Simultaneous rapid estimation of sedimentation coefficient and molecular weight

Data obtained from the early portion of sedimentation velocity experiments may be analyzed to simultaneously estimate both s and s/D. The C versus r data obtained are analyzed using a nonlinear least squares algorithm and an approximate solution to the Lamm equation. This procedure was tested both with simulated noisy data and with experimental data obtained using ribonuclease, ovalbumin, and somatostatin.dodecylsulfate. The procedure assumes that both s and D are independent of concentration. The results suggest that optimal estimation of both s and s/D is obtained at values of (= 2D/(s.omega(2).r(a)(2))) in the range of 0.002 to 0.01 and values of tau(= 2 somega(2)t) less than 0.04. Appropriate selection of rotor speed allows the estimation of both s and s/D for nearly globular macromolecules in the range of 10(4) to 10(6) daltons with data obtained during the first 3000-5000 seconds of a sedimentation velocity experiment.     

根表面养分吸收通量和根围溶质浓度的近似解析解

该文用Nye-Tinker-Barber模型来研究植物根系表面的养分吸收通量和根围溶质浓度的近似解析解。将根围区域分为远场区域和近场区域, 在远场用相似变量, 在近场用尺度变换, 将远场解在根表面展开并与近场解进行待定函数的匹配, 从而获得对流扩散方程根表面通量和浓度的一阶近似解析解, 该解能够简化到扩散方程的解的形式。对氮、钾、硫、磷、镁、钙的养分吸收通量和氮、钾的浓度分别进行数值模拟, 比较模型的数值解、Roose的近似解析解和该文的近似解析解。结果表明: 在扩散方程中, 6种元素通量的解析解与Roose解析解相近, 但均高于数值解, 钾和磷的通量在短时间内迅速衰减; 钾和氮浓度的全局近似解析解与Roose解析解接近, 并与数值解的变化趋势一致。在对流扩散方程中, 除氮外的5种元素通量的近似解较Roose的解析解更接近于数值解, 且没有奇性。     

Approximate analytical solutions of root surface nutrient uptake flux and rhizosphere solute concentrations

该文用Nye-Tinker-Barber模型来研究植物根系表面的养分吸收通量和根围溶质浓度的近似解析解。将根围区域分为远场区域和近场区域, 在远场用相似变量, 在近场用尺度变换, 将远场解在根表面展开并与近场解进行待定函数的匹配, 从而获得对流扩散方程根表面通量和浓度的一阶近似解析解, 该解能够简化到扩散方程的解的形式。对氮、钾、硫、磷、镁、钙的养分吸收通量和氮、钾的浓度分别进行数值模拟, 比较模型的数值解、Roose的近似解析解和该文的近似解析解。结果表明: 在扩散方程中, 6种元素通量的解析解与Roose解析解相近, 但均高于数值解, 钾和磷的通量在短时间内迅速衰减; 钾和氮浓度的全局近似解析解与Roose解析解接近, 并与数值解的变化趋势一致。在对流扩散方程中, 除氮外的5种元素通量的近似解较Roose的解析解更接近于数值解, 且没有奇性。     

Two-dimensional nuclear Overhauser enhancement investigation of the solution structure and dynamics of the DNA octamer [d(GGTATACC)]2

The resonances of nearly all 70 of the non-exchangeable protons of the duplex [d(GGTATACC)]2 in aqueous solution are assigned by proton two-dimensional nuclear Overhauser enhancement (2D NOE) spectra obtained in pure absorption phase at 500 MHz. Experimental and theoretical 2D NOE spectra are compared at each mixing time (100, 175, 250 and 400 ms) using two B-DNA structures: a standard B-form and an energy-minimized form. The GG and CC ends of the octamer duplex are well represented by the regular B-DNA structure. But large discrepancies from these models are observed for the 'TATA' box. All 2D NOE data are consistent with nanosecond correlation times, as indicated by non-selective proton spin-lattice relaxation times, but small variations in the correlation time are observed, suggesting that there are some local differences in mobility within the octamer duplex structure in solution.     

Investigation of the solution structure of a DNA octamer [d(GGAATTCC)]2 using two-dimensional nuclear Overhauser enhancement spectroscopy

Proton two-dimensional nuclear Overhauser enhancement (2D NOE) spectra in the pure absorption phase were obtained at 500 MHz for [d(GGAATTCC)]2 in aqueous solution at a series of mixing times. The experimental data were analyzed by comparison with theoretical spectra calculated using the complete 70 X 70 relaxation matrix including all proton dipole-dipole interactions and spin diffusion [Keepers, J. W. & James, T. L. (1984) J. Magn. Reson. 57, 404-426]. The theoretical spectra at each mixing time were calculated using two structures: a standard B-form DNA structure and an energy-minimized structure based on the similarity of the six internal residues of the title octamer with those of the dodecamer [d(CGCGAATTCGCG)]2, for which the crystal structure has been determined. Neither the standard B-form nor the energy-minimized structure will yield theoretical 2D NOE spectra which accurately reproduce all peak intensities in the experimental spectra. However, many features of the experimental spectra can be represented by both the B-form and the energy-minimized structure. Sequence-dependent structural characteristics are manifest in the 2D NOE spectra, in particular at the purine-pyrimidine junction as noted previously in the crystal structure. On the whole, the energy-minimized structure appears to yield theoretical 2D NOE spectra which mimic many, if not all, aspects of the experimental spectra. All 2D NOE data were consistent with nanosecond correction times as implied by proton spin-lattice relaxation time measurements. But better fits of some of the 2D NOE data using small variations in an effective isotropic correlation time suggest that there may be some local variations in mobility within the octamer duplex structure in solution.     

Self diffusion of water in frog muscle.

Self diffusion of cell water has been measured at diffusion times ranging form 0.3 ms to 2.4 s for three muscle types of Rana pipiens, using various magnetic field gradient nuclear magnetic resonance methods. Intracellular diffusion coefficients and membrane permeabilities are calculated with the aid of previous theoretical results for regularly spaced permeable planar barriers. The intracellular diffusion coefficient is 1.6 x 10-5 cm2/s, in approximate agreement with other literature values for skeletal muscles. The outer membrane permeabilities are estimated at 0.01 cm/s for two of the muscle types, and much higher for the other one.     

New Moment Closures Based on A Priori Distributions with Applications to Epidemic Dynamics

Recently, research that focuses on the rigorous understanding of the relation between simulation and/or exact models on graphs and approximate counterparts has gained lots of momentum. This includes revisiting the performance of classic pairwise models with closures at the level of pairs and/or triples as well as effective-degree-type models and those based on the probability generating function formalism. In this paper, for a fully connected graph and the simple SIS (susceptible-infected-susceptible) epidemic model, a novel closure is introduced. This is done via using the equations for the moments of the distribution describing the number of infecteds at all times combined with the empirical observations that this is well described/approximated by a binomial distribution with time dependent parameters. This assumption allows us to express higher order moments in terms of lower order ones and this leads to a new closure. The significant feature of the new closure is that the difference of the exact system, given by the Kolmogorov equations, from the solution of the newly defined approximate system is of order 1/N(2). This is in contrast with the O(1/N) difference corresponding to the approximate system obtained via the classic triple closure. The fully connected nature of the graph also allows us to interpret pairwise equations in terms of the moments and thus treat closures and the two approximate models within the same framework. Finally, the applicability and limitations of the new methodology is discussed in detail.     

Analysis of the anisotropy decay of trans-parinaric acid in lipid bilayers.

An analysis is presented of the complex anisotropy behavior of trans-parinaric acid in single component DEPC lipid bilayers. It is shown that a model involving two species with distinct lifetime and motional behavior is required, and is adequate, to explain the observed data. In particular, the observed increase in the anisotropy at long times demonstrates the presence of a species with a long fluorescence lifetime that has a high anisotropy. The time dependence of the anisotropy for these two environments is treated using both a purely mathematical sum of exponentials and a constrained fit based on an approximate solution of the anisotropic diffusion problem. In this latter model the anisotropy is described in terms of the second and fourth rank order parameters, (P2) and (P4), and a single dynamical parameter, D1, the perpendicular diffusion coefficient for this uniaxial probe. The parameters of both models are accurately determined from the fits to the data when two environments coexist and an association is made between lifetime components and distinct rotational sites. The values of the parameters obtained demonstrate the "solid-like" and "fluidlike" nature of these two coexisting environments.     

An approximate solution for a transient two-phase stirred tank bioreactor with nonlinear kinetics

The derivation of an approximate solution method for models of a continuous stirred tank bioreactor where the reaction takes place in pellets suspended in a well-mixed fluid is presented. It is assumed that the reaction follows a Michaelis-Menten-type kinetics. Analytic solution of the differential equations is obtained by expanding the reaction rate expression at pellet surface concentration using Taylor series. The concept of a pellet's dead zone is incorporated; improving the predictions and avoiding negative values of the reagent concentration. The results include the concentration expressions obtained for (a) the steady state, (b) the transient case, imposing the quasi-steady-state assumption for the pellet equation, and (c) the complete solution of the approximate transient problem. The convenience of the approximate method is assessed by comparison of the predictions with the ones obtained from the numerical solution of the original problem. The differences are in general quite acceptable.     

A fast method for approximating maximum likelihoods of phylogenetic trees from nucleotide sequences

We have developed a rapid parsimony method for reconstructing ancestral nucleotide states that allows calculation of initial branch lengths that are good approximations to optimal maximum-likelihood estimates under several commonly used substitution models. Use of these approximate branch lengths (rather than fixed arbitrary values) as starting points significantly reduces the time required for iteration to a solution that maximizes the likelihood of a tree. These branch lengths are close enough to the optimal values that they can be used without further iteration to calculate approximate maximum-likelihood scores that are very close to the "exact" scores found by iteration. Several strategies are described for using these approximate scores to substantially reduce times needed for maximum-likelihood tree searches.     

Dynamic parameters of the dipole layer formed during pulsed photoemission discharging of a plane vacuum diode

The parameters of the current and dipole moment that arise during the discharging of a plane vacuum diode by a short photoemission pulse are studied analytically and numerically. Electron emission is induced by the ionizing radiation incident obliquely on the cathode. An approximate analytic model is developed that, under certain conditions, makes it possible to reduce the problem to that having a known solution for the normally incident ionizing radiation. In the case of a short pulse, scaling relationships for the parameters of the dipole layer are obtained as functions of the diode parameters (the interelectrode gap and applied voltage) and the angle of incidence of the ionizing radiation.     

Free energy of helix propagation in short polyalanine chains determined from peptide growth simulations of La3+-binding model peptides. Comparison with experimental data

Molecular dynamics (MD) is, at present, a unique tool making it possible to study, at the atomic level, conformational transitions in peptides and proteins. Nevertheless, because MD calculations are always based on a more or less approximate physical model, using a set of approximate parameters, their reliability must be tested by comparison with experimental data. Unfortunately, it is very difficult to find a peptide system in which conformational transitions can be studied both experimentally and using MD simulations so that a direct comparison of the results obtained in both ways could be made. Such a system, containing a rigid alpha-helix nucleus stabilized by La(3+) coordination to a 12-residue sequence taken from an EF-hand protein has recently been used to determine experimentally the helix propagation parameters in very short polyalanine segments (Goch et al. (2003) Biochemistry 42: 6840-6847). The same parameters were calculated here for the same peptide system using the peptide growth simulation method with, alternatively, charmm 22 and cedar potential energy functions. The calculated free energies of the helix-coil transition are about two times too large for cedar and even three times too large for charmm 22, as compared with the experimental values. We suggest that these discrepancies have their origin in the incorrect representation of unfolded peptide backbone in solution by the molecular mechanics force fields.     

Moving approximate entropy applied to surface electromyographic signals

The objective of this study was to investigate the surface electromyographic signals using moving approximate entropy from 20 healthy participants’ wrist muscles (flexor carpi ulnaris and flexor carpi radialis). The participants were required to voluntary performed wrist flexion/extension, co-contraction and isometric contraction. A moving data window of 200 values was applied to the data and a moving approximate entropy series was obtained from the analysis. The results demonstrate that there are distinct drops of the approximate entropy values at the start and end of a contraction, and high (less regularity) approximate entropy in the middle. Mean values of approximate entropy of 0.54 and 0.55 were found for the start of a contraction compared to 0.79 and 0.77 during the middle, for the flexor and extensor, respectively. At the end, there are values of 0.46 and 0.5, respectively.     

Immobilization of yeast cells on various supports for ethanol production

An immobilization technique has been developed for a packed bed fermenter which is being considered as one stage of a process for the production of fuel-grade ethanol from sugar solutions. Relatively inexpensive beech wood chips have been successfully used as the support material and relatively high cell loadings of 188 mg DW cells/g DW support have been achieved for a test system of Saccharomyces cerevisiae cultures.No washout of adsorbed cells occurs below a superficial liquid velocity of 8.9 × 10^-2 cm/s which can be increased to 9.7 × 10^-2 cm/s by including up to 1% Hercofloc solution in the reactor medium during the immobilization procedure. The immobilization procedure is practically unaffected by pH and temperature in the range 3.5 to 5.0 and 22 °C to 37 °C respectively.Typical ethanol productivity of 21.8g/l·hr has been obtained with wood-chip-adsorbed cells, which compares well with optimal values of 18 to 32g/l·hr obtained using free-suspension cultures in stirred-tank fermenters with cell recycle.     

NMR relaxation of protein and water protons in diamagnetic hemoglobin solutions

We have measured T1 and T2 of protein and water protons in hemoglobin solutions using broad-line pulse techniques; selective excitation and detection methods enabled the intrinsic protein and water relaxation rates, as well as the spin-transfer rate between them, to be obtained at 5, 10, and 20 MHz. Water and protein T1 data were also obtained at 100 and 200 MHz for hemoglobin in H2O/D2O mixtures by using commercial Fourier-transform instruments. The T1 data conform to a simple model of two well-mixed spin systems with single intrinsic relaxation times and an average spin-transfer rate, with each phase recovering from a radio-frequency excitation with a biexponential time dependence. At low frequencies, protein T1 and T2 agree reasonably with a model of dipolar relaxation of an array of fixed protons tumbling in solution, explicitly calculating methyl and methylene relaxation and using a continuum approximation for the others. Differing values in H2O and D2O are mainly ascribed to solvent viscosity. For water-proton relaxation, T1, T2, and spin transfer were measured for H2O and HDO, which enabled a separation of inter-and intramolecular contributions to relaxation. Despite such detail, few firm conclusions could be reached about hydration water. But it seems clear that few long-lived hydration sites are needed to explain T1 and T2, and the spin-transfer value mandates fewer than five sites with a lifetime longer than 10(-8) s.     

Influence of transition rates and scan rate on kinetic simulations of differential scanning calorimetry profiles of reversible and irreversible protein denaturation.

The thermodynamic parameters characterizing protein folding can be obtained directly using differential scanning calorimetry (DSC). They are meaningful only for reversible unfolding at equilibrium, which holds for small globular proteins; however, the unfolding or denaturation of most large, multidomain or multisubunit proteins is either partially or totally irreversible. The simplest kinetic model describing partially irreversible denaturation requires three states: Formula [see text] We obtain numerical solutions for N, U, and D as a function of temperature for this model and derive profiles of excess specific heat (Cp) in terms of the reduced variables v/ki and k1/k3, where v is the scan rate. The three-state model reduces to the two-state reversible or irreversible models for very large or very small values of k1/k3, respectively. The apparent transition temperature (Tapp) is always reduced by the irreversible step (U-->D). For all values of k3, Tapp is independent of v/k1 at sufficiently slow scan rates, even when denaturation is highly irreversible, but increases identically for all models at fast scan rates in which case the excess specific heat profile is determined by the rate of unfolding. Accurate values of delta H and delta S can be obtained for the reversible step only when k1 is more than 2000-50,000 times greater than k3. In principle, approximate values for the ratio k1/k3 can be obtained from plots of fraction unfolded vs fraction irreversibly denatured as a function of temperature; however, the fraction irreversibly denatured is difficult to measure accurately by DSC alone.(ABSTRACT TRUNCATED AT 250 WORDS)     

Measurement of diffusion within the cell wall in living roots of Arabidopsis thaliana

To quantify the diffusion constant of small molecules in the plant cell wall, fluorescence from carboxyfluorescein (CF) in the intact roots of Arabidopsis thaliana was recorded. Roots were immersed in a solution of the fluorescent dye and viewed through a confocal fluorescence microscope. These roots are sufficiently transparent that much of the apoplast can be imaged. The diffusion coefficient, D(cw), of CF in the cell wall was probed using two protocols: fluorescence recovery after photobleaching and fluorescence loss following perfusion with dye-free solution. Diffusion coefficients were obtained from the kinetics of the fluorescent transients and modelling apoplast geometry. Apoplastic diffusion constants varied spatially in the root. In the elongation zone and mature cortex, D(cw)=(3.2+/-1.4)x10(-11) m(2) s(-1), whereas in mature epidermis, D(cw)=(2.5+/-0.7)x10(-12) m(2) s(-1), at least an order of magnitude lower. Relative to the diffusion coefficient of CF in water, these represent reductions by approximately 1/15 and 1/195, respectively. The low value for mature epidermis is correlated with a suberin-like permeability barrier that was detected with either autofluorescence or berberine staining. This study provides a quantitative estimate of the permeability of plant cell walls to small organic acids-a class of compounds that includes auxin and other plant hormones. These measurements constrain models of solute transport, and are important for quantitative models of hormone signalling during plant growth and development.     

Protein Fibrillation Lag Times During Kinetic Inhibition

Protein aggregation is linked to more than 30 human pathologies, including Alzheimer’s and Parkinson’s diseases. Since small oligomers that form at the beginning of the fibrillation process probably are the most toxic elements, therapeutic strategies involving fibril fragmentation could be detrimental. An alternative approach, named kinetic inhibition, aims to prevent fibril formation by using small ligands that stabilize the parent protein. The factors that govern fibrillation lag times during kinetic inhibition are largely unknown, notwithstanding their importance for designing effective long-term therapies. Inhibitor-bound species are not likely to be incorporated into the core of mature fibrils, although their presence could alter the kinetics of the fibrillation process. For instance, inhibitor-bound species may act as capping elements that impair the nucleation process and/or fibril growth. Here, we address this issue by studying the effect of two natural inhibitors on the fibrillation behavior of lysozyme at neutral pH. We analyzed a set of 79 fibrillation curves obtained in lysozyme alone and a set of 37 obtained in the presence of inhibitors. We calculated the concentrations of the relevant species at the beginning of the curves using the inhibitor-binding constants measured under the same experimental conditions. We found that inhibitor-bound protein species do not affect fibrillation onset times, which are mainly determined by the concentration of unbound protein species present in equilibrium. In this system, knowledge of the fibrillation kinetics and inhibitor affinities suffices to predict the effect of kinetic inhibitors on fibrillation lag times. In addition, we developed a new methodology to better estimate fibrillation lag times from experimental curves.     

Protein Fibrillation Lag Times During Kinetic Inhibition

Protein aggregation is linked to more than 30 human pathologies, including Alzheimer’s and Parkinson’s diseases. Since small oligomers that form at the beginning of the fibrillation process probably are the most toxic elements, therapeutic strategies involving fibril fragmentation could be detrimental. An alternative approach, named kinetic inhibition, aims to prevent fibril formation by using small ligands that stabilize the parent protein. The factors that govern fibrillation lag times during kinetic inhibition are largely unknown, notwithstanding their importance for designing effective long-term therapies. Inhibitor-bound species are not likely to be incorporated into the core of mature fibrils, although their presence could alter the kinetics of the fibrillation process. For instance, inhibitor-bound species may act as capping elements that impair the nucleation process and/or fibril growth. Here, we address this issue by studying the effect of two natural inhibitors on the fibrillation behavior of lysozyme at neutral pH. We analyzed a set of 79 fibrillation curves obtained in lysozyme alone and a set of 37 obtained in the presence of inhibitors. We calculated the concentrations of the relevant species at the beginning of the curves using the inhibitor-binding constants measured under the same experimental conditions. We found that inhibitor-bound protein species do not affect fibrillation onset times, which are mainly determined by the concentration of unbound protein species present in equilibrium. In this system, knowledge of the fibrillation kinetics and inhibitor affinities suffices to predict the effect of kinetic inhibitors on fibrillation lag times. In addition, we developed a new methodology to better estimate fibrillation lag times from experimental curves.