate in biological films and particles

Summary Particle supported biofilms of uniform thickness were generated in an aerobic fluidized-bed reactor with phenol as the carbon source. A method was developed for determining the effective diffusivities of oxygen and phenol using trypan blue, a vital stain as the tracer. The effective diffusivities of oxygen and phenol were found to be 2.72×10^–6 cm²/s and 1.12×10^–6 cm²/s respectively.Nomenclature C_i initial solute concentration in bulk, g/cm³ - C_t solute concentration in bulk at time t, g/cm³ - C bulk solute concentration at equilibrium, g/cm³ - D molecular diffusivity, cm²/s - D effective diffusivity, cm²/s - D_o D_p D_tb molecular diffusivity of oxygen, phenol and trypan blue, cm²/s - D_o, D_p, D_tb effective diffusivity of oxygen, phenol and trypan blue, cm²/s - D_s molecular diffusivity of substrate, cm²/s - D_s effective diffusivity of substrate, cm²/s - K partition coefficient - M_t amount of solute in the particle at time t, g - M amount of solute in the particle at equilibrium, g - r particle radius, cm - r _bp radius of the particle with biofilm, cm - S substrate concentration, g/cm³ - S_b substrate concentration in bulk, g/cm³ - S_i initial substrate concentration, g/cm³ - V₁ solute molar volume, cm³/g mol Greek Symbols bf porosity of the biofilm - tortuosity factor     

Direct evidence for Ca++-induced lateral phase separation in black membranes of lipid mixtures by the analysis of gramicidin A single-channels

Single-channel conductance fluctuations are analysed for gramicidin A incorporated into binary-mixed black lipid membranes of charged phosphatidic acid and neutral lecithin in different molar ratios. At very low Ca⁺⁺ concentrations in the electrolyte (i.e. in the presence of EDTA) homogeneous lipid mixtures are identified through their conductance and life time probability distributions for integral gramicidin pores. As for the pure lipid components, the conductance histograms each show a single maximum with regular width and for all channels a single mean lifetime is found.For Ca⁺⁺-levels (10^-6–10^-5 M) that are close to the critical demixing concentration (10^-4 M) unusually broad conductance distributions and reduced lifetimes are found provided the PC content, x, of the membrane is close to the critical mixture (x _crit0.5). We interpret this as a first example of the coupling of a membrane function (the transport of ions) to a lipid matrix with locally fluctuating composition close to a critical demixing point.For the conductance histogram of gramicidin A in an equimolar mixture of PA and PC shows two well-separated maxima. A correlation analysis between conductance and lifetime of the single pores shows that the two channel populations also differ significantly in their mean channel lifetime, ^*. This finding is interpreted as being direct evidence for Ca⁺⁺-induced lateral phase separation in black lipid membranes, as has been postulated recently.Abbreviations used HEPES N-2-hydroxyethyl-piperazine-N-2-ethane-sulfonic acid - EDTA ethylenediaminetetraacetic acid