A novel dialysis procedure for the crystallization of proteins

Various dialysis methods are commonly employed for the crystallization of proteins. Typical procedures include the use of dialysis bags, dialysis buttons or Zeppezauer microdiffusion cells. The general principle involved is that the protein solution is gradually brought to a point of supersaturation by imposing a gradient of ionic strength or organic solvent concentration across the wall of the dialysis membrane. However, in some cases, the imposition of this gradient across the dialysis membrane can result in the formation of a large number of crystal nucleation sites, thereby giving rise to a reduction in the maximum size of the crystals which can be obtained. A novel 'double-dialysis' procedure which incorporates a second dialysis membrane, thus reducing the rate of equilibration in the crystallization experiment, has been developed in our laboratory. The system has been employed successfully on the delta toxin of Staphylococcus aureus resulting in a useful increase in crystal size. A more quantitative analysis of the technique has been carried out on rat liver malic enzyme. The results of a limited series of crystallization trials with this protein have shown that employment of the 'double-dialysis' technique allows a fine control of the rate of crystal nucleation and therefore provides a mechanism for the controlled growth of large crystals.     

Theoretical study of flow,pressure and solute concentration in double membrane systems

A model system consisting of two rigidly held membranes in series was investigated through the application of the Kedem and Katchalsky thermodynamic single membrane flow equations. This analysis results in predictions of the steady state flow properties as well as values for the solute concentration and pressure of the internal compartment when the system is under the influence of a constant solute concentration or hydrostatic pressure gradient. It is demonstrated that although the flow properties and internal compartment pressure are complicated functions of the membrane permeability coefficients and driving gradient across the system, the relationships are greatly simplified by the explicit appearance of the internal compartment steady state solute concentration in the equations. It is shown that the steady state volume flow rate depends on the absolute value of the solute concentration in the external compartments, as well as the solute concentration gradient across the system. The properties of non-linear dependence of volume flow on concentration gradient, and rectification of volume flow are discussed and shown to be independent properties of the system. For the system under the influence of a solute concentration gradient, the internal compartment pressure can be greater or less than the ambient pressure, and depends mainly on the order in which the membranes are encountered by the volume flow. These properties are qualitatively correlated with certain available experimental observations in biological systems.     

A mathematical model of solute coupled water transport in toad intestine incorporating recirculation of the actively transported solute

A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241-251), computations predict that 60-80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived.     

The Mechanism of Isotonic Water Transport

The mechanism by which active solute transport causes water transport in isotonic proportions across epithelial membranes has been investigated. The principle of the experiments was to measure the osmolarity of the transported fluid when the osmolarity of the bathing solution was varied over an eightfold range by varying the NaCl concentration or by adding impermeant non-electrolytes. An in vitro preparation of rabbit gall bladder was suspended in moist oxygen without an outer bathing solution, and the pure transported fluid was collected as it dripped off the serosal surface. Under all conditions the transported fluid was found to approximate an NaCl solution isotonic to whatever bathing solution used. This finding means that the mechanism of isotonic water transport in the gall bladder is neither the double membrane effect nor co-diffusion but rather local osmosis. In other words, active NaCl transport maintains a locally high concentration of solute in some restricted space in the vicinity of the cell membrane, and water follows NaCl in response to this local osmotic gradient. An equation has been derived enabling one to calculate whether the passive water permeability of an organ is high enough to account for complete osmotic equilibration of actively transported solute. By application of this equation, water transport associated with active NaCl transport in the gall bladder cannot go through the channels for water flow under passive conditions, since these channels are grossly too impermeable. Furthermore, solute-linked water transport fails to produce the streaming potentials expected for water flow through these passive channels. Hence solute-linked water transport does not occur in the passive channels but instead involves special structures in the cell membrane, which remain to be identified.     

Breakthrough performance of plasmid DNA on ion-exchange membrane columns

Breakthrough performance of plasmid DNA adsorption on ion-exchange membrane columns was theoretically and experimentally investigated using batch and fixed-bed systems. System dispersion curves showed the absence of flow non-idealities in the experimental arrangement. Breakthrough curves (BTC) were significantly affected by inlet flow rate and solute concentration. In the theoretical analysis, a model was integrated by the serial coupling of the membrane transport model and the system dispersion model. A transport model that considers finite kinetic rate and column dispersed flow was used in the study. A simplex optimization routine, coupled to the solution of the partial differential model equations, was employed to estimate the maximum adsorption capacity constant, the equilibrium desorption constant, and the forward interaction rate constant, which are the parameters of the membrane transport model. The analysis shows that as inlet concentration or flow rate increases, the deviation of the model from the experimental behavior decreases. The BTCs displacement as inlet concentration increases was explained in terms of a greater degree of column saturation reached and more efficient operation accomplished. The degree of column saturation was not influenced by inlet flow rate. It was necessary to consider in the column model the slight variation in the BTC produced by the axial dispersion, in order to accomplish the experimental curve dispersion. Consequently, the design criteria that for Pe > 40 the column axial dispersion can be neglected should be taken with precaution.     

Mathematical Model of a Countercurrent Flow Multi-fibre Dialyser

Summary The closed form solution to a distributed parameter mathematical model of a countercurrent flow dialyser is presented. The model consisting of a bundle of hollow fibres in a shell accounts for axial convection and radial diffusion. The proposed model relates the fractional removal of a solute to mass transfer parameters such as Sherwood number, length Peclet number and system geometry. Excellent agreement with experimental beer dialysis data is demonstrated for the removal of alcohol using 8-lm thick 200-lm diameter cuprophane hollow-fibre membrane fibres. Potentially, this model could be very helpful in designing new processes involving dialysis. For example, removal efficiency better than 90% is achievable in systems operating with a Sherwood number of 2.0, length Peclet number of 5 · 105, unit tube-side/shell-side volumetric flow and length-to-diameter ratio of 5000. Results were obtained in this work from only the first eigenvalue and the case of no solute in the incoming dialysate stream.     

Magnesium influx in dialyzed squid axons

Summary The influx of magnesium from seawater into squid giant axons has been measured under conditions where internal solute control in the axon was maintained by dialysis. Mg influx is smallest (1 pmol/cm² sec) when both Na and ATP have been removed from the axoplasm by dialysis. The addition of 3mm ATP to the dialysis fluid gives a Mg influx of 2.5 pmol/cm² sec while the addition of [Na] _i and [ATP] _i gives 3 pmol/cm² sec as a value for Mg influx; this corresponds well with fluxes measured in intact squid giant axons.The Mg content of squid axons is 6 mmol/kg axoplasm; this is unaffected by soaking axons in Li or Na seawater for periods of up to 100 min.     

A Molecular Structural Basis for the Excitation Properties of Axons

A structural model is suggested for axon membranes consisting of a double layer of lipid and phospholipid molecules in which the polar ends of certain phospholipids change their orientation and combining properties under the influence of an electric field. The phosphate groups act as ion exchange “gates” for the control of ion flow through the membrane. Expressions are developed for the calculation of membrane current components as functions of time, potential, and ionic environment. Approximate solutions show fairly good agreement with existing experimental data in a number of different respects such as steady-state current-voltage relations, the effect of calcium on steady-state current, potassium tracer flux ratios, initial current and rate of change of current, and the dependence of the time constants of current change on membrane potential.     

Preparation of giant liposomes

A method is described for the preparation of giant unilamellar lipid vesicles that are stable in electrolyte solution. In general, it involves dialysis of lipid and indifferent solute in a water-miscible organic solvent against an aqueous buffer. During dialysis the concentration of organic solvent decreases so that vesicles form under conditions where their internal contents are continuously hyperosmotic. Interlamellar attractive forces are neutralized, even between bilayer membranes with no net charge, and giant vesicles are generated in large numbers. The population is heterogeneous but most large vesicles have diameters between 10 and 100 μm. The method is simple. One procedure involves dialysis for a day or more of a methanol solution of phosphatidylcholine, supersaturated with methylglucoside, against an aqueous phase containing up to 1 M univalent electrolyte. The procedure is effective over a wide range of temperature and pH.     

Water Flow in Beta vulgaris Storage Tissue

The relative magnitudes of the hydraulic resistances, water capacities, and water potential equilibration time constants for the single cell, for the apoplast, and for the symplast in higher plant tissue are assessed. Swelling of beetroot (Beta vulgaris, var. `Detroit Red') storage tissue sections in pure water is measured using a displacement transducer. This method of measurement avoids the difficulty of solute diffusion in the apoplast. Theoretical analysis of the experimental results shows that the main path of water flow into the tissue is the apoplast rather than the symplast, that the main resistance to water flow into the cells is usually the cell membrane rather than the apoplast, but that in some cases the apoplast resistance and water capacity can contribute significantly to the water potential equilibration time constant of the tissue.     

An exact analysis for a solute transport,due to simultaneous dialysis and ultrafiltration,in a hollow-fibre artificial kidney

Transport of a uremic solute effected by a combined dialysis and ultrafiltration procedure in a hollow-fibre artificial kidney, is investigated theoretically under standard assumptions. An exact analytical solution for the concentration profile in a blood channel is obtained by using the method of separation of variables. The necessary requirement that the solution must tend to that of pure dialysis, in the limit ultrafiltration tending to zero, is fulfilled. Exact analytical expressions are derived for the eigenconstants of the solution. In using the solution, the solute clearance is emphasized. Diffusive and ultrafiltration components of the solute clearance are defined and studied. The combined procedure is examined for middle versus small molecules and for polyacrylonitrile versus cuprophan hollow-fibres.     

不同甘油浓度与平衡时间对食蟹猴精液冷冻效果的影响

探讨了不同甘油浓度(3%、5%、7%、11%)和不同平衡时间(30、60、90、120min)对食蟹猴(Macaca fascicularis)精液冷冻效果的影响,以建立和优化食蟹猴精液冷冻的程序。参照TTE稀释液成分组成改良型TTE,冷冻前和解冻后均检测精子的活力、畸形率、质膜完整性、顶体完整率。结果显示,平衡时间为30min时精子的冷冻解冻后活力、复苏率均高于平衡时间90min和120min组,差异显著(P<0.05),比60min组稍好;甘油浓度为3%、5%组的精子冷冻解冻后活力及复苏率均高于甘油浓度11%组,差异显著(P<0.05),比7%组好;不同甘油浓度各组间以及不同平衡时间各组间畸形率、质膜完整性、顶体完整率差异不显著(P<0.05)。由此得出如下结论,在食蟹猴精液冷冻中,在改良TTE中加入3%~5%的甘油且平衡30min可以获得较好效果,精子冻后活率和复苏率达到45%和62%。     

Solute concentration effect on osmotic reflection coefficient

A theory for the effect of concentration on osmotic reflection coefficient, correct to first order, was developed at the molecular level by considering the effect of solute-solute interactions on solute concentration and the fluid stress tensor within a solvent-filled pore. The solvent was modeled as a continuous fluid and potential energies between solute molecules and the pore wall were assumed to be pairwise additive. Although the theory is more general, calculations are presented only for excluded volume effects (hard-sphere for solute, hard-wall for pore). The relationship between the first-order concentration effect and the infinite dilution value of reflection coefficient appears to be geometry independent. The theory is discussed in light of experimental studies of osmotic flow that have recently appeared in the literature.     

尿素动力学模型及尿素反弹的实验研究

综述了尿素动力学模型的研究进展,并分析了几种模型的优缺点。建立了串联双室模型实验系统,研究了在透析间期尿素反弹的情况。该系统通过控制泵流量（F）来模拟两室室间溶质清除率（KIE）;用KCl代替尿素,通过实验曲线拟合得到KIE、R^2;通过与临床数据比较,获得了适合于尿素反弹系统的KIE,并研究了非灌注室浓度（A）对KIE的影响。结果显示,F=580ml／min较好地匹配了患者透析的尿素动力学特征;基于F=580ml／min进行的A对KIE影响的实验中,A与KIE没有必然联系,KIE平均值为512ml／min,标准差为10．25。且室间溶质浓度达到平衡所需的时间均为35-5min。尿素反弹的串联双室模型实验系统能够对患者透析后的尿素动力学进行较好的模拟,并具有较强的稳定性。     

Effects of internal and external ionic environment on excitability of squid giant axon. A macromolecular approach

The effects of ten cations and fifteen anions on the excitability of the squid giant axon were studied. The method of intracellular perfusion used in these investigations is described in detail. Empirical criteria were established for evaluating the relative favorability of any salt solution for maintaining the normal excitability of the membrane of the axon. It was found that both cations and anions could be ordered in sequences of relative favorability, which are directly related to the classic lyotropic sequences found for protein macromolecules and in colloid chemistry in general. The effects of concentration, salt mixtures, non-electrolyte carriers, enzymes, metabolic inhibitors, pH, and external media were also studied. The results are interpreted in terms of current concepts of the interactions between water structure, charged macromolecules, and their ionic environments. A macromolecular approach is given to the physicochemical nature of the "two stable states" of the excitable membrane, to describe the time-dependent potential changes observed.     

Network thermodynamic analysis and stimulation of isotonic solute-coupled volume flow in leaky epithelia: an example of the use of network theory to provide the qualitative aspects of a complex system and its verification by stimulation

A network thermodynamic model was developed to provide insights into the nature of isotonic solute-coupled volume flow in "leaky" epithelia, where the transepithelial volume flow is assumed to be primarily through the cellular pathway. The coupled flows of solute and volume at each membrane in this four membrane model are described by the practical phenomenological equations as developed by Kedem & Katchalsky (1958). The model contains one permeable non-electrolyte solute (s) and a fixed amount of an impermeable non-electrolyte (i) inside the cell. The cell is assumed to be capable of volume regulation under the steady-state experimental conditions simulated. A solute-pump, located in the basolateral membrane, uses feedback regulation to adjust Cs in the cell in order to maintain cell volume at or near control levels in all simulations. Model behavior is, in general, very consistent with experimental observations with respect to tonicity and magnitude of volume flow over a wide range of experimental conditions. Examination of the parameter space suggests the following important features when isotonic solute-coupled volume flow moves primarily through the cellular pathway: (1) the apical membrane reflection coefficient must be less than that of the basolateral membrane; (2) the basement membrane reflection coefficient must be small; (3) the apical membrane solute permeability and reflection coefficient are the two most "sensitive" parameters and need to vary in an inverse manner in order to maintain isotonicity when both solute and volume flows increase; and (4) relationships (1) and (3) above imply the need for at least two separate solute pathways in the apical membrane, one that is shared with volume flow and one that is not.     

Fluid mechanical and electrostatic study on the osmotic flow through cylindrical pores

When two solutions differing in solute concentration are separated by a porous membrane, the osmotic pressure will generate a net volume flux of the suspending fluid across the membrane; this is termed osmotic flow. We consider the osmotic flow across a membrane with circular cylindrical pores when the solute and the pore walls are electrically charged, and the suspending fluid is an electrolytic solution containing small cations and anions. Under the condition in which the radius of the pores and that of the solute molecules greatly exceed those of the solvent as well as the ions, a fluid mechanical and electrostatic theory is introduced to describe the osmotic flow in the presence of electric charge. The interaction energy, including the electrostatic interaction between the solute and the pore wall, plays a key role in determining the osmotic flow. We examine the electrostatic effect on the osmotic flow and discuss the difference in the interaction energy determined from the nonlinear Poisson-Boltzmann equation and from its linearized equation (the Debye-Hückel equation).     

Voltage dependence of the Na/Ca exchange in voltage-clamped, dialyzed squid axons. Na-dependent Ca efflux

A combination of the voltage-clamp and the intracellular dialysis techniques has been used to study the membrane potential dependence of the Nao-dependent Ca efflux in squid giant axons. In order to improve axon survival, experiments were carried out using internal solutions prepared with large impermeant organic anions and cations, which did not affect the operation of the Na/Ca exchange mechanism. In axons dialyzed with solutions prepared without internal Na, the Nao-dependent Ca efflux had a small sensitivity to membrane potential changes. For a 25-mV membrane displacement in the hyperpolarizing direction, the basal Ca efflux increased by only 7.4% (n = 13). When the dialysis medium contained Na (from 20 to 55 mM), the efflux increased 32.3% (n = 25) for the same membrane potential change. The K1/2 for this effect is approximately 5 mM Na, and saturation appears to occur at a Na concentration above 20 mM. Adding ATP to the dialysis medium increased the magnitude of the Nao-dependent Ca efflux without changing its voltage sensitivity. Wide changes in the intracellular ionized Ca concentration (from 0.1 to 230 microM) did not modify the voltage sensitivity of the exchange system. Elimination of the reversal of Na/Ca exchange (Nai-dependent Ca influx) by removing Cao did not modify the voltage sensitivity of the Nao-dependent Ca efflux. When the axon membrane potential was submitted to prolonged changes, the corresponding changes in the Ca efflux were not sustained, but declined exponentially to intermediate values. This effect may indicate a slow inactivation process in the Na/Ca exchange mechanism. Voltage-clamp pulse experiments revealed: (a) the absence of a fast inactivation process in the Na/Ca exchange, and (b) that the activation of the carrier for hyperpolarizing pulses occurs as rapidly as 1 ms.     

Concentration Polarization in an Ultrafiltering Capillary

Concentration polarization, the accumulation of retained solute next to an ultrafiltering membrane, elevates osmotic pressure above that which would exist in the absence of polarization. For ultrafiltration in a cylindrical tube, use of the radially averaged solute concentration results in an underestimate of osmotic pressure, yielding an effective hydraulic permeability (k) less than the actual membrane hydraulic permeability (k_m). The extent to which k and k_m might differ in an ultrafiltering capillary has been examined theoretically by solution of the momentum and species transport equations for idealized capillaries with and without erythrocytes. For diameters, flow velocities, protein concentrations and diffusivities, and ultrafiltration pressures representative of the rat glomerular capillary network, results indicate that the effects of polarization are substantial without erythrocytes (k/k_m = 0.7) and persist, but to a lesser extent, with erythrocytes (k/k_m = 0.9), the reduction in polarization in the latter case being due to enhanced plasma mixing. In accord with recent experimental findings in rats, k is found to be relatively insensitive to changes in glomerular plasma flow rate.     

Effect of equilibration period on the viability of frozen-thawed mouse morulae after rapid freezing

Mouse morulae were frozen with 1.5-4.0 M glycerol + 0.25 M lactose solution by direct plunging into liquid nitrogen vapor 0.5-30 min after equilibration at room temperature. After thawing, embryos were cultured in vitro, and the highest survival rates were obtained after exposure for 3 min at 3.0 and 4.0 M and for 5 min at 1.5 and 2.0 M glycerol levels. Significant reductions in the survival rates (P less than 0.05) were observed when equilibration periods were extended for 3-5 min at 3.0 and 4.0 M and for 5-10 min at 1.5 and 2.0 M glycerol levels. These results clearly demonstrate that the equilibration time of embryos in glycerol-lactose mixture is one of the most important factors in the present rapid freezing conditions. To clarify the factors that lower embryo viability after prolonged equilibration, we performed further experiments on the effects of exposure to glycerol-lactose mixture on the developmental potential of embryos without freezing and on the volume changes of embryos during the exposure to glycerol solution with or without lactose. It was suggested that the detrimental effects of prolonged equilibration are due not only to the toxicity and osmotic injury of higher concentrations of cryoprotectant solution but also to the influx of water into embryonic cells caused by the hypotonic salt concentration of the extracellular (freezing) solution.