Residual motion of hemoglobin-bound spin labels and protein dynamics: viscosity dependence of the rotational correlation times

The residual motion of spin labels bound to cysteine 93 and to lysines of methemoglobin has been studied by electron paramagnetic resonance spectroscopy. To separate the influences of the solvent and the protein environment of the label fluctuations, the correlation times, , were analyzed as a function of temperature for fixed solvent viscosities, . Results show that over a wide range of viscosity the dependence of on may be empirically described by a power law ^k . The exponent k depends strongly on the location of the label on the protein surface. If one regards the spin labels as artificial amino acid side chains, characteristic values of correlation times and amplitudes of the rotational motion at the surface can be given. For =1 cP and T=297 K the correlation time of the labels bound to lysines is found to be =9 · 10^–10 s and the rotational diffusion is nearly isotropic. The spin label bound to cysteine 93 occupies a protein pocket, its rotational motion is therefore restricted. The correlation time of the label motion within a limited motion cone of semi angle =30° ± 3° is found to be =1.3 · 10^–9 s for =1 cP and T=297 K.     

Internal motions of apo-neocarzinostatin as studied by 13C NMR methine relaxation at natural abundance

Summary Dynamics of the backbone and some side chains of apo-neocarzinostatin, a 10.7 kDa carrier protein, have been studied from ¹³C relaxation rates R1, R2 and steady-state ¹³C-{¹H} NOEs, measured at natural abundance. Relaxation data were obtained for 79 nonoverlapping C resonances and for 11 threonine C single resonances. Except for three C relaxation rates, all data were analysed from a simple two-parameter spectral density function using the model-free approach of Lipari and Szabo. The corresponding C–H fragments exhibit fast (_e < 40 ps) restricted libration motions (S²=0.73 to 0.95). Global examination of the microdynamical parameters S² and _e along the amino acid sequence gives no immediate correlation with structural elements. However, different trends for the three loops involved in the binding site are revealed. The -ribbon comprising residues 37 to 47 is spatially restricted, with relatively large _e values in its hairpin region. The other -ribbon (residues 72 to 87) and the large disordered loop ranging between residues 97–107 experience small-amplitude motions on a much faster (picosecond) time scale. The two N-terminal residues, Ala¹ and Ala², and the C-terminal residue Asn¹¹³, exhibit an additional slow motion on a subnanosecond time scale (400–500 ps). Similarly, the relaxation data for eight threonine side-chain C must be interpreted in terms of a three-parameter spectral density function. They exhibit slower motions, on the nanosecond time scale (500–3000 ps). Three threonine (Thr⁶⁵, Thr⁶⁸, Thr⁸¹) side chains do not display a slow component, but an exchange contribution to the observed transverse relaxation rate R2 could not be excluded at these sites. The microdynamical parameters (S², _e and R2_ex) or (S _infslow ^sup2 , S _inffast ^sup2 and _slow) were obtained from a straightforward solution of the equations describing the relaxation data. They were calculated assuming an overall isotropic rotational correlation time _e for the protein of 5.7 ns, determined using standard procedures from R2/R1 ratios. However, it is shown that the product (1–S²)× _e is nearly independent of _e for residues not exhibiting slow motions on the nanosecond time scale. In addition, this parameter very closely follows the heteronuclear NOEs, which therefore could be good indices for local fast motions on the picosecond time scale.     

Maxi K+ channels from the apical membranes of rabbit oviduct epithelial cells

Large conductance (approximately 210 pS), K⁺-selective channels were identified in excised, insideout patches obtained from the apical membranes of both ciliated and nonciliated epithelial cells grown as monolayers from the primary culture of rabbit oviduct. The open probability of channels showing stable gating was increased at positive membrane potentials and was sensitive to the concentration of free calcium ions at the cytosolic surface of the patch ([Ca²⁺] _i ). In these respects, the channel resembled maxi K⁺ channels found in a number of other cell types. The distributions of dwell-times in the open state were most consistently described by two exponential components. Four exponential components were fitted to the distributions of dwelltimes in the closed state. Depolarizations and [Ca²⁺] _i increases had similar effects on the distribution of open dwell-times, causing increases in the two open time constants ( _o1 and _o2) and the fraction of events accounted for by the longer component of the distribution. In contrast, calcium ions and voltage had distinct effects on the distribution of closed dwelltimes. While the three shorter closed time constants ( _c1, _c2 and _c3) were reduced by depolarizing membrane potentials, increases in [Ca²⁺] _i caused decreases in the longer time constants ( _c3 and _c4). It is concluded that oviduct large conductance Ca²⁺-activated K⁺ channels can enter at least two major open states and four closed states.A.F.J. was supported by a research fellowship from the Japan Society for the Promotion of Science and received a grant for laboratory expenses from the Ministry of Education, Science and Culture, Japan. The authors wish to thank Dr. Shigetoshi Oiki for valuable discussion of the analysis of gating kinetics and Dr. Jeman Kim (Kyoto Pharmaceutical University) for making the transmission electron micrographs.     

Effects of zwitterionic detergents on the electronic structure of the primary donor and the charge recombination kinetics of P+Q A − in native and mutant reaction centers from Rhodobacter sphaeroides

The effects of detergents on the electronic structure of the oxidized primary donor P⁺ and the time constant _AP of the P⁺Q _A ^– charge recombination at ambient temperatures have been investigated in native and mutant reaction centers (RCs) from Rhodobacter sphaeroides. It is shown that N-lauryl-N,N-dimethyl-3-ammonio-1-propane sulfonate (SB12) induces a transition to a second distinct conformation of the RC. In the case of the wild type and the mutant FY(M197), in which a hydrogen bond is introduced to the 2-acetyl group of the dimer half of P that is associated with the M-subunit of the RC, the conformational change causes a more asymmetric spin density distribution between the two bacteriochlorophyll moieties of P⁺ in favor of the L-half. For both types of RCs the time constant _AP depends on the SB12/RC ratio as does the position of the long-wavelength band of P, _max. The increase of _AP by 30 ms and the shift of _max from 866 nm to 851 nm are indicative for the conformational change. In addition, a smaller linear increase of _AP with increasing SB12/RC ratio is superimposed on the variation of _AP due to the conformational change. Similar effects of SB12 on the optical spectra as well as on _AP are also observed for the two heterodimer mutants HL(L173) and HL(M202), in which one of the bacteriochlorophylls of P is replaced by a bacteriopheophytin. There are no clear indications for a correlation of _AP with the localization of the positive charge in P⁺. Furthermore, it is concluded from the dependence of _AP on the SB12/RC ratio that the single-site mutations do not affect the standard free energy difference of the two conformations to a measurable extent.     

An empirical relationship between rotational correlation time and solvent accessible surface area

Structure–dynamics interrelationships are important in understanding protein function. We have explored the empirical relationship between rotational correlation times (_c and the solvent accessible surface areas (SASA) of 75 proteins with known structures. The theoretical correlation between SASA and _c through the equation SASA = K_rc ^(2/3) is also considered. SASA was determined from the structure, _c ^calc was determined from diffusion tensor calculations, and _c ^expt was determined from NMR backbone¹³ C or ¹⁵N relaxation rate measurements. The theoretical and experimental values of _c correlate with SASA with regression analyses values of K_r as 1696 and 1896 m²s^-(2/3), respectively, and with corresponding correlation coefficients of 0.92 and 0.70.     

Growth and reproduction of the Nile perch,Lates niloticus,an introduced predator,in the Nyanza Gulf,Lake Victoria,East Africa

Synopsis Length-frequency data suggest Nile perch, Lates niloticus, from the Nyanza Gulf grew to a total length of 9 cm by age 118 days and 23 cm by age 287 days. A modified von Bertalanffy growth curve _t = 1.35·L(1-e^–K(t-t _o)) with the parameters L = 93.1, K = 0.272 and t_o = 0.046, is suggested to describe growth up to 5 years of age and the relationship _t = 1.35·(31.96 + 7.681t) for fish aged 6 years and above. Length-weight relationships were = 0.0234·-gt^2.74 for fish between 7 and 15.9 cm total length, = 0.0151·^2.94 for fish between 16 and 45.9 cm total length, and = 0.0023·^3.44 for fish between 46 and 120 cm total length. Male Nile perch first matured between 50 and 55 cm total length when they were probably 2 years old; female Nile perch first matured between 80 and 85 cm total length when they were probably 4 years old. Small males were common, large males were rare, with the reverse holding for females. Sex change, from male to female, is a possible explanation for this size dimorphism.     

Modelling endplate currents: dependence on quantum secretion probability and decay of miniature current

Quantification of the time course and amplitude of endplate currents (EPC) was made with respect to dispersion of quanta secretion and to changes in the exponential decay of miniature endplate currents (_mepc). The relationship between RPC amplitude and _mepc follows a double-exponential curve with ₁= 0.3 ms and ₂ = 6 ms. If the amplitude of fully synchronised EPC is taken as 100%, then the loss of EPC amplitude is already 42% with physiological parameters of dispersion (the half-rise and decay constant of distribution of secretion probability = 0.5 ms, _mepc =1 ms). This loss is even more substantial if secretion is more dispersed or miniature endplate currents decay faster. Correspondence to: F. Vyskocil     

Interaction among anion,cation and glucose transport proteins in the human red cell

Summary The time course of binding of the fluorescent stilbene anion exchange inhibitor, DBDS (4,4-dibenzamido-2,2-stilbene disulfonate), to band 3 can be measured by the stopped-flow method. We have previously used the reaction time constant, _DBDS, to obtain the kinetic constants for binding and, thus, to report on the conformational state of the band 3 binding site. To validate the method, we have now shown that the ID₅₀ (0.3±0.1 m) for H₂-DIDS (4,4-diisothiocyano-2,2-dihydrostilbene disulfonate) inhibition of _DBDS is virtually the same as the ID₅₀ (0.47±0.04 m) for H₂-DIDS inhibition of red cell Cl^– flux, thus relating _DBDS directly to band 3 anion exchange. The specific glucose transport inhibitor, cytochalasin B, causes significant changes in _DBDS, which can be reversed with intracellular, but not extracellular,d-glucose. ID₅₀ for cytochalasin B modulation of _DBDS is 0.1±0.2 m in good agreement withK _D =0.06±0.005 m for cytochalasin B binding to the glucose transport protein. These experiments suggest that the glucose transport protein is either adjacent to band 3, or linked to it through a mechanism, which can transmit conformational information. Ouabain (0.1 m), the specific inhibitor of red cell Na⁺,K⁺-ATPase, increases red cell Cl^– exchange flux in red cells by a factor of about two. This interaction indicates that the Na⁺,K⁺-ATPase, like the glucose transport protein, is either in contact with, or closely linked to, band 3. These results would be consistent with a transport proteincomplex, centered on band 3, and responsible for the entire transport process, not only the provision of metabolic energy, but also the actual carriage of the cations and anions themselves.     

Conformational dynamics of the anticodon loop in yeast tRNAPhe as sensed by the fluorescence of wybutine

Conformational and dynamic properties of the anticodon loop of yeast tRNA^Phe were investigated by analyzing the time resolved fluorescence of wybutine serving as a local structural probe adjacent to the anticodon GmAA on its 3 side. The influence of Mg²⁺, important for stabilizing the tertiary structure of tRNA, and of the complementary anticodon s²UUC of E. coli tRNA ₂ ^Glu were investigated.Fluorescence lifetimes and anisotropies were measured with ps time resolution using time correlated single photon counting and a mode locked synchronously pumped and frequency doubled dye laser as excitation source. From the analysis of lifetimes () and rotational relaxation times ( _R ) we conclude that wybutine occurs in various structural states: (i) one stacked conformation where the base has no free mobility and the only rotational motion reflects the mobility of the whole tRNA molecule (=6 ns, _R =19 ns), (ii) an unstacked conformation where the base can freely rotate (=100 ps, _R = 370 ps) and (iii) an intermediary state (=2 ns, _R = 1.6 ns).Under biological conditions, i. e. in the presence of Mg²⁺ and neutral salts, wybutine is found in a stacked and immobile state which is consistent with the crystallographic picture. In the presence of the complementary codon however, as exemplified by the E. coli-tRNA ₂ ^Glu anticodon, our analysis indicates that the codon-anticodon complex exists in an equilibrium of structural states with different rotational mobility of wybutine. The conformation with wybutine freely mobile is the predominant one and suggests that this conformation of the codon-anticodon structure differs from the canonical 3–5 stack.     

Comparison of 15N- and 13C-determined parameters of mobility in melittin

Backbone and tryptophan side-chain mobilities in the 26-residue, cytolytic peptide melittin (MLT) were investigated by ¹⁵N and ¹³C NMR. Specifically, inverse-detected ¹⁵N T₁ and steady-state NOE measurements were made at 30 and 51 MHz on MLT at 22 °C enriched with ¹⁵N at six amide positions and in the Trp¹⁹ side chain. Both the disordered MLT monomer (1.2 mM peptide at pH 3.6 in neat water) and -helical MLT tetramer (4.0 mM peptide at pH 5.2 in 150 mM phosphate buffer) were examined. The relaxation data were analyzed in terms of the Lipari and Szabo model-free formalism with three parameters: _m, the correlation time for the overall rotation; S², a site-specific order parameter which is a measure of the amplitude of the internal motion; and _e, a local, effective correlation time of the internal motion. A comparison was made of motional parameters from the ¹⁵N measurements and from ¹³C measurements on MLT, the latter having been made here and previously [Kemple et al. (1997) Biochemistry, 36, 1678–1688]. _m and _e values were consistent from data on the two nuclei. In the MLT monomer, S² values for the backbone N-H and C-H vectors in the same residue were similar in value but in the tetramer the N-H order parameters were about 0.2 units larger than the C-H order parameters. The Trp side-chain N-H and C-H order parameters, and _e values were generally similar in both the monomer and tetramer. Implications of these results regarding the dynamics of MLT are examined.     

Hydraulic model of a gas-lift bioreactor with flocculating yeast

The hydraulic model of a gas lift bioreactor, during a continuous alcoholic fermentation by using a strongly flocculating yeast, is analysed. Sucrose at two different concentrations (50 and 100 g/l) was used as substrate and the dilution rate for all the experiments was 1 h^–1. The biomass concentrations were between 85 and 110 g dry weight/1. A stimulus response technique was used to obtain the Residence Time Distribution curves, a pulse of a lactose solution being used as the tracer. Mixing time was determined by means of the response to a pulse of an acid tracer. These experiments were carried out by using an on-line data-acquisition system. The bioreactor behaviour is completely homogeneous, except for high substrate and biomass concentrations. A two parameters combined model is necessary, in this case, to fit the experimental data. Mixing times are very low, in the order of 10 seconds.List of Symbols C _T1 Tracer concentration of the tank 1 (g/l) - C _T10 Reference tracer concentration (g/l) - C Normalized tracer concentration (dimensionless) - Q ₀ Feed flowrate (l/h) - Q ₁ Flow exchanged between tank 1 and 2 (l/h) - [S] Substrate concentration (g/l) - t Time (s) - t _mix Mixing time (s) - t _c Circulation time (s) - V Reactor total volume (l) - X Biomass concentration expressed as dry weigh (g d.w./l) - Fraction of the total volume occupied by the highly agitated region - Fraction of the total flow which is exchanged between reactor 1 and 2 - Mean residence time (s), = V/Q ₀ - Dimensionless time, = t/ The stay of E. Roca at the ISIM in Montpellier (France) was supported by a grant from the CICYT (project BIO92 0568) of the Spanish Government.     

Interactions between anion exchange and other membrane proteins in rabbit kidney medullary collecting duct cells

Summary In separated outer medullary collecting duct (MCD) cells, the time course of binding of the fluorescent stilbene anion exchange inhibitor, DBDS (4,4-dibenzamido-2,2-stilbene disulfonate), to the MCD cell analog of band 3, the red blood cell (rbc) anion exchange protein, can be measured by the stopped-flow method and the reaction time constant, _DBDS, can be used to report on the conformational state of the band 3 analog. In order to validate the method we have now shown that the ID_50,DBDS,MCD (0.5±0.1 m) for the H₂-DIDS (4,4-diisothiocyano-2,2-dihydrostilbene disulfonate) inhibition of _DBDS is in agreement with the ID_50,Cl ^–,_MCD (0.94±0.07 m) for H₂-DIDS inhibition of MCD cell Cl^– flux, thus relating _DBDS directly to anion exchange. The specific cardiac glycoside cation transport inhibitor, ouabain, not only modulates DBDS binding kinetics, but also increases the time constant for Cl^– exchange by a factor of two, from _Cl=0.30±0.02 sec to 0.56±0.06 sec (30mm NaHCO₃). The ID_50,DBDS,MCD for the ouabain effect on DBDS binding kinetics is 0.003±0.001 m, so that binding is about an order of magnitude tighter than that for inhibition of rbc K⁺ flux (K _I,K ⁺,_rbc=0.017 m). These experiments indicate that the Na⁺,K^–-ATPase, required to maintain cation gradients across the MCD cell membrane, is close enough to the band 3 analog that conformational information can be exchanged. Cytochalasin E (CE), which binds to the spectrin/actin complex in rbc and other cells, modulates DBDS binding kinetics with a physiological ID_50,DBDS,MCD (0.076±0.005 m); 2 m CE also more than doubles the Cl^– exchange time constant from 0.20±0.04 sec to 0.50±0.08 sec (30mm NaHCO₃). These experiments indicate that conformational information can also be exchanged between the MCD cell band 3 analog and the MCD cell cytoskeleton.     

Molecular motion of small nonelectrolyte molecules in lecithin bilayers

Summary We have used magnetic resonance spectroscopy, both ESR and¹³C spin relaxation, to measure translational and rotational mobilities and partition coefficients of small nitroxide solutes in dipalmitoyl lecithin liposomes. Above the bilayer transition temperature,T _c, the bilayer interior is quite fluid, as determined from the solutes' rapid rotational and moderately rapid translational motion; the rotational and translational viscosities within the bilayer are _R <1cP and =6–10cP, respectively. and _R are independent of molecular size for all solutes studied, but all were small compared to the size of the phospholipids. , and probably _R , are relatively independent of temperature aboveT _c, but both increase very sharply as temperature is lowered belowT _c; at 32°C, _R increases to 6cP and is greater than 1000 cP. Anisotropy of rotational motion increases gradually as temperature is lowered toT _c, and changes little belowT _c; anisotropy of translational motion was not investigated.¹³C nuclear spin relaxation measurements indicate that translational motion of nitroxide solutes is more rapid in the center of the bilayer than near the polar interface. It takes at least 100 nsec for a solute molecule to cross the bilayer/water interface. We estimate a lower limit of 2 sec/cm for the interfacial resistance to solute diffusion; this result indicates that interfacial resistance dominates permeation across the membrane. The relative solubility, or partition coefficient, is a strong function of solute structure, and decreases abruptly on cooling through the transition temperature. From the partition coefficient and its temperature dependence we calculate the free energy, enthalpy, and entropy of partition. Effects of cholesterol on partition and diffusion coefficients are compatible with the interpretation that bilayers containing cholesterol consist of two phases.     

Sodium channel opening as a precursor to inactivation

The time constant of the process producing the delay in Na inactivation development as determined by the two pulse method (_delay) was extracted and compared to that of the slowest Na activation process ₃ for the I _Na during the conditioning pulse of that same determination. _delay and two pulse inactivation _c values were computer generated using a nonlinear least squares algorithm. _h and single pulse inactivation _h values were independently generated for each determination also with the aid of the computer using the same non-linear least squares algorithm. In one determination at 2 mV, _c was 4.68 and _delay 0.494 ms while _h was 4.70 and ₃ 0.491 ms for a _c/_h of 0.996 and a _delay/₃ of 1.006. Mean _delay/₃ from five determinations in four axons, both Cs and K perfused, and spanning a potential range of-27 to 2mV was 1.068. The precursor process to inactivation is channel opening. Some fraction of channels presumably inactivate via another route where prior channel opening is not required.     

NMR exchange broadening arising from specific low affinity protein self-association: Analysis of nitrogen-15 nuclear relaxation for rat CD2 domain 1

Nuclear spin relaxation monitored by heteronuclear NMR provides a useful method to probe the overall and internal molecular motion for biological macromolecules over a variety of time scales. Nitrogen-15 NMR relaxation parameters have been recorded for the N-terminal domain of the rat T-cell antigen CD2 (CD2d1) in a dilution series from 1.20 mM to 40 M (pH 6.0, 25 °C). The data have been analysed within the framework of the model- free formalism of Lipari and Szabo to understand the molecular origin of severely enhanced transverse relaxation rates found for certain residues. These data revealed a strong dependence of the derived molecular correlation time _c upon the CD2d1 protein concentration. Moreover, a number of amide NH resonances exhibited exchange broadening and chemical shifts both strongly dependent on protein concentration. These amide groups cluster on the major -sheet surface of CD2d1 that coincides with a major lattice contact in the X-ray structure of the intact ectodomain of rat CD2. The complete set of relaxation data fit well to an equilibrium monomer–dimer exchange model, yielding estimates of exchange rate constants (k_ON=5000 M^-1 s^-1; k_OFF=7 s^-1) and a dissociation constant (K_D 3–6 mM) that is consistent with the difficulty in detecting the weak interactions for this molecule by alternative biophysical methods. The self-association of CD2d1 is essentially invariant to changes in buffer composition and ionic strength and the associated relaxation phenomena cannot be explained as a result of neglecting anisotropic rotational diffusion in the analysis. These observations highlight the necessity to consider low affinity protein self-association interactions as a source of residue specific exchange phenomena in NMR spectra of macromolecular biomolecules, before the assignment of more elaborate intramolecular conformational mechanisms.     

Application of the Criterion of Biological Time (τ n /τ0) to the Studies of Embryogenesis in Birds

It was shown on the example of chick embryo that the number ₀ ( _n /₀) can be recommended as a measure of biological time and, for this purpose, the duration of the minimal mitotic cycle during synchronous cleavage divisions should be determined (in minutes) in various avian species. Based on the preliminary data, one can propose the comparability and similarity of the temporal programs of gastrulation and somitogenesis in the chick embryo and embryos of some fish and amphibians.     

Holling's “hungry mantid” model for the invertebrate functional response considered as a Markov process. Part I: The full model and some of its limits

In this paper we give an analytical reformulation of Holling's (1966) simulation model for invertebrate predatory behaviour. To this end we represent a population of predators as a frequency distribution over a space of (physiological) states. The functional response of a predator is calculated from the (stable) equilibrium distribution of its state as a function of prey density.Starting from the general model various other models are obtained by limit processes, some of them new and some of them old. The more interesting of which will be studied in further papers in this series.List of Notation a rate constant of digestion - b maximum of rate constant of prey encounter in the mantid - b maximum pursuit duration in the mantid (_p(0)) - c satiation threshold for search - c satiation threshold for pursuit in the mantid: c=c(b-D_s/v)/b - D _m maximum sighting distance - D _p pursuit distance - D _s strike distance - expectation operator - f, f ₀ rate of change of satiation during search - f ₁ rate of change of satiation during prey handling - F functional response: number of prey eaten per unit of time by one predator - g rate constant of effective prey encounter in the gobbler and sucker - g₀ rate constant of prey encounter - g₁ probability of no prey loss from pursuit - g₂ probability of no prey escaping during pursuit - H Holling secretary correction factor in the sucker: fraction of the time spent searching - k _R density of R - k_T probability density of maximum prey handling time - K probability that maximum prey handling time is _e, i.e. pursuit duration is zero - K _R distribution function of R - N number of prey caught - p (marginal) density of S - p₀ density of S in search - p₁ simultaneous density of S and T - P probability - p ₁ marginal density of S in handling prey - q probability of strike success - R ratio of realized to maximum sighting distance - s, S satiation - satiation axis - t time - handling time axis - u eating speed - U homogeneous(0,1) random variable - v pursuit speed - V exponential(1) random variable - w prey weight - W exponential(_m) random variable - x prey density - ratio of maximum successful pursuit duration to meal duration (_pm/_e) - _pm - relative duration of successful pursuit (_p/_pm) - ratio of shortest to largest sighting distance - x_e - time already spent handling a prey item - rate of prey loss during prey handling - prey escape rate during pursuit - prey biomass density (xw) - , T maximum time still to be spent handling a prey item - _e meal duration - _m maximum handling time ( _e+ _p) - _p duration of successful pursuit - _pm maximum duration of successful pursuit (_p(0)) - hazard rate - _m maximum of hazard rate - scaled functional response (wF) - minimal i-state space     

A novel device for the assessment of shear effects on suspended microbial cultures

Summary A novel device has been designed for the evaluation of the effects of shear on microorganisms. The device consists of a combination of a coaxial cylinder plus cone and plate viscometers and enables cultures of both eukaryotic and prokaryotic microorganisms to be grown under fully defined and controlled fluid dynamic characteristics for serveral generations. In the preliminary tests performed a change in cell length was observed in Escherichia coli, and with Penicillium chrysogenum the septal length, hyphal diameter, and branching frequency all changes as shear was increased.Symbols L Height of liquid (m) - r Radius of cone/bob (m) - r _m Arithmetic mean of R and r (m) - R Radius of cup (m) - T Torque (Nm) - Shear rate (s^-1) - ₀ Angle of cone (rad) - Shear stress (Nm^-2) - Annular velocity (rad s^-1)     

Determination of protein rotational correlation time from NMR relaxation data at various solvent viscosities

An accurate determination of the overall rotation of a protein plays a crucial role in the investigation of its internal motions by NMR. In the present work, an innovative approach to the determination of the protein rotational correlation time _R from the heteronuclear relaxation data is proposed. The approach is based on a joint fit of relaxation data acquired at several viscosities of a protein solution. The method has been tested on computer simulated relaxation data as compared to the traditional _R determination method from T₁/T₂ ratio. The approach has been applied to ribonuclease barnase from Bacillus amyloliquefaciens dissolved in an aqueous solution and deuterated glycerol as a viscous component. The resulting rotational correlation time of 5.56 ± 0.01 ns and other rotational diffusion tensor parameters are in good agreement with those determined from T₁/T₂ ratio.