Kinetics of polymerization of deoxyhemoglobin S and mixtures of hemoglobin A and hemoglobin S at high hemoglobin concentrations

Transverse water proton relaxation times (T₂) have been measured as a function of time after deoxygenation of solutions containing hemoglobin S. The shortened T₂ values observed upon deoxygenation of hemoglobin S result from an increase in the correlation time (τ_c) of the water fraction irrotationally bound to deoxyhemoglobin S as it polymerizes. Therefore, the change in τ_c as a function of time after deoxygenation can be used to measure the rate of polymer formation. The change in τ_c observed is reasonably fit by the first-order equation τ = τ₀ (1 ? e^?kt) + τ_oxy. At a total hemoglobin concentration of approximately 300 mg/ml, the pseudo-first-order rate constant in a heterozygous AS sample is 25 times slower than in a homozygous S sample, k = 0.019 and 0.47 s^?1, respectively. Since the transit time for an erythrocyte in vivo is approximately 15 s, these results suggest that the heterozygous A/S erythrocyte would traverse the circulation and become reoxygenated before extensive polymerization and, therefore, cell sickling could occur. For the homozygous S/S erythrocyte, there is ample time for polymerization and for cell sickling during circulation.     

Analysis of Sub-τc and Supra-τc Motions in Protein Gβ1 Using Molecular Dynamics Simulations

The functions of proteins depend on the dynamical behavior of their native states on a wide range of timescales. To investigate these dynamics in the case of the small protein Gβ1, we analyzed molecular dynamics simulations with the model-free approach of nuclear magnetic relaxation. We found amplitudes of fast timescale motions (sub-τ_c, where τ_c is the rotational correlation time) consistent with S² obtained from spin relaxation measurements as well as amplitudes of slow timescale motions (supra-τ_c) in quantitative agreement with S² order parameters derived from residual dipolar coupling measurements. The slow timescale motions are associated with the large variations of the ³J couplings that follow transitions between different conformational substates. These results provide further characterization of the large structural fluctuations in the native states of proteins that occur on timescales longer than the rotational correlation time.     

Spin label studies of microsomal membranes from Acanthamoeba castellanii in different states of differentiation

Two fatty acid spin labels—[I(1,14)], stearic acid bearing a paramagnetic nitroxide group on carbon 16, and [I(12,3)], stearic acid bearing a paramagnetic nitroxide group on carbon 5—have been used to compare the physical properties of lipid in rough and smooth microsomal membranes from trophozoites and cysts of Acanthamoeba castellanii. Arrhenius plots of rotational correlation times (τ_c) calculated from the spectra for I(1,14) showed an abrupt discontinuity in slope for membranes from both trophozoites and cysts. This occurred at temperatures ranging from ?3 to 1 °C for smooth microsomes and from 8 to 11 °C for rough microsomes for both cysts and amoebae. The value of τ_c at 29 °C, the culturing temperature, in effect scores fluidity of the membrane matrix, and did not show any significant difference for either rough or smooth microsomes during the transition from exponential to stationary phase growth. However, smooth microsomes from cysts showed a 14% increase in fluidity relative to trophozoites, and the fluidity of rough microsomes from cysts tended to be lower. An order parameter (S) calculated from spectra for I(12,3) did not change as a function of encystment for the smooth membranes and increased only slightly for rough microsomes. The activation energy (E_a) for Arrhenius plots of τ_c above the inflection temperature increased as a result of encystment, indicating a greater degree of molecular interaction within the cyst membranes. Moreover, the τ_c plots for both rough and smooth microsomal membranes from trophozoites tended to converge at 29 °C, the growth temperature, whereas plots for cyst membranes were virtually parallel, bracketing those for the trophozoite membranes. This suggests that the trophozoite is able to regulate its membrane fluidity and that cysts, which are resting cells, have lost this regulatory capacity.     

Redox-controlled backbone dynamics of human cytochrome c revealed by N NMR relaxation measurements

Redox-controlled backbone dynamics in cytochrome c (Cyt c) were revealed by 2D ¹⁵N NMR relaxation experiments. ¹⁵N T₁ and T₂ values and ¹H-¹⁵N NOEs of uniformly ¹⁵N-labeled reduced and oxidized Cyt c were measured, and the generalized order parameters (S²), the effective correlation time for internal motion (τ_e), the ¹⁵N exchange broadening contributions (R_ex) for each residue, and the overall correlation time (τ_m) were estimated by model-free dynamics formalism. These dynamic parameters clearly showed that the backbone dynamics of Cyt c are highly restricted due to the covalently bound heme that functions as the stable hydrophobic core. Upon oxidation of the heme iron in Cyt c, the average S² value was increased from 0.88 ± 0.01 to 0.92 ± 0.01, demonstrating that the mobility of the backbone is further restricted in the oxidized form. Such increases in the S² values were more prominent in the loop regions, including amino acid residues near the thioether bonds to the heme moiety and positively charged region around Lys87. Both of the regions are supposed to form the interaction site for cytochrome c oxidase (CcO) and the electron pathway from Cyt c to CcO. The redox-dependent mobility of the backbone in the interaction site for the electron transfer to CcO suggests an electron transfer mechanism regulated by the backbone dynamics in the Cyt c-CcO system.     

Saturation transfer electron paramagnetic resonance spectroscopy of spin labeled tobacco mosaic virus protein.

The coat protein of Tobacco Mosaic Virus is covalently labeled with a maleimide spin label at the single SH-group of the protein. Saturation transfer electron paramagnetic resonance spectroscopy, a technique that is sensitive to very slow molecular motion with rotational correlation times τ_c in the range 10^?7 to 10^?3 sec, shows the dissociation of large oligomers of spin labeled protein with τ_c～10^?4 sec at pH 5.5 to smaller oligomers at higher pH.     

Internal noise enhanced oscillation in a delayed circadian pacemaker

The effect of internal noise in a delayed circadian oscillator is studied by using both chemical Langevin equations and stochastic normal form theory. It is found that internal noise can induce circadian oscillation even if the delay time τ is below the deterministic Hopf bifurcation τ_h. We use signal-to-noise ratio (SNR) to quantitatively characterize the performance of such noise induced oscillations and a threshold value of SNR is introduced to define the so-called effective oscillation. Interestingly, the τ-range for effective stochastic oscillation, denoted as Δτ_EO, shows a bell-shaped dependence on the intensity of internal noise which is inversely proportional to the system size. We have also investigated how the rates of synthesis and degradation of the clock protein influence the SNR and thus Δτ_EO. The decay rate K_d could significantly affect Δτ_EO, while varying the gene expression rate K_e has no obvious effect if K_e is not too small. Stochastic normal form analysis and numerical simulations are in good consistency with each other. This work provides us comprehensive understandings of how internal noise and time delay work cooperatively to influence the dynamics of circadian oscillations.     

Open-State Occupancy Prevents Gating Charge Relaxation of N-type (CaV2.2) Calcium Channels

N-type and L-type channels have significant gating differences, and we wondered whether some of these differences are linked to the relationship between charge movement and channel opening. The time constants for N-channel closing (τ_Deact) and Off-gating charge movement (τQ_Off) were compared over a range of voltages. τQ_Off was significantly larger than τ_Deact at voltages < −10 mV, and the voltage dependence of the τQ_Off was less steep than that for τ_Deact, which suggests that gating charge relaxation does not limit channel closing. Roscovitine, a drug that slows N-channel closing by holding the channel in a high open-probability state, was found to slow both τQ_Off and τ_Deact, and thus the time courses of channel closing and gating charge relaxation were similar. Our gating current results were reproduced with the addition of a voltage-independent, closed-closed transition to our previously published two-open-state N-channel model. This work suggests that, like L-type channels, there is a voltage-independent transition along the N-channel activation/deactivation pathway, but this transition occurs between closed states instead of the closed-open states of the L-channel. Also unlike L-type channels, the gating charge appears to be locked into the activated position by the N-channel open state.     

Macromolecular composition of bacteria

Equations are presented that describe the macromolecular composition in exponential bacterial cultures as functions of five parameters: doubling time of the culture (τ), protein per origin of replication (P₀), chromosome replication time (C-period), peptide chain elongation rate (c_p), and the time between termination of replication and cell division (D-period). Implicit in the value for some of these parameters is a specific macromolecular control system: the control of the growth rate (τ), the timing of initiation of rounds of chromosome replication (P₀), and the regulation of cell division (D). The utility of these relations is illustrated by using updated measurements of the macromolecular composition of E. coli B/r to calculate values for the fundamental parameters and to predict the composition of a mutant which has a defect in the control of DNA replication. Furthermore, the meaning of several often-cited physiological parameters (RNA/protein, RNA/cell and RNA/genome) is examined. The relations presented here show that these parameters and their variation with growth rate are not directly relevant to arguments about control of ribosome synthesis or culture growth.     

Elevated Proton Leak of the Intermediate OH in Cytochrome c Oxidase

The kinetics of the formation and relaxation of transmembrane electric potential (Δψ) during the complete single turnover of CcO was studied in the bovine heart mitochondrial and the aa₃-type Paracoccus denitrificans enzymes incorporated into proteoliposome membrane. The real-time Δψ kinetics was followed by the direct electrometry technique. The prompt oxidation of CcO and formation of the activated, oxidized (O_H) state of the enzyme leaves the enzyme trapped in the open state that provides an internal leak for protons and thus facilitates dissipation of Δψ (τ^app ≤ 0.5-0.8 s). By contrast, when the enzyme in the O_H state is rapidly re-reduced by sequential electron delivery, Δψ dissipates much slower (τ^app > 3 s). In P. denitrificans CcO proteoliposomes the accelerated Δψ dissipation is slowed down by a mutational block of the proton conductance through the D-, but not K-channel. We concluded that in contrast to the other intermediates the O_H state of CcO is vulnerable to the elevated internal proton leak that proceeds via the D-channel.     

Would transformation of C3 crop plants with foreign Rubisco increase productivity? A computational analysis extrapolating from kinetic properties to canopy photosynthesis

Genetic modification of Rubisco to increase the specificity for CO₂ relative to O₂ (τ) would decrease photorespiration and in principle should increase crop productivity. When the kinetic properties of Rubisco from different photosynthetic organisms are compared, it appears that forms with high τ have low maximum catalytic rates of carboxylation per active site (k^c_c). If it is assumed that an inverse relationship between k^c_c and τ exists, as implied from measurements, and that an increased concentration of Rubisco per unit leaf area is not possible, will increasing τ result in increased leaf and canopy photosynthesis? A steady‐state biochemical model for leaf photosynthesis was coupled to a canopy biophysical microclimate model and used to explore this question. C₃ photosynthetic CO₂ uptake rate (A) is either limited by the maximum rate of Rubisco activity (V_cmax) or by the rate of regeneration of ribulose‐1,5‐bisphosphate, in turn determined by the rate of whole chain electron transport (J). Thus, if J is limiting, an increase in τ will increase net CO₂ uptake because more products of the electron transport chain will be partitioned away from photorespiration into photosynthesis. The effect of an increase in τ on Rubisco‐limited photosynthesis depends on both k^c_c and the concentration of CO₂ ([CO₂]). Assuming a strict inverse relationship between k^c_c and τ, the simulations showed that a decrease, not an increase, in τ increases Rubisco‐limited photosynthesis at the current atmospheric [CO₂], but the increase is observed only in high light. In crop canopies, significant amounts of both light‐limited and light‐saturated photosynthesis contribute to total crop carbon gain. For canopies, the present average τ found in C₃ terrestrial plants is supra‐optimal for the present atmospheric [CO₂] of 370 µmol mol^?1, but would be optimal for a CO₂ concentration of around 200 µmol mol^?1, a value close to the average of the last 400 000 years. Replacing the average Rubisco of terrestrial C₃ plants with one having a lower and optimal τ would increase canopy carbon gain by 3%. Because there are significant deviations from the strict inverse relationship between k^c_c and τ, the canopy model was also used to compare the rates of canopy photosynthesis for several Rubiscos with well‐defined kinetic constants. These simulations suggest that very substantial increases (> 25%) in crop carbon gain could result if specific Rubiscos having either a higher τ or higher k^c_c were successfully expressed in C₃ plants.     

Structural stability,alternate descriptions and information

The inactivation properties of a model of the nerve membrane are examined. The inactivation kinetics are closely first order and may be characterized by Hodgkin-Huxley (H-H) parameters h_∞ and τ_h which depend on potential in agreement with experiments. Some differences from the H-H equations are identified. The forms predicted for τ_h variation with hyper-polarization and change of external [K⁺] agree with available data. While the inactivation time delay predicted by the model is too small to be detected experimentally, there are grounds for expecting that it may be larger in other tissues, as observed in Myxicola giant axons. The variation of the delay with test potential is predicted to be exponential. Although the model is coupled in the sense defined by Hoyt, it gives rise to an inactivation shift of negligible magnitude. However, introducing a simple variability in one physical parameter leads to the observed form of both the peak transient current voltage relation and the inactivation shift. Inactivation shift thus does not unambiguously indicate coupling; that it results from parametric heterogeneity may be a better hypothesis, and is readily testable. The inactivation shift dependence on current ratio, from experimental data, can be used to correct for the effects of parametric heterogeneity and obtain the value of a previously predicted fundamental parameter of excitable membranes. It is suggested that the effects of parametric heterogeneity must be considered in interpreting experiments and designing models for excitable systems.     

Accessing ns–μs side chain dynamics in ubiquitin with methyl RDCs

This study presents the first application of the model-free analysis (MFA) (Meiler in J Am Chem Soc 123:6098–6107, 2001; Lakomek in J Biomol NMR 34:101–115, 2006) to methyl group RDCs measured in 13 different alignment media in order to describe their supra-τ _c dynamics in ubiquitin. Our results indicate that methyl groups vary from rigid to very mobile with good correlation to residue type, distance to backbone and solvent exposure, and that considerable additional dynamics are effective at rates slower than the correlation time τ _c. In fact, the average amplitude of motion expressed in terms of order parameters S ² associated with the supra-τ _c window brings evidence to the existence of fluctuations contributing as much additional mobility as those already present in the faster ps-ns time scale measured from relaxation data. Comparison to previous results on ubiquitin demonstrates that the RDC-derived order parameters are dominated both by rotameric interconversions and faster libration-type motions around equilibrium positions. They match best with those derived from a combined J-coupling and residual dipolar coupling approach (Chou in J Am Chem Soc 125:8959–8966, 2003) taking backbone motion into account. In order to appreciate the dynamic scale of side chains over the entire protein, the methyl group order parameters are compared to existing dynamic ensembles of ubiquitin. Of those recently published, the broadest one, namely the EROS ensemble (Lange in Science 320:1471–1475, 2008), fits the collection of methyl group order parameters presented here best. Last, we used the MFA-derived averaged spherical harmonics to perform highly-parameterized rotameric searches of the side chains conformation and find expanded rotamer distributions with excellent fit to our data. These rotamer distributions suggest the presence of concerted motions along the side chains.     

Shear stress and sediment resuspension in relation to submersed macrophyte biomass

We examined the impacts of macrophyte beds dominated by a canopy-forming (Myriophyllum sibiricum) and a meadow-forming (Chara canescens) species on bottom shear stress (τ) and resuspension in shallow Lake Christina, Minnesota (U.S.A.). Studies were conducted in late summer, 1998, when macrophyte biomass levels exceeded 200 g m^?2, and in early summer, 2000, when biomass was greatly reduced (<20 g m^?2) in both plant beds. The critical shear stress (τ_c) of sediments, measured experimentally in the laboratory, was low (1.4 dynes cm^?2) indicating potential for resuspension in the absence of macrophytes. During 1998, turbidity was low at the M. sibiricum and Chara station, rarely increasing when calculated bottom τ (calculated from wave theory assuming no biomass obstruction) exceeded τsub c sub, indicating that both beds reduced sediment resuspension at high biomass levels. In situτ (estimated τ), measured via gypsum sphere dissolution, did not exceed τ_c above the sediment interface in either bed during 1998. In contrast, sediment resuspension occurred in both beds during similar high winds in 2000. However, estimated τ was lower than calculated bottom τ, suggesting that at low biomass, macrophytes were having some impact on τ.     

Putrescine distribution in Escherichia coli studied in vivo by 13C nuclear magnetic resonance

In order to study the intracellular polyamine distribution in Escherichia coli, ¹³C-NMR spectra of [1,4-¹³C]putrescine were obtained after addition of the latter to intact bacteria. The ¹³C-enriched methylene signal underwent line broadening. When the cells were centrifuged after 90 min the cell-bound putrescine peak had a linewidth of 23 Hz, while the supernatant liquid showed an unbound putrescine signal with a linewidth smaller than 1 Hz. By using ¹³C-enriched internal standards it could be shown that the linewidening was not due to the heterogeneity of the medium or to an in vivo paramagnetic effect. Cell-bound putrescine was liberated by addition of trichloroacetic acid and was therefore non-covalently linked to macromolecular cell structures. Cell-bound [¹³C]putrescine could be displaced by addition of an excess of [¹²C]putrescine. When samples of membranes, soluble protein, DNA, tRNA and ribosomes from E. coli were incubated with [1,4-¹³C]putrescine, strong binding was detected only in the ribosomal and membrane fractions. The ribosome-putrescine complex showed properties similar to those determined with the intact cells. By measuring the nuclear Overhauser enhancements η, it was possible to estimate that only about 50% of the polyamine was linked to the macromolecules. Determination of the T₁ values of free and ribosomal-bound putrescine allowed the calculation of a correlation time, τ_c = 4·10^?7 s for the latter. T₁ and τ_c value for the ribosome-putrescine complex were those expected for a motional regime of slowly tumbling molecules.     

Temporal Modulation of Sodium Current Kinetics in Neuron Cells by Near-Infrared Laser

Near-infrared laser provides a novel nerve stimulation modality to regulate the cell functions. Understanding its physiological effect is a prerequisite for clinic laser therapy applications. Here, the whole-cell sodium (Na) channel kinetics of neuron cell was employed to determine the temporal roles of infrared laser. The Na currents were elicited by electrical pulses that were synchronized at the rising and falling edges of the 980 nm laser pulses, respectively, to investigate the different infrared effect on cell functions. The time constants of activation (τ _m) and inactivation (τ _h) kinetics were extracted from fitting of the Na current (m³h) according to the Hodgkin–Huxley (HH) model. By comparing the time constants without and with the laser irradiation, we obtained that laser pulses changed the Na current kinetics by accelerating τ _h-phase and slowing down τ _m-phase at the beginning of the laser pulse, whereas both phases were accelerated at the end of the pulse. After relating the ratios of the time constants to the temperature characteristics of Na channel by Q ₁₀, we found that the accelerating in Na current kinetics could be related to the average temperature of extracellular solution in the corresponding time span by choosing Q ₁₀ = 2.6. The results of this study demonstrated that there was a positive correlation between the acceleration of the Na current kinetics and increases in temperature of the extracellular solution.     

Mechanisms of β-Adrenergic Modulation of IKs in the Guinea-Pig Ventricle: Insights from Experimental and Model-Based Analysis

Detailed understanding of I_Ks gating complexity may provide clues regarding the mechanisms of repolarization instability and the resulting arrhythmias. We developed and tested a kinetic model to interpret physiologically relevant I_Ks properties, including pause-dependence and modulation by β-adrenergic receptors (β-AR). I_Ks gating was evaluated in guinea-pig ventricular myocytes at 36°C in control and during β-AR stimulation (0.1 μmol/L isoprenaline (ISO)). We tested voltage dependence of steady-state conductance (Gss), voltage dependence of activation and deactivation time constants (τ_act, τ_deact), and pause-dependence of τ_act during repetitive activations (τ_react). The I_Ks model was developed from the Silva and Rudy formulation. Parameters were optimized on control and ISO experimental data, respectively. ISO strongly increased Gss and its voltage dependence, changed the voltage dependence of τ_act and τ_deact, and modified the pause-dependence of τ_react. A single set of model parameters reproduced all experimental data in control. Modification of only three transition rates led to a second set of parameters suitable to fit all ISO data. Channel unitary conductance and density were unchanged in the model, thus implying increased open probability as the mechanism of ISO-induced Gss enhancement. The new I_Ks model was applied to analyze ISO effect on repolarization rate-dependence. I_Ks kinetics and its β-AR modulation were entirely reproduced by a single Markov chain of transitions (for each channel monomer). Model-based analysis suggests that complete opening of I_Ks channels within a physiological range of potentials requires concomitant β-AR stimulation. Transient redistribution of state occupancy, in addition to direct modulation of transition rates, may underlie β-AR modulation of I_Ks time dependence.     

Fluctuation analysis of Na+ channels modified by batrachotoxin in myelinated nerve

(1) Single myelinated nerve fibres of Rana esculenta were treated with the steroidal alkaloid batrachotoxin, and Na⁺ currents and Na⁺-current fluctuations were measured near the resting potential under voltage-clamp conditions. Between test pulses fibres were held at hyperpolarizing membrane potentials. (2) The spectral density of Na⁺-current fluctuations was fitted by the sum of a $\text{1}\text{f}$ component and a Lorentzian function. The time constant $\text{τ}{}_{\mathrm{<mtext>c</mtext>}}\text{= 1/(2π?}{}_{\mathrm{<mtext>c</mtext>}}\text{)}$ obtained from the corner frequency ?_c of the Lorentzian function approximately agreed with the activation time constant τ_m of the macroscopic currents. (3) The conductance γ of a single Na⁺ channel modified by batrachotoxin was calculated from the integral of the Lorentzian function and the steady-state Na⁺ current. At the resting potential V = O we obtained γ = 1.6 pS, higher γ-values of 3.2 and 3.45 pS were found at V = ?8 and ?16 mV, respectively. (4) The conductance of a modified Na⁺ channel is significantly lower than the values 6.4 to 8.85 pS reported in the literature for normal Na⁺ channels. Hence, our experiments are in agreement with the view that batrachotoxin acts in an ‘all-or-none’ manner on Na⁺ channels and creates a distinct population of modified channels.     

Proton magnetic relaxation and anion effect in solutions of acid ferricytochrome c.

Measurements of the longitudinal relaxation rates of water protons in aqueous solutions of ferricytochrome c and their temperature dependence, were used for the elucidation of the heme iron ligands at acid pH. The relaxation rates increased with a decrease in pH and pK values of 2.5 and 4.48 were evaluated for the aqueous and 6 m urea solutions, respectively. The results at acid pH are compatible with a structure in which two water molecules exchange rapidly between the coordination sphere of high spin heme iron and the bulk. They suggest that concomitantly with the low-high spin transition the histidine-18 and methionine-80 iron bonds break simultaneously. Addition of various anions, including methanesulfonate at pH 1.95 caused a 85% decrease in the net longitudinal relaxation rate. However, neither the chemical shift nor the width of the methyl proton nmr line of methanesulfonate in solution of acid ferricytochrome c were affected indicating that the effect of anions is not due to a direct binding to the heme iron. The relaxation mechanism of the water molecules in the first coordination sphere of the ferric ion in acid cytochrome c is discussed. It appears that the longitudial relaxation rate is modulated by the electronic correlation time of the ferric ion which was calculated to be τ_s = 6 × 10^?11 sec at 60 MHz.     

Probing the fluorescence emission kinetics of the photosynthetic apparatus of Rhodopseudomonas sphaeroides, strain 1760-1, on a picosecond pulse fluorometer

Using the pulse picosecond fluorometric technique the fluorescence properties of intact cells, isolated chromatophores and photosynthetic reaction centres were studied in bacteria Rhodopseudomonas sphaeroides, strain 1760-1.The fluorescent emission from reduced reaction centres excited by 694.3 nm light has a biphasic character, the lifetimes of the components being τ₁ = 15±8 ps and τ₂ = 250 ps. The faster component, τ₁, contributes to the integral fluorescence in the long wavelength region. It disappears with oxidation of the reaction centres and is attributed to photoactive bacteriochlorophyll P870. The slow component, τ, is apparently due to both bacteriochlorophyll P800 and bacteriopheophytin. The fluorescence from intact cells exhibits a monophasic pattern and decays with τ = 200 ps.The fluorescence emitted by chromatophores comprises two components with τ₃ = 200 ps and τ₄ = 4200 ps. The duration of fluorescence τ₃ increases to its maximum of 500–550 ps, as P870 is oxidized chemically or photochemically, while τ₄ remains unchanged. The fluorescence with a lifetime of 200 ps was ascribed to the photosystem and the 4200-ps fluorescence to bacteriochlorophyll which had lost its functional links with the photosystem.The rise time of the fluorescence emitted by chromatophores varies from 60 or 70 ps to 350 ps depending on the wavelength of the exciting light and the recorded spectral region. On the basis of our findings the rate for energy migration was estimated to be 10⁹ s^?1.