Determination of dendrigraft poly-L-lysine diffusion coefficients by taylor dispersion analysis

This work focuses on the physicochemical characterization of dendrigraft poly-L-lysines (DGLs) obtained by polymerization of N-carboxyanhydride in buffered water (pH 6.5). Diffusion coefficients (D) and hydrodynamic radii (Rh) of five successive DGL generations were determined by Taylor dispersion analysis (TDA). To our knowledge, this is the first experimental work using TDA for the characterization of dendrimer-like structures. Experimental Rh values obtained by TDA were compared to those derived from dynamic light scattering and size exclusion chromatography coupled to a triple detection (refractive index, viscosimetry, and static light scattering). Significant differences were obtained, especially for the highest generations, as a result of the inherent contribution of aggregates to the light scattering intensity. For that reason, TDA was found to be the most appropriate technique for determining the D values of these hyperbranched macromolecules. Regarding their physicochemical behavior, the experimental results confirm that DGLs are very similar to trifunctional dendrimers (exponential growth of the molar mass, almost linear variation of the hydrodynamic radius, high branching density, and maximum of the intrinsic viscosity or of the free volume fraction for generation 4).     

Determination of diffusion coefficients in biofilms by confocal laser microscopy

Microbial exopolymer may hinder the diffusion of nutrients, antibiotics, and other materials to the cell surface. Studies of diffusion in biofilms have been limited to indirect measurements. This study demonstrated the use of fluorescein and size-fractionated fluor-conjugated dextrans in conjunction with scanning confocal laser microscopy to directly monitor and determine diffusion coefficients within biofilms. The monitoring approaches were simple and, when combined with computerized image collection, allowed assembly of a data set suitable for calculation of one-dimensional diffusion coefficients for biofilm regions. With these techniques, it was shown that regional variability in the mobility of the dextrans occurred within mixed-species biofilms. Some regions exhibited rapid diffusion of all test molecules, while adjacent regions were only penetrated by the lower-molecular-weight compounds. The effective diffusion coefficients (D(e)) determined in a mixed-species biofilm were a function of the molecular radius of the probe (i.e., fluorescein, D(e) = 7.7 x 10 cm s; 4,000 molecular weight, D(e) = 3.1 x 10 cm s; and 2,000,000 molecular weight, D(e) = 0.7 x 10 cm s). These results demonstrated that diffusion in the biofilm was hindered relative to diffusion in the bulk solution. The study indicated that in situ monitoring by scanning laser microscopy is a useful approach for determining the mobility of fluorescently labeled molecules in biofilms, allowing image acquisition, appropriate scales of study, both xy and xz monitoring, and calculation of D(e) values.     

Determination of diffusion and permeability coefficients in muscle

A theory is presented for the study of diffusion in heterogeneous tissue-like structures. It is applicable to a common type of measurement in which the change of the amount of substance remaining in the tissue is determined as the substance diffuses from the tissue into an adjacent medium, for instance, Ringer's solution. The main objective of this paper is to obtain a method for the calculation of the diffusion coefficient in the intercellular space and of the permeability coefficients between this space and the cells, based on the type of measurement mentioned above. Although the fundamental ideas upon which the theory is based are applicable to any type of tissue, the formulae derived are limited to the case in which the cells form a flat bundle of parallel fibers. The theory is applied to the experimental results of E. J. Harris and G. P. Burn on diffusion of sodium in the sartorius muscle of the frog. We find that if we know the ratio of the cellular and intercellular volumes of the muscle the ratio of the equilibrium concentrations of sodium outside and inside the cells can be determined. A very simple mathematical analysis of the experimental relation between the amount of substance diffusing out of the muscle and the time of diffusion gives us this ratio. The ratio of the equilibrium sodium concentrations in the case of the sartorius frog muscle is between about 10 and 30, depending on the muscle used. The same mathematical analysis makes it possible to obtain the permeability coefficients of muscle fibers through simple calculations, if their sizes are known. The permeability coefficients for the experimental work mentioned above using sodium are 1.25 to 11.5×10⁻⁸ cm/sec for the flow into the fibers and 3.2 to 16×10⁻⁷ cm/sec for the flow in the opposite direction. The determination of the diffusion coefficient in the intercellular space is more laborious and yields only an order of magnitude: 10⁻⁶ cm²/sec.     

Determination of diffusion coefficients of proteins in stationary phases by frontal chromatography

A strategy to determine effective diffusion coefficients of proteins in chromatographic gels is presented in this article. An experimental methodology based on frontal liquid chromatography was combined with a numerical methodology based on a mathematical model describing the chromatographic process including the extra-column dispersion, the dispersion due to the packed bed, the external mass transfer from the bulk phase to the stationary phase, and the diffusive transport within the stationary phase. The methodology has several advantages compared to previously reported methods to determine diffusion coefficients in that no other equipment than an HPLC is required, any class of stationary phases can be investigated as long as the experiments are performed under non-binding conditions, and no modification, e.g., moulding of slabs or membranes, to the stationary phase is required. To show the applicability of the methodology, the effective diffusion coefficients of lysozyme, bovine serum albumin, and immunoglobulin gamma in Sepharose CL-4B were determined and shown to be comparable with those determined with other methods.     

An automated method for rapid determination of diffusion coefficients via measurements of boundary spreading

The use of a simple device by which a layer of solvent may be deposited onto a solution of an optically absorbing solute in a cylindrical quartz tube, without substantial mixing of solution and solvent, is described. The spreading of the boundary thus formed may be monitored as a function of time using an automated absorbance scanning device previously described [A. K. Attri and A. P. Minton (1983) Anal. Biochem. 133, 142-152]. A semiautomatic procedure for determining the diffusion coefficient from the time dependence of the shape of the boundary is described and is particularly well-suited for real-time data analysis with a laboratory microcomputer. The diffusion coefficients of several proteins have been measured using the technique reported, and the results are generally in good agreement with values reported in the literature. The feasibility of using this technique in combination with a previously described method for measuring the sedimentation coefficient [A. K. Attri and A. P. Minton (1984) Anal. Biochem. 136, 407-415] to rapidly determine the molecular weight of a protein is established.     

Determination of glucose diffusion coefficients in biofilms with micro-electrodes

A glucose micro-electrode was developed for direct measurements inside biofilms, and applied for the determination of effective diffusion coefficients in a model system of agar beads containing immobilized yeast cells. Two methods were used, one based on concentration gradients present at the liquid/solid interface of an active biofilm under steady-state conditions, the other based on the rate of glucose redistribution in an inactivated biofilm under transient-state conditions. Additional measurements with pH and oxygen micro-electrodes were performed and thus allowed for in-situ correction of the glucose electrode signal. From the micro-electrode measurements in the model system it was concluded that the glucose micro-sensor is a useful tool with which to obtain effective diffusion coefficients in biofilms.     

Determination of diffusion and permeability coefficients in nerve trunks

A mathematical theory is developed which permits the determination of certain parameters of an inhomogenous tissue, such as a nerve trunk without its epineurium. The parameters are the permeability coefficients for entrance into an exit of a substance from the nerve fibers, and the diffusion coefficient of the interstitial material. The experimental data required are the dimensions of the cross-section, the average diameter of the fibers, and the ratio of the cross-sectional are of the fibers to the total cross-section, as well as the time course of the decrease of the fraction of the substance left in the nerve trunk, when the trunk is immersed in a bathing solution containing none of it.     

Root histogenesis from tobacco thin cell layers

Summary Internode stem expiants ofNicotiana tabacum cv. Samsun, consisting of eight cell layers: epidermis, subepidermal chlorenchyma, collenchyma and cortical parenchyma (i.e., thin cell layers), were cultured under conditions inducing rhizogenesis. The aim was to investigate the histological sequence of adventitious root formation in this system. The earliest cytological events in culture (12 h) were nucleolar extrusions and amitotic nuclear divisions. Though not restricted to a specific cell layer, the two phenomena were more frequent in the subepidermal chlorenchyma, and characterized the first phases (12-96 h) of cell proliferation mainly occurring in this layer. Amitoses were followed by the formation of thin walls within the original cells, resulting in the formation of intracellular clusters. These subepidermal clusters were separated by enlarged cells of the parent tissue, whose nuclei showed nucleolar extrusion. At day 3 the first mitoses were observed in cells having abundant starch inclusions. Amitotic divisions also continued, but less frequently. The increasing frequency of mitoses in the subepidermal chlorenchyma (day 4), as well as in the two underlying collenchymatous layers, contributed to the growth of the superficial clusters, in which small clumps of meristematic cells were formed; these, later (day 9), gave rise to root domes. The 5th cell layer remained undivided for a relatively long time (two weeks). The 6th and 7th layers proliferated mitotically later (from day 8 onwards) than the superficial layers and formed root domes following the same histological sequence. Wound callus, generated by the innermost layer, increased markedly in the last two weeks of culture and concomitantly formed vascular clumps surrounded by meristematic layers; these produced root primordia which were frequently anomalous (day 26–27). Regardless of its origin (i.e., superficial or deep layers of the expiant, or wound callus cells), root tip formation was always preceded by the differentiation of a sheath of starch-containing cells, from which the root cap developed.Abbreviations LS longitudinal section - S.E. standard error - TVS transverse section     

Determination of diffusion coefficients and diffusion characteristics for chlorferon and diethylthiophosphate in Ca-alginate gel beads

Diffusion characteristics of chlorferon and diethylthiophosphate (DETP) in Ca-alginate gel beads were studied to assist in designing and operating bioreactor systems. Diffusion coefficients for chlorferon and DETP in Ca-alginate gel beads determined at conditions suitable for biodegradation studies were 2.70 x 10(-11) m(2)/s and 4.28 x 10(-11) m(2)/s, respectively. Diffusivities of chlorferon and DETP were influenced by several factors, including viscosity of the bulk solution, agitation speed, and the concentrations of diffusing substrate and immobilized cells. Diffusion coefficients increased with increasing agitation speed, probably due to poor mixing at low speed and some attrition of beads at high speeds. Diffusion coefficients also increased with decreasing substrate concentration. Increased cell concentration in the gel beads caused lower diffusivity. Theoretical models to predict diffusivities as a function of cell weight fraction overestimated the effective diffusivities for both chlorferon and DETP, but linear relations between effective diffusivity and cell weight fraction were derived from experimental data. Calcium-alginate gel beads with radii of 1.65-1.70 mm used in this study were not subject to diffusional limitations: external mass transfer resistances were negligible based on Biot number calculations and effectiveness factors indicated that internal mass transfer resistance was negligible. Therefore, the degradation rates of chlorferon and DETP inside Ca-alginate gel beads were reaction-limited.     

Oxygen diffusion from capillary layers with concurrent flow

Oxygen transport from capillary layers with concurrent flow is considered for symmetric and asymmetric distributions of oxygen concentration between the layers. The analysis is based on the solution previously obtained by the author [1]. Solutions for the symmetric case are shown to be very close to the corresponding solutions of the Krogh cylinder model. Asymmetry in oxygen distribution is introduced systematically by considering different velocities of blood in the alternate capillary layers, different inlet capillary oxygen tensions, and different capillary hematocrits. It is shown that increase of the degree of asymmetry leads to diminution of the mean oxygen tension.     

Determination of diffusion coefficients in a solution by the transport of a solute through porous membranes

The possibility of determining the coefficients of diffusion in solution by the transport of solutes through porous polymeric membrane was studied. Reliable and reproducible results can be obtained by using nucleoporous filters with cylindrical pores. The method enables the selective determining of the diffusion coefficients of solutes being in complex mixtures, which is of special interest for biochemical research. The possibilities of the method are illustrated on the pattern of some globular proteins, polyethylene glycols and proteolytic enzymes.     

Determination of glucose and ethanol effective diffusion coefficients in Ca-alginate gel.

Glucose and ethanol diffusion coefficients in 2% Ca-alginate gel were measured using the experimental technique based on solute diffusion into or out of gel beads in a well-stirred solution. The aim of the study was to make the measurements under typical conditions found in alcoholic fermentations, such as the concentrations of glucose (100 g l-1) and ethanol (50 g l-1), the simultaneous counter-diffusion of glucose and ethanol, and the presence of cells in the gel beads at a level of 10(9) cells g-1 of beads. Previously, an evaluation of the error associated with the methodology used indicated how the experimental procedure would minimize the error. The individual measurement of glucose and ethanol coefficients in 2% Ca-alginate with no cells gave values of 5.1 and 9.6 x 10(-6) cm2 s-1, respectively, which are lower than those in water. When the effect of counter-diffusion was investigated, both coefficients decreased: glucose by 14% and ethanol by 28%. When cells were incorporated into the beads, only the ethanol coefficient decreased significantly, while the glucose coefficient apparently increased its value to 6.9 10(-6) cm2 s-1.     

Determination of catecholamine permeability coefficients for passive diffusion across phospholipid vesicle membranes

Summary A convenient catecholamine transport assay has been developed which permits continuous, instantaneous monitoring of transmembrane flux. Epinephrine transport has been examined by spectrophotometrically monitoring adrenochrome formation resulting from the passive diffusion of catecholamine into unilamellar phospholipid vesicles containing entrapped potassium ferricyanide. Ferricyanide oxidation of epinephrine under the conditions employed is fast compared to membrane transport, which obviates the need for intravesicular concentration or volume determinations. Epinephrine transport data over a pH 6 to 7 range have been fitted to an integrated rate equation from which a permeability coefficient for neutral epinephrine of 2.7±1.5×10^–6 cm/sec has been obtained.     

Plant regeneration from thin cell layers in Spinacia oleracea

Caulogenesis and somatic embryogenesis were induced from transverse thin cell layers (tTCLs) of two European (Spinacia oleracea L.) spinach genotypes. Regeneration occurred mostly when tTCLs had been excised from seedlings grown on a preconditioning medium consisting of White's macroelements, Nitsch's microelements, Murashige and Skoog's (MS) vitamins, 6 g l^–1 agar and 20 g l^–1 glucose. The explants were cultured on MS medium supplemented with sucrose (10, 30, 50 or 80 g l^–1) or fructose (5, 10 or 30 g l^–1) and several combinations of indole-3-acetic acid (IAA), -naphtalene acetic acid (NAA), 6-benzylaminopurine (BAP) and gibberellic acid (GA₃). Most of the regeneration events were obtained from root explants of the cultivar Carpo. The best result was observed on MS medium supplemented with 50 g l^–1 sucrose, 100 M NAA, 1 M BAP and 10 M GA₃. After an 8-week culture, the calluses were transferred onto MS medium where shoots and somatic embryos appeared 1 week later. The best root development was obtained on MS medium supplemented with 4.9 M indole-3-butyric acid (IBA) and 8 g l^–1 Phytagel. The plantlets were, then, transferred to soil and developed into well-conformed, fertile plants.     

Propagators and time-dependent diffusion coefficients for anomalous diffusion

Complex diffusive dynamics are often observed when one is investigating the mobility of macromolecules in living cells and other complex environments, yet the underlying physical or chemical causes of anomalous diffusion are often not fully understood and are thus a topic of ongoing research interest. Theoretical models capturing anomalous dynamics are widely used to analyze mobility data from fluorescence correlation spectroscopy and other experimental measurements, yet there is significant confusion regarding these models because published versions are not entirely consistent and in some cases do not appear to satisfy the diffusion equation. Further confusion is introduced through variations in how fitting parameters are reported. A clear definition of fitting parameters and their physical significance is essential for accurate interpretation of experimental data and comparison of results from different studies acquired under varied experimental conditions. This article aims to clarify the physical meaning of the time-dependent diffusion coefficients associated with commonly used fitting models to facilitate their use for investigating the underlying causes of anomalous diffusion. We discuss a propagator for anomalous diffusion that captures the power law dependence of the mean-square displacement and can be shown to rigorously satisfy the extended diffusion equation provided one correctly defines the time-dependent diffusion coefficient. We also clarify explicitly the relation between the time-dependent diffusion coefficient and fitting parameters in fluorescence correlation spectroscopy.     

Prediction of diffusion coefficients of proteins

A correlation for predicting the diffusion coefficients of proteins at standard conditions is proposed by adapting the Stokes-Einstein equation to a model for the equivalent hydrodynamic sphere. The radius of gyration, which accounts for the size and shape of protein molecules in solution, was used in deriving the new correlation. The correlation successfully predicted the diffusion coefficients of proteins, for which experimental data were available, with a higher degree of accuracy than achieved by previous correlation methods.     

Production of isolated somatic embryos from sunflower thin cell layers

We describe here a two step procedure which allows the easy isolation of somatic embryos from Sunflower (Helianthus annuus L.) hypocotyl tissues. Thin cell layers composed of the epidermis plus 3 to 6 parenchyma cell layers were incubated for 5 days in a basal Murashige and Skoog medium using an auxin to cytokinin weight ratio of 1/1. The epidermis layers were then transferred to a Gamborg medium containing a high level of sucrose. After one week of incubation in this medium, many somatic embryos started to be released from the parental epidermal tissue. Even though the germination of these embryos is difficult, we have been able to induce secondary embryos and regenerate fertile plants.Abbreviations NAA 1-naphthalene acetic acid - IAA indole-3-acetic acid - BAP 6-benzylamino-purine - MS Murashige and Skoog medium - B5 Gamborg medium