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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↗

Estimation of oxygen distribution in RIF-1 tumors by diffusion model-based interpretation of pimonidazole hypoxia and eppendorf measurements.

Numerical simulations of oxygen diffusion from the capillaries in tumor tissue were used to predict the capillary oxygen supply within and near hypoxic regions of the RIF-1 tumor. A finite element method to simulate the oxygen distribution from a histology section is presented, along with a method to iteratively estimate capillary oxygen concentrations. Pathological structural data for these simulations came from sections of the tumor stained with hematoxylin and eosin and were used to define the capillary positions and shapes, while overlapping regions of low oxygen concentration were defined by the hypoxia marker pimonidazole. These simulations were used to calculate spatial maps of the oxygen concentration and were tested for their ability to reproduce Eppendorf pO(2) histograms from the same tumor line. This simulation study predicted that capillary oxygen concentrations ranged from zero to above 20 microM, with a dominant peak in the hypoxic regions showing 78% of capillaries with less than 1 microM oxygen concentration, compared to only 12% in the non-hypoxic regions. The results were not highly sensitive to the metabolic oxygen consumption rate, within the range of 2 to 16 microM/s. This numerical method for oxygen capillary simulation is readily adaptable to histology sections and provides a method to examine the heterogeneity of oxygen within the capillaries and throughout the tumor tissue section being examined.

Animals↗

A diffuse biosemiotic model for cell-to-tissue computational closure.

The adoption of diffuse rationality creates a practical bridge between biosemiotics and computation in formulating local-to-global self-consistent criteria for cellular-to-tissue interfacing and for the emergence of life and consciousness. Nature is always complex, the more so at biological membranic inter-scalar interfaces. We present an evolutionary model of the relationship between autonomy and dependence across scales, and describe the implications of its alternating complex-rational-complex nature.

Biological Evolution↗

Drifting towards a diffuse control model of exploratory motor learning: A comparison of global and within-trial performance measures.

Accurate measurement is crucial for understanding the processes that underlie exploratory patterns in motor learning. Accordingly, measures of learning should be sensitive to the changes that take place during skill acquisition. Most studies, however, use trial-based global measures that assess performance but do not actually measure gradual changes taking place within trials. The present study attempted to remedy this shortcoming by analysing a visual adaptation task, and comparing traditional global measures of learning with new, within-trial measures. Movement time was the only global measure sensitive to changes in the movement trajectory during learning. Three new measures were expected to reveal changes to the movement trajectory that are associated with learning: (i) the length of runs, (ii) change of trajectory angle in relation to the target, and (iii) drift (change in distance from the target). All three measures were sensitive to learning and indicated a gradual straightening of the movement trajectories over trials. Furthermore, three different methods to partition trajectories into segments were examined. The new within-trial measures, irrespective of partitioning method, prove promising for the development of a diffuse control model of exploratory learning.

Exploratory Behavior↗

Spatial embedding of neuronal trees modeled by diffusive growth.

The relative importance of the intrinsic and extrinsic factors determining the variety of geometric shapes exhibited by dendritic trees remains unclear. This question was addressed by developing a model of the growth of dendritic trees based on diffusion-limited aggregation process. The model reproduces diverse neuronal shapes (i.e., granule cells, Purkinje cells, the basal and apical dendrites of pyramidal cells, and the axonal trees of interneurons) by changing only the size of the growth area, the time span of pruning, and the spatial concentration of 'neurotrophic particles'. Moreover, the presented model shows how competition between neurons can affect the shape of the dendritic trees. The model reveals that the creation of complex (but reproducible) dendrite-like trees does not require precise guidance or an intrinsic plan of the dendrite geometry. Instead, basic environmental factors and the simple rules of diffusive growth adequately account for the spatial embedding of different types of dendrites observed in the cortex. An example demonstrating the broad applicability of the algorithm to model diverse types of tree structures is also presented.

Animals↗

Neutral evolution of model proteins: diffusion in sequence space and overdispersion.

We stimulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves (1) the structure of the ground state, (2) its thermodynamic stability and (3) its kinetic accessibility. All other mutations are considered lethal and are rejected. We adopt a lattice model, amenable to a reliable solution of the protein folding problem. We prove the existence of extended neutral networks in sequence space-sequences can evolve until their similarity with the starting point is almost the same as for random sequences. Furthermore, we find that the rate of neutral mutations has a broad distribution in sequence space. Due to this fact, the substitution process is overdispersed (the ratio between variance and mean is larger than 1). This result is in contrast with the simplest model of neutral evolution, which assumes a Poisson process for substitutions, and in qualitative agreement with the biological data.

Animals↗

Effects of sales promotion on smoking among U.S. ninth graders.

OBJECTIVE: The purpose of this study was to examine the association between tobacco marketing efforts and daily cigarette smoking by adolescents. DESIGN: This was a longitudinal study of uptake of smoking on a daily basis with smoking data from the Monitoring the Future project. Diffusion modeling was used to generate expected rates of daily smoking initiation, which were compared with actual rates. Study data were from a national survey, administered annually from 1978 through 1995. Between 4,416 and 6,099 high school seniors participated per year, for a total of 94,652. The main outcome measure was a deviation score based on expected rates from diffusion modeling vs actual rates of initiation of daily use of cigarettes by ninth graders. Annual data on cigarette marketing expenditures were reported by the Federal Trade Commission. RESULTS: The deviation scores of expected vs actual rates of smoking initiation for ninth graders were correlated with annual changes in marketing expenditures. The correlation between sales promotion expenditures and the deviation score in daily smoking initiation was large (r = 0. 769) and statistically significant (P = 0.009) in the 1983-1992 period. Correlations between sales promotion and smoking initiation were not statistically significant in 1978-1982. Correlations between advertising expenditures and smoking initiation were not significant in either period. CONCLUSIONS: In years of high promotional expenditures, the rate of daily smoking initiation among ninth graders was higher than expected from diffusion model predictions. Large promotional pushes by cigarette marketers in the 1980s and 1990s appear to be linked with increased levels of daily smoking initiation among ninth graders.

Adolescent↗

From periodic travelling waves to travelling fronts in the spike-diffuse-spike model of dendritic waves.

In the vertebrate brain excitatory synaptic contacts typically occur on the tiny evaginations of neuron dendritic surface known as dendritic spines. There is clear evidence that spine heads are endowed with voltage-dependent excitable channels and that action potentials invade spines. Computational models are being increasingly used to gain insight into the functional significance of a spine with an excitable membrane. The spike-diffuse-spike (SDS) model is one such model that admits to a relatively straightforward mathematical analysis. In this paper we demonstrate that not only can the SDS model support solitary travelling pulses, already observed numerically in more detailed biophysical models, but that it has periodic travelling wave solutions. The exact mathematical treatment of periodic travelling waves in the SDS model is used, within a kinematic framework, to predict the existence of connections between two periodic spike trains of different interspike interval. The associated wave front in the sequence of interspike intervals travels with a constant velocity without degradation of shape, and might therefore be used for the robust encoding of information.

Action Potentials↗

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↗

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↗

Radiocesium contamination in a submediterranean semi-natural ecosystem following the Chernobyl accident: measurements and models.

Radiocesium dynamics in a Quercus conferta Kit ecosystem in Northern Greece have been extensively studied over the years 1993-1995. Radiocesium distribution in the different parts of the ecosystem was measured. A total 137Cs inventory of 243+/-66 MBq ha(-1) due to the Chernobyl accident was measured in all parts of the ecosystem. Almost 90% of this inventory is still in the upper layers of the soil and the forest floor. In particular 13.4% is in the forest floor, 52.6% in the Ah horizon, and 23.4% in the upper 5 cm of the soil. Only 2.2% of this inventory is in the above ground biomass. The mean total 137Cs deposited on the forest floor from the above ground biomass is 0.18 MBq ha(-1) y(-1). Cesium leaching from the forest floor is negligible. The radiocesium distribution in soil is fixed and in equilibrium, at least since 1993. Most of radiocesium is not available for migration. Cesium migration in soil was modeled by a) an "equivalent diffusion" model with different initial conditions and b) a "compartment" model derived from a diffusion-advection model. A compartment model for the contamination of living biomass is proposed. The total absorbed dose rate in air as well as the contribution due to 137Cs from the Chernobyl accident was determined inside the forest, by in-situ gamma spectrometry.

Biomass↗

Ultrastructural observation of effect of moderate hypothermia on axonal damage in an animal model of diffuse axonal injury.

OBJECTIVE: To investigate the effect of moderate hypothermia on responses of axonal cytoskeleton to axonal injury in the acute stage of injury. METHODS: Of fifteen adult guinea pigs, twelve animals were subjected to stretch injury to the right optic nerves and divided into the normothermic group (n = 6) in which the animal's core temperature was maintained at 36.0-37.5 degrees C and the hypothermia group (n = 6) in which the core temperature was reduced to 32.0-32.5 degrees C after stretch injury. Remaining three animals sustained no injury to the right optic nerves and served as control group. Half of injured animals (n = 3) of either normothermic group or hypothermic group were killed at either 2 hours or 4 hours after injury. The ultrastructural changes of axonal cytoskeleton of the right optic nerve fibers from the animals were examined under a transmission electron microscope and analyzed by quantitative analysis with a computer image analysis system. RESULTS: At 2 hours after stretch injury, there was a significant reduction in the mean number of microtubules (P < 0.001), and a significant increase in the mean intermicrotubule spacing (P < 0.05 or P < 0.01) in axons of all sizes in normothermic animals. The mean number of neurofilaments also decreased statistically (P < 0.01) in large and medium subgroups of axons in the same experimental group at 2 hours. By 4 hours, the large subgroup of axons in normothermic animals still demonstrated a significant decline in the mean number of microtubules (P < 0.01) and an increase in the mean intermicrotubule spacing (P < 0.05), while the medium and small subgroups of axons displayed a significant increase in the mean number of neurofilaments (P < 0.05) and reduction in the mean interneurofilament spacing (P < 0.05). On the contrary, either the mean number of microtubules and the mean intermicrotubule spacing, or the mean number of neurofilaments and interneurofilament spacing in axons of all sizes in hypothermic stretch-injured animals was not significant different from the mean values of sham-operated animals. CONCLUSIONS: Posttraumatic moderate hypothermia induced immediately after axonal injury results in substantial protection of axonal cytoskeleton and ameliorates axonal damage.

Animals↗

Measles dynamics and vaccination diffusion. A model and an application.

Although numerous mathematical models focusing on measles dynamics have been proposed in the literature, efforts in this area have concentrated essentially on the mechanisms of measles propagation. If present, vaccination diffusion is treated as an exogenous factor. Here we propose a model focused on the course of measles in France in which the mechanisms of vaccination diffusion are explicitly modeled. The parameters in this model are estimated by an original method based on an expectation-maximization algorithm. This model gives indications of the way in which measles propagation and vaccination diffusion interact. It also allows discussion of the possibility of eliminating this disease in France in the near future.

Journal Article↗

Dynamic model of biomolecular diffusion through two-dimensional nanochannels.

The molecular diffusion dynamics in unconstrained cases has been studied thoroughly during the last two centuries, leading to the well-known Fick's diffusion laws and Stokes-Einstein equation. More recently, a new impulse to the study of this topic has been provided by the necessity of understanding the behavior of solute particles in the presence of environmental constraints of size comparable to the molecular dimensions. In this work, we investigate the diffusion kinetics of biomolecules, such as bovine serum albumin, interferon, and lysozyme, through microfabricated silicon membranes, having pores of nanometric size in only one dimension, in the range from few to tens of nanometers (the other dimensions are in the mum range). Experimental results show that the diffusion profiles, in some cases, deviate substantially from those predicted by Fick's laws. In light of these results, a new diffusion mathematical model is proposed, which can reasonably explain the phenomenon and, at the same time, recovers the classical diffusion laws in the unconstrained case. Moreover, a physical description, derived from van der Waals equation of state, is presented, and it is compared with the results obtained by the mathematical model.

Animals↗

Nephrotic mice (ICGN strain): a model of diffuse mesangial sclerosis in infantile nephrotic syndrome.

The ICGN mouse strain is a unique model for naturally occurring nephrotic syndrome. In the present study, we examined the onset of the clinical manifestation of nephrotic syndrome and determined the sequence of intraglomerular events associated with progression of nephrotic conditions. Laboratory analysis revealed that homozygous (nep/nep) mice showed urinary albumin excretion during the suckling stage, rapidly leading to hypoalbuminemia accompanied by body growth failure. Renal pathology demonstrated that an initial intraglomerular event in the nephrotic mice was observed 3 weeks after birth in the form of mesangiolytic lesions, characterized by microaneurysm, platelet accumulation and capillary ballooning. In 6-week-old homozygous mice, mesangial sclerosis, characterized by mesangial expansion and glomerular hypertrophy, was observed in a diffuse fashion. Immunohistochemistry revealed that the glomerular cells in the 3-week-old homozygous suckling mice were positive for alpha-smooth muscle actin, suggesting a phenotypic change in the mesangial cells. Mesangial expansion, confirmed by the over-deposition of type I collagen, was evident until 6 weeks after weaning, while it was of interest that fibrogenic cytokines such as platelet-derived growth factor and transforming growth factor-beta were not detected in the sclerotic glomeruli throughout the observations. Furthermore, the nephrotic features were shown to be resistant to steroid therapy with a high dose of prednisolone. Our results suggest that diffuse mesangial sclerosis, a hereditary glomerular disease, may be genetically generated through early myofibroblast formation, which occurs and develops probably independently of up-regulation of these fibrogenic cytokines. In conclusion, the homozygous nephrotic mouse (ICGN strain) is believed to be a good model for investigating not only nephrotic conditions but also cellular and molecular pathogenesis of diffuse mesangial sclerosis in steroid-resistant infantile nephrotic syndrome.

Albuminuria↗

Modeling hydrophobic recovery of electrically discharged polydimethylsiloxane elastomers.

Theoretical models are proposed to account for the hydrophobic recovery kinetics of electrically discharged silicone elastomers, in which the effects of both the diffusion and adsorption of in situ produced low molecular weight (LMW) species are considered. A homogeneous solid diffusion model or a pore diffusion model well represents the surface restructuring of silicone elastomers exposed to partial electrical discharges. The computed diffusivity of the in situ produced LMW species through an inorganic, silica-like layer to the outermost part of the oxidized polymer is much smaller than that calculated from the absorption experiment of a silicone elastomer. At severe discharge intensity, no significant difference in the hydrophobic recovery is observed for extracted samples and those doped with free dimethylsiloxane fluid, whereas fluorinated siloxane fluid containing samples recover their hydrophobicity faster than the others. Modeling studies indicate that the faster recovery of the later samples may be due to the faster diffusion of the species produced from the fragmentation of the fluorinated siloxane fluid preexisting in the polymer during electrical discharge.

Journal Article↗