Brownian dynamics simulations of probe and self-diffusion in concentrated protein and DNA solutions.

We have developed a Brownian dynamics algorithm for simulating probe and self-diffusion in concentrated solutions of DNA and protein. In these simulations, proteins are represented as spheres with radii given by their hydrodynamic radii, while DNA is modeled as a wormlike chain of hydrodynamically equivalent spherical frictional elements. The molecular interaction potentials employed by the program allow for intramolecular stretching and bending motions of the DNA chains, short-range Lennard-Jones interactions, and long-range electrostatic interactions. To test the program, we have carried out simulations of bovine serum albumin (BSA) probe diffusion and DNA self-diffusion in solutions of short-chain DNA as a function of both DNA concentration and solution ionic strength. In addition, we report on simulations of BSA self-diffusion as a function of BSA concentration and ionic strength. Based on a comparison to available experimental data, we find that our simulations accurately predict these transport properties under conditions of physiological salt concentration and predict the stronger concentration dependence observed at lower salt concentrations. These results are discussed in light of the nature of the intermolecular interactions in such systems and the approximations and limitations of the simulation algorithm.     

Analysis of diffusion and relaxation behavior of water in apple parenchymal cells

It has been demonstrated by an example of apple parenchymal cells that NMR spectroscopy can be used to analyze the relaxation and diffusion of water molecules in plant cells. With small diffusion times, three relaxation components have been distinguished, which correspond to water in a vacuole, in the cytoplasm, and in intercellular liquid. The coefficient of self-diffusion corresponding to these components have been determined. With large diffusion times, it is possible to distinguish two components. For the slowly relaxing component (which corresponds to water in a vacuole), the regime of restricted diffusion was observed. For a quickly relaxing component, an anomalous increase in the coefficient of self-diffusion with the time of diffusion took place.     

On the relative contribution of viscous flow vs. diffusional (frictional) flow to the stationary state flow of water through a "tight" membrane

The practice of calculating the diffusion contribution to the total pressure-driven flow of water through a tight membrane by using the self-diffusion coefficient for tritiated water is examined by a theoretical analysis. Equations of motion for water and membrane in pressure-driven water flow and water, membrane, and tritiated water in self-diffusion of tritiated water are adapted from Bearman and Kirkwood (1958). These equations of motion are used to develop an equation for the pressure-driven flow of water. Because of the lack of specific information about the detailed structure of most membranes, as well as considerations of the need to eliminate some of the mathematical difficulties, an "equivalent capillary" model is used to find a solution to the equation of motion. The use of the equivalent capillary model and possible ambiguities in distinctions between diffusion and hydrodynamic flow are discussed     

Combined analysis of diffusion and relaxation behavior of water in apple parenchyma cells

With apple parenchymal cells as an example, we demonstrate the expedience of combined analysis of the relaxation and diffusion of water molecules in plant cells by NMR spectroscopy. At small diffusion times, our approach discerns three relaxation components pertaining to water in the vacuole, cytoplasm, and intercellular space. The corresponding self-diffusion coefficients are determined. At long diffusion times, it is possible to distinguish two components. For the slow-relaxing component (vacuolar water) we observe the mode of restricted diffusion. For the fast-relaxing components, the diffusion coefficient anomalously increases with time.     

Diffusion of water in the endosperm tissue of wheat grains as studied by pulsed field gradient nuclear magnetic resonance.

Pulsed field gradient nuclear magnetic resonance has been used to measure water self-diffusion coefficients in the endosperm tissue of wheat grains as a function of the tissue water content. A model that confines the water molecules to a randomly oriented array of capillaries with both transverse dimension less than 100 nm has been used to fit the data and give a unique diffusion coefficient at each water content. The diffusion rates vary from 1.8 x 10(-10) m2s-1 at the lowest to 1.2 x 10(-9) m2s-1 at the highest moisture content. This variation can be explained in terms of an increase in water film thickness from approximately 0.5 to approximately 2.5 nm over the moisture range investigated (200-360 mg g-1).     

N.m.r. imaging of intact biological systems

Internal images of structured objects may be obtained with n.m.r. by labelling component parts with different magnetic field strengths and therefore recognizably different n.m.r. frequencies. A linear field gradient generates a one-dimensional projection of nuclear density and a variety of techniques are employed to manipulate this one-dimensional probe to yield internal images in two and three dimensions. In the past few years, n.m.r. imaging, sometimes also called zeugmatography or spin mapping, has been applied progressively to provide proton images of small phantoms, fruit, vegetables and small animals, and finally to in vivo imaging of the human body; it promises to provide a valuable means of interior investigation of intact biological systems generally. For medical imaging the method is non-invasive, does not use ionizing radiations, appears to be without hazard and penetrates bony cavities without attenuation. Furthermore, other n.m.r. parameters, for example, relaxation times and fluid flow, may also be mapped; there is evidence that the relaxation times from tumours are significantly longer than those from corresponding normal tissue. Effort to date has mostly been concentrated on proton n.m.r., but some work has been done with other nuclei. Three examples are shown of n.m.r. images of intact biological systems: a fruit, an animal and a human system. The discussion includes the quantitative nature of the images, tissue discrimination, the relation between the resolution in the image and image acquisition time, attenuation and phase shift of the r.f. field in the biological tissue, and magnets suitable for n.m.r. imaging. In principle, all conventional n.m.r. techniques can be combined with n.m.r. methods in order to investigate heterogeneous systems. Overhauser imaging is briefly discussed.     

Computing the self-diffusion coefficient for TIP4P water

A molecular dynamics study was made for the TIP4P model of liquid water. Thermal dependences of water density and radial distribution functions were calculated for model verification. Different methods were used to calculate the self-diffusion coefficient, and assessed for sensitivity to molecular system size and trajectory length. The Green-Kubo formula deriving the diffusion coefficient from the velocity autocorrelation function is preferable in short MD simulations with a high sampling rate, whereas the Einstein equation for diffusion is the method of choice in long simulations. The latter approach yields more stable and reliable results, especially at very short times and for a small number of molecules, if the diffusion coefficient is estimated not from the limit ratio of mean squared displacement to time, but from the slope of the time plot of mean squared displacement.     

Microscopic diffusion and hydrodynamic interactions of hemoglobin in red blood cells

The cytoplasm of red blood cells is congested with the oxygen storage protein hemoglobin occupying a quarter of the cell volume. The high protein concentration leads to a reduced mobility; the self-diffusion coefficient of hemoglobin in blood cells is six times lower than in dilute solution. This effect is generally assigned to excluded volume effects in crowded media. However, the collective or gradient diffusion coefficient of hemoglobin is only weakly dependent on concentration, suggesting the compensation of osmotic and friction forces. This would exclude hydrodynamic interactions, which are of dynamic origin and do not contribute to the osmotic pressure. Hydrodynamic coupling between protein molecules is dominant at short time- and length scales before direct interactions are fully established. Employing neutron spin-echo-spectroscopy, we study hemoglobin diffusion on a nanosecond timescale and protein displacements on the scale of a few nanometers. A time- and wave-vector dependent diffusion coefficient is found, suggesting the crossover of self- and collective diffusion. Moreover, a wave-vector dependent friction function is derived, which is a characteristic feature of hydrodynamic interactions. The wave-vector and concentration dependence of the long-time self-diffusion coefficient of hemoglobin agree qualitatively with theoretical results on hydrodynamics in hard spheres suspensions. Quantitative agreement requires us to adjust the volume fraction by including part of the hydration shell: Proteins exhibit a larger surface/volume ratio compared to standard colloids of much larger size. It is concluded that hydrodynamic and not direct interactions dominate long-range molecular transport at high concentration.     

Relationship between Recrystallization Rate of Ice Crystals in Sugar Solutions and Water Mobility in Freeze-Concentrated Matrix

To better understand the relation between recrystallization rate and water mobility in freeze-concentrated matrix, isothermal ice recrystallization rates in several sugar aqueous solutions and self-diffusion coefficients of water component in corresponding freeze-concentrated matrix were measured. The sugars used were fructose, glucose, maltose, and sucrose. The sugar concentrations and temperature were varied so that ice contents for all samples were almost equal. Neither recrystallization rates nor diffusion coefficients depended uniformly on temperature. The recrystallization rates increased with increasing the diffusion coefficients, and a direct relationship was found between recrystallization rate and diffusion coefficient. This indicated that self-diffusion coefficient of water component in freeze-concentrated matrix is a useful parameter for predicting and controlling recrystallization rate in sugar solutions relevant to frozen desserts.     

Interactions of spermidine and methylspermidine with DNA studied by nuclear magnetic resonance self-diffusion measurements.

The NMR pulsed field gradient self-diffusion method has been used to study the self-diffusion of the polyamine spermidine and the polyamine analog methylspermidine (completely N-methylated spermidine). The self-diffusion coefficient, D, was measured in solutions of calf thymus DNA prepared from nucleosome core particles (with an average length of 120 base pairs) as a function of the concentration ratio of polyamine to DNA phosphate. A study of the self-diffusion quotient, D/Do (where Do is the diffusion coefficient for free polyamine, not associated with DNA), in additions of spermidine and methyl-spermidine to solutions of NaDNA/NaCl, gave almost identical results with complete association of polyamine to DNA in the initial part of the titrations, indicating similar affinities for DNA. A large influence on the measured self-diffusion coefficients was detected for methylspermidine in NaDNA solutions with different concentrations of NaCl, which shows a considerable salt effect on the polyamine-DNA association. No notable differences in D/Do for methylspermidine were observed in competitive titrations of solutions of Li- and NaDNA, indicating that sodium and lithium ions behave similarly in their interactions with DNA. In titration experiments of methylspermidine into MgDNA solution, the results showed that the polyamine association is less effective than in the case of NaDNA, because of competition from magnesium binding to DNA. Comparisons with calculations based on the electrostatic Poisson-Boltzmann cell model were performed. It is suggested that the interaction is primarily of electrostatic nature, with no binding to specific sites on the DNA molecule.     

Self-diffusion of polymers in cartilage as studied by pulsed field gradient NMR

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) was used to investigate the self-diffusion behaviour of polymers in cartilage. Polyethylene glycol and dextran with different molecular weights and in different concentrations were used as model compounds to mimic the diffusion behaviour of metabolites of cartilage. The polymer self-diffusion depends extremely on the observation time: The short-time self-diffusion coefficients (diffusion time Delta approximately 15 ms) are subjected to a rather non-specific obstruction effect that depends mainly on the molecular weights of the applied polymers as well as on the water content of the cartilage. The observed self-diffusion coefficients decrease with increasing molecular weights of the polymers and with a decreasing water content of the cartilage. In contrast, the long-time self-diffusion coefficients of the polymers in cartilage (diffusion time Delta approximately 600 ms) reflect the structural properties of the tissue. Measurements at different water contents, different molecular weights of the polymers and varying observation times suggest that primarily the collagenous network of cartilage but also the entanglements of the polymer chains themselves are responsible for the observed restricted diffusion. Additionally, anomalous restricted diffusion was shown to occur already in concentrated polymer solutions.     

PFG-NMR measurements of the self-diffusion coefficients of water in equilibrium poly(HEMA-co-THFMA) hydrogels

The self-diffusion coefficients for water in a series of copolymers of 2-hydroxyethyl methacrylate, HEMA, and tetrahydrofurfuryl methacrylate, THFMA, swollen with water to their equilibrium states have been studied at 310 K using PFG-NMR. The self-diffusion coefficients calculated from the Stejskal-Tanner equation, D(obs), for all of the hydrated polymers were found to be dependent on the NMR storage time, as a result of spin exchange between the proton reservoirs of the water and the polymers, reaching an equilibrium plateau value at long storage times. The true values of the diffusion coefficients were calculated from the values of D(obs) in the plateau regions by applying a correction for the fraction of water protons present, obtained from the equilibrium water contents of the gels. The true self-diffusion coefficient for water in polyHEMA obtained at 310 K by this method was 5.5 x 10(-10) m(2)s-1. For the copolymers containing 20% HEMA or more a single value of the self-diffusion coefficient was found, which was somewhat larger than the corresponding values obtained for the macroscopic diffusion coefficient from sorption measurements. For polyTHFMA and copolymers containing less than 20% HEMA, the PFG-NMR stimulated echo attenuation decay curves and the log-attenuation plots were characteristic of the presence of two diffusing water species. The self-diffusion coefficients of water in the equilibrium-hydrated copolymers were found to be dependent on the copolymer composition, decreasing with increasing THFMA content.     

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.     

Nonexponential Diffusion Extinction of Spin Echo from Water Protons in Wheat Root

The method of NMR spin echo with the magnetic field pulse gradient was used for studying self-diffusion of water molecules in the radial root direction. It was shown on the basis of physiologopharmacological methods of modification of the object that the coefficients of water self-diffusion resulting from computer decomposition of nonexponential diffusion extinction of the relative echo amplitude in the root to components are related to the subcellular and supercellular organization (structure) of the root and reflect changes in water permeability of the two transport channels of plasmodesmas.     

Generalized concentration dependence of globular protein self-diffusion coefficients in aqueous solutions.

The self-diffusion coefficients of globular proteins (myoglobin, bovine serum albumin, barstar, lysozyme) in aqueous solutions at different temperatures and pH values are obtained by pulsed-gradient spin-echo NMR, and their concentration dependence is analyzed. The generalized concentration dependence of globular protein self-diffusion coefficients is empirically established, and compared to the concentration dependence of diffusion coefficients of flexible polymers and rigid Brownian particles.     

NMR-investigation of restricted self-diffusion of oil in rape seeds

The self-diffusion of oil and water in rape seeds (Brassica napus L.) was measured with the NMR pulsed field gradient technique. The self-diffusion of oil was found to be completely restricted for diffusion times > 30 ms. The experiments could be explained in terms of the model of diffusion within spherical droplets and a Gaussian mass distribution of the droplet radii. The mean droplet radius was found to be about 0.7 m; this value decreased somewhat with increasing moisture content of the seeds. The experiments could also be explained with a Gaussian number distribution of droplet radii and a fraction of immobile protons in the NMR signal of 5 ... 10%, possibly arising from lipid protons. Though the transverse nuclear magnetic relaxation decay of the oil protons is not a single exponential we observe one uniform diffusive mobility for the oil molecules. The water self-diffusion coefficient at maximum moisture content of about 40% was determined to be 4.2 · 10^-10 m² s^-1 which is typical for swollen polymer-solvent systems at such a concentration. Offprint requests to: P. W. Kuchel     

三峡库区古夫河着生藻类叶绿素a的时空分布特征及其影响因素

古夫河系长江三峡水库湖北省境内香溪河的一条支流,发源于神农架林区并最终汇入三峡水库香溪河库湾,是流域生态学研究的热点水体。本文对古夫河2010年9月至2011年8月干流及主要支流21个样点的着生藻类叶绿素a和14项环境因子进行了调查,采用多元统计方法对调查数据进行了方差分析、聚类分析、偏相关分析和逐步回归分析,研究了着生藻类叶绿素a的时空分布特征及其主要环境影响因子。结果表明：叶绿素a含量范围为0.07—145.96 mg/m2,平均值为11.63 mg/m2。不同样点的叶绿素a含量差异显著,其中古夫河干流上游低于下游,支流竹园河上游高于下游,表现为人为影响大的区域高于人为影响小的区域;不同季节着生藻类叶绿素a含量差异显著,表现出冬春季高、夏秋季低的趋势。古夫河着生藻类叶绿素a与总磷和硬度呈极显著正相关,与电导率、氨氮和总氮呈显著正相关,而与流速呈极显著负相关;水体总磷是古夫河流域着生藻类生长的第一限制因子,流速对着生藻类的生长具有显著抑制作用;古夫河着生藻类生物量空间格局可能由其生境尺度（营养盐）和流域尺度（硬度和电导率）的特征决定,而古夫河着生藻类生物量时间变化主要受水动力（流速）的影响。     

Concentration dependence of protein diffusion.

The concentration dependence of protein self-diffusion constants is described by a free volume diffusion theory which accounts for the effects of local protein concentration fluctuations.     

Macromolecular diffusion of biological polymers measured by confocal fluorescence recovery after photobleaching.

Fluorescence recovery after photobleaching with an unmodified confocal laser scanning microscope (confocal FRAP) was used to determine the diffusion properties of network forming biological macromolecules such as aggrecan. The technique was validated using fluorescein isothiocyanate (FITC)-labeled dextrans and proteins (molecular mass 4-2000 kDa) at 25 degrees C and with fluorescent microspheres (207 nm diameter) over a temperature range of 5-50 degrees C. Lateral diffusion coefficients (D) were independent of the focus position, and the degree and extent of bleach. The free diffusion coefficient (Do) of FITC-aggrecan determined by confocal FRAP was 4.25 +/- 0.6 x 10(-8) cm2 s-1, which is compatible with dynamic laser light scattering measurements. It appeared to be independent of concentration below 2.0 mg/ml, but at higher concentrations (2-20 mg/ml) the self-diffusion coefficient followed the function D = Do(e)(-Bc). The concentration at which the self-diffusion coefficient began to fall corresponded to the concentration predicted for domain overlap. Multimolecular aggregates of aggrecan ( approximately 30 monomers) had a much lower free diffusion coefficient (Do = 6.6 +/- 1.0 x 10(-9) cm2 s-1) but showed a decrease in mobility with concentration of a form similar to that of the monomer. The method provides a technique for investigating the macromolecular organization in glycan-rich networks at concentrations close to those found physiologically.