A kinetic lattice model of the chain-melting phase transition in lipid membrane: its experimental calibration and physiological implications

A kinetic lattice model of chain-melting phase transition has been developed. Its time scale has been calibrated with the acoustic relaxation spectroscopic data. The model presents a tool for the analysis and predictions of kinetic features of those physiological processes in biological membranes whose mechanism is based on the phase transition in the lipid component. It has been shown that the phase-transitional mechanism can provide a high rate of synaptic exocytosis known for the fastest synapses in the central nervous system. It was also demonstrated that this mechanism can serve as an essential factor of synaptic plasticity.     

Phase transition in lipids and the problem of homoiothermia

Why such a high stability of temperature is necessary for warm-blooded animals? Why the range of body temperatures of various warm-blooded species is several-fold narrower than the range of environmental temperatures? What were the physicochemical factors that determined such results of the biological evolution? A hypothesis presented in this short communication provides answers to these basic questions of the problem of homoiothermia. The hypothesis implies that the Ca(2+)-induced chain-ordering phase transition in the lipid component of synaptic membranes plays a key role at the last step of the mechanism of synaptic transmission, namely, the step of neurotransmitter release. The physicochemical substantiation of a possible molecular mechanism of the release involving the phase transition is presented, and the main kinetic and evolutionary issues of the mechanism are considered in brief.     

Properties of a model of Ca(++)-dependent vesicle pool dynamics and short term synaptic depression

We explore the properties of models of synaptic vesicle dynamics, in which synaptic depression is attributed to depletion of a pool of release-ready vesicles. Two alternative formulations of the model allow for either recruitment of vesicles from an unlimited reserve pool (vesicle state model) or for recovery of a fixed number of release sites to a release-ready state (release-site model). It is assumed that, following transmitter release, the recovery of the release-ready pool of vesicles is regulated by the intracellular free Ca(++) concentration, [Ca(++)](i). Considering the kinetics of [Ca(++)](i) after single presynaptic action potentials, we show that pool recovery can be described by two distinct kinetic components. With such a model, complex kinetic and steady-state properties of synaptic depression as found in several types of synapses can be accurately described. However, the specific assumption that enhanced recovery is proportional to [Ca(++)](i), as measured with Ca(++) indicator dyes, is not confirmed by experiments at the calyx of Held, in which [Ca(++)](i)-homeostasis was altered by adding low concentrations of the exogenous Ca(++) buffer, fura-2, to the presynaptic terminal. We conclude that synaptic depression at the calyx of Held is governed by localized, near membrane [Ca(++)](i) signals not visible to the indicator dye, or else by an altogether different mechanism. We demonstrate that, in models in which a Ca(++)-dependent process is linearly related to [Ca(++)](i), the addition of buffers has only transient but not steady-state consequences.     

Mechanistic origin of the kinetic cooperativity of hexokinase type L1 from wheat germ

A theoretical analysis is presented which shows that initial velocity data for hexokinase L1 catalysis of glucose phosphorylation by MgATP cannot be reconciled with the observed rate of the 'mnemonical' conformational transition which has been proposed to account for the kinetic cooperativity of the enzyme. The basic kinetic properties of hexokinase L1 and other allegedly 'mnemonical' enzymes appear to be fully consistent with an ordered ternary-complex mechanism in which the leading substrate participates in abortive-complex formation. It is concluded that, so far, no enzyme displaying kinetic cooperativity has been convincingly demonstrated to operate by a 'mnemonical' type of reaction mechanism.     

The allosteric transition of GroEL induced by metal fluoride-ADP complexes

To understand the mechanism of a functionally important ATP-induced allosteric transition of GroEL, we have studied the effect of a series of metal fluoride-ADP complexes and vanadate-ADP on GroEL by kinetic fluorescence measurement of pyrene-labeled GroEL and by small-angle X-ray scattering measurement of wild-type GroEL. The metal fluorides and vanadate, complexed with ADP, are known to mimic the gamma-phosphate group of ATP, but they differ in geometry and size; it is expected that these compounds will be useful for investigating the strikingly high specificity of GroEL for ATP that enables the induction of the allosteric transition. The kinetic fluorescence measurement revealed that aluminium, beryllium, and gallium ions, when complexed with the fluoride ion and ADP, induced a biphasic fluorescence change of pyrenyl GroEL, while scandium and vanadate ions did not induce any kinetically observed change in fluorescence. The burst phase and the first phase of the fluorescence kinetics were reversible, while the second phase and subsequent changes were irreversible. The dependence of the burst-phase and the first-phase fluorescence changes on the ADP concentration indicated that the burst phase represents non-cooperative nucleotide binding to GroEL, and that the first phase represents the allosteric transition of GroEL. Both the amplitude and the rate constant of the first phase of the fluorescence kinetics were well understood in terms of a kinetic allosteric model, which is a combination of transition state theory and the Monod-Wyman-Changeux allosteric model. From the kinetic allosteric model analysis, the relative free energy of the transition state in the metal fluoride-ADP-induced allosteric transition of GroEL was found to be larger than the corresponding free energy of the ATP-induced allosteric transition by more than 5.5kcal/mol. However, the X-ray scattering measurements indicated that the allosteric state induced by these metal fluoride-ADP complexes is structurally equivalent to the allosteric state induced by ATP. These results suggested that both the size and coordination geometry of gamma-phosphate (and its analogs) are related to the allosteric transition of GroEL. It was therefore concluded that the tetrahedral geometry of gamma-phosphate (or its analogs) and the inter-atomic distance ( approximately 1.6A) between phosphorus (vanadium, or metal atom) and oxygen (or fluorine) are both important for inducing the allosteric transition of GroEL, leading to the high selectivity of GroEL for ATP about ligand adenine nucleotides, which function as the preferred allosteric ligand.     

Differential scanning calorimetric studies of ethanol interactions with distearoylphosphatidylcholine: transition to the interdigitated phase

It is well established that ethanol and other amphipathic molecules induce the formation of a fully interdigitated gel phase in saturated like-chain phosphatidylcholines (PC's). We have previously shown that the induction of interdigitation in PC's by ethanol is dependent upon the alcohol concentration, the lipid chain length, and the temperature [Nambi, P., Rowe, E. S. & McIntosh, T. J. (1988) Biochemistry 27, 9175-9182]. In the present study, we have used high-sensitivity differential scanning calorimetry to investigate the transitions of distearoylphosphatidylcholine between the noninterdigitated and the interdigitated phases. The enthalpy of the L beta' to L beta I transition is approximately half that of the L beta' to P beta' transition which occurs in the absence of ethanol. The reversibility of these transitions has also been investigated by employing both heating and cooling scans in order to establish the most stable phases as a function of temperature and ethanol concentration. It has been demonstrated that the transition to the interdigitated phase is reversible as a function of temperature. Kinetic studies on the reverse transition (L beta I to L beta') demonstrate that this transition can be very slow, requiring weeks to reach completion. The rate depends upon temperature and ethanol concentration. The slow phase changes mean that the lipid can exist for long periods of time in a phase structure which is not the most stable state. The biological significance of this type of lipid behavior is the implication that the phase structure of biological membranes may depend not only on the most stable phase structure of the lipids present but also on the synthetic pathway or other kinetic variables.     

Intramolecular conformational transitions "random coil-helix-folded structure" in polypeptides.

A general theory has been developed for conformational intramolecular transitions in a single macromolecule with a high degree of polymerization (an infinite length model) capable of forming two types of ordered structures: the α-helix and the folded β-structure, as well as acquiring the random coil conformation. The phase diagram analysis of this system has shown that the regular β-structure state is separated from all other states of the chain by the phase boundary line. Any intersection of the phase boundary is a phase transition which can be either of the first order or second order, depending on values of the energy parameters of the system. Mechanisms of intramolecular rearrangements: β-structure–random coil and α-helix–β-structure have been discussed. It has been shown that there exist two different mechanisms for each of these rearrangements, and the regions of parameter variation corresponding to each mechanism have been specified.     

The mechanism of abrupt transition between theta and hyper-excitable spiking activity in medial entorhinal cortex layer II stellate cells

Recent studies have shown that stellate cells (SCs) of the medial entorhinal cortex become hyper-excitable in animal models of temporal lobe epilepsy. These studies have also demonstrated the existence of recurrent connections among SCs, reduced levels of recurrent inhibition in epileptic networks as compared to control ones, and comparable levels of recurrent excitation among SCs in both network types. In this work, we investigate the biophysical and dynamic mechanism of generation of the fast time scale corresponding to hyper-excitable firing and the transition between theta and fast firing frequency activity in SCs. We show that recurrently connected minimal networks of SCs exhibit abrupt, threshold-like transition between theta and hyper-excitable firing frequencies as the result of small changes in the maximal synaptic (AMPAergic) conductance. The threshold required for this transition is modulated by synaptic inhibition. Similar abrupt transition between firing frequency regimes can be observed in single, self-coupled SCs, which represent a network of recurrently coupled neurons synchronized in phase, but not in synaptically isolated SCs as the result of changes in the levels of the tonic drive. Using dynamical systems tools (phase-space analysis), we explain the dynamic mechanism underlying the genesis of the fast time scale and the abrupt transition between firing frequency regimes, their dependence on the intrinsic SC's currents and synaptic excitation. This abrupt transition is mechanistically different from others observed in similar networks with different cell types. Most notably, there is no bistability involved. 'In vitro' experiments using single SCs self-coupled with dynamic clamp show the abrupt transition between firing frequency regimes, and demonstrate that our theoretical predictions are not an artifact of the model. In addition, these experiments show that high-frequency firing is burst-like with a duration modulated by an M-current.     

Consideration of the Possibility that the slow step in protein denaturation reactions is due to cis-trans isomerism of proline residues.

A model is proposed to account for the observation that the denaturation of small proteins apparently occurs in two kinetic phases. It is suggested that only one of these phases--the fast one--is actually an unfolding process. The slow phase is assumed to arise from the cis-trans isomerism of proline residues in the denaturated protein. From model compound data, it is shown that the expected rate for isomerism is in satisfactory agreement with the rates actually observed for protein folding. It is also shown that a simple model of protein unfolding based on the isomerism concept is very successful in accounting for many known experimental characteristics of the kinetics and thermodynamic of protein denaturation. Thus, the model is able to predict that two kinetic phases will be seen in the transition region while none are seen in the base-line regions, that both the fast and slow refolding phases lead to the native protein as the product, that the fast phase becomes the only observable phase for jumps ending far in the denatured base-line region, that most or all small proteins show a limiting low-temperature activation energy of ca. 20,000 cal, and that the relaxtion time for the slow phase seen in cytochrome c denaturation is much shorter than for all other small proteins. By utilizing "double-jump" experiments, it is shown directly that the slow phase is not part of the unfolding process but that it corresponds to a transition among two or more denatured forms which have identical spectroscopic (286.5 nm) properties. Thus, the slow relaxation is "invisible" except in the transition region where it couples to the fast unfolding equilibrium. Finally, since the present model assumes that only one of the major kinetic phases seen in denaturation reactions is concerned with the denaturation process per se, it is in agreement with numerous thermodynamic studies which show consistency with the two-state model for unfolding.     

Equilibrium and kinetics of the allosteric transition of GroEL studied by solution X-ray scattering and fluorescence spectroscopy

We have studied the ATP-induced allosteric structural transition of GroEL using small angle X-ray scattering and fluorescence spectroscopy in combination with a stopped-flow technique. With X-ray scattering one can clearly distinguish the three allosteric states of GroEL, and the kinetics of the transition of GroEL induced by 85 microM ATP have been observed directly by stopped-flow X-ray scattering for the first time. The rate constant has been found to be 3-5s(-1) at 5 degrees C, indicating that this process corresponds to the second phase of the ATP-induced kinetics of tryptophan-inserted GroEL measured by stopped-flow fluorescence. Based on the ATP concentration dependence of the fluorescence kinetics, we conclude that the first phase represents bimolecular non-cooperative binding of ATP to GroEL with a bimolecular rate constant of 5.8 x 10(5)M(-1)s(-1) at 25 degrees C. Considering the electrostatic repulsion between negatively charged GroEL (-18 of the net charge per monomer at pH 7.5) and ATP, the rate constant is consistent with a diffusion-controlled bimolecular process. The ATP-induced fluorescence kinetics (the first and second phases) at various ATP concentrations (< 400 microM) occur before ATP hydrolysis by GroEL takes place and are well explained by a kinetic allosteric model, which is a combination of the conventional transition state theory and the Monod-Wyman-Changeux model, and we have successfully evaluated the equilibrium and kinetic parameters of the allosteric transition, including the binding constant of ATP in the transition state of GroEL.     

Modeling the Spontaneous Activity of the Auditory Cortex

We present a rate model of the spontaneous activity in the auditory cortex, based on synaptic depression. A Stochastic integro-differential system of equations is derived and the analysis reveals two main regimes. The first regime corresponds to a normal activity. The second regime corresponds to epileptic spiking. A detailed analysis of each regime is presented and we prove in particular that synaptic depression stabilizes the global cortical dynamics. The transition between the two regimes is induced by a change in synaptic connectivity: when the overall connectivity is strong enough, an epileptic activity is spontaneously generated. Numerical simulations confirm the predictions of the theoretical analysis. In particular, our results explain the transition from normal to epileptic regime which can be induced in rats auditory cortex, following a specific pairing protocol. A change in the cortical maps reorganizes the synaptic connectivity and this transition between regimes is accounted for by our model. We have used data from recording experiments to fit synaptic weight distributions. Simulations with the fitted distributions are qualitatively similar to the real EEG recorded in vivo during the experiments. We conclude that changes in the synaptic weight function in our model, which affects excitatory synapses organization and reproduces the changes in cortical map connectivity can be understood as the main mechanism to explain the transitions of the EEG from the normal to the epileptic regime in the auditory cortex. D.H is incumbent to the Hass Russell Career Chair Development.     

Mechanism of pH-triggered collapse of phosphatidylethanolamine liposomes stabilized by an ortho ester polyethyleneglycol lipid

The mechanism of pH-triggered destabilization of liposomes composed of a polyethyleneglycol-orthoester-distearoylglycerol lipid (POD) and phosphatidyl ethanolamine (PE) has been studied using an ANTS/DPX leakage and a lipid-mixing assay. We developed a kinetic model that relates POD hydrolysis to liposome collapse. This minimum-surface-shielding model describes the kinetics of the pH-triggered release of POD/PE liposomes. In the model, when acid-catalyzed hydrolysis lowers the mole percentage of POD on the liposome surface to a critical level, intervesicular lipid mixing is initiated, resulting in a burst of contents release. Two phases of content leakage are observed: a lag phase and a burst phase. During the lag phase, less than 20% of liposomal contents are released and the leakage begins to accelerate when approaching to the transition point. During the burst phase, the leakage rate is dependent on interbilayer contact. The burst phase occurs when the surface density of the PEG lipid is 2.3 +/- 0.6 mol%, regardless of the pH. Vesicles containing 4 mol% of a pH-insensitive PEG-lipid conjugate and 10% POD did not leak contents or collapse at any pH. These data are consistent with the stalk theory to describe the lamellar-to-inverted hexagonal phase transition and set a lower bound of approximately 16 PE lipids on the external monolayer as the contact site required for lipid mixing between two bilayers.     

Chromatophore heterogeneity explains phenomena seen in Rhodobacter sphaeroides previously attributed to supercomplexes

It is generally considered that metabolic reactions are well described by homogeneous kinetic models in which the reaction phase is statistically uniform. In membranes, especially in photosynthetic systems where the protein complement is high, it has recently been recognized that effects of local heterogeneity might contribute additional factors that perturb the kinetic behavior, and require more extensive treatment. We show in this paper that statistical heterogeneity in vesicular systems can also contribute to quite marked discrepancies from the behavior expected from standard kinetic and thermodynamic models, for reactions involving free diffusion in the aqueous phase. We explain the kinetic and thermodynamic effects observed in studies of photosynthetic electron transfer in cells and chromatophores from Rhodobacter sphaeroides previously attributed to supercomplexes, in terms of a model based on heterogeneity in distribution of electron transfer components among the chromatophore population. We discuss examples of data inconsistent with the supercomplex model, but well explained by the heterogeneity model.     

Mechanism of Agrobacterium beta-glucosidase: kinetic studies.

The beta-glucosidase from Agrobacterium faecalis (previously Alcaligenes faecalis) has been subjected to a detailed kinetic investigation with a range of substrates to probe its specificity and mechanism. It has a relatively broad specificity for the substrate sugar moiety and exhibits a classical pH dependence for its kinetic parameters with three different substrates and an identical pH dependence for its inactivation by a mechanism-based inactivator, cyclophellitol. Measurement of kcat and Km values for a series of aryl glucoside substrates has allowed construction of a Bronsted plot, the concave-downward shape of which is consistent with the anticipated two-step mechanism involving a glucosyl-enzyme intermediate which is formed and hydrolyzed via oxocarbonium ion-like transition states. The slope of the leaving group-dependent portion of the Bronsted plot (beta 1g = -0.7) indicates a large degree of bond cleavage at the transition state. Secondary deuterium kinetic isotope effects measured for five different aryl glucosides are also consistent with this mechanism and further suggest that the transition state for formation of the glucosyl-enzyme intermediate, probed with the slower substrates for which kH/kD = 1.06, is more SN2-like than that for its hydrolysis (for which kH/kD = 1.11). Reasons for this difference are proposed, and values of Ki for several ground-state and transition-state analogue inhibitors are presented which support the concept of sp2-hybridized transition states.     

Some Kinetic Singularities of Mg2+-Dependent Mn-ATPase in Rat Brain Synaptic Membranes

Mn(2+) stimulated change of Mg-ATPase activity has been found in the synaptic fraction of rat brain that was named Mn-ATPase. Investigation of the molecular mechanism has shown that Mn-ATPase is a multi-sited enzyme system whose minimum functional unit is a dimer. Its substrate is the MgATP complex. The number of sites for Mn(2+) as for essential activators and that of full-effect inhibitors are equal, n?=?m?=?1. Studying regulation of the Mn-ATPase system by Mg(2+) has shown that Mg(2+) represents a double-sided effect modifier, namely, it activates the enzyme system at low concentration but inhibits at high concentration. Supposedly, binding-release of MgATP and Mg(2+) from the enzyme would be performed by a randomized mechanism. When analyzing experiments by using the kinetic method of complex curves, a "minimal model" for Mn-ATPase has been created.     

On the relationship between the Hill coefficients for steady-state and transient kinetic data: A criterion for concerted transitions in allosteric proteins

A frequently used measure for the extent of cooperativity in ligand binding by allosteric proteins is the Hill coefficient. Hill coefficients can be measured for steady-state kinetic data and also for transient kinetic data. Here, the relationship between the two types of Hill coefficients is analysed. It is shown that a value of 1 for the ratio of the two Hill coefficients is a test for a concerted ligand-induced transition between two conformations of the protein, in accordance with the Monod-Wyman-Changeux model. A value of 1 for this ratio has recently been observed for a series of chaperonin GroEL mutants suggesting that ATP-induced allosteric transitions in this protein are concerted.     

Dynamics of the cluster model of protein folding

The cluster model of protein folding [Kanehisa, M. I. & Tsong, T. Y. (1978) J. Mol. Biol. 124 , 177–194] is further investigated for the thermodynamic and kinetic properties of protein folding–unfolding transitions. A cluster is a locally formed ordered region in the polypeptide chain due to cooperative interactions among residues. In the cluster model a cooperative term is assigned as proportional to the surface area of a globular cluster. This assignment is compared with that for the helix–coil transition of homopolypeptides, where the cooperative term is proportional to the two ends of a linear helical sequence. The dynamics of the cluster model exhibit a slow phase, which is well-separated from other faster phases, because of the cooperative interaction of the macrosystem. This slow phase not only appears within the transition region, but can also persist well below the transition region if the cooperativity depends on the external condition. The amplitudes of certain kinetic phases can vary depending on the choice of physical parameters monitoring the reaction. Thus the same reaction may display different time courses. The qualitative aspects of the folding dynamics are as follows. In one case the rate-limiting formation of a critical-size cluster is followed by its rapid growth, while in the other the rate-limiting step appears in a later stage, where preformed smaller clusters merge into larger ones. The former case is similar to the dynamics of the helix–coil transition, and the latter represents a stepwise mechanism of protein structure formation.     

Kinetics and mechanism of the barotropic lamellar gel/lamellar liquid crystal phase transition in fully hydrated dihexadecylphosphatidylethanolamine: a time-resolved x-ray diffraction study using pressure jump.

The kinetics and mechanism of the barotropic lamellar gel (L beta')/lamellar liquid crystal (L alpha) phase transition in fully hydrated 1,2-dihexadecyl-sn-glycero-3-phosphoethanolamine (DHPE) has been studied using time-resolved x-ray diffraction (TRXRD). The phase transition was induced by pressure jumps of varying amplitudes in both the pressurization and depressurization directions at controlled temperature (78 degrees C). Both low- and wide-angle diffracted x rays were recorded simultaneously in live time using an x-ray-sensitive image intensifier coupled to a CCD camera and Super-VHS videotape recorder. Such an arrangement allowed for the direct and quantitative characterization of the long- (lamellar repeat spacing) and short-range order (chain packing) during a kinetic experiment. The image-processed live-time x-ray diffraction data were fitted using a nonlinear least-squares model, and the parameters of the fits were monitored continuously throughout the transition. The pressure-induced transitions from the L alpha to the L beta' phase and from the L beta' to the L alpha phase was two-state (no formation of intermediates apparent during the transition) to within the sensitivity limits of the method. The corresponding transit time (the time during which both phases coexist) associated with the long- and short-range order of the pressurization-induced L alpha-to-L beta' phase transition decreased to a limiting value of approximately 50 ms with increasing pressure jump amplitude. This limiting value was close to the response time of the detector/recording system. Thus, the intrinsic transit time of this transition in fully hydrated DHPE at 78 degrees C was less than or equal to 50 ms. In contrast, the depressurization-induced L beta'-to-L alpha phase transition was slower, taking approximately 1 s to complete, and occurred with no obvious dependence of the transit time on pressure jump amplitude. In the depressurization jump experiment, the lipid responded rapidly to the pressure jump in the L beta' phase up to the rate-determining L beta'-to-L alpha transition. Such behavior was examined carefully, as it could complicate the interpretation of phase transition kinetic measurements.     

Dynamical changes in neurons during seizures determine tonic to clonic shift

A tonic-clonic seizure transitions from high frequency asynchronous activity to low frequency coherent oscillations, yet the mechanism of transition remains unknown. We propose a shift in network synchrony due to changes in cellular response. Here we use phase-response curves (PRC) from Morris-Lecar (M-L) model neurons with synaptic depression and gradually decrease input current to cells within a network simulation. This method effectively decreases firing rates resulting in a shift to greater network synchrony illustrating a possible mechanism of the transition phenomenon. PRCs are measured from the M-L conductance based model cell with a range of input currents within the limit cycle. A large network of 3000 excitatory neurons is simulated with a network topology generated from second-order statistics which allows a range of population synchrony. The population synchrony of the oscillating cells is measured with the Kuramoto order parameter, which reveals a transition from tonic to clonic phase exhibited by our model network. The cellular response shift mechanism for the tonic-clonic seizure transition reproduces the population behavior closely when compared to EEG data.     

Interaction of mannose-6-phosphate with the hysteretic transition in glucose-6-phosphate hydrolysis in intact liver microsomes.

We showed previously that glucose-6-phosphatase activity was characterised in intact liver microsomes by a hysteretic transition between a rapid and a slower catalytic form of the enzyme. We have now further investigated the substrate specificity of these two kinetic forms. It was found that the pre-incubation of intact microsomes with mannose-6-phosphate or glucose-6-phosphate (50 microM for 30 s) suppressed the burst in glucose-6-phosphatase activity, that the hysteretic transition was reversible and that mannose-6-phosphate inhibited glucose-6-phosphate hydrolysis during the first seconds of incubation, but not anymore after the burst. Our results indicate (i) that mannose-6-phosphate is recognised by the enzyme and can promote the hysteretic transition and (ii) that the transient phase is part of the catalytic mechanism itself.