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PubMed1990

Mathematical models of the spatial distribution of retinal oxygen tension and consumption, including changes upon illumination.

To better understand oxygen utilization by the retina, a mathematical model of oxygen diffusion and consumption in the cat outer, avascular retina was developed by analyzing previously recorded profiles of oxygen tension (PO2) as a function of retinal depth. Simple diffusion modelling of the oxygen distribution through the outer retina is possible because the PO2 depends only on diffusion from the choroidal and retinal circulations and on consumption within the tissue. Several different models were evaluated in order to determine the best one from the standpoints of their ability to represent the data and to agree with physiological reality. For the steady state one-dimensional diffusion model adopted (the special three-layer diffusion model), oxygen consumption was constant through the middle layer and zero in the layers near the choroid and near the inner retina. On the average, the oxygen consuming layer, as found by nonlinear regression for each profile, extended from about 75% to 85% of the retinal depth from the vitreous. This is a narrow band through the mid-region of the photoreceptors. Oxygen consumption of the entire avascular retina, determined from fitting eight PO2 profiles measured in light-adapted retinas, averaged 2.7 ml O2(STP)/(100 g tissue.min), while the value determined from fitting thirty-two PO2 profiles measured in dark-adapted retinas averaged 4.4 ml O2(STP)/(100 g tissue.min). Consumption in the light was thus only 60% of that in the dark. This suggests that the outer retina is at greater risk of hypoxic injury in the dark than in the light, a finding of considerable clinical significance.

Animals↗
PubMed1979

Quantitative aspects of a unified model of diffusion mediated receptor--cyclase coupling.

A quantitative model is presented of diffusion mediated coupling of adenylate cyclase to multivalent plasma membrane receptors which accounts for a wide range of phenomena including non linear occupation-activation plots with either positive or negative second derivatives, spare receptors, silent receptors, and negative and positive binding cooperativity. A non linear least square fit of the predicted equation for cyclase activation to available data predicts translational diffusion coefficients in the range of (10(-10) - 10(-11))cm2/s.

Adenylyl Cyclases↗
PubMed1979

The role of diffusion in the photoresponse of an extraretinal photoreceptor of Aplysia.

1. Membrane currents produced by flashes and steps of light (photo-current) were recorded from the ventral photoresponsive neurone of Aplysia californica. The effects of background illumination and changes in temperature were also examined. 2. The falling phase of the response wave form may be separated into two components with time constants of 10--12 sec and 50 sec. 3. Background illumination reduced the response amplitude to light impulses without appreciably altering the response wave form. 4. Lowering the temperature greatly reduced the amplitude of the photo-current with a Q10 of 2.91 (25--15 degrees C) and greatly prolonged the duration of the response. 5. Because of the relatively large distance between the plasma membrane and the pigmented cytoplasmic lipochondria where light is absorbed, a diffusion-based model with Ca as the internal-transmitter (Andresen & Brown, 1979) was developed. 6. In this model diffusion of Ca2+ released from the lipochondria upon photon absorption is slowed by the reversible uptake of Ca2+ at cytoplasmic binding sites. Ca2+ interacts with sites at the plasma membrane to increase GK and Ca2+ levels are subsequently restored by irreversible uptake processes. Ca2+ release and its adsorption and desorption from the more numerous plasma membrane binding sites were assumed to be instantaneous with respect to the duration of the light-evoked response. 7. The linearized model equations adequately predict the experimental response wave forms, the effects of temperature, and saturation of the steady-state amplitude--stimulus relationship. Aside from amplitude scaling, no curve-fitting was used. 8. The model also gives realistic values for the cytoplasmic diffusion coefficient of Ca and the net rate of Ca efflux required to restore dark Ca activity.

Animals↗
PubMed2026

Conditional Diffusion Model-Based Method for Annotation of Antibiotic Resistance Gene Properties.

The crisis of bacterial antibiotic resistance, which has led to a decline in the effectiveness of antibiotics originally used to combat bacterial infections, has emerged as an urgent challenge for public health. Antibiotic resistance genes (ARGs) are one of the key reasons for bacteria to develop resistance to antibiotics. Therefore, accurately identifying and annotating the critical properties of ARGs is of great importance for addressing the antibiotic resistance emergency. Although existing deep learning models demonstrate remarkable effectiveness in extracting local features from sequence data, they still face limitations in the capacity to further gain the enriched latent representations within the data. To address the critical challenge of extracting higher-quality representations from ARGs sequence data, we propose a novel ARGs properties annotation method based on the conditional diffusion model which is used to learn latent representations through domain-specific knowledge injection. Specifically, during the conditional information integration phase, we systematically incorporate ARGs' domain knowledge to guide the diffusion process in generating high-quality latent representations. To overcome information redundancy caused by direct concatenation of conditional information and intermediate features, we design a cross-attention mechanism that enables feature fusion between heterogeneous information sources, thereby enhancing further the quality of obtained representations. Experimental results on widely used data sets demonstrate the framework's effectiveness in achieving superior prediction performance compared to existing methods.

Anti-Bacterial Agents↗
PubMed1986

The effects of transmural transport in the microcirculation: a two gas species model.

Diffusion of oxygen and carbon dioxide across the walls of noncapillary vessels in the microcirculation has been suggested by several studies. The formulation and steady-state solutions to a nine-compartment mathematical model of the microcirculation of skeletal muscle with transmural gas diffusion in all vessels are presented. The simultaneous transport of oxygen and carbon dioxide between arterioles, capillaries, and venules, and connective and muscle tissue at rest and exercise are described. Special attention is paid to the interactions of these gases in blood. This model predicts a longitudinal intravascular gradient in oxygen tension from large to small vessel with the tension at the precapillary vessels relatively insensitive to changes in the input tension. At rest, there is significant small arteriolar oxygen flux. However, during exercise, the precapillary transmural flux of oxygen is only a small fraction of the total metabolic demand. The model predicts large noncapillary fluxes of carbon dioxide, and also that tissue PCO2 is dependent on input tensions. The model also predicts that Bohr shifts due to either changes in input PCO2 or increased precapillary PCO2 due to increased metabolism may cause physiologically significant changes in precapillary PO2. Countercurrent shunting was predicted by the model to be significant only for carbon dioxide.

Animals↗
PubMedDate not supplied

[A model of diffusion of anti-cataract drugs into the lens tissue].

For modeling anticataract drugs diffusion into the lens surface tension of drugs, their solubility in nonpolar solvent and drug adsorption at air-water and water-lipid monolayer surface were measured. It has been shown that diffusion of many drugs into the lens is limited by their low solubility in a monolayer phase of the membrane. Catachrom concentration in the lens should be the highest, because it can concentrate at interfaces.

Cataract↗
PubMed1989

Effect of Ca2+ diffusion on the time course of neurotransmitter release.

The three-dimensional (3D) diffusion model of Fogelson, A. L., and R. S. Zucker (1985. Biophys. J. 48: 1003-1017) has been employed as the basis of a refined version of the "Ca theory" for neurotransmitter release. As such, it has been studied here as to its ability to predict the time course of release under various conditions. In particular, conditions were chosen in which the temporal variations in intracellular Ca2+ concentration, the sole factor controlling the release according to the Ca theory, were modified and tested experimentally. The predictions of this model were compared with the experimental results. It is shown that the 3D diffusion model, similarly to earlier simpler versions of the Ca theory, predicts that the time course of release is highly sensitive to both the level of depolarization and the level of the resting concentration of intracellular Ca2+ Moreover, the 3D diffusion model predicts that the time course of release is insensitive to changes in temperature. In contrast, the experimental results show that the time course of release is invariant to the level of depolarization and to the resting level in intracellular Ca2+, but highly sensitive to variations in temperature.

Animals↗
PubMed1977

Amphiphile diffusion in model membrane systems studied by pulsed NMR.

The translational diffusion of the amphiphilic molecules in a number of lyotropic liquid crystalline phases has been measured with the pulsed NMR pulsed magnetic field gradient method. The amphiphiles studied were soaps, monoglycerids and lecithins. Measurements were performed both for oriented lamellar and for cubic phases. The order of magnitude of the diffusion coefficients was found to be the same as in neat liquids of analogous compounds. It was also found that the difussion coefficient depend markedly on the amphiphile end group in a way that parallels the area per polar head group as determined in X-ray studies. When corrections for geometrical factors has been made the diffusion rate is approximately equal in cubic and lamellar phases containing the same amphiphile.

Chemical Phenomena↗
PubMed1989

Axonal injury in the optic nerve: a model simulating diffuse axonal injury in the brain.

A new model of traumatic axonal injury has been developed by causing a single, rapid, controlled elongation (tensile strain) in the optic nerve of the albino guinea pig. Electron microscopy demonstrates axonal swelling, axolemmal blebs, and accumulation of organelles identical to those seen in human and experimental brain injury. Quantitative morphometric studies confirm that 17% of the optic nerve axons are injured without vascular disruption, and horseradish peroxidase (HRP) studies confirm alterations in rapid axoplasmic transport at the sites of injury. Since 95% to 98% of the optic nerve fibers are crossed, studies of the cell bodies and terminal fields of injured axons can be performed in this model. Glucose utilization was increased in the retina following injury, confirming electron microscopic changes of central chromatolysis in the ganglion cells and increased metabolic activity in reaction to axonal injury. Decreased activity at the superior colliculus was demonstrated by delayed HRP arrival after injury. The model is unique because it produces axonal damage that is morphologically identical to that seen in human brain injury and does so by delivering tissue strains of the same type and magnitude that cause axonal damage in the human. The model offers the possibility of improving the understanding of traumatic damage of central nervous system (CNS) axons because it creates reproducible axonal injury in a well-defined anatomical system that obviates many of the difficulties associated with studying the complex morphology of the brain.

Animals↗
PubMed1991

Kinetic analysis of cAMP-activated Na+ current in the molluscan neuron. A diffusion-reaction model.

cAMP-activated Na+ current (INa,cAMP) was studied in voltage-clamped neurons of the seaslug Pleurobranchaea californica. The current response to injected cAMP varied in both time course and amplitude as the tip of an intracellular injection electrode was moved from the periphery to the center of the neuron soma. The latency from injection to peak response was dependent on the amount of cAMP injected unless the electrode was centered within the cell. Decay of the INa,cAMP response was slowed by phosphodiesterase inhibition. These observations suggest that the kinetics of the INa,cAMP response are governed by cAMP diffusion and degradation. Phosphodiesterase inhibition induced a persistent inward current. At lower concentrations of inhibitor, INa,cAMP response amplitude increased as expected for decreased hydrolysis rate of injected cAMP. Higher inhibitor concentrations decreased INa,cAMP response amplitude, suggesting that inhibitor-induced increase in native cAMP increased basal INa,cAMP and thus caused partial saturation of the current. The Hill coefficient estimated from the plot of injected cAMP to INa,cAMP response amplitude was close to 1.0. An equation modeling INa,cAMP incorporated terms for diffusion and degradation. In it, the first-order rate constant of phosphodiesterase activity was taken as the rate constant of the exponential decay of the INa,cAMP response. The stoichiometry of INa,cAMP activation was inferred from the Hill coefficient as 1 cAMP/channel. The equation closely fitted the INa,cAMP response and simulated changes in the waveform of the response induced by phosphodiesterase inhibition. With modifications to accommodate asymmetric INa,cAMP activation, the equation also simulated effects of eccentric electrode position. The simple reaction-diffusion model of the kinetics of INa,cAMP may provide a useful conceptual framework within which to investigate the modulation of INa,cAMP by neuromodulators, intracellular regulatory factors, and pharmacological agents.

1-Methyl-3-isobutylxanthine↗
PubMed1990

Restricted diffusion of molecules in porous affinity chromatography adsorbents.

A restricted diffusion model is constructed and solved in order to study the permeability of large adsorbate molecules in the pores of affinity chromatography media, when the adsorbate molecules are adsorbed onto immobilized ligands. The combined effects of steric hindrance at the entrance to the pores and frictional resistance within the pores, as well as the effects of pore size distribution, pore connectivity of the adsorbent, molecular size of adsorbate and ligand, and the fractional saturation of adsorption sites (ligands), are considered. Affinity adsorbents with dilute and high ligand concentrations are examined, and the permeability of the adsorbate in porous networks of connectivity nT is studied by means of effective medium approximation (EMA) numerical solutions. As expected, the permeability of the adsorbate decreases as the size of the adsorbate and/or ligand molecule increases. The permeability also decreases when the fractional saturation of the ligands increases, as well as when the pore connectivity of the network decreases. The dependence of the permeability on the pore connectivity tends to be less marked in adsorbents with concentrated ligand than in porous media with dilute ligand concentration. The conditions are also presented for which the percolation threshold is attained in a number of different systems. The restricted diffusion model and results of this work may be of importance in studies involving the modeling, prediction of the dynamic behavior, design, and control of affinity chromatography (biospecific adsorption) systems employing porous adsorbents. The theoretical results may also have important implications in the selection of a ligand as well as in the selection and construction of an affinity porous matrix, so that the adsorbate of interest can be efficiently separated from a given solution. Furthermore, with appropriate modifications this restricted diffusion model may be used in studies involving the immobilization of ligands or enzymes in porous solids.

Adsorption↗
PubMed1976

A unified mathematical model for diffusion from drug-polymer composite tablets.

The derivation and experimental verification of a unified mathematical model for the estimation of drug release rate from drug-polymer composite tablets are presented. Cylindrical coordinates are utilized in the solution of the diffusion equation for a three-dimensional system. The model is applicable to tablets that range from the shape of a flat disk (radius greater than thickness) to that of a cylindrical rod (radius less than thickness). The general solution for the fraction of drug released at a time t is (see article). This approach to a three-dimensional system, utilizing cylindrical coordinates, presents a comprehensive method for the estimation of drug release rates from sustained release tablets with drug distributed homogeneously throughout a polymer matrix. The calculated and experimental drug diffusion rate of pyrimethamine from pyrimethamine-silicone rubber composite tablets that range in shape from that of a disk to a cylinder, and of hydrocortisone from EVA, polycaprolactone, and PVA terpolymer, are compared.

Caprolactam↗
PubMed1991

Microscopic versus macroscopic diffusion in model membranes by electron spin resonance spectral-spatial imaging.

The macroscopic and the microscopic diffusion coefficients of a phospholipid spin label (16-PC) in the model membrane 1-palmitoyl-2-oleoyl-sn-glycero-phosphatidylcholine have been measured simultaneously in the same sample utilizing the new technique of spectral-spatial electron spin resonance imaging. The macroscopic diffusion coefficient Dmacro for self-diffusion of 16-PC spin label is obtained from imaging the concentration profiles as a function of time, and it is (2.3 +/- 0.4) x 10(-8) cm2/s at 22 degrees C. The microscopic diffusion coefficient Dmicro for relative diffusion of the spin probes is obtained from the variation of the spectral line broadening with spin label concentration, which is due to spin-spin interactions. Dmicro is found to be substantially greater than Dmacro for the same sample at the same conditions, and is estimated to be at least (1.0 +/- 0.4) x 10(-7) cm2/s. Possible sources for their difference are briefly discussed in terms of the models used for Dmicro.

Cyclic N-Oxides↗
PubMed1977

The respiratory gas exchange of sea turtle nests (Chelonia, Caretta).

Sea turtles lay about 100 leathery-shelled eggs in a 25 cm diameter chamber carefully excavated about 50 cm deep in a nesting beach, where the eggs exchange gases (at approximately 28 degrees C) during their 60-day incubation period. The sand surrounding the spherical nest chamber restricts the diffusion of gases into and out of the nest so that as embryonic development progresses, PO2 decreases and PCO2 increases in the gas inside the nest. PO2 falls to 80-100 torr and PCO2 rises to 40-60 torr inside 100-egg man-made Chelonia and Caretta nests. The change in gas tensions in the nest during development is very similar to that seen in the air cell of the chicken egg. Gas tensions inside the turtle nest and in the sand surrounding the nest can be described by a radial steady-state diffusion model. The rate of diffusion of gases in the sand is 30-50% of the rate found in the nest and 6-12% of the rate found in an equal volume of air. The sand surrounding the turtle nest appears to determine the gas exchange of the eggs in the nest and is functionally analogous to the shell surrounding the chicken embryo. The female sea turtle may construct her nest so as the maximize its gas exchange and minimize gas partial pressure gradients inside the nest.

Animals↗
PubMed1990

Exact solution of a model of diffusion in an infinite chain or monolayer of cells coupled by gap junctions.

Analytic solutions are found for an infinite chain of cells coupled by gap junctions under two initial conditions: (a) One inner cell initially filled uniformly to a fixed concentration and (b) inner cell maintained indefinitely at constant concentration. The solution can be extended by the product method (Carslaw and Jaeger. 1959. Conduction of Heat in Solids. Oxford University Press.) to monolayers. We can also incorporate leakage through the plasma membrane by the product method. We demonstrate the utility of these results by fitting diffusion data from the septate axon of earthworm and by plots of theoretical profiles from monolayers of cells. Use of these analytic solutions enables one to overcome the limitations of methods that lump the effects of cytoplasmic diffusion and junctional permeability into an effective diffusion coefficient.

Animals↗