Numerical solutions of the Lamm equation. II. Equilibrium sedimentation

The Lamm equation has been solved numerically for conditions corresponding to equilibrium runs for a nonlinear concentration dependence of the form s/s₀ = (1 + kc)^?1. It is shown that the approach to equilibrium is very close to being exponential (in time) as in the case k = 0. We also compare results for the nonlinear case given above with results obtained for linear c-dependence of the form s/s₀ = 1 – kc. For relatively high speeds the time required to attain equilibrium may be greatly underestimated by use of the latter approximation. Finally, we present analytic approximations for the concentration distribution at equilibrium and as a function of time.     

Analysis of copper corrosion in compacted bentonite clay as a function of clay density and growth conditions for sulfate‐reducing bacteria

Aims: To investigate the relationships between sulfate‐reducing bacteria (SRB), growth conditions, bentonite densities and copper sulfide generation under circumstances relevant to underground, high‐level radioactive waste repositories. Methods and Results: Experiments took place 450 m underground, connected under in situ pressure to groundwater containing SRB. The microbial reduction of sulfate to sulfide and subsequent corrosion of copper test plates buried in compacted bentonite were analysed using radioactive sulfur (³⁵SO₄^2?) as tracer. Mass distribution of copper sulfide on the plates indicated a diffusive process. The relationship between average diffusion coefficients (D_s) and tested density (ρ) was linear. D_s (m² s^?1) = ?0·004 × ρ (kg m^?3) + 8·2, decreasing by 0·2 D_s units per 50 kg m^?3 increase in density, from 1·2 × 10^?11 m² s^?1 at 1750 kg m^?3 to 0·2 × 10^?11 m² s^?1 at 2000 kg m^?3. Conclusions: It is possible that sulfide corrosion of waste canisters in future radioactive waste repositories depends mainly on sulfide concentration at the boundary between groundwater and the buffer, which in turn depends on SRB growth conditions (e.g., sulfate accessibility, carbon availability and electron donors) and geochemical parameters (e.g., presence of ferrous iron, which immobilizes sulfide). Maintaining high bentonite density is also important in mitigating canister corrosion. Significance and Impact of the Study: The sulfide diffusion coefficients can be used in safety calculations regarding waste canister corrosion. The work supports findings that microbial activity in compacted bentonite will be restricted. The study emphasizes the importance of growth conditions for sulfate reduction at the groundwater boundary of the bentonite buffer and linked sulfide production.     

Stomatal behaviour in a beech canopy: an analysis of Bowen ratio measurements compared with porometer data

On the basis of measurements or stand transpiration and microclimate, the bulk stomatal or bulk leaf conductance (g_L) of a beech forest in northern Germany was calculated for periods in which leaves were fully expanded and the canopy was dry. This conductance depends strongly on light and humidity conditions above the forest. During periods with photosynthetic photon flux densities Q > 1200 μmol m^?2s^?1, g_L was reduced from 1500mmol m^?2s^?1 at a vapour pressure deficit D= 0.5kPa to 500 mmol m^?2s^?1 at D= 2kPa. Light saturation of g_L was not reached until Q= 1200 μmol m^?2s^?1 at low D, or until even higher Q at higher D. The dependence of g_L, on Q and D was described mathematically by a non-linear equation that requires two empirical parameters. Values for g_L as simulated by this equation provided a satisfactory agreement with independent porometer data collected on single leaves and scaled up to the canopy. A comparison of stomatal and aerodynamic conductances showed a strong coupling between the forest canopy and the atmosphere, indicating that transpiration of the beech forest is controlled mainly by the stomata.     

Translational and rotational diffusion of tobacco mosaic virus from polarized and depolarized light scattering

The translational and rotational dynamics of tobacco mosaic virus in sodium phosphate buffer (pH =7.5) solutions has been investigated by polarized and depolarized light scattering Rayleigh linewidth studies. For concentrations ranging from 1.75 × 10^?4 g ml^?1 to 0.25 × 10^?4 g ml^?1 the translational diffusion coefficient (D_T) has been found to be slightly concentration dependent and extrapolation to zero concentration gives D₀^20°C = 0.34 ± 0.01 × 10^?7 cm²S^?1. A full analysis of the polarized spectra obtained at high and low scattering angles and the depolarized spectra at near zero scattering angles has enabled these techniques to be compared and the rotational diffusion constant D_R to be determined. At a solution concentration of 1.75 × 10^?4 g ml^?1 a mean value is found to be D_R^20°C = 350 ± 30s^?1. These values of D_T and D_R are in approximate agreement with calculations based on models of the tobacco mosaic virus molecule as a cylindrical rod.     

Dynamic light scattering from thin rigid rods: Anisotropy of translational diffusion of tobacco mosaic virus

An Exact theoretical expression for the apparent diffusion coefficient D_app(K) of a thin rigid rod with arbitrary anisotropy of its translational diffusion diffusion coefficient is derived from the first cumulant of its dynamic structure factor. D_app(K) is predicted to reach a limiting plateau value at extermely large values of KL, where K is the scattering vector and L the rod length. Howerver, that limiting plateau value is approached only very slowly along a quasi-plateau with a very gradual slope. Dynamic light-scattering studies have been performed on tobacco mosaic virus from K² = (0.4–20) × 10¹⁰ cm^?2 using 632-8-nm laser radiation. The present data yield D₀ = (4.19 ± 0.10) × 10^?8 cm²/s (corrected to 20,w conditions) and, with literature data to establish L = 2980 Å and the rotational diffusion coefficient D_R = 318s^?1, yield also Δ ≡ D_∥ ? D_⊥ = (1.79 ± 0.38) × 10^?8 cm²/s. The experimental data closely follow the curve of D_app(K) vs K² calcuated for these parameters. The present value of D₀ substantially exceeds all previous dynamic light-scattering values, but is in good aggreement with previous sedimentation data, which were confirmed for the presemt sample. The anisotropy ratio Δ/D₀ = 0.43 ± 0.09 is in accord with theoretical predictions based on the modified Kirkwood algorithm, despite the fact the D₀ lies significantly below its corresponding theoretical value. The present data largely predlude the possibility that both D₀ and Δ/D₀ could simultaneously match their theoretical predictions. We present a detailed comparison of the experimental data with the calculations of Tirado and Garcia de la Torre based on the modified Kirkwood algorithm and with the Broersma formulas.     

Evaluation of diffusion coefficients by means of an approximate steady-state condition in sedimentation velocity distributions

This investigation examined the feasibility of manipulating the rotor speed in sedimentation velocity experiments to spontaneously generate an approximate steady-state condition where the extent of diffusional spreading is matched exactly by the boundary sharpening arising from negative s–c dependence. Simulated sedimentation velocity distributions based on the sedimentation characteristics for a purified mucin preparation were used to illustrate a simple procedure for determining the diffusion coefficient from such steady-state distributions in situations where the concentration dependence of the sedimentation coefficient, s = s⁰/(1 + Kc), was quantified in terms of the limiting sedimentation coefficient as c → 0 (s⁰) and the concentration coefficient (K). Those simulations established that spontaneous generation of the approximate steady state could well be a feature of sedimentation velocity distributions for many unstructured polymer systems because the requirement that Kc_oω²s⁰/D be between 46 and 183 cm⁻² is not unduly restrictive. Although spontaneous generation of the approximate steady state is also a theoretical prediction for structured macromolecular solutes exhibiting linear concentration dependence of the sedimentation coefficient, s = s⁰(1 − kc), the required value of k is far too large for any practical advantage to be taken of this approach with globular proteins.     

Thermal denaturation of Na- and Li-DNA in salt-free solutions

Thermal denaturation of Na- and Li-DNA from chicken erythrocytes was studied by means of scanning microcalorimetry in salt-free solutions at DNA concentrations (C_p) from 4.5 · 10^?2 to 1 · 10^?3 moles of nucleotides/liter (M). Linear dependencies of DNA melting temperature (T_m) vs lgC_p were obtained: ((1)) ((2)) for Na- and Li-DNA, respectively. Microcalorimetry data were compared with the results of spectrophotometric studies at 260 nm of DNA thermal denaturation in Me-DNA + MeCl solutions at C_p ? (6–8) · 10^?5 M and C_s = 0–40 mM (Me is Na or Li, C_s is salt concentration). It was found that Eqs. (1) and (2) are valid in DNA salt-free solutions over the C_p range 6 · 10^?5?4.5 · 10^?2M. Protonation of DNA bases due to the absorption of CO₂ from air in Na-DNA + NaCl solutions affects DNA melting parameters at C_s < 4 mM. Linear dependence of T_m on lga₊ is found in Na-DNA + NaCl at C_s > 0.4 mMin the absence of contact of solutions with CO₂ from air (a₊ is cation activity). A dependence of [dT_m/dlga₊] on Li⁺ activity was observed in Li-DNA + LiCl solutions at C_s < 10 mM: [dT_m/dlga₊] increases from 17°–18° at C_s > 10 mM to 28°–30° at C_s ? 0.2–0.4 mM. Spectrophotometric measurements at 282 nm show that this effect was caused by protonation of bases in fragments of denatured DNA in neutral solutions. The Poisson–Boltzmann (PB) equation was solved for salt-free DNA at the melting point. The linear dependence of T_m vs lgC_p was interpreted in terms of Manning's condensation theory. PB and Manning's theories fit the experimental data if charge density parameter (ξ) of denatured DNA is in the range 1.8–2.1 (assuming for native DNA ξ = 4.2). Specificity of Li ions in interactions with DNA is discussed. © 1994 John Wiley & Sons, Inc.     

Flow injection chemiluminescence study of acridinium ester stability and kinetics of decomposition

Decomposition of phenyl acridinium-9-carboxylate is monitored using electrogenerated chemiluminescence in a flow system. The formation of the pseudobase from the acridinium ester [AE] is described by rate = k′₁[AE] + k″₁[AE][OH^?]^0.5, where k′₁ = 0.020 ± 0.006 s^?1 and k″₁ = 2.1 ± 0.8 (L/mol)^?0.5 s^?1. Irreversible decomposition of the pseudobase is described by rate = k′₂[AE][OH^?], where k′₂ = 20.1 ± 3.8 (L/mol s). These kinetic equations, plus measurement of variation in emission intensity for constant acridinium ester concentration, are used to predict the resulting emission intensity v. pH behaviour given various contact times (in the 0.25 to 25 s range) for the acridinium ester to be in an alkaline solution prior to initiation of the chemiluminescence reaction.     

The concentration dependence of sedimentation for polysaccharides

The relationship between the sedimentation coefficient s₀ and its concentration coefficient k_s obtained in experiments on velocity sedimentation for polysaccharides is discussed. The values of s₀, k_s and an independently determined molecular weight reported by different authors for different polysaccharides are considered. It was established that the scaling relation. k_s∼ s₀ ^v unambiguously relates to the scaling relation s₀∼ M^b. The values of the sedimentation parameter β _s introduced on the basis of Svedberg's equation for s₀ and on the basis of the expression k_s = B 〈h²〉^3/2M^–1 are discussed and the generalized Wales-van Holde-Rowe equation M_KS = (N_A/β _S)^3/2[s]^3/2 k_S ^1/2 is used for evaluation of the molecular weights of polysaccharides. The adequacy of this evaluation is illustrated by taking as an example the determination of the unit length weight of an extra-rigid polysaccharide chain and of the equilibrium rigidity of rigid-chain, semi-rigid-chain and flexible-chain polysaccharides. The pair of experimental values s₀ and k_S obtained in a single series of experiments give the same information as may be obtained from the other pairs of hydrodynamic values such as [η] and s₀ or [η] and D₀, where [η] is the intrinsic viscosity and D₀ is the translational diffusion coefficient. Accepted: 11 December 1996     

Inducibility of Rat Liver Drug-Metabolizing Enzymes as an Index of Food-Screeing for Safety Assessment

D-Lactate dehydrogenase (D-LDH) from Pediococcus pentosaceus ATCC 25745 was found to produce D-3-phenyllactic acid from phenylpyruvate. The optimum pH and temperature for enzyme activity were pH 5.5 and 45 °C. The Michaelis-Menten constant (K _m), turnover number (k _cat), and catalytic efficiency (k _cat?K _m) values for the substrate phenylpyruvate were estimated to be 1.73 mmol/L, 173 s^?1, and 100 (mmol/L)^?1 s^?1 respectively.     

Dynamic light scattering from collagen solutions. I. Translational diffusion coefficient and aggregation effects

Solutions of native collagen extracted from rat tail tendons in neutral salt solution have been studied by dynamic light scattering. The spectra obtained are consistent with the presence in solution of both single rod-shaped collagen molecules and aggregates of molecules. No contribution to the spectrum has been detected at any scattering angle from rotational diffusion of single molecules, although a measurable broadening effect is expected at high angles. The translational diffusion coefficient D of single molecules, calculated from the broader spectral component, shows an anomalous dependence on collagen concentration with a maximum value of D_20,w = 8.6 ± 0.2 × 10^?12 m²/sec near the concentration 0.04% by weight. Above 0.05% D falls linearly with increasing concentration and takes the value D _20,w = 8.1 ± 0.2 × 10^?12 m²/sec at 0.064% collagen.     

Dynamics of molecular organization in agarose sulphate

Nongelling solutions of structurally regular chain segments of agarose sulphate show disorder–order and order–disorder transitions (as monitored by the temperature dependence of optical rotation) that are closely similar to the conformational changes that accompany the sol–gel and gel–sol transitions of the unsegmented polymer. The transition midpoint temperature (T_m) for formation of the ordered structure on cooling is ～25 K lower than T_m for melting. Salt-induced conformational ordering, monitored by polarimetric stopped-flow, occurs on a millisecond time scale, and follows the dynamics expected for the process 2 coil ? helix. The equilibrium constant for helix growth (s) was calculated as a function of temperature from the calorimetric enthalpy change for helix formation (ΔH_cal = ?3.0 ± 0.3 kJ per mole of disaccharide pairs in the ordered state), measured by differential scanning calorimetry. The temperature dependence of the nucleation rate constant (k_nuc), calculated from the observed second-order rate constant (k_obs) by the relationship k_obs = k_nuc(1 ? 1/s) gave the following activation parameters for nucleation of the ordered structure of agarose sulphate (1 mg mL^?1; 0.5M Me₄NCl or KCl): ΔH* = 112 ± 5 kJ mol^?1; ΔS* = 262 ± 20 J mol^?1 K^?1; ΔG*₂₉₈ = 34 ± 6 kJ mol^?1; (k_nuc)₂₉₈ = (7.5 ± 0.5) × 10⁶ dm³ mol^?1 s^?1. The endpoint of the fast relaxation process corresponds to the metastable optical rotation values observed on cooling from the fully disordered form. Subsequent slow relaxation to the true equilibrium values (i.e., coincident with those observed on heating from the fully ordered state) was monitored by conventional optical rotation measurements over several weeks and follows second-order kinetics, with rate constants of (2.25 ± 0.07) × 10^?4 and (3.10 ± 0.10) × 10^?4 dm³ mol^?1 s^?1 at 293.7 and 296.2 K, respectively. This relaxation is attributed to the sequential aggregation processes helix + helix → dimer, helix + dimer → trimer, etc., with depletion of isolated helix driving the much faster coil–helix equilibrium to completion. Light-scattering measurements above and below the temperature range of the conformational transitions indicate an average aggregate size of 2–3 helices.     

Static and dynamic light scattering from dilute insulin solutions

Static and dynamic light-scattering measurements are reported on zinc-insulin at room temperature (21 ± l°C) and pH = 6.88 in 0.1M NaCl aqueous solution. The experiments were performed at very low concentration, in the range 0.12 × 10^?4 to 0.90 × 10^?4 g cm^?3. Within experimental error, we find no evidence for a critical micellar concentration in this system. The aggregation phenomenon starts immediately after preparation of the solutions, and takes several days to come to stable equilibrium. The concentration dependence of the diffusion coefficients, D _z, = D_o (1 — k_DC), is negative, and k_D was observed to decrease as a function of time, while the aggregate size was found to increase. The equivalent concentration coefficient, ?2BM _W, obtained from static light scattering, showed a similar behavior, and, within experimental error, was found to be numerically equal to k_D. From the relation found between the diffusion coefficient at infinite dilution and the molecular weight of the aggregates, log D₀ = ?0.240 log M _w ? 5.077, we deduce that the insulin aggregates are compact structures with a characteristic radius of 0.71 Å/(dalton)^1/3, surrounded by a hydration layer of a thickness of 8.0 Å. The equilibrium aggregation number is approximately 10.     

Biomass and leaf‐level gas exchange characteristics of three African savanna C4 grass species under optimum growth conditions

C₄ savanna grass species, Digitaria eriantha, Eragrostis lehmanniana and Panicum repens, were grown under optimum growth conditions with the aim of characterizing their above‐ and below‐ground biomass allocation and the response of their gas exchange to changes in light intensity, CO₂ concentration and leaf‐to‐air vapour pressure deficit gradient (D_l). Digitaria eriantha showed the largest above‐ and below‐ground biomass, high efficiency in carbon gain under light‐limiting conditions, high water use efficiency (WUE) and strong stomatal sensitivity to D_l (P = 0.002; r² = 0.5). Panicum repens had a high aboveground biomass and attained high light saturated photosynthetic rates (A_sat, 47 μmol m^?2 s^?1), stomatal conductance, (g_sat, 0.25 mol m^?2 s^?1) at relatively high WUE. Eragrostis lehmanniana had almost half the biomass of other species, and had similar A_sat and g_sat but were attained at lower WUE than the other species. This species also showed the weakest stomatal response to D_l (P = 0.19, r² = 0. 1). The potential ecological significance of the contrasting patterns of biomass allocation and variations in gas exchange parameters among the species are discussed.     

Li+ counterion self-diffusion in ordered DNA

The anisotropic self-diffusion coefficient of ⁷Li⁺ (I = 3/2) counterions has been studied in hydrated, macroscopically oriented Li-(B)DNA fibers at relatively high water contents, corresponding to approximate DNA-DNA helix axis distances of 22–35 Å, using the pulsed field gradient hmr spin-echo method. Self-diffusion coefficients parallel (D_∥) and perpendicular (D_?) to the DNA helix axis increase with increasing salt content and with increasing DNA-DNA helix axis distance. The observed anisotropy D_∥/D_? decreases from 1.6 to 1.2 with the DNA-DNA separation increasing from 22 to 35 Å in the salt-free sample. This result can be understood by the obstruction effect caused by the DNA molecules themselves. The values of the Li⁺ self-diffusion coefficients in the most water-rich system with no added salt (corresponding to an approximate distance of 35 Å between the DNA helix axes) were D_∥ ～ 1.15 × 10^?10 m² s^?1 and D_? ～ 0.98 × 10^?10 m² s^?1, compared to 9.14 × 10^?10 m² s^?1 for the diffusion of Li⁺ in an aqueous solution of LiCl (～ 2.1M). The possible occurrence of restriction effects in the DNA fibers have also been studied by determining the self-diffusion coefficient at different effective diffusion times. The self-diffusion coefficient of Li⁺ in the sample with the largest DNA-DNA helix axis distance seems to be independent of the effective diffusion time, which indicates that the lithium ions are not trapped within impermeable barriers. The possibility of diffusion through permeable barriers has also been investigated, and is discussed. © 1994 John Wiley & Sons, Inc.     

An attempt to establish a synthetic model of photosynthesis-transpiration based on stomatal behavior for maize and soybean plants grown in field

A synthetic model of photosynthesis-transpiration was established based on a comprehensive consideration of models of CO₂ and H₂O fluxes controlled by stomata of plant leaves.The synthetic model was developed by introducing the internal conductance to CO₂ assimilation, g_ic, and the general equation of stomatal conductance model to H₂O diffusion, g_sw = g₀+a₁A_mf(D_s)/(C_s-Γ), into models of CO₂ and H₂O diffusion through the plant leaves stomata. In the above expression, g₀ and a₁ are coefficients, C_s ambient CO₂ concentration at leaf surface, Γ CO₂ compensation point, and f(D_s) the general function describing the response of stomatal conductance to humidity. Using the data observed in maize (Zea mays L.) and soybean (Glycine max Merr.) plants grown in the field, the parameters in the model were identified, and the applicability of the model was examined. The verification indicated that the developed model could be used to estimate net assimilation rate, transpiration rate, and water use efficiency with a high enough level of precision. The examination also showed that when f(D_s) = h_s or f(D_s) = (1+D_s/D₀)⁻¹ was employed, the estimation precision of the synthetic model was highest. In the study, the parameter g_ic was estimated by means of a linear function of Q_P because it was shown to be mostly correlated with photosynthetic photon flux, Q_P, among various environmental factors.     

Transient electric birefringence of T-even bacteriophages. I. T4B in the absence of tryptophan and fiberless T4 particles

Measurements of the electric birefringence of suspensions of T4B in the absence of tryptophan and of fiberless T4 particles show that both kinds of particles are hydrodynamically equivalent. Their rotational diffusion coefficients corrected to 25°C and water viscosity (D_25,w) are 280 ± 9 sec^?1 and 295 ± 10 sec^?1, respectively. These corrected rotational diffusion coefficients are almost independent of buffer concentration and temperature. The sedimentation coefficient (s_20,w) of T4 B is equal to 1023 ± 12 S, a value which is likewise independent of buffer concentration. By analysis of the field strength dependence of the steady-state birefringence and by reversing pulse experiments it could be shown that the orientation in an electric field is largely due to a permanent dipole moment. This dipole moment is somewhat dependent on buffer concentration and amounts to about 24,000 debye for T4B and 95,000 debye for fiberless T4. An approximate calculation shows that the difference in dipole moment may be ascribed to positive charges on the fiber tip (at least ten per fiber), to negative charges along the fiber or (and) positive charges on the fiberless particle at those places where the fibers are attached in normal particles.     

Standard metabolism and growth dynamics of laboratory‐reared larvae of Sardina pilchardus

This study provides the first measurements of the standard respiration rate (R_S) and growth dynamics of European sardine Sardina pilchardus larvae reared in the laboratory. At 15° C, the relationship between R_S (µl O₂ individual^?1 h^?1) and larval dry mass (M_D, µg) was equal to: R_S = 0·0057(±0·0007, ± s.e.)·M_D^{0·8835(±0·0268)}, (8–11% M_D day^?1). Interindividual differences in R_S were not related to interindividual differences in growth rate or somatic (Fulton's condition factor) or biochemical‐based condition (RNA:DNA).     

Cryopreservation of Atlantic salmon Salmo salar sperm: effects on sperm physiology

The objective of this study was to determine the effect of freezing on the function in Atlantic salmon Salmo salar spermatozoa. The semen was frozen in Cortland's medium + 1.3M dimethyl sulphoxide + 0.3M glucose + 2% bovine serum albumin (final concentration) in a ratio of 1:3 (semen:cryoprotectant) as the treatment (T) and fresh semen as the control (F). Straws of 0·5 ml of sperm suspension were frozen in 4 cm of N₂L. They were thawed in a thermoregulated bath (40° C). After thawing, the percentage of spermatozoa with fragmented DNA [transferase dUTP (deoxyuridine triphosphate) nick‐end labelling (TUNEL)], plasma membrane integrity (SYBR‐14/PI) and mitochondrial membrane potential (ΔΨMMit, JC‐1) were evaluated by flow cytometry and motility was evaluated by optical microscope under stroboscopic light. The fertilization rates of the control and treatment semen were tested at a sperm density of 1·5 × 10⁷ spermatozoa oocyte^?1, by observation of the first cleavages after 16 h incubation at 10° C. In the cryopreserved semen (T), the mean ± s.d . DNA fragmentation was 4·8 ± 2·5%; plasma membrane integrity 75·2 ± 6·3%; mitochondrial membrane potential 51·7 ± 3·6%; motility 58·5 ± 5·3%; curved line velocity (V_CL) 61·2 ± 17·4 µm s^?1; average‐path velocity (V_AP) 50·1 ± 17·3 µm s^?1; straight‐line velocity (V_SL) 59·1 ± 18·4 µm s^?1; fertilization rate 81·6 ± 1·9%. There were significant differences in the plasma membrane integrity, mitochondrial membrane potential, motility, fertilization rate, V_CL, V_AP and V_SL compared with the controls (P < 0·05). Also the mitochondrial membrane potential correlated with motility, fertilization rate, V_CL and V_SL (r = 0·75; r = 0·59; r = 0·77 and r = 0·79, respectively; P < 0·05); and the fertilization rate correlated with V_CL and V_SL (r = 0·59 and r = 0·55, respectively).