Simulations of NMR-detected diffusion in suspensions of red cells: the "signatures" in q-space plots of various lattice arrangements

Coherence effects from pulsed field-gradient spin-echo (PGSE) nuclear magnetic resonance diffusion experiments have been observed and characterized for diffusants in many heterogeneous systems, ranging from porous materials to cell suspensions. The resulting coherence patterns appear in plots of the normalized PGSE signal intensities as a function of the spatial wave vector Q in a so-called q-space plot. The origin of these phenomena and their mathematical and physical underpinnings are now well established. We have conducted a number of studies of diffusion-coherence phenomena in suspensions of red blood cells and have made extensive use of computer simulations of molecular diffusion in virtual lattices of cells to aid in the interpretation and analysis of experimental data. In the current work we extended the canonical model used in these studies to investigate the effect that varying the packing arrangement of cells in the suspension has on the coherence patterns, as seen in q-space plots. We show that changes in the packing arrangement of cells are reflected in the q-space plots and in the results of diffusion tensor analysis and thus we speculate upon the possible clinical importance of these findings.     

Simulations of molecular diffusion in lattices of cells: insights for NMR of red blood cells

The pulsed field-gradient spin-echo (PGSE) nuclear magnetic resonance (NMR) experiment, conducted on a suspension of red blood cells (RBC) in a strong magnetic field yields a q-space plot consisting of a series of maxima and minima. This is mathematically analogous to a classical optical diffraction pattern. The method provides a noninvasive and novel means of characterizing cell suspensions that is sensitive to changes in cell shape and packing density. The positions of the features in a q-space plot characterize the rate of exchange across the membrane, cell dimensions, and packing density. A diffusion tensor, containing information regarding the diffusion anisotropy of the system, can also be derived from the PGSE NMR data. In this study, we carried out Monte Carlo simulations of diffusion in suspensions of "virtual" cells that had either biconcave disc (as in RBC) or oblate spheroid geometry. The simulations were performed in a PGSE NMR context thus enabling predictions of q-space and diffusion tensor data. The simulated data were compared with those from real PGSE NMR diffusion experiments on RBC suspensions that had a range of hematocrit values. Methods that facilitate the processing of q-space data were also developed.     

Simulations of NMR-detected diffusion in suspensions of red cells: the effects of variation in membrane permeability and observation time

Monte Carlo random-walk simulations of diffusion in virtual lattices of cells have been used to study and characterize diffusion-coherence phenomena that arise when pulsed field-gradient spin-echo (PGSE) nuclear magnetic resonance (NMR) experiments are conducted on human red blood cell (RBC; erythrocytes) suspensions. These coherence effects are manifest as diffraction-like patterns when the normalized PGSE signal intensities are plotted as a function of the spatial wave vector q in so-called q-space plots. q-Space analysis is sensitive to small changes in cell morphology, cell size, membrane transport rates, hematocrit, and packing arrangement. In the present study we used simulations to predict the effect of varying the time over which diffusion is measured (the "observation time" or "diffusion time") and the permeability of the membrane on the form of q-space plots. Thus we predict that inhibiting water exchange across the human RBC membrane, such that the value of the permeability coefficient is reduced by approximately an order of magnitude below the normal physiological value, will effectively render the membrane impermeable on the timescale of the PGSE NMR experiment; further inhibition will therefore result in negligible reduction in the measured root-mean-square displacement (r.m.s.d.) of diffusing water as a function of the observation time. The work also underscores the importance of using an appropriate experimental observation time if q-space data are to be used to estimate compartment dimensions and interbarrier spacing, and illustrates an expeditious method for determining this value.     

电穿孔下离子型药物透皮扩散的一类数学模型及其建模方法论

在分子型模型的基础上,导出了离子型药物经皮渗透过程的一类数学模型,并用计算机模拟了其特性、而且针对分子型和离子型模型中,待估参数相对于实验样本点而言过多,同时需处理大批在不同实验控制条件下的数据资料的情形,讨论了其建模方法论问题。     

Determination of the content of nonfilterable cells in erythrocyte suspensions as a function of the medium osmolality

The results of most filtration assays for deformability of erythrocytes do not distinguish whether the entire population or only its small fraction exhibits abnormal rheological properties. We developed a simple filtration method for determination of the percentage of nonfilterable cells in erythrocyte suspension using membrane filters with mean pore diameter of 3.1 microns. This method makes it possible to detect even minor abnormal subpopulations in erythrocyte suspensions. The flow rate of buffer depends on the number of free pores of a filter. The plot of the number of pores clogged by nonfilterable cells vs the total number of erythrocytes that were allowed to pass through the filter had a linear portion, with a slope representing the relative content, Z%, of nonfilterable cells in the suspension. We determined Z% for various medium osmolalities u and used the data to derive the distribution of erythrocytes in ucr (ucr is the maximum value of u at which an erythrocyte cannot pass through a pore of a given filter because of geometric limitations). The distribution of ucr in suspension of normal erythrocytes has a maximum of about 200 mOsm/kg and a half-width of about 20 mOsm/kg. The distributions of ucr are altered in normal erythrocyte suspensions at decreased pH values, in cryopreserved and ATP-depleted erythrocyte suspensions and in erythrocytes from a xerocytosis patient.     

Electroporation of red blood cell membrane and its use as a drug carrier system.

Application of external electric field to cell suspension maintained at ice temperature induces pores in the cell membrane. At this stage, a drug added to the cell suspension equilibrates across the membrane. On raising the temperature to 37 degrees C, the pores appear to be sealed as the drug is retained in the cells. This method was used for encapsulation of Co-57 labelled cynocobalamin in rabbit erythrocytes. It was seen from the in vivo biokinetic study of the drug-loaded erythrocytes that the rate of elimination of the drug was considerably reduced as compared to that of the free drug, indicating that drug delivery by electroencapsulation can give a sustained release of the drug.     

Mathematical analysis of the effects of geometric parameters and mechanical properties of erythrocytes on the filterability of nonuniform suspensions

Approaches to determination of the pattern of erythrocytes distribution with regard to the rates of their passage through pores (3 microm in diameter) of a membrane filter by processing the data on changes in the flow rates of erythrocyte suspensions with time (filtration curves) are discussed. We considered the case when the suspension consisted of two subpopulations of erythrocytes differing in a single parameter. Using a model describing the erythrocyte passage through a pore and a model describing filtration of a nonuniform suspension, we analyzed the dependences of filtration kinetics of such suspensions on the relative contents of the subpopulations and their rheological characteristics. It has been shown that the filtration rates of the major subpopulation and the minor abnormal subpopulation, and their relative contents can be determined from the analysis of filtration curves. This can be done when the filtration rate of cells from the minor subpopulation is at least one order of magnitude lower than the filtration rate of cells from the major subpopulation. Thus we can register the presence of the minor subpopulation in the range of 0.5-1%. If filtration rates are recorded at different osmolalities, their analysis makes it possible to determine the surface area, intracellular viscosity, and membrane rigidity of cells of the major subpopulation and, in certain cases, the same parameters for the cells of the minor subpopulation.     

Spectroscopic investigations on the interactions of potent platinum(II) anticancer agents with bovine serum albumin

The interactions of three platinum(II)-based anticancer complexes [(5,6-dimethyl-1,10-phenanthroline)(1S,2S-diaminocyclohexane)platinum(II)]²⁺, [(5,6-dimethyl-1,10-phenanthroline)(1R,2R-diaminocyclohexane)platinum(II)]²⁺, and [(5,6-dimethyl-1,10-phenanthroline)(1,2-diaminoethane)platinum(II)]²⁺ (56MEEN) with BSA have been examined by circular dichroism (CD), fluorescence and ¹H pulsed gradient spin–echo (PGSE) diffusion NMR spectroscopy. The number of association constants and sites differed depending upon the spectroscopic method. This may be because each technique monitors different types of interaction/s and/or as a consequence of the different concentration ranges required for each technique. The titration of BSA with the achiral 56MEEN as monitored by CD indicates a reduction in the α-helical nature of the albumin, with the association constant calculated to be ~5 × 10⁶ M⁻¹ for one site. Due to the chiral nature of the other two complexes, their association with albumin was not monitored using CD but was examined using fluorescence and PGSE diffusion NMR. Titration of BSA with any of the three metal complexes resulted in quenching of fluorescence, with the number of association sites calculated to be ~1.1, with an association constant of ~2 × 10⁵ M⁻¹. PGSE diffusion NMR provided insights into interactions occurring with the BSA in its entirety, rather than with individual regions. Metal complex binding sites were estimated (~10 equivalent) from the diffusion data, with the average association constant for all sites ~10²–10³M⁻¹. These experiments highlight the information that can be elucidated from complementary spectroscopic techniques and demonstrate the usefulness of PGSE diffusion NMR in monitoring multiple weak binding sites, which is of great importance in studying drug-biomolecule interactions.     

Biopolymer and water dynamics in microbial biofilm extracellular polymeric substance

Nuclear magnetic resonance (NMR) is a noninvasive and nondestructive tool able to access several observable quantities in biofilms such as chemical composition, diffusion, and macroscale structure and transport. Pulsed gradient spin echo (PGSE) NMR techniques were used to measure spectrally resolved biomacromolecular diffusion in biofilm biomass, extending previous research on spectrally resolved diffusion in biofilms. The dominant free water signal was nulled using an inversion recovery modification of the traditional PGSE technique in which the signal from free water is minimized in order to view the spectra of components such as the rotationally mobile carbohydrates, DNA, and proteins. Diffusion data for the major constituents obtained from each of these spectral peaks demonstrate that the biomass of the biofilm contains both a fast and slow diffusion component. The dependence of diffusion on antimicrobial and environmental challenges suggests the polymer molecular dynamics measured by NMR are a sensitive indicator of biofilm function.     

Theory of sound attenuation in the blood and erythrocyte suspensions]

Mechanisms of the ultrasound attenuation in blood and erythrocyte suspension in the long wave range are examined. It is shown that the theory proposed for dilute suspension of structured microobjects has a good coincidence with the known experimental data, both on erythrocyte suspensions and on blood. The contribution of viscous losses to attenuation are decreased with frequency and reach 44% in water suspensions of erythrocytes and 24% in the whole blood at 1 MHz.     

Purification and characterization of a pore-forming protein from the marine sponge Tethya lyncurium.

A pore-forming protein was detected and purified for the first time from a marine sponge (Tethya lyncurium). The purified protein has a polypeptide molecular mass of 21 kDa and a pI of 6.4. Tethya pore-forming protein (also called Tethya hemolysin) rapidly lysed erythrocytes from a variety of organisms. After binding to target membranes, the hemolysin resisted elution with EDTA, salt or solutions of low ionic strength and hence resembled an integral membrane protein. Erythrocytes could be protected from hemolysis induced by Tethya hemolysin by addition of 30 mM dextran 4 (4-6 kDa; equivalent hydrodynamic diffusion radius, 1.75-2.3 nm) to the extracellular medium, but not by addition of uncharged molecules of smaller size [sucrose, raffinose and poly(ethylene glycol) 1550; equivalent hydrodynamic diffusion radii, 0.46, 0.57 and 1.2 nm, respectively]. This result indicates that hemolysin is able to form stable transmembrane pores with an effective diameter of about 2-3 nm. Treatment of osmotically protected erythrocytes with Tethya hemolysin caused a rapid efflux of intracellular K+ and ATP, and a rapid influx of extracellularly added Ca2+ and sucrose. In negative-staining electron microscopy, target erythrocyte membranes exposed to purified Tethya hemolysin displayed ultrastructural lesions but without visible pores.     

A modification of the filtration method for studying the content of nonfilterable cells in erythrocyte suspension

The results of filtration assays provide estimates of the deformability of erythrocytes averaged over the entire suspension. These assays do not distinguish whether the entire population or only its small fraction exhibits abnormal rheological properties. We developed a simple method using a filtrometer to determine the percentage of non-filterable (under given conditions) cells in the erythrocyte suspension. Membrane filters made of a polyethylene terphthalate film had the mean pore diameter of 3.1 microns and the length of cylindrical micropores of 7 microns. The buffer flow rate tb depends on the number of free pores in a filter. The plot of the number of pores clogged by non-filterable cells versus the total number of erythrocytes passed through the filter had a linear portion whose slope represents the relative content Z of non-filterable cells in the suspension. We determined Z for various medium osmolarities u. These data were used to derive the distribution of erythrocytes in ucr, the value of u at which an erythrocyte cannot pass through a pore of a given filter because of geometric limitations. The distribution maximum corresponded to 190-200 mOsm/kg for erythrocytes from the normal blood. This means that normal erythrocytes have the median values of their surface area and area-to-volume ratio of 155-151 microns2 and 1.72-1.68 microns-1, respectively. The half-width of the distribution was approximately 30 mOsm/kg. This finding suggests that the normal blood contains a certain fraction of erythrocytes with a decreased area-to-volume ratio. Our results showed that the distribution is altered in various forms of anemia and in ATP-depleted erythrocyte suspensions.     

A First-Passage Time Approach to Diffusion in Liquids and Superionic Conductors

Abstract

As a new tool to investigate single-particle motion in condensed matter, a first-passage time (FPT) approach to diffusion is developed and applied to the molecular dynamics simulations of simple liquids and superionic conductor CaF₂. It is shown that a continuous diffusion model reproduces the observed FPT distribution quite well for both liquids and CaF₂, which enables us to evaluate diffusion constants with good accuracy by our method. On a length scale as small as a lattice constant, however, the effect of hopping appears in the FPT distribution of F^? ions, which can not be described by a continuous diffusion model. A simple hopping diffusion model is proposed and examined from the FPT viewpoint.     

The binding of G-protein to rod outer segment phospholipids at the nitrogen-water interface

In the visual process, one photoexcited rhodopsin (R*) catalyzes the activation of hundreds of G-proteins. It remains to be determined whether G-protein and R* find one another by membrane surface diffusion of these components (diffusion model) or by diffusion of G-protein through the aqueous phase (hopping model). A monolayer of each main rod outer segment (ROS) phospholipid interacting with a subphase containing G-protein, has been used to simulate the interaction of G-protein with the cytoplasmic surface of discal membranes. The possible diffusion of G-protein through the aqueous phase was then measured by observing its adsorption-desorption in the monolayer of each main ROS phospholipid. From examination of surface pressure and ellipsometric isotherms at the nitrogen-water interface, we have determined that once incorporated into the monolayer, the G-protein remains associated, independent of surface pressure, thus providing evidence against the hopping model.     

STRUCTURE IN NUCLEATED ERYTHROCYTES

The structure of the nucleated erythrocyte of frog and chicken has been investigated by electron microscopy and correlated with the distribution of haemoglobin and DNA-containing material determined by haem absorption and Feulgen staining in the light microscope. The nuclei of both species are found to contain haemoglobin which is continuous with the haemoglobin in the cytoplasm through holes or pores in the nuclear envelope. In addition the nucleus of the frog erythrocyte sometimes contains a single invagination which is lined by the nuclear envelope. The structure of the nuclear envelope and the pores and the organisation of the nucleus are similar to those already described for other somatic cells. Erythrocytes differ from the cells previously studied in that a continuity, via the nuclear pores, of chemical substance in the interior of the nucleus and in the cytoplasm can be directly demonstrated. This is due to the fact that the cytoplasm of erythrocytes is simple, consisting predominantly of haemoglobin, and that haemoglobin is easily recognised by its specific absorption. The static pictures obtained by electron microscopy have been supplemented by observations in phase-contrast of the changes in refraction of the cell contents due to the diffusion of the haemoglobin from the nucleus into the cytoplasm during haemolysis.     

An Analytical Model for Estimating Water Exchange Rate in White Matter Using Diffusion MRI

Substantial effort is being expended on using micro-structural modeling of the white matter, with the goal of relating diffusion weighted magnetic resonance imaging (DWMRI) to the underlying structure of the tissue, such as axonal density. However, one of the important parameters affecting diffusion is the water exchange rate between the intra- and extra-axonal space, which has not been fully investigated and is a crucial marker of brain injury such as multiple sclerosis (MS), stroke, and traumatic brain injury (TBI). To our knowledge, there is no diffusion analytical model which includes the Water eXchange Rate (WXR) without the requirement of short gradient pulse (SGP) approximation. We therefore propose a new analytical model by deriving the diffusion signal for a permeable cylinder, assuming a clinically feasible pulse gradient spin echo (PGSE) sequence. Simulations based on Markov Random Walk confirm that the exchange parameter included in our model has a linear correlation (R²>0.88) with the actual WXR. Moreover, increasing WXR causes the estimated values of diameter and volume fraction of the cylinders to increase and decrease, respectively, which is consistent with our findings from histology measurements in tissues near TBI regions. This model was also applied to the diffusion signal acquired from ex vivo brains of 14 male (10 TBI and 4 normal) rats using hybrid diffusion imaging. The estimated values of axon diameter and axonal volume fraction are in agreement with their corresponding histological measurements in normal brains, with 0.96 intra-class correlation coefficient value resulting from consistency analysis. Moreover, a significant increase (p = 0.001) in WXR and diameter and decrease in axonal volume fraction in the TBI boundary were detected in the TBI rats compared with the normal rats.     

Protein Sliding along DNA: Dynamics and Structural Characterization

Efficient search of DNA by proteins is fundamental to the control of cellular regulatory processes. It is currently believed that protein sliding, hopping, and transfer between adjacent DNA segments, during which the protein nonspecifically interacts with DNA, are central to the speed of their specific recognition. In this study, we focused on the structural and dynamic features of proteins when they scan the DNA. Using a simple computational model that represents protein-DNA interactions by electrostatic forces, we identified that the protein makes use of identical binding interfaces for both nonspecific and specific DNA interactions. Accordingly, in its one-dimensional diffusion along the DNA, the protein is bound at the major groove and performs a helical motion, which is stochastic and driven by thermal diffusion. A microscopic structural insight into sliding from our model, which is governed by electrostatic forces, corroborates previous experimental studies suggesting that the active site of some regulatory proteins continually faces the interior of the DNA groove while sliding along sugar-phosphate rails. The diffusion coefficient of spiral motion along the major groove of the DNA is not affected by salt concentration, but the efficiency of the search can be significantly enhanced by increasing salt concentration due to a larger number of hopping events. We found that the most efficient search comprises ∼ 20% sliding along the DNA and ∼ 80% hopping and three-dimensional diffusion. The presented model that captures various experimental features of facilitated diffusion has the potency to address other questions regarding the nature of DNA search, such as the sliding characteristics of oligomeric and multidomain DNA-binding proteins that are ubiquitous in the cell.     

The Behaviour of Ions in Narrow Water-Filled Pores

Today, the equilibrium behavior of ions in solution may be predicted with some confidence, essentially because rapid ionic diffusion over small distances ensures homogeneity throughout the solution. Equilibrium concepts such as ionic strength and pH apply. However, when attempting to understand the behavior of ions passing rapidly through narrow pores such as ion channels, no such equilibrium state may be assumed. The passing solution may have been in equilibrium with conditions at the mouth of the pore but will not be in equilibrium with charged molecules on the pore wall. In addition, the water in narrow pores will be partially ordered by contact with the pore walls and will not behave like bulk water.To illustrate this difference, a simple equilibrium calculation of the ion concentrations near a plastic sheet penetrated by narrow pores and containing in its surface partially ionized carboxyl groups is shown to be in good agreement with experiment. However, to predict the non-equilibrium behavior within the narrow pores is much more difficult. To illustrate the difficulty, a Monte Carlo computer model is described which attempts to predict the rapid switching of ion current observed experimentally with these narrow pores.     

The binding of noradrenaline to human erythrocytes.

When human erythrocytes are incubated in a suspension medium containing noradrenaline, they take up noradrenaline in a reaction proceeding in two phases. In a rapid first reaction noradrenaline is bound by the cells by adsorption at pH-values above 6.0; this reaction follows Freundlich's isotherms. Subsequently, noradrenaline is taken up much more slowly by transmembranous diffusion into the cells. Neither reaction can be influenced by inhibitors such as N-ethyl maleinimide, ouabain, alpha- or beta-receptor blockers.