Reduction of Dimensionality in Monte Carlo Simulation of Diffusion in Extracellular Space Surrounding Cubic Cells.

The real-time iontophoretic method has measured volume fraction and tortuosity of the interstitial component of extracellular space in many regions and under different conditions. To interpret these data computer models of the interstitial space (ISS) of the brain are constructed by representing cells as Basic Cellular Structures (BCS) surrounded by a layer of ISS and replicating this combination to make a 3D ensemble that approximates brain tissue with a specified volume fraction. Tortuosity in such models is measured by releasing molecules of zero size into the ISS and allowing them to execute random walks in the ISS of the ensemble using a Monte Carlo algorithm. The required computational resources for such simulations may be high and here we show that in many situations the 3D problem may be reduced to a quasi-1D problem with consequent reduction in resources. We take the simplest BCS in the form of cubes and use MCell software to perform the Monte Carlo simulations but the analysis described here may be extended in principle to more complex BCS and an ISS that has a defined viscosity and an extracellular matrix that interacts with diffusing molecules. In the course of this study we found that the original analytical description of the relation between volume fraction and tortuosity for an ensemble of cubes may require a small correction.

Unified model of brain tissue microstructure dynamically binds diffusion and osmosis with extracellular space geometry.

We present a universal model of brain tissue microstructure that dynamically links osmosis and diffusion with geometrical parameters of brain extracellular space (ECS). Our model robustly describes and predicts the nonlinear time dependency of tortuosity (λ=sqrt[D/D^{*}]) changes with very high precision in various media with uniform and nonuniform osmolarity distribution, as demonstrated by previously published experimental data (D = free diffusion coefficient, D^{*} = effective diffusion coefficient). To construct this model, we first developed a multiscale technique for computationally effective modeling of osmolarity in the brain tissue. Osmolarity differences across cell membranes lead to changes in the ECS dynamics. The evolution of the underlying dynamics is then captured by a level set method. Subsequently, using a homogenization technique, we derived a coarse-grained model with parameters that are explicitly related to the geometry of cells and their associated ECS. Our modeling results in very accurate analytical approximation of tortuosity based on time, space, osmolarity differences across cell membranes, and water permeability of cell membranes. Our model provides a unique platform for studying ECS dynamics not only in physiologic conditions such as sleep-wake cycles and aging but also in pathologic conditions such as stroke, seizure, and neoplasia, as well as in predictive pharmacokinetic modeling such as predicting medication biodistribution and efficacy and novel biomolecule development and testing.

Brain Extracellular Space as a Diffusion Barrier.

The extracellular space (ECS) consists of the narrow channels between brain cells together with their geometrical configuration and contents. Despite being only 20-60 nm in width, the ECS typically occupies 20% of the brain volume. Numerous experiments over the last 50 years have established that molecules moving through the ECS obey the laws of diffusion but with an effective diffusion coefficient reduced by a factor of about 2.6 compared to free diffusion. This review considers the origins of the diffusion barrier arising from the ECS and its properties. The paper presents a brief overview of software for implementing two point-source paradigms for measurements of localized diffusion properties: the real-time iontophoresis or pressure method for small ions and the integrative optical imaging method for macromolecules. Selected results are presented. This is followed by a discussion of the application of the MCell Monte Carlo simulation program to determining the importance of geometrical constraints, especially dead-space microdomains, and the possible role of interaction with the extracellular matrix. It is concluded that we can predict the impediment to diffusion of many molecules of practical importance and also use studies of the diffusion of selected molecular probes to reveal the barrier properties of the ECS.

Ouabain protects against adverse developmental programming of the kidney.

The kidney is extraordinarily sensitive to adverse fetal programming. Malnutrition, the most common form of developmental challenge, retards the formation of functional units, the nephrons. The resulting low nephron endowment increases susceptibility to renal injury and disease. Using explanted rat embryonic kidneys, we found that ouabain, the Na,K-ATPase ligand, triggers a calcium-nuclear factor-κB signal, which protects kidney development from adverse effects of malnutrition. To mimic malnutrition, kidneys were serum deprived for 24 h. This resulted in severe retardation of nephron formation and a robust increase in apoptosis. In ouabain-exposed kidneys, no adverse effects of serum deprivation were observed. Proof of principle that ouabain rescues development of embryonic kidneys exposed to malnutrition was obtained from studies on pregnant rats given a low-protein diet and treated with ouabain or vehicle throughout pregnancy. Thus, we have identified a survival signal and a feasible therapeutic tool to prevent adverse programming of kidney development.

Mechanical properties of primary cilia regulate the response to fluid flow.

The primary cilium is a ubiquitous organelle present on most mammalian cells. Malfunction of the organelle has been associated with various pathological disorders, many of which lead to cystic disorders in liver, pancreas, and kidney. Primary cilia have in kidney epithelial cells been observed to generate intracellular calcium in response to fluid flow, and disruption of proteins involved in this calcium signaling lead to autosomal dominant polycystic kidney disease, implying a direct connection between calcium signaling and cyst formation. It has also been shown that there is a significant lag between the onset of flow and initiation of the calcium signal. The present study focuses on the mechanics of cilium bending and the resulting calcium signal. Visualization of real-time cilium movements in response to different types of applied flow showed that the bending is fast compared with the initiation of calcium increase. Mathematical modeling of cilium and surrounding membrane was performed to deduce the relation between bending and membrane stress. The results showed a delay in stress buildup that was similar to the delay in calcium signal. Our results thus indicate that the delay in calcium response upon cilia bending is caused by mechanical properties of the cell membrane.

Intraparticle transport and release of dextran in silica spheres with cylindrical mesopores.

The transport of oligomeric molecules in silica spheres with cylindrical mesopores has been quantified and related to the structural features of the spherical particles and the interactions at the solid-liquid interface. An emulsion-solvent evaporation method was used to produce silica spheres having cylindrical mesopores with an average pore diameter of 6.5 nm. The transport of dextran molecules (fluorescently tagged) with molecular weights of 3000 and 10,000 g/mol was quantified using confocal laser scanning microscopy (CLSM). The intraparticle concentration profiles in the dextran-containing spheres were flat at all times, suggesting that the release is not isotropic and not limited by diffusion. The release of dextran into the solution is characterized by an initial burst, followed by long-term sustained release. The release follows a logarithmic time dependency, which was rationalized by coupling concentration-dependent effective diffusion constants with adsorption/desorption.

Release and molecular transport of cationic and anionic fluorescent molecules in mesoporous silica spheres.

We describe here a method for study of bulk release and local molecular transport within mesoporous silica spheres. We have analyzed the loading and release of charged fluorescent dyes from monodisperse mesoporous silica (MMS) spheres with an average pore size of 2.7 nm. Two different fluorescent dyes, one cationic and one anionic, have been loaded into the negatively charged porous material and both the bulk release and the local molecular transport within the MMS spheres have been quantified by confocal laser scanning microscopy. Analysis of the time-dependent release and the concentration profiles of the anionic dye within the spheres show that the spheres are homogeneous and that the release of this nonadsorbing dye follows a simple diffusion-driven process. The concentration of the cationic dye varies radially within the MMS spheres after loading; there is a significantly higher concentration of the dye close to the surface of the spheres (forming a "skin") compared to that at the core. The release of the cationic dye is controlled by diffusion after an initial period of rapid release. The transport of the cationic dye within the MMS spheres of the dye from the core to near the surface is significantly faster compared to the transport within the surface "skin". A significant fraction of the cationic dye remains permanently attached to the negatively charged walls of the MMS spheres, preferentially near the surface of the spheres. Relating bulk release to the local molecular transport within the porous materials provides an important step toward the design of new concepts in controlled drug delivery and chromatography.