Approximation of continuous growth of Cephalotaxus harringtonia plant cell cultures using fed-batch operation

In Cephalotaxus harringtonia plant cell cultures, periods of batch growth that are limited by hexose uptake are too short to make an accurate estimate of the Monod saturation constant. Continuous cultures are infeasible on a laboratory scale, and semicontinuous cultures require too frequent sampling. Fed-batch operation, consisting of intermittent removal from a culture that is fed continuously, was investigated as a possible solution to these problems. For a constant feed rate, computer simulations showed that a steady state can be achieved which is useful for studying growth at different specific growth rates. In terms of the dilution rate it was confirmed that the operation is essentially equivalent to continuous culture when the samples represent a small fraction of the total culture volume. Experiments with glucose or fructose as the carbon source were carried out in shake flasks fed by a multichannel syringe pump. Results indicate that Monod kinetics based on medium glucose levels cannot adequately describe growth under these conditions. Monod's expression for specific growth rate using internal glucose concentration gives an improved correlation.     

The osmotic migration of cells in a solute gradient.

The effect of a nonuniform solute concentration on the osmotic transport of water through the boundaries of a simple model cell is investigated. A system of two ordinary differential equations is derived for the motion of a single cell in the limit of a fast solute diffusion, and an analytic solution is obtained for one special case. A two-dimensional finite element model has been developed to simulate the more general case (finite diffusion rates, solute gradient induced by a solidification front). It is shown that the cell moves to regions of lower solute concentration due to the uneven flux of water through the cell boundaries. This mechanism has apparently not been discussed previously. The magnitude of this effect is small for red blood cells, the case in which all of the relevant parameters are known. We show, however, that it increases with cell size and membrane permeability, so this effect could be important for larger cells. The finite element model presented should also have other applications in the study of the response of cells to an osmotic stress and for the interaction of cells and solidification fronts. Such investigations are of major relevance for the optimization of cryopreservation processes.     

Quantitative Aspects of a Theory of Translocation

An analysis is made of two aspects of the behaviour of a proposedmechanism of translocation based on the mixing effect withina sieve-tube of streaming transcellular strands of protoplasmpassing through the sieve-pores and through a vacuole-like reservoirof sucrose solution in each sieve-element. First, the behaviour of the model is considered when it is transportinga solute (sucrose, for example) in the steady-state conditionof constant consumption and supply. It is found that the concentrationsof solute in the regions of the model are readily determinedat all points of the sieve-tube, and that the gradients of concentrationare all equal, the concentrations differing by constant amountsat all points. Transport is analogous to diffusive transferin that the steepness of the concentration gradient is proportionalto the rate of transfer and simple expressions are derived forthe net transport of solute and for the apparent diffusion coefficientin terms of the properties of the model. Transfer is found tobe rapid over a short path and slower over a longer path; thereis a maximum distance beyond which a given rate of transfercannot take place. Second, an analysis is made of the unsteady behaviour of themodel when changing concentrations of solute are introducedinto the system. The concept of strand diffusion time is introduced.This is the time taken for the concentration in the strand surroundedby an infinite reservoir to fall to I/e of its initial value.The results of this analysis are used to determine how radioactivesolute will become distributed when it is introduced into thesteady-state model. If the time over which the translocationof radioactive solute has proceeded is small compared with thestrand diffusion time, a wave-like profile of radioactivitywith distance is produced, and if large, the profile is of adiffusive kind; intermediate conditions give a profile displayingboth characteristics which is termed the transition type. Thesethree types of profile of radioactivity are exemplified by experimentsin different plants (Salix, Tropaeolum, and Helianthus), andthe experimental profiles are used to estimate (1) the apparentdiffusion coefficient of translocated sucrose in the sense ofMason and Maskell, and (2) the permeability constant of thestrand-reservoir boundary. The close correspondence betweenthese two sets of figures derived from the radioactive profileswith the experimental values obtained directly is regarded asstrong confirmation of the theory.     

Diffusion through a membrane: Approach to equilibrium

The transfer of solute through a membrane separating two aqueous solutions is studied with the time-dependent diffusion equation for composite media. By introducing new independent and dependent variables it is shown that the differential equations and boundary conditions can be transformed into a dimensionless form which does not explicitly depend on the diffusivities of the media. Laplace transforms are used to derive explicit solutions for the solute concentration as a function of position and time. It is shown that at large time the concentration approaches the equilibrium distribution exponentially. Explicit results are given for the decay time as a function of the parameters of the system. In addition, an accurate and simplified expression is derived for the decay time for the case of small membrane permeability. The accuracy of the analytic solutions for the concentration profiles is tested by comparing them with numerical results obtained by solving the diffusion equations by the method of finite differences. Excellent agreement is found. Research supported in part by a grant from the National Science Foundation.     

Determinants of the translational mobility of a small solute in cell cytoplasm

The purposes of this study were: (a) to measure the translational mobility of a small solute in cell cytoplasm; (b) to define quantitatively the factors that determine solute translation; and (c) to compare and contrast solute rotation and translation. A small fluorescent probe, 2,7-bis-(2-carboxyethyl)-5-(and 6-)- carboxyfluorescein (BCECF), was introduced into the cytoplasm of Swiss 3T3 fibroblasts. BCECF translation was measured by fluorescence recovery after photo-bleaching; rotation was measured by Fourier transform polarization microscopy. Diffusion coefficients relative to those in water (D/D0) were determined by comparing mobility in cytoplasm with mobility in standard solutions of known viscosity. At isosmotic cell volume, the relative diffusion coefficients for BCECF translation and rotation in cytoplasm were 0.27 +/- 0.01 (SEM, n = 24, 23 degrees C) and 0.78 +/- 0.03 (n = 4), respectively. As cell volume increased from 0.33 to 2 times isosmotic volume, the relative translational diffusion coefficient increased from 0.047 to 0.32, while the relative rotational diffusion coefficient remained constant. The factors determining BCECF translation were evaluated by comparing rotation and translation in cytoplasm, and in artificial solutions containing dextrans (mobile barriers) and agarose gels (immobile barriers). It was concluded that the hindrance of BCECF translation in cytoplasm could be quantitatively attributed to three independent factors: (a) fluid-phase cytoplasmic viscosity is 28% greater than the viscosity of water (factor 1 = 0.78); (b) 19% of BCECF is transiently bound to intracellular components of low mobility (factor 2 = 0.81); and most importantly, (c) translation of unbound BCECF is hindered 2.5- fold by collisions with cell solids comprising 13% of isosmotic cell volume (factor 3 = 0.40). The product of the 3 factors is 0.25 +/- 0.03, in good agreement with the measured D/D0 of 0.27 +/- 0.01. These results provide the first measurement of the translational mobility of a small solute in cell cytoplasm and define quantitatively the factors that slow solute translation.     

Capsule walls as barriers to oxygen availability: Implications for the development of brooded embryos by the estuarine gastropod Crepipatella dilatata (Calyptraeidae)

Encapsulation of developing embryos imposes potential restrictions, because the capsule wall must allow for adequate inward diffusion of oxygen and for increased diffusion of oxygen as metabolic demand increases with continued development. Samples of egg capsules from the gastropod Crepipatella dilatata were used to document surface characteristics, composition of the different capsule wall layers, and alterations in wall thickness during development. The diffusion coefficient and capsule wall permeability were determined experimentally for capsules containing embryos at different developmental stages. We also determined oxygen consumption rates for various embryonic stages and for nurse eggs, which provide food for embryos during development. The capsule wall of C. dilatata possesses 2 differentiated layers: the external capsular wall (ECW) and the internal capsular wall (ICW). The ECW is compact and fibrous, features that remain invariable during development, and lacks surface features that might make some portions of the capsule wall more permeable to oxygen than others. On the other hand, the ICW is initially spongy and thick, but significantly decreases in thickness over time, particularly before the embryos begin feeding on nurse eggs. Although the capsule wall is a serious barrier to diffusion, permeability to oxygen increases over time by 112% due to the dramatic thinning of the inner capsule wall layer. Nurse eggs consume oxygen but at very low rates, supporting the idea that they correspond to living embryonic cells that have stopped their development. Respiration measurements indicated that embryos are initially supplied with enough oxygen within the egg capsules to carry out the activities characteristic of embryogenesis, even though the capsular walls show their maximum thickness and lowest permeability at this time. However, as the embryo develops its velum and becomes more active, capsule wall thickness decreases and capsule permeability to oxygen increases. Correspondingly, the oxygen demands of metamorphosed but still encapsulated specimens are approximately 135% higher than those of pre-metamorphosed sibling embryos.     

Determination of effective diffusion coefficients and distribution constants in polysaccharide gels with non-steady-state measurements

A non-steady-state method has been used for determining the effective diffusion coefficient, D(e), and a distribution constant, K(i), of small molecules in alginate gel beads. A mathematical model based on Pick's law and includingexternal film diffusion resistance describe the diffusion process. Criticalexperimental parameters for the estimation of D(e) and K(i), for both one- and two-parameter methods were the initial solute concentration in the bulk liquid, the void fraction inthe reactor, and the experimental starting point. In our analysis, the two-parameter method is preferable. Incorporation of an estimate of the film resistance into the overall model increased the estimated values of D(e) significantly and improved the stability of the term over a range of reactor agitation rates. (c) 1995 John Wiley & Sons Inc.     

Modeling the Role of Diffusion Coefficients on Turing Instability in a Reaction-diffusion Prey-predator System

The paper is concerned with the effect of variable dispersal rates on Turing instability of a non-Lotka-Volterra reaction-diffusion system. In ecological applications, the dispersal rates of different species tends to oscillate in time. This oscillation is modeled by temporal variation in the diffusion coefficient with large as well as small periodicity. The case of large periodicity is analyzed using the theory of Floquet multipliers and that of the small periodicity by using Hill's equation. The effect of such variation on the resulting Turing space is studied. A comparative analysis of the Turing spaces with constant diffusivity and variable diffusivities is performed. Numerical simulations are carried out to support analytical findings.     

Concentration wave of a solute in an artery: the influence of curvature

Mass transport and diffusion phenomena in the arterial lumen are studied through a mathematical model. Blood flow is described by the unsteady Navier-Stokes equation and solute dynamics by an advection-diffusion equation, the convective field being provided by the fluid velocity. A linearization procedure over the steady state solution is carried out and an asymptotic analysis is used to study the effect of a small curvature with respect to the straight tube. Analytical and numerical solutions are found: the results show the characteristics of the long wave propagation and the role played by the geometry on the solute distribution and demonstrate the strong influence of curvature induced by the fluid dynamics.     

A new method of monitoring ventilatory activity in mussels and its use in a study of the ventilatory patterns of Mytilus edulis L.

An apparatus for measuring pumping rates in mussels, based on the delivery of exhaled sea water into a constant flow of fresh water, is described. When food is available, pumping is continuous for several days although there are signs of satiation after ≈ 1 wk. When food is withdrawn pumping does not cease for several hours especially in animals which have been food-deprived for some time before feeding. Food-deprived mussels often fail to pump for periods of > 24 h and ventilatory bursts are carried out at flow rates well below maximum. Shell valve movements and diffusion of oxygen through the gape between open valves can supplement ciliary ventilation.     

Selective extraction using preferential transport through adsorptive membranes

Selective extraction of a protein from a mixture can be accomplished using an adsorptive membrane and low displacement recuperative parametric pumping. Low displacement recuperative parametric pumping can lead to the preferential transport of an adsorbing solute and the rejection of nonadsorbing solutes by the adsorptive membrane. Using a protein mixture consisting of lysozyme and myoglobin, we have found the conditions under which lysozyme is preferentially transported through an ion-exchange membrane cartridge while myoglobin is rejected by the membrane. Trends observed when parameters such as the desorbent concentration, feed concentration, and flow rate are varied agree with the predictions of a mathematical model. Comparison with facilitated diffusion shows that preferential transport can lead to higher solute fluxes, albeit at lower selectivity. Additionally, preferential transport can be used to transport a solute up a concentration gradient and to selectively extract a solute from a feed that contains suspended solids. (c) 1996 John Wiley & Sons, Inc.     

Transport of neutral solute in articular cartilage: effect of microstructure anisotropy

Due to the avascular nature of articular cartilage, solute transport through its extracellular matrix is critical for the maintenance and the functioning of the tissue. What is more, diffusion of macromolecules may be affected by the microstructure of the extracellular matrix in both undeformed and deformed cartilage and experiments demonstrate diffusion anisotropy in the case of large solute. However, these phenomena have not received sufficient theoretical attention to date. We hypothesize here that the diffusion anisotropy of macromolecules is brought about by the particular microstructure of the cartilage network. Based on this hypothesis, we then propose a mathematical model that correlates the diffusion coefficient tensor with the structural orientation tensor of the network. This model is shown to be successful in describing anisotropic diffusion of macromolecules in undeformed tissue and is capable of clarifying the effects of network reorientation as the tissue deforms under mechanical load. Additionally, our model explains the anomaly that at large strain, in a cylindrical plug under unconfined compression, solute diffusion in the radial direction increases with strain. Our results indicate that in cartilage the degree of diffusion anisotropy is site specific, but depends also on the size of the diffusing molecule. Mechanical loading initiates and/or further exacerbates this anisotropy. At small deformation, solute diffusion is near isotropic in a tissue that is isotropic in its unstressed state, becoming anisotropic as loading progresses. Mechanical loading leads to an attenuation of solute diffusion in all directions when deformation is small. However, loading, if it is high enough, enhances solute transport in the direction perpendicular to the load line, instead of inhibiting it.     

Bipartite expressions for diffusional mass transport in biomembranes

Analytical expressions for solute diffusion through a membrane barrier for different initial and boundary conditions are available in the literature. The three commonest initial and boundary conditions are for a membrane without solute respectively immersed in a solution of constant concentration, immersed in such a solution for one side but with the other side isolated, and immersed in such a solution for one side and with the other side kept at zero concentration. The physical quantities for the first two initial and boundary conditions are concentration and average concentration (the total solute entering the membrane) with amperometric current (flux) and solute that permeates through the membrane (charge passed) for the third initial and boundary condition. Expressions for these methods in the literature are inconvenient for practical applications because of the infinite mathematical series required. An investigation of convergence of these expressions was therefore carried out. Simple but accurate bipartite expressions for these methods were constructed and provided theoretical support for studies on mass transport characterization of biomembranes. As a specific application, these expressions enabled a direct fit of the simulated observables to experimental values to obtain diffusion coefficients. For these initial and boundary conditions and corresponding physical quantities, simple one point methods for diffusion coefficient estimation are also suggested. These latter diffusion coefficients can be initial values for numerical fit methods.     

Cytoplasmic viscosity near the cell plasma membrane: translational diffusion of a small fluorescent solute measured by total internal reflection-fluorescence photobleaching recovery.

Total internal reflection-fluorescence recovery after photobleaching (TIR-FRAP) was applied to measure solute translational diffusion in the aqueous phase of membrane-adjacent cytoplasm. TIR fluorescence excitation in aqueous solutions and fluorescently labeled cells was produced by laser illumination at a subcritical angle utilizing a quartz prism; microsecond-resolution FRAP was accomplished by acousto-optic modulators and electronic photomultiplier gating. A mathematical model was developed to determine solute diffusion coefficient from the time course of photobleaching recovery, bleach time, bleach intensity, and evanescent field penetration depth; the model included irreversible and reversible photobleaching processes, with triplet state diffusion. The validity and accuracy of TIR-FRAP measurements were first examined in aqueous fluorophore solutions. Diffusion coefficients for fluorescein isothiocyanate-dextrans (10-2000 kDa) determined by TIR-FRAP (recovery t1/2 0.5-2.2 ms) agreed with values measured by conventional spot photobleaching. Model predictions for the dependence of recovery curve shape on solution viscosity, bleach time, and bleach depth were validated experimentally using aqueous fluorescein solutions. To study solute diffusion in cytosol, MDCK epithelial cells were fluorescently labeled with the small solute 2',7'-bis-2-carboxyethyl-5-carboxyfluorescein-acetoxymethyl-ester (BCECF). A reversible photobleaching process (t1/2 approximately 0.5 ms) was identified that involved triplet-state relaxation and could be eliminated by triplet-state quenching with 100% oxygen. TIR-FRAP t1/2 values for irreversible BCECF bleaching, representing BCECF translational diffusion in the evanescent field, were in the range 2.2-4.8 ms (0.2-1 ms bleach times), yielding a BCECF diffusion coefficient 6-10-fold less than that in water. These results establish the theory and the first experimental application of TIR-FRAP to measure aqueous-phase solute diffusion, and indicate slowed translational diffusion of a small solute in membrane-adjacent cytosol.     

Adaptation to salinity at the plant cell level

Summary Various mechanisms of adaptation of plant cells to salinity are reviewed: (1) protection of enzymes and maintenance of turgor by organic solutes; (2) prevention of ion toxicity by compartmentation; and (3) energization of solute transport by the proton pump. All these mechanisms seem to play a role in adaptation. The particular advantages of using salt-adapted cells in suspension culture to identify mechanisms of adaptation are pointed out.     

Design and validation of a dynamic flow perfusion bioreactor for use with compliant tissue engineering scaffolds

In tissue engineering, flow perfusion bioreactors can be used to enhance nutrient diffusion while mechanically stimulating cells to increase matrix production. The goal of this study was to design and validate a dynamic flow perfusion bioreactor for use with compliant scaffolds. Using a non-permanent staining technique, scaffold perfusion was verified for flow rates of 0.1-2.0 mL/min. Flow analysis revealed that steady, pulsatile and oscillatory flow profiles were effectively transferred from the pump to the scaffold. Compared to static culture, bioreactor culture of osteoblast-seeded collagen-GAG scaffolds led to a 27-34% decrease in cell number but stimulated an 800-1200% increase in the production of prostaglandin E(2), an early-stage bone formation marker. This validated flow perfusion bioreactor provides the basis for optimisation of bioreactor culture in tissue engineering applications.     

The effective diffusion coefficient and the distribution constant for small molecules in calcium-alginate gel beads

The effective diffusion coefficient, D(e), and the distribution constant, K(i), for selected mono- and disaccharides and organic acids were determined in homogeneous calcium-alginate gel with and without entrapped bacteria. Results were obtained from transient concentration changes in well-stirred solutions of limited volume, in which the gel beads were suspended. The effective diffusioncoefficients and the distribution constants were estimated by fitting mathematical model predictions to the experimental data using a nonlinear model fitting program (MODFIT). Both single solute diffusion and multiple solute diffusion were performed. A small positive effect was obtained onthe values of D(e) for the system of multiple solute diffusion; however, the values of K(i) were not significantly influenced. For the nine solutes tested, D(e) for 2% Ca-alginate gel beads was found to be approximately 85% of the diffusivity measured in water. The effects on D(e) and K(i), for lactose and lactic acid were determined for variations of alginate concentration, pH, temperature, and biomass content in the beads. D(e) decreased linearly for both lactose and lactic acid with increasing cell concentration in the Ca-alginate gel. K(i), was constant for both lactose and lactic acid with increasing cell concentration. D(e) was significantly lower at pH 4.5 than at pH 5.5 and 6.5 for both lactose and lactic acid. Furthermore, D(e) seemed to decrease with increased alginate concentration in the range of 1% to 4%. The diffusion rate increased with increasing temperature, and the activation energy for the diffusion process for both lactose and lactic acid was constant in the temperature range tested. (c) 1995 John Wiley & Sons Inc.     

A Model of Solute Transport through Stratum Corneum Using Solute Capture and Release

A one-dimensional model of solute transport through the stratum corneum is presented. Solute is assumed to diffuse through lipid bi-layers surrounding impermeable corneocytes. Transverse diffusion (perpendicular to the skin surface) through lipids separating adjacent corneocytes, is modeled in the usual way. Longitudinal diffusion (parallel to the skin surface) through lipids between corneocyte layers, is modeled as temporary trapping of solute, with subsequent release in the transverse direction. This leads to a linear equation for one-dimensional transport in the transverse direction. The model involves an arbitrary function whose precise form is uncertain. For a specific choice of this function, closed form expressions for the Laplace transform of solute out-flux at the inner boundary, and for the time lag are obtained in the case that a constant solute concentration is maintained at the outer skin surface, with the inner boundary of the stratum corneum kept at zero concentration, and with the stratum corneum initially free of solute.     

Continuous cultures limited by a gaseous substrate: Development of a simple, unstructured mathematical model and experimental verification with Methanobacterium thermoautotrophicum

This article presents a simple, unstructured mathematical model describing microbial growth in continuous culture limited by a gaseous substrate. The model predicts constant gas conversion rates and a decreasing biomass concentration with increasing dilution rate. It has been found that the parameters influencing growth are primarily the gas transfer rate and the dilution rate. Furthermore, it is shown that, for correct simulation of growth, the influence of gaseous substrate consumption on the effective gas flow through the system has to be taken into account.Continuous cultures of Methanobacterium thermoautotrophicum were performed at three different gassing rates. In addition to the measurement of the rates of biomass production, product formation, and substrate consumption, microbial heat dissipation was assessed using a reaction calorimeter. For the on-line measurement of the concentration of the growth-limiting substrate, H(2), a specially developed probe has been used. Experimental data from continuous cultures were in good agreement with the model simulations. An increase in gassing rate enhanced gaseous substrate consumption and methane production rates. However, the biomass yield as well as the specific conversion rates remained constant, irrespective of the gassing rate. It was found that growth performance in continuous culture limited by a gaseous substrate is substantially different from "classic" continuous culture in which the limiting substrate is provided by the liquid feed. In this report, the differences between both continuous culture systems are discussed.