Diffusion of [3H]dexamethasone in rat subcutaneous slices after injection measured by digital autoradiography

A relatively simple method for the determination of the diffusion coefficient of a substance that has been injected into tissue is described. We illustrate this method using [3]dexamethasone injected into the subcutaneous tissue of rats. Digital autoradiography was used to measure the distribution of the [3H] dexamethasone within the subcutaneous tissue at 2.5 and 20 min after injection. Measured concentration profiles of the injection were compared to a mathematical model of drug diffusion from an injection. There was good agreement between the experimental data and the mathematical model. The diffusion coefficient found using this simple injection method was (4.01 +/- 2.01) x 10(-10) m2/s. This D value was very close to the value of D = (4.11 +/- 1.77) x 10(-10) m2/s found previously using different mathematical and experimental techniques with osmotic pumps implanted for 6, 24, and 60 h in rats (1). The simple method given here for the determination of the diffusion coefficient is general enough to be applied to other substances and tissues as well.     

Primordial transport of sugars and amino acids via Schiff bases

Experimental support is given for a model concerning the origin of a primordial transport system. The model is based on the facilitated diffusion of amino acids stimulated by aliphatic aldehyde carriers and sugars stimulated by aliphatic amine carriers. The lipid-soluble diffusing species is the Schiff base. The possible role of this simple transport system in the origin of an early protocell is discussed.     

Diffusion measurement of fluorescence-labeled amphiphilic molecules with a standard fluorescence microscope.

The lateral diffusion of fluorescence-labeled amphiphilic tracer molecules dissolved within a two-dimensional matrix of lipids was measured by continuous illumination of an elongated rectangular region. The resulting spatial concentration profile of unbleached tracer molecules was observed with a standard epifluorescence microscope and analyzed with digital image-processing techniques. These concentration profiles are governed by the mobility of the tracers, their rate of photolysis, and the geometry of the illuminated area. For the case of a long and narrow illuminated stripe, a mathematical analysis of the process is given. After prolonged exposure, the concentration profile can be approximated by a simple analytical function. This fact was used to measure the quotient of the rate of photolysis, and the diffusion constant of the fluorescent probe. With an additional measurement of the rate of photolysis, the mobility of the tracer was determined. As prototype experiments we studied the temperature dependence of the lateral diffusion of N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)-dipalmitoylphosphatidyl++ + ethanolamine in glass-supported bilayers of L-alpha-dimyristoylphosphatidylcholine. Because of its simple experimental setup, this technique represents a very useful method of determining the lateral diffusion of fluorescence-labeled membrane molecules.     

Calculation of time constants for intracellular diffusion in whole cell patch clamp configuration.

We present a simplified model to identify and analyze the important variables governing the diffusion of substances from pipettes into canine cardiac Purkinje cells in the whole cell patch clamp configuration. We show that diffusion of substances through the pipette is the major barrier for equilibration of the pipette and cellular contents. We solve numerically the one-dimensional diffusion equation for different pipette geometries, and we derive a simple analytic equation which allows one to estimate the time necessary to reach the steady state of intracellular concentration. The time constant of the transient to steady state is given by a pipette geometric factor times the cell volume divided by the diffusion coefficient of the substance of interest. The geometric factor is shown to be given by the ratio of pipette resistance to the resistivity of the filling solution. Additionally from our modeling, we concluded that pipette perfusion at distances greater than 20 microns from the pipette tip would not substantially reduce the time necessary to achieve the steady state.     

A countercurrent mechanism with transverse diffusion

A simple treatment is given for the stationary state distribution of a substance dissolved in two liquids flowing in opposite directions in two tubes with a common wall that is permeable to the substance. The transverse diffusion is taken into account. It is shown how in the case of sufficiently fast diffusion the permeability constant of the wall can be obtained from the concentrations of the substance at the ends of the tubes, the velocities in the tubes, and the length of the tubes.     

Restricted Diffusion in Cellular Media: (1+1)-Dimensional Model

We consider the diffusion of molecules in a one-dimensional medium consisting of a large number of cells separated from the extra-cellular space by permeable membranes. The extra-cellular space is completely connected and allows unrestricted diffusion of the molecules. Furthermore, the molecules can diffuse within a given cell, i.e., the intra-cellular space; however, direct diffusion from one cell to another cell cannot occur. There is a movement of molecules across the permeable membranes between the intra- and extra-cellular spaces. Molecules from one cell can cross the permeable membrane into the extra-cellular space, then diffuse through the extra-cellular space, and eventually enter the intra-cellular space of a second cell. Here, we develop a simple set of model equations to describe this phenomenon and obtain the solutions using an eigenfunction expansion. We show that the solutions obtained using this method are particularly convenient for interpreting data from experiments that use techniques from nuclear magnetic resonance imaging.     

Hydrodynamics of a permeable patch in the fluid membrane.

A patch of cross-linked proteins in the fluid membrane is considered for the case in which the patch is permeable (porous) for the lipid flow in the membrane. The Bretscher flow field is studied quantitatively and the distribution of Brownian particles over the surface of the cell is given. This leads to a simple quantitative criterion for cap formation. Finally, explicit expressions for the rotational and translational diffusion coefficients of a permeable patch, as calculated from hydrodynamics, are given.     

Image blurring by thermal diffusion in the observation of hydrated biomolecules with soft X-ray microscopy.

A simple model is presented for the estimation of image blurring in X-ray microscopy of biological specimens in a hydrated environment. The model is essentially based on thermal diffusion of an object to be imaged. The degree of image blurring by diffusion depends on the following situations of the object. The object is free from, is tightly fixed to, or is partially connected to the surrounding structures. The proper imaging time required to achieve a given resolution in X-ray microscopy of biological structures was estimated with the present method. The results suggest that imaging time shorter than 3 msec (free) to 1.4 sec (tightly fixed) is required for the observation of a cell (30 microns in diameter) at the resolution of 100 nm. The model is also applicable to a fragmented object caused by imaging X-rays.     

Mechanismen des Wassertransportes bei der Getreideweiche

A simple method for the investigation of the water transport velocity in cereal kernel is described. The mechanism of the water transport is discussed. It is explained that data, place and strength of the effect of hydrolytic enzymes can be determined on the basis of the changed transport resistance from the temporal change of the different diffusion coefficient. The fundamentals of the modelling of steeping processes are given.     

Computer simulation of stochastic processes through model-sampling (Monte Carlo) techniques

A simple Monte Carlo simulation program is outlined which can be used for the investigation of random-walk problems, for example in diffusion, or the movement of tracers in the blood circulation. The results given by the simulation are compared with those predicted by well-established theory, and it is shown how the model can be expanded to deal with drift, and with reflexion from or adsorption at a boundary.     

An Ion Displacement Membrane Model

The usual assumption in treating the diffusion of ions in an electric field has been that the movement of each ion is independent of the movement of the others. The resulting equation for diffusion by a succession of spontaneous jumps has been well stated by Parlin and Eyring. This paper will consider one simple case in which a different assumption is reasonable. Diffusion of monovalent positive ions is considered as a series of jumps from one fixed negative site to another. The sites are assumed to be full (electrical neutrality). Interaction occurs by the displacement of one ion by another. An ion leaves a site if and only if another ion, not necessarily of the same species, attempts to occupy the same site. Flux ratios and net fluxes are given as functions of the electrical potential, concentration ratios, and number of sites encountered in crossing the membrane. Quantitative comparisons with observations of Hodgkin and Keynes are presented.     

An approach to the mathematical biophysics of biological self-regulation and of cell polarity

In a cell, in which the permeability to a metabolite is a function of the concentration of that metabolite, situations may occur, in which the diffusion field will exhibit certain assymetric patterns, even though the cell may possess geometrically spherical symmetry. This pattern results in a polarity of the cell. Moreover, the pattern being the result of a dynamic equilibrium, it possesses the property of self-regulation. Dividing the cell in two results in the appearance of a similar patterns in each half-cell. Another case when such self regulation and polarity occur is given by considerations of the action of the diffusion forces upon colloidal particles, which affect catalytically the metabolic reactions. A simple case is treated mathematically.     

Diffusion coefficients of segmentally flexible macromolecules with two spherical subunits

The translational and rotational diffusion coefficients have been calculated for a simple, segmentally flexible model: the hinged dumbbell (HD). In the HD, two spherical subunits are attached to an universal joint by means of frictionless connectors. In addition to the case in which hydrodynamic interactions are neglected (NI), we have also considered two more cases, including hydrodynamic interaction by means of the Kirkwood-Riseman approximate treatment (KR) and using accurate procedure based in the series expansions for the two-sphere diffusion tensor (SE). Expressions for the friction coefficients of the HD are given for the three cases, and the diffusion coefficients are evaluted inverting the 9 × 9 resistance matrix, for two HDs with different dimensions. The KR treatment, which includes a contribution from the finite volume of the subunits, is shown to be an excellent approximation to the more rigorous procedure. In the NI case for rotation, the various coefficients present different deviations with respect to the SE results. A rough estimate of the errors of the NI relaxation times indicates that they may be smaller than 15% for a HD with identical beads. However, the influence of hydrodynamic interaction should be more important for the rotational diffusivity of a small sphere attached to a larger one. The error of the NI result for the translational diffusion coefficient is of about 25% for the two HDs.     

Limiting sedimentation and diffusion coefficients of polyelectrolytes. The charge effect

General expressions relating the sedimentation and diffusion constants of polyelectrolytes to the friction properties of ionic components in multicomponent systems have been derived. A quantitative explanation of the charge effect with respect to the addition of a low-molecular-weight salt is given; special attention is laid on limiting laws according to the salt-to-polymer concentration ratio. The theory is applied to a simple model, the infinitely long rod-like model, to illustrate the peculiar aspect of the charge effect in presence of salt.     

Steady-state diffusion through a finite pore into an infinite reservoir: An exact solution

An outline is given of an analysis that leads to an exact solution for the problem of steady-state diffusion through a finite thick pore into an infinite region surrounding the mouth of the pore. From this exact formula a simple expression for the flux is derived. This expression approximates the flux with a relative error of less than 3.42 per cent independently of the ratiol/a wherel is the length of the pore anda its radius. If desired, more accurate expressions for the flux can be obtained from the exact solution. This research was supported in part by Contract Nonr 595(17), Office of Naval Research, U.S. Navy.     

Anomalous Diffusion Induced by Cristae Geometry in the Inner Mitochondrial Membrane

Diffusion of inner membrane proteins is a prerequisite for correct functionality of mitochondria. The complicated structure of tubular, vesicular or flat cristae and their small connections to the inner boundary membrane impose constraints on the mobility of proteins making their diffusion a very complicated process. Therefore we investigate the molecular transport along the main mitochondrial axis using highly accurate computational methods. Diffusion is modeled on a curvilinear surface reproducing the shape of mitochondrial inner membrane (IM). Monte Carlo simulations are carried out for topologies resembling both tubular and lamellar cristae, for a range of physiologically viable crista sizes and densities. Geometrical confinement induces up to several-fold reduction in apparent mobility. IM surface curvature per se generates transient anomalous diffusion (TAD), while finite and stable values of projected diffusion coefficients are recovered in a quasi-normal regime for short- and long-time limits. In both these cases, a simple area-scaling law is found sufficient to explain limiting diffusion coefficients for permeable cristae junctions, while asymmetric reduction of the junction permeability leads to strong but predictable variations in molecular motion rate. A geometry-based model is given as an illustration for the time-dependence of diffusivity when IM has tubular topology. Implications for experimental observations of diffusion along mitochondria using methods of optical microscopy are drawn out: a non-homogenous power law is proposed as a suitable approach to TAD. The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes.     

Highly protective alkalinization by ammonia vapor diffusion in viscosimetric DNA damage assessment

A method for the measurement of viscosities correlated to DNA alterations in alkaline homogenate suspensions is described. The alkaline pH shift to afford cell lysis, DNA unfolding, and denaturation is attained by gaseous ammonia diffusion, thus avoiding shear stress from mechanical mixing. At the same time a stabilizing density gradient is established. This solution is run through a plastic measuring tube that is wide enough to minimize the influence of uneven swelling of the lysing DNA-containing components. Flow times under a carefully controlled water head are registered, and their ratios to control solutions are evaluated. The relative viscosities show a strong and irreversible dependence on shear and on DNase treatment and therefore are considered as essentially DNA derived. The time dependence of the lysate viscosities with and without the DNA-damaging agent bleomycin is given and the dose:activity curves of this agent with sponge homogenates from two orders of Porifera are given with their 50% effective concentration values. The dose:activity curve of an extract from a polluted marine point source is demonstrated. The concentration changes in sponges exposed at differently polluted marine sites are shown. The idea of alkalinization through gaseous diffusion in conjunction with a simple measuring device has already proven a sensitive, reliable, and specific tool in the assessment of DNA damage produced under both laboratory and field conditions.     

Noise-triggered regime shifts in a simple aquatic model

We examined the effects of random fluctuations and diffusion on regime shifts in bistable aquatic ecosystems, using a simple two-component reaction–diffusion model with nutrients and phytoplankton. The corresponding mean-field model generates two stable attractors: one is a nutrient-dominated (ND) state or a clear-water state, and the other is a phytoplankton-dominated (PD) state or a turbid-water state. According to our simulations of the reaction–diffusion model without fluctuations, either of two stable states can be dominant corresponding to the given parameters and the configuration of two states, meaning that the long-term coexistence of these two states is difficult. The dominant state expands gradually eliminating the other non-dominant one, which results in the homogeneous distribution of the dominant state in the whole lake. Further simulations including the effects of temporally changing fluctuations show that the regime shifts driven by external noise proceed even within a bistable region, which complicates the detection of hysteresis in real aquatic ecosystems.     

A Model for Bacterial Colonization of Sinking Aggregates

Sinking aggregates provide important nutrient-rich environments for marine bacteria. Quantifying the rate at which motile bacteria colonize such aggregations is important in understanding the microbial loop in the pelagic food web. In this paper, a simple analytical model is presented to predict the rate at which bacteria undergoing a random walk encounter a sinking aggregate. The model incorporates the flow field generated by the sinking aggregate, the swimming behavior of the bacteria, and the interaction of the flow with the swimming behavior. An expression for the encounter rate is computed in the limit of large Péclet number when the random walk can be approximated by a diffusion process. Comparison with an individual-based numerical simulation is also given.