Phase transition kinetics of phosphatidic acid bilayers A stopped-flow study of the electrostatically induced transition

The kinetics of the electrostatically induced phase transition of dimyristoyl phosphatidic acid bilayers was followed using the stopped-flow technique. The phase transition was triggered by a fast change in the pH or the magnesium ion concentration and followed by recording the time dependence of the absorbance. When the phase transition was induced by a pH jump the time course of the absorbance could be described by two exponentials, their time constants displaying the for cooperative processes characteristic maximum at the transition midpoint. The time constants are in the 10 and 100 ms range for the H⁺ triggered transition from the fluid to the ordered state. A third slower process shows no appreciable temperature dependence and is probably caused by vesicle aggregation. For the OH^--induced transition fron the ordered to the fluid state the time constants are in the 100 and 1000 ms range. The fluid-ordered transition could also be triggered by addition of magnesium ions. Of the several observed processes only the fastest in the 10–100 ms time range could definitely be assigned to the fluid-ordered transition while the others are due to aggregation phenomena. The experimental data were compared with results obtained from pressure jump experiments and could be interpreted on the basis of theories for non-equilibrium relaxation.     

Kinetic properties and the electric field effect of the helix-coil transition of poly(gamma-benzyl L-glutamate) determined from dielectric relaxation measurements

Dielectric relaxation of poly(γ-benzyl L -glutamate) in solution has been studied in the 5 kcps-10 Mcps range for various values of the helix content. The results give first experimental evidence for three effects of major significance. (1) The system exhibits dielectric relaxation due to a chemical rate process (namely helix formation). This confirms recent theoretical predictions. (2) The mean relaxation time τ* of the helix–coil transition could be evaluated as a function of the degree of transition. The results are in excellent agreement with a previously developed theory. At the midpoint of transition it is found τ*_max = 5 × 10^?7 sec. The elementary process of helical growth turns out to be practically diffusion-controlled (with a rate constant of hydrogen bond formation of 1.3 × 10¹⁰ sec^?1). (3) There is a considerable electric field effect of the helix–coil transition. This indicates that conformation changes in biological systems could be potentially caused by direct action of an electric field.     

Kinetic studies of the helix–coil transition in aqueous solutions of poly(L-lysine)

The rate of conformational change of aqueous poly(α-L -lysine) solutions was measured using the electric field pulse relaxation method with conductivity detection. The relaxation time as a function of pH exhibits two maxima. One is assigned to a proton transfer reaction and the other to the helix–coil conformational transition. The helix nucleation parameter and the maximum relaxation time yield the rate constant of helix growth process (k_F) according to Schwarz's kinetic theory as k_F = 2 × 10⁷ sec^?1, which is comparable to that of the poly(glutamic acid) solution. The thermodynamic parameters of the helix growth process are compared with those of poly(glutamic acid).     

Model calculations on the kinetics of oligonucleotide double helix coil transitions. Evidence for a fast chain sliding reaction

Relaxation data obtained previously for the double helix coil transition of oligoriboadenylates and oligoribouridylates are compared to the results of numerical calculations according to various models. In these models the helix coil transition is described by individual rate constants for the first steps of helix formation, whereas the rate constants of the following steps of helix chain growth are assumed to be uniform. The existence of various helix intermediates containing the same number of base pairs is accounted for by statistical factors. First a quasistationary treatment of a zipper model is used for an analysis of the influence of various model parameters. Then relaxation spectra are calculated including helix coil intermediates explicitly without any assumption of quasistationarity. The relaxation spectrum calculated for any chain length N comprises N—1 fast processes with time constants in the range of 0.1 to 0.5 μs and one slow process with a time constant τ depending upon the nucleotide concentration (τ is usually in the ms time range). The fast processes are associated mainly with the unzippering at helix ends and are usually characterized by relatively small amplitudes, whereas the slow process represents the overall helix coil transition usually characterized by a very large amplitude.Consideration of staggered helix series (where the different helix scries are coupled to each other by the single stranded state) leads to a spectrum of slow relaxation processes with one separate relaxation process for each helix series. It is shown that this “non-sliding” staggering zipper model is not consistent with the experimental results. The measured relaxation curves can be represented by single exponentials for nucleotide chain lengths 8 to 11 (within experimental accuracy). This is also true for conditions where several, clearly separated time constants should be expected according to the theoretical model. The experimental data suggest the existence of a direct coupling between different series of staggered helices by a chain sliding mechanism with a time constant < 1ms. Chain sliding may be explained by diffusion of helix defects along the double helix such as diffusion of small loops. A simple model calculation for the diffusion of a bulge loop assuming quasistationarity suggests a sliding time constant around 100 μs for a helix comprising 10 base pairs.Finally some thermodynamic and kinetic parameters are evaluated according to the “sliding” staggering zipper model: The negative activation enthalpy observed for helix recombination can he described using a series of nucleation parameters indicating reduced stability constants for the first three base pairs. Nucleation may usually be achieved with the formation of the third or fourth base pair depending upon the magnitude of the chain growth parameter. The rate constant of helix chain growth is around 10⁶ s^?1 at 0.05 M [Na⁺] and increases to about 4 × 10⁶ s^?1 at 0.17 M [Na⁺].     

Helix–coil transition kinetics in aqueous poly(α,L-glutamic acid)

A polarimetric electric-field-jump relaxation apparatus is described and used to determine the relaxation spectrum for the helix–coil transition of poly(α,L -glutamic acid) in water at 24°C. A maximum relaxation time of 1.7 μc occurs at the transition midpoint (pH = 5.9) yielding a rate constant for helical growth of 6 × 10⁷ sec^?1.     

Viscoelastic relaxations in solutions of poly(glutamic acid) and gelatin at ultrasonic frequencies

Complex shear viscosity η* = η′ – iη″ of poly (L -glutarmic acid) solution was measured by the torsional crystal method at 50 kc./sec. as a function of pH. A sharp peak was found at the midpoint of the helix-coil transition region in both η′ and η″. The relaxation time is calculated from η′ and η″ assuming a single relaxation process and the peak value at the midpoint of transition is estimated at 10^?6 sec. Such behavior agrees well with the prediction from the theory of Schwarz. The attenuation of longitudinal sound waves at,3 Me./sec. was measured as a function of pH for solutions of poly(glutamic acid), glutamic acid, and gelatin. A small attenuation peak was observed for the three solutions, the peak height being almost, the same for them. The peak is interpreted in terms of the dissociation reaction of side chains.     

Sol–gel transition of alginate solution by the addition of various divalent cations: 13C-nmr spectroscopic study

¹³C-NMR spectroscopic studies have been made on alginate solutions undergoing sol–gel transition induced by four different divalent cations: Ca, Cu, Co, and Mn. From the analysis of nmr spectra and relaxation times, we have found different interaction modes existing between the Ca–alginate systems and the transition metal (Cu, Co, and Mn)–alginate systems. In the Ca–alginate systems, there exists a specific interaction characterized by a strong autocooperative binding between guluronate residues and calcium ions, and all functional groups in guluronate residues are considered to involve the interaction with calcium ions. On the other hand, in transition metal (Cu, Co, and Mn)–alginate systems, sol–gel transition is characterized by a complex formation in which the carboxyl groups in both mannuronate and guluronate residues are coordinated to metal ions. The other functional groups, like hydroxyl groups, do not participate in the binding to metal ions. It is suggested by relaxation time measurements that from a microscopic point of view the sol–gel transition phenomena can be explained as a dynamic process in which the low frequency molecular motions are dominant and increase their proportions with the formation of three-dimensional cross-links. © 1993 John Wiley & Sons, Inc.     

Rheology and dynamic light scattering of octa-ethyleneglycol-monododecylether/chitosan solutions

In this work we used rheometry and DLS to probe relaxation phenomena in solutions of chitosan and octa-ethyleneglycol-monododecylether. The dispersions had a marked pseudoplastic behavior, which became less evident, as surfactant concentration was increased. Arrhenius plots showed that systems with surfactant presented a characteristic temperature at which apparent enthalpy of activation (varying from 3 to 40 kJ mol⁻¹) changed: this change was correlated to a possible transition of colloidal aggregates to a wormlike configuration. DLS intensity correlation functions were described by KWW equation: pure chitosan solutions had relaxation rate distributions centered at a characteristic relaxation rate around 4.6 × 10⁻⁶ μS⁻¹; as surfactant was added, a new component, with a faster characteristic relaxation rate with a magnitude order of 10⁻³ μs⁻¹, appeared. It was shown that the dependence between these relaxation rates and surfactant concentration could be used to describe DLS-related relaxation phenomena as an Arrhenius-activated process, agreeing with results obtained using rheometry.     

Nuclear magnetic resonance investigation of human erythrocytes in the presence of manganese ions. Evidence for a thermal transition

Water proton transverse relaxation was investigated in whole blood and washed erythrocytes samples, respectively, at various temperatures and manganese concentrations. Water diffusional exchange controls proton relaxation in whole blood samples at higher Mn²⁺ concentrations (20–30 mM) or in washed erythrocyte samples at low Mn²⁺ content (1–5 mM). Mn²⁺ uptake is significant in washed normal erythrocyte samples when its concentrations is about 18 mM or higher in the medium, at temperatures below about 26°C. The thermal transition as revealed by the NMR doping method represents a switch from a water exchange process, mainly seen in the higher temperature range, to a paramagnetic ion controlled water proton relaxation in the lower temperature range.     

Sodium ion and solvent nuclear relaxation results in aqueous solutions of DNA

The field-dependent ²³Na nuclear relaxation in aqueous DNA solutions has been obtained for a range of temperatures, including the DNA melting region. At least two correlation times are needed to characterize the spectral density function for the ²³Na relaxation. For the slow process (with the largest correlation time), the temperature dependence of the coupling constant and the correlation time were determined, and important premelting effects were observed. Possible origins of the slow process are discussed. The last process is shown to be correlated with the properties of the hydration water of DNA as reflected by the ¹⁷O relaxation rates in these solutions. The influence of the polyelectrolyte and NaCl concentrations on the ²³Na relaxation rate is compared with previous results from solutions of linear flexible polyelectrolytes.     

Molecular states in single-stranded adenylate chains by relaxation analysis

The single-strand helix-coil transition in various oligo- and polyadenylates is characterized by means of an improved cable temperature-jump technique. In all the polymers studied {poly(rA), poly(dA), poly[A(m^2′)] and poly[A(e^2′)]} helix-coil relaxation is observed in the time range from 30 to 1000 nsec. Relaxation-time constants observed at wavelengths λ<280 nm (τ_α) are different from those found at λ >280 nm (τβ), indicating the presence of more than two conformational states. The time constants τ_α increase in the series poly(dA), poly[A(m^2′)], constants τ_β/τ_α is approximately 2.5, except in poly(dA) where τ_β/τ_α ≈ 9. Relaxation measurements with r(A)_n- oligomers show a decrease in conformational mobility with increasing chain length. The relaxation curves also demonstrate that “internal” residues have lower reaction rates than residues at the ends of the oligomer chain. Measurement in D₂O reveal a solvent isotope effect for τ_α of +87% for poly(rA), and of +53% for poly(dA), whereas no isotope effect is found in τ_β. The absence of “slow” relaxation processes in the model compound 9,9′ -trimethylenebisadenine shows that the relatively low rate of the single-strand helix-coil transitions is due to the coupling of base stacking with the folding of the sugar–phosphate chain. The absence of a seprate relaxation process (corresponding to τ_β) in 9,9′-trimethylenebisadenine, as well as in the dinucleotides ApC and CpA, suggests that this relaxation process is dependent upon the presence of both the sugar–phosphate chain and of adjacent adenine bases. The experimental data provide evidence that there is more than one ordered conformation in various single-stranded oligo- and polyadenylates and that the transition between these conformations is influenced by the sugar conformation.     

Phase transition kinetics of lipid bilayer membranes studied by time-resolved pressure perturbation calorimetry

The relaxation kinetics of aqueous lipid dispersions after a pressure jump (p-jump) was investigated using time-resolved pressure perturbation calorimetry (PPC). Analysis of the calorimetric response curves by deconvolution with the instrumental response function gives information about slow processes connected with the lipid phase transition. The lipid transition from the gel to the liquid-crystalline state was found to be a multi-step process with relaxation constants in the seconds range resolvable by time-resolved PPC and faster processes with relaxation times shorter than ca. 5 s that could not be resolved by the instrument. The faster processes comprise ca. 50% of the total heat uptake at the transition midpoint. This is the first calorimetric measurement showing the multi-step nature of the transition. The results are in good agreement with data obtained with other detection methods and with molecular modelling experiments describing the transition as a multi-step process with nucleation and growth steps.     

Thermodynamic aspects of vitrification

Vitrification is a process in which a liquid begins to behave as a solid during cooling without any substantial change in molecular arrangement or thermodynamic state variables. The physical phenomenon of vitrification is relevant to both cryopreservation by freezing, in which cells survive in glass between ice crystals, and cryopreservation by vitrification in which a whole sample is vitrified. The change from liquid to solid behavior is called the glass transition. It is coincident with liquid viscosity reaching 10¹³ Poise during cooling, which corresponds to a shear stress relaxation time of several minutes. The glass transition can be understood on a molecular level as a loss of rotational and translational degrees of freedom over a particular measurement timescale, leaving only bond vibration within a fixed molecular structure. Reduced freedom of molecular movement results in decreased heat capacity and thermal expansivity in glass relative to the liquid state. In cryoprotectant solutions, the change from liquid to solid properties happens over a ∼10 °C temperature interval centered on a glass transition temperature, typically near −120 °C (±10 °C) for solutions used for vitrification. Loss of freedom to quickly rearrange molecular position causes liquids to depart from thermodynamic equilibrium as they turn into a glass during vitrification. Residual molecular mobility below the glass transition temperature allows glass to very slowly contract, release heat, and decrease entropy during relaxation toward equilibrium. Although diffusion is practically non-existent below the glass transition temperature, small local movements of molecules related to relaxation have consequences for cryobiology. In particular, ice nucleation in supercooled vitrification solutions occurs at remarkable speed until at least 15 °C below the glass transition temperature.     

Dielectric relaxation and molecular motions in C14-lecithin-water systems

The dependence of the complex permittivity on the frequency has been measured between 10⁵ and 6 × 10¹⁰ Hz for aqueous solutions of dimyristoylphosphatidylcholine at several temperatures around the crystalline/liquid-crystalline phase transition temperature of the samples. To the observed data is fitted a sum of Cole-Cole functions and also a model relaxation function to yield various relaxation parameters. The variation of these parameters with temperature is discussed.A noteworthy result is that there exists a pronounced cooperativity effect in the diffusive motions of the phosphorylcholine groups at the bilayer surface and that the mobility of the cationic trimethylammonium head group is dramatically smaller than with lysolecithin micelles in aqueous solutions. As another remarkable result the hydration water relaxation time appears to be distinctly smaller than the reorientation time of the molecules in the pure solvent at the same temperature.     

Stopped-flow rapid kinetics of anesthetic-induced phase transition in phospholipid vesicle membranes: nonlocalized fluctuation

Kinetics of the gel to liquid-crystalline phase transition of dipalmitoylphosphatidylcholine vesicle membrane was studied by the stopped-flow technique with turbidity detection. The observed change in turbidity was well characterized by a single-exponential decay curve with relaxation time in the millisecond range, although the existence of a faster process than the dead-time of the stopped-flow apparatus was inferred from the amplitude analysis. Relaxation times were determined as functions of 1-hexanol concentration and temperature just below phase transition. From the analysis based on the theories of nonequilibrium relaxation, it is concluded that the phase transition induced by 1-hexanol is governed by a nonlocalized fluctuation mechanism. The anesthetic-induced nonequilibrium state is unstable rather than metastable.     

The reaction of aromatic peptides with double helical DNA. Quantitative characterisation of a two step reaction scheme

The binding of LysTrpLys and LysTyrLys to calf thymus DNA has been investigated by the field jump method using fluorescence detection. Two separate relaxation processes, clearly distinguished on the time scale and by opposite ampli- tudes, are observed for the binding of LysTrpLys to DNA with ~ 30000 base pairs. The concentration dependence of the relaxation time constants demonstrates a mechanism with a bimolecular step followed by a slow intramolecular transition with a forward rate of 6.4 X 103 s^?1 and an equilibrium constant of 11. Measurements at various degrees of peptide binding demonstrate that the binding mechanism associated with low binding rates is restricted to a rather low number of binding sites (roughly one site in 15 base pairs). The binding of LysTyrLys to the same DNA is not associated with relaxation pro- cesses of opposite amplitudes; nevertheless two processes could be identified and assigned to a two step mechanism corre- sponding to that observed in the case of LysTrpLys. In the presence of sonicated DNA both peptides show a single relaxa- tion process with characteristics similar to those observed for the slow process in the binding to high molecular DNA. The data indicate that the intramolecular step is faster for low than for high molecular DNA. These results suggest an assignment of the intramolecular step to an insertion of the aromatic residues into the DNA associated with bending of the helix. The increase in the rate of the intramolecular step with decreasing chain length of the DNA may then be explained by a higher flexibility of the double helix at lower chain lengths.     

Kinetics of denaturation of DNA

The kinetics of denaturation of DNA have been studied by relaxation techniques. Examination of the terminal relaxation times for a variety of DNA's under a variety of conditions has shown that DNA denaturation is principally a hydrodynamically limited process. Measurements within the helix–coil transition have demonstrated that the experimentally measured terminal relaxation times are a function of the following: (1) position in the helix–coil transition; (2) ionic strength of the solvent; (3) solvent viscosity; (4) DNA concentration; (5) molecular weight; (6) number and position of single-strand breaks. The dependence of the terminal relaxation time on the above mentioned factors can be attributed to hydrodynamic effects. Thus a hydrodynamic model for DNA unwinding is required. The model which best fits the data involves the assumption of a rotational frictional coefficient independent of molecular weight. This assumption is suggested by the fact that the relaxation time is proportional to the first power of the molecular weight.     

Multiple conformational states of the hammerhead ribozyme, broad time range of relaxation and topology of dynamics

The dynamics of a hammerhead ribozyme was analyzed by measurements of fluorescence-detected temperature jump relaxation. The ribozyme was substituted at different positions by 2-aminopurine (2-AP) as fluorescence indicator; these substitutions do not inhibit catalysis. The general shape of relaxation curves reported from different positions of the ribozyme is very similar: a fast decrease of fluorescence, mainly due to physical quenching, is followed by a slower increase of fluorescence due to conformational relaxation. In most cases at least three relaxation time constants in the time range from a few microseconds to ~200 ms are required for fitting. Although the relaxation at different positions of the ribozyme is similar in general, suggesting a global type of ribozyme dynamics, a close examination reveals differences, indicating an individual local response. For example, 2-AP in a tetraloop reports mainly the local loop dynamics known from isolated loops, whereas 2-AP located at the core, e.g. at the cleavage site or its vicinity, also reports relatively large amplitudes of slower components of the ribozyme dynamics. A variant with an A→G substitution in domain II, resulting in an inactive form, leads to the appearance of a particularly slow relaxation process (τ ≈200 ms). Addition of Mg²⁺ ions induces a reduction of amplitudes and in most cases a general increase of time constants. Differences between the hammerhead variants are clearly demonstrated by subtraction of relaxation curves recorded under corresponding conditions. The changes induced in the relaxation response by Mg²⁺ are very similar to those induced by Ca²⁺. The relaxation data do not provide any evidence for formation of Mg²⁺-inner sphere complexes in hammerhead ribozymes, because a Mg²⁺-specific relaxation effect was not visible. However, a Mg²⁺-specific effect was found for a dodeca-riboadenylate substituted with 2-AP, showing that the fluorescence of 2-AP is able to indicate inner sphere complexation. Amplitudes and time constants show that the equilibrium constant of inner sphere complexation is 1.2, corresponding to 55% inner sphere state of the Mg²⁺ complexes; the rate constant 6.6 × 10³ s^–1 for inner sphere complexation is relatively low and shows the existence of some barrier(s) on the way to inner sphere complexes.     

Studies of fibrin film. I. Stress relaxation and birefringence

Measurements of stress relaxation in uniaxial extension and associated time-dependent birefringence have been made on bovine fibrin film, prepared by gentle compaction of coarse fibrin clots, containing 13–22% fibrin plasticized with either aqueous buffer or glycerol. Both unligated and ligated (i.e., with α-α and γ-γ ligation by fibrinoligase, factor XIIIa) films were studied. Both types showed two stages of stress relaxation, with time scales of approximately 10 and 10³–10⁴ s, respectively, with a plateau region between. In the plateau, the nominal (engineering) stress for ligated glycerol-plasticized film is proportional to In λ, where λ is the stretch ratio, up to λ ? 2, and it decreases with increasing temperature. For unligated glycerol-plasticized film, the stresses are smaller by a factor of one-half to one-third. For ligated film, the second stage of relaxation is relatively slight, and recovery after release of stress is often nearly complete. For unligated film, the second stage involves a substantial drop in stress, and after recovery there is a significant permanent set. A second relaxation for ligated film reproduces the first, but for unligated film it reproduces the first only if the initial relaxation is terminated before the second stage; otherwise, the second relaxation shows a weaker structure. The behavior of water-plasticized film is similar to that of glycerol-plasticized except that the second stage of relaxation occurs at shorter times. During the first stage of stress relaxation, up to about 100 s, the birefringence and the stress-optical coefficient increase; during the plateau zone of stress relaxation, the birefringence of ligated films is approximately constant and is proportional to 2λ²/(λ² + 1) ? 1, where λ is the stretch ratio. This dependence is predicted by a two-dimensional model in which rodlike elements in the plane of the film are oriented with independent alignment. During the final stage of stress relaxation, the birefringence of ligated films decreases slightly; that of unligated films decreases substantially, but less rapidly than the stress, corresponding to a further increase in the stress-optical coefficient. With additional information from small-angle x-ray scattering reported in an accompanying paper, the first stage of relaxation is attributed to partial release of bending forces in the fibers by orientation, accompanied by increased birefringence. The second stage is attributed, for ligated films, to an internal transition in the fibrin units accompanied by elongation of some of the fibers; and in the unligated films, to a combination of the latter transition with slippage of protofibrils lengthwise within the fiber bundles that causes some loss of orientation, which diminishes the birefringence.     

Kinetics of luminal proton binding to the SR Ca-ATPase

An open membrane preparation containing SR Ca-ATPase was prepared from sarcoplasmic-reticulum vesicles to study the ion binding kinetics in the P-E₂ conformation. Because Ca²⁺ and H⁺ binding are electrogenic reactions, fluorescent styryl dyes could be used to determine changes in the binding site occupation in equilibrium titration experiments and time-resolved relaxation processes triggered by a pH jump. By photo release from caged proton the pH of the electrolyte could be decreased in a step of 0.1 pH units by a single ultraviolet-laser flash. Analysis of the pH-jump induced relaxation process in the P-E₂ conformation showed that three Ca-ATPase-specific processes could be identified, fast H⁺ binding (τ < 100 μs) and pH-insensitive conformational relaxations after the release of the Ca²⁺ ion (τ ∼160 ms), and a slow process (τ ∼3.4 s) whose origin could not be unambiguously revealed. The Ca²⁺-binding affinity in the P-E₂ conformation was reduced with increasing pH, a behavior that can be explained by a reversible transition of the empty P-E₂ state to an inactivated state of the ion pump. All findings are interpreted in the framework of the Post-Albers pump cycle introduced previously, supplemented by an additional transition to an inhibited state of the ion pump.