Quantal Behavior Research Articles

Classical limit of a quantal nano-magnet in an anisotropic environment

The time evolution of a model quantal magnetic moment proportional to an angular momentum, S, is studied and compared to that of a classical magnetic moment. The presence of an anisotropy quadratic term in the Hamiltonian makes classical and quantal behaviours qualitatively different for small values of the angular momentum, S. When S is increased, the classical behaviour is retrieved for a finite amount of time, even in the presence of magnetic anisotropy terms; however, in general, this limit is only reached for very large S values. The classical vs quantal behaviour is discussed in terms of three characteristic times of the system: the classical precession time, the quantal revival time and the spreading time. This allows showing that the closer to equilibrium the initial conditions are, the easier the classical limit is reached.

Beyond the Dirac Phase Factor: Dynamical Quantum Phase-Nonlocalities in the Schrödinger Picture

Generalized solutions of the standard gauge transformation equations are presented and discussed in physical terms. They go beyond the usual Dirac phase factors and they exhibit nonlocal quantal behavior, with the well-known Relativistic Causality of classical fields affecting directly the phases of wavefunctions in the Schroedinger Picture. These nonlocal phase behaviors, apparently overlooked in path-integral approaches, give a natural account of the dynamical nonlocality character of the various (even static) Aharonov-Bohm phenomena, while at the same time they seem to respect Causality. Indeed, for particles passing through nonvanishing magnetic or electric fields they lead to cancellations of Aharonov-Bohm phases at the observation point, generalizing earlier semiclassical experimental observations (of Werner & Brill) to delocalized (spread-out) quantum states. This leads to a correction of previously unnoticed sign-errors in the literature, and to a natural explanation of the deeper reason why certain time-dependent semiclassical arguments are consistent with static results in purely quantal Aharonov-Bohm configurations. These nonlocalities also provide a remedy for misleading results propagating in the literature (concerning an uncritical use of Dirac phase factors, that persists since the time of Feynman's work on path integrals). They are shown to conspire in such a way as to exactly cancel the instantaneous Aharonov-Bohm phase and recover Relativistic Causality in earlier "paradoxes" (such as the van Kampen thought-experiment), and to also complete Peshkin's discussion of the electric Aharonov-Bohm effect in a causal manner. The present formulation offers a direct way to address time-dependent single- vs double-slit experiments and the associated causal issues -- issues that have recently attracted attention, with respect to the inability of current theories to address them.

Mechanism of the Mitochondrial Cytochrome C Release Wave in Bid-Induced Apoptosis

Bid, a BH3-only Bcl2 family protein, plays a central role in apoptosis. Bid is cleaved by caspase-8 and other enzymes forming tBid that induce mitochondrial outer membrane (OMM) permeabilization and cytochrome c (cyto-c) release. However a mystery remains how Bid synchronizes the function of a large number of discrete organelles, particularly in mitochondria-rich liver or muscle cells. Here we showed that tBid (0.5-50nM) elicited progressive OMM permeabilization and complete cyto-c release with a dose-dependent lag time and rate in H9c2 cell populations. Once started, the OMM permeabilization was not prevented by tBid washout. In contrast, the dose-response for digitonin-induced OMM permeabilization displayed quantal behavior. In single cell imaging studies, permeabilized H9c2 and primary human cardiac cells transfected with cyto-c-GFP showed complete tBid-induced cyto-c-GFP release closely followed by mitochondrial depolarization. The cyto-c-GFP release started at discrete sites and propagated through the mitochondria with a constant velocity and a relatively stable kinetic of release in each organelle. Similar tBid-induced cyto-c-GFP release wave was documented in intact H9c2 cells transfected with tBid. The waves were not dependent on Ca2+, caspase activation or permeability transition pore opening. However, treatment with MnTMPyP, a ROS scavenger or overexpression of mitochondrial superoxide dismutase suppressed the coordinated cyto-c release and also inhibited tBid-induced cell death. On the other hand, both superoxide and hydrogen peroxide sensitized mitochondria to the tBid-induced permeabilization. Thus, tBid engages a ROS-dependent inter-mitochondrial signaling mechanism for spatial amplification of the apoptotic signal by mitochondrial waves.

The Role of the Pore-forming Region in the Regulation of IP3 Receptor by Luminal Ca2+

It is well known that submaximal concentrations of IP3 release only a portion of the intracellular Ca2+ store via the IP3 receptor (IP3R), a phenomenon known as “quantal” Ca2+ release. Such quantal behavior of IP3R is thought to be due to the feedback regulation of the channel by luminal Ca2+. A high level of luminal Ca2+ enhances the sensitivity of IP3R to IP3, while a reduced luminal Ca2+ level desensitizes IP3R. Despite its importance, the molecular basis underling the regulation of IP3R by luminal Ca2+ is unknown. Ryanodine receptors (RyRs), another family of intracellular Ca2+ release channels, also exhibit quantal Ca2+ release in response to agonists, and are regulated by luminal Ca2+. We have recently demonstrated that mutations in the TM10 helix (the pore inner helix) of the RyR2 channel markedly alter the sensitivity of the channel to activation by luminal Ca2+. Given the high degree of sequence homology in the channel pore-forming region between RyR and IP3R, we hypothesize that the TM6 helix in IP3R, corresponding to TM10 in RyR, is also important for luminal Ca2+ regulation of IP3R. To test this hypothesis, we have generated a number of mutations in the TM6 of IP3R and established stable, inducible HEK293 cell lines expressing these mutants. By monitoring the ER luminal Ca2+ level using a fluorescent ER Ca2+ sensor protein, D1ER, we found that mutations in TM6 either increase or decrease the rate of IP3-induced Ca2+ release in permeablized mutant cells. These mutations also affect the sensitivity of ATP-triggered Ca2+ release in intact cells. Further studies at the single channel level should provide new insights into the role of the pore-forming region in the luminal Ca2+ regulation of IP3R.

Distinct Quantal Features of AMPA and NMDA Synaptic Currents in Hippocampal Neurons: Implication of Glutamate Spillover and Receptor Saturation

Excitatory postsynaptic currents (EPSCs) were studied in the CA1 pyramidal cells of rat hippocampal slices. Components mediated by α-amino-3-hydroxy-5-methylisoxazole-4-proprionic acid (AMPA) and by N-methyl-D-aspartate (NMDA) receptors were separated pharmacologically. Quantal parameters of AMPA and NMDA receptor-mediated EPSCs were obtained using both maximal likelihood and autocorrelation techniques. Enhancement of transmitter release with 4-aminopyridine caused a significant increase in quantal size of NMDA EPSC. This was accompanied by a slowing of the EPSC decay. The maximal number of quanta in the NMDA current was unchanged, while the probability of quantal event dramatically enhanced. In contrast, neither the quantal size nor the kinetics of AMPA EPSC was altered by 4-aminopyridine, while the maximal number of quanta increased. These changes in the quantal parameters are consistent with a transition to multivesicular release of the neurotransmitter. Spillover of excessive glutamate on the nonsynaptic areas of dendritic spines causes an increase in the quantal size of NMDA synaptic current. The difference in quantal behavior of AMPA and NMDA EPSCs implies that different mechanisms underlie their quantization: the additive response of nonsaturated AMPA receptors contrasts with the variable involvement of saturated intrasynaptic and nonsaturated extrasynaptic NMDA receptors.

Polarized expression of G protein-coupled receptors and an all-or-none discharge of Ca2+ pools at initiation sites of [Ca2+]i waves in polarized exocrine cells.

In the present work we examined localization and behavior of G protein-coupled receptors (GPCR) in polarized exocrine cells to address the questions of how luminal to basal Ca(2+) waves can be generated in a receptor-specific manner and whether quantal Ca(2+) release reflects partial release from a continuous pool or an all-or-none release from a compartmentalized pool. Immunolocalization revealed that expression of GPCRs in polarized cells is not uniform, with high levels of GPCR expression at or near the tight junctions. Measurement of phospholipase Cbeta activity and receptor-dependent recruitment and trapping of the box domain of RGS4 in GPCRs complexes indicated autonomous functioning of G(q)-coupled receptors in acinar cells. These findings explain the generation of receptor-specific Ca(2+) waves and why the waves are always initiated at the apical pole. The initiation site of Ca(2+) wave at the apical pole and the pattern of wave propagation were independent of inositol 1,4,5-trisphosphate concentration. Furthermore, a second Ca(2+) wave with the same initiation site and pattern was launched by inhibition of sarco/endoplasmic reticulum Ca(2+)-ATPase pumps of cells continuously stimulated with sub-maximal agonist concentration. By contrast, rapid sequential application of sub-maximal and maximal agonist concentrations to the same cell triggered Ca(2+) waves with different initiation sites. These findings indicate that signaling specificity in pancreatic acinar cells is aided by polarized expression and autonomous functioning of GPCRs and that quantal Ca(2+) release is not due to a partial Ca(2+) release from a continuous pool, but rather, it is due to an all-or-none Ca(2+) release from a compartmentalized Ca(2+) pool.

Analysis of synaptic quantal depolarizations in smooth muscle using the wavelet transform.

The time-frequency characteristics of synaptic potentials contain valuable information about the process of neurotransmission between nerves and their target organs. For example, at the synapse between autonomic nerves and smooth muscle, two central issues of neurophysiology, i.e., 1) the probability of neurotransmitter release and 2) the quantal behavior of transmission can be deduced from analysis of the rising phases of evoked excitatory junction potentials (eEJP's) recorded from smooth muscle. eEJP rising phases are marked by prominent inflexions, which reflect these features of neuronal activity. Since these inflexions contain time-varying frequency information, we have applied recent techniques of time-frequency analysis based upon wavelet transforms to eEJP's recorded from the guinea-pig vas deferens in vitro. We find that these techniques allow accurate and convenient characterization of neuronal release sites, and that their probability of release falls between 0.001-0.004. We have also analyzed eEJP's recorded in the presence of the chemical 1-heptanol, which reveals quantal depolarizations. These results have helped clarify the nature of the quantal depolarizations that underly eEJP's. The present method offers significant advantages over those previously employed for these tasks, and holds promise as a novel approach to the analysis of synaptic potentials.

Implications of quantal motor action in biological systems.

We demonstrate in this paper that quantal behavior is a central feature of biological motile and contractile systems. Step-like behavior has been demonstrated in the interaction between single molecules and filaments both in the kinesin-microtubule system and in the myosin-actin filament system. We show here that the step-like molecular features appear also in the single intact sarcomere. We studied single sarcomeres of single bumble-bee myofibrils, both in the unactivated and activated states. Myofibril-length changes induced by a motor-imposed ramp were accompanied by corresponding sarcomere-length changes. However, the sarcomere-length changes were stepwise. Computer analysis of the stepwise shortening patterns revealed a step-size distribution containing multiple peaks. In the activated state, the peaks were separated by 2.7 nm per half-sarcomere which is the linear actin-subunit spacing. Thus, translation steps are an integer multiple of the actin-subunit spacing. This result parallels the one observed in the kinesin-tubulin spacing, where step size is a multiple of the tubulin-subunit spacing. In the muscle system, however, the steps are preserved on a macroscopic scale, implying high synchrony. The quantal steps are easily explained by a model in which the actin filament propels itself over stationary cross-bridges: if actin binds to the cross-bridges between steps, then the observed quantal result is inevitable. As probes of contractile phenomena approach the molecular level, the discrete unitary events underlying contraction begin to emerge. Thus, step-like behavior is observed as the single kinesin molecule translates along the microtubule, as the single myosin molecule translates over the actin filament, and as the single isolated titin molecule is stretched.

Evidence for hybrid classical - quantal behaviour in state- and angle-resolved atom - diatom scattering

We present measurements of the state-to-state differential scattering cross section (DCS) for with Xe using a new sub-Doppler spectroscopic method and compare results with those obtained using molecular beam techniques on the same system; the agreement is good. Criteria for comparison are based on the recent finding (McCaffery A J and Wilson R J 1996 Phys. Rev. Lett. 77 48) that simple quasiclassical vector relations determine the direction of the initial relative velocity vector and the scattering angle. The incident velocity direction is such that the perpendicular component just opens the inelastic channel and the parallel component is scattered. The relationship is Newtonian but is modified by the molecule's characteristic quantum structure. Angular distributions from a range of experiments are found to obey the vector relation, suggesting that atom - molecule collisions are controlled by a quantum-modified Newtonian mechanics, the modification arising as a consequence of the internal energy level structure of the molecule. We introduce the term quantum-constrained kinematics to describe the hybrid mechanics and suggest that this may also influence other collisional events.

Incremental Ca2+ mobilization by inositol trisphosphate receptors is unlikely to be mediated by their desensitization or regulation by luminal or cytosolic Ca2+.

The kinetics of Ins(1,4,5)P3 (InsP3)-stimulated Ca2+ release from intracellular stores are unusual in that submaximal concentrations of InsP3 rapidly release only a fraction of the InsP3-sensitive Ca2+ stores. By measuring unidirectional 45Ca2+ efflux from permeabilized rat hepatocytes, we demonstrate that such quantal responses to InsP3 occur at all temperatures between 2 and 37 degrees C, but at much lower rates at the lower temperatures. Preincubation with submaximal concentrations of InsP3, which themselves evoked quantal Ca2+ release, had no effect on the sensitivity of the stores to further additions of InsP3. The final Ca2+ content of the stores was the same whether they were stimulated with two submaximal doses of InsP3 or a single addition of the sum of these doses. Such incremental responses and the persistence of quantal behaviour at 2 degrees C indicate that InsP3-evoked receptor inactivation is unlikely to be the cause of quantal Ca2+ mobilization. Reducing the Ca2+ content of the intracellular stores by up to 45% did not affect their sensitivity to InsP3, but substantially reduced the time taken for each submaximal InsP3 concentration to exert its full effect. These results suggest that neither luminal nor cytosolic Ca2+ regulation of InsP3 receptors are the determinants of quantal behaviour. Our results are not therefore consistent with incremental responses to InsP3 depending on mechanisms involving attenuation of InsP3 receptor function by cytosolic or luminal Ca2+ or by InsP3 binding itself. We conclude that incremental activation of Ca2+ release results from all-or-nothing emptying of stores with heterogeneous sensitivities to InsP3. These characteristics allow rapid graded recruitment of InsP3-sensitive Ca2+ stores as the cytosolic InsP3 concentration increases.

Quantum fluctuation effects on nuclear fragment formation

Multifragmentation in Au+Au collisions is investigated at incident energies in the range 100–400 MeV per nucleon by means of a recently developed quantal Langevin model. The inclusion of quantum fluctuations enhances the average multiplicity of intermediate mass fragments, especially in central collisions. This is mainly because the excitation energies of fragments are reduced due to the quantal behavior of intrinsic specific heat.

Quantal Motor Action in Muscle Contraction

AbstractIt is becoming clear that quantal behavior is a central feature of contractile systems. Steplike behavior has been demonstrated in the kinesin - microtubule system and in the myosin - actin filament system-both on molecular scale. We show here that step-like features appear also in the single intact sarcomere. We studied single sarcomeres of single bumblebee myofibrils. Motorimposed ramp length changes on activated myofibrils resulted in sarcomere-length changes that were stepwise. Computer analysis of the stepwise shortening patterns revealed a step-size distribution containing multiple peaks. The peaks were separated by 2.7 nm per half-sarcomere which is the linear actin-subunit spacing. Thus, translation steps are an integer multiple of the actin-subunit spacing. This result parallels the one observed in the kinesin-tubulin spacing where step size is a multiple of the tubulin-subunit spacing. In the muscle system, however, the steps are preserved on a macroscopic scale, implying high synchrony. The quantal steps are easily explained by a model in which the actin filament propels itself over stationary cross-bridges: if actin binds to the cross-bridges between steps, then the observed quantal result is inevitable.

Mechanisms responsible for quantal Ca2+ release from inositol trisphosphate-sensitive calcium stores.

Activation of cells by hormones, growth factors or neurotransmitters leads to an increased production of inositol trisphosphate (InsP3) and, after activation of the InsP3 receptor (InsP3R), to Ca2+ release from intracellular Ca2+ stores. The release of intracellular Ca2+ is characterised by a graded response when submaximal doses of agonists are used. The basic phenomenon, called "quantal Ca2+ release", is that even the maintained presence of a submaximal dose of agonist or of InsP3 for long time periods (up to 20 min) provokes only a partial release of Ca2+. This partial, or quantal, release phenomenon is due to the fact that the initially very rapid InsP3-induced Ca2+ release eventually develops into a much slower release phase. Physiologically, quantal release allows the Ca2+ stores to function as increment detectors and to induce local Ca2+ responses. The basic mechanism for quantal release of Ca2+ is presently not known. Possible mechanisms to explain the quantal behaviour of InsP3- induced Ca2+ release include the presence of InsP3Rs with varying sensitivities for InsP3, heterogeneous InsP3R distribution, intrinsic inactivation of the InsP3Rs, and regulation of the InsP3Rs by Ca2+ store content. This article reviews critically the evidence for the various mechanisms and evaluates their functional importance. A Ca2+-mediated conformational change of the InsP3R is most likely the key feature of the mechanism for quantal Ca2+ release, but the exact mode of operation remains unclear. It should also be pointed out that in intact cells more than one mechanism can be involved.

Regulation of inositol trisphosphate receptors by luminal Ca2+ contributes to quantal Ca2+ mobilization.

The quantal behaviour of inositol trisphosphate (InsP3) receptors allows rapid graded release of Ca2+ from intracellular stores, but the mechanisms are unknown. In Ca2+-depleted stores loaded with Fura 2, InsP3 caused concentration dependent increases in the rates of fluorescence quench by Mn2+ that were unaffected by prior incubation with InsP3, indicating that InsP3 binding did not cause desensitization. When Fura 2 was used to report the luminal free [Ca2+] after inhibition of further Ca2+ uptake, submaximal concentrations of InsP3 caused rapid, partial decreases in fluorescence ratios. Subsequent addition of a maximal InsP3 concentration caused the fluorescence to fall to within 5% of that recorded after ionomycin. Addition of all but the lowest concentrations of InsP3 to stores loaded with the lower affinity indicator, Calcium Green-5N, caused almost complete emptying of the stores at rates that increased with InsP3 concentration. The lowest concentration of InsP3 (10 nM) slowly emptied approximately 80% of the stores, but within 3 min the rate of Ca2+ release slowed leaving approximately 7 microM Ca2+ within the stores, which was then rapidly released by a maximal InsP3 concentration. In stores co-loaded with both indicators, InsP3-evoked Ca2+ release appeared quantal with Fura 2 and largely non-quantal with Calcium Green-5N; the discrepancy is not, therefore, a direct effect of the indicators. The fall in luminal [Ca2+] after activation of InsP3 receptors may, therefore, cause their inactivation, but only after the Ca2+ content of the stores has fallen by approximately 95% to < or = 10 microM.

Semiclassical dynamics of a bound system in a high-frequency field

The quantal behaviour of a particle in a one-dimensional triangular potential well, driven by a monochromatic electric field, is studied. A classical high-frequency expansion together with semiclassical uniform methods are used to obtain an explicit form of the Floquet evolution operator in the unperturbed basis. A local exact solution is found for the eigenvalue equation of this operator under certain conditions. The local solution provides a tool for the quantitative investigation of the eigenstates. It predicts the appearance of quasi-resonances, or photonic states, and gives their location, shape and width as a function of parameters. It also predicts a local crossover from a decaying region to a more extended region as a function of n, with a point of crossover nc between them. The results concerning the local structures are used to justify and extend a previously suggested method for the investigation of the asymptotic properties of the eigenstates. These are found to decay with a power depending on the field parameters (first proposed by Benvenuto et al., 1991). The specific system studied here is suggested as a prototype model for a class of driven one-dimensional bound systems. Whose main characteristic is an increasing density of states as a function of energy.

Quantal behaviour of magnetically kicked electron

The problem of a free electron periodically kicked by a magnetic field has been solved. The system shows a transition from quantum recurrence to instability at ωT=2 where ω is the Larmor frequency andT is the period of the kick. The existence of recurrent behaviour amounts to the confinement of the electron by magnetic kicking. Since the theory holds for all types of charged particles, it has many practical applications.

Gaussian wave-packet dynamics: Semiquantal and semiclassical phase-space formalism.

Gaussian wave packets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an extended potential formulation. We develop Gaussian semiquantal dynamics to provide a phase-space formalism, and construct a propagator with desirable qualities. We qualitatively evaluate the behavior of these semiquantal equations, and show that they reproduce the quantal behavior better than the standard Gaussian semiclassical dynamics. We also show that these semiclassical equations arise as non-self-consistent (in \ensuremath{\Elzxh}) truncations to semiquantal dynamics. This enables us to introduce an extended semiclassical dynamics that retains the power of the Hamiltonian phase-space formulation. Finally, we show how to obtain approximate eigenvalues and eigenfunctions in this formalism, and demonstrate with an example that this works well even for a classically strongly chaotic Hamiltonian.

Compartmentalization of Ca2+ signaling and Ca2+ pools in pancreatic acini. Implications for the quantal behavior of Ca2+ release.

Streptolysin O-permeabilized pancreatic acini were used to study compartmentalization of Ca2+ signaling and Ca2+ pools. In these cells, the inositol 1,4,5-trisphosphate (IP3)-dependent Ca2+ channels could be activated by a number of agonists (carbachol, cholecystokinin, or bombesin) or by activation of the entire cellular phospholipase C pool with GTP gamma S. Surprisingly, each of the antagonists interacting with acinar cells inactivated the channels after stimulation with GTP gamma S. In addition, when permeabilized cells were stimulated with more than one agonist, any antagonist to the specific agonists employed inactivated the channels. The aberrant behavior of the antagonists in permeable cells was not related to a loss of specificity since (a) when added before GTP gamma S, the antagonists had no effect on Ca2+ release and (b) when cells were stimulated with a single agonist, the antagonists prevented only the effect of their specific agonist. The differential behavior of the antagonists in intact and permeable cells suggests a compartmentalization of Ca2+ signaling into separate, agonist-specific units that is modified by cell permeabilization. Further evidence for compartmentalization of signaling was obtained by showing that the partial agonist (the CCK octapeptide analogue JMV-180) can access and release only 50% of the cholecystokinin- or IP3-mobilizable Ca2+ pool in intact and permeable cells. Kinetic measurements revealed a multiphasic time course of agonist-evoked Ca2+ release in permeable cells. At high agonist concentrations, all phases were fast and merged into an apparent single event of Ca2+ release. The phases were separated by three independent protocols: reduction in agonist concentrations, addition of heparin, or addition of guanosine-5'-O-(thio)diphosphate. Since all protocols that caused phase separation reduce IP3-mediated Ca2+ release, these findings demonstrate heterogeneity in the affinity for IP3 of channels present in compartmentalized Ca2+ pools of the same cells. Compartmentalization of signaling and the heterogeneity in the affinity for IP3 resulted in a quantal agonist-evoked Ca2+ release. The overall findings are discussed in the context of an integrated model of compartmentalization of signaling complexes, Ca2+ pools, and IP3-activated Ca2+ channels.

Radiological assessment of pulmonary oedema: a new principle. Oleic acid lung injury

Histological and physiological evidence suggests that in pulmonary ooedema the sequence of fluid accumulation in the lung is quantal (all-or-one). We have proposed that increased variation in radiographic density with respiration in pulmonary oedema can be attributed to quantal alveolar behaviour: the more severe the oedema, the greater the variation. To test this hypothesis CT scans of the chest were performed in 5 pigs on inspiratory and expiratory breath-holding at baseline and at various degrees of oleic acid pulmonary oedema. Extravascular lung water (EVLW) was monitored with the double indicator dilution technique to match these observations. At baseline, during induction and throughout the course of pulmonary oedema variation of radiographic attenuation with respiration correlated well with EVLW (R = 0.98). With extensive alveolar oedema this variation did not match EVLW. It is concluded that the principle of quantal alveolar behaviour is a useful model for analysis of pulmonary oedema and its realtionship with respiration.

Quantum instability for a wave packet kicked periodically by a quadratic potential

The quantal behaviour of wave packet periodically kicked by a quadratic potential has been investigated using Floquet theory. The wave function of the particle afterN kicks has been determined. This wave function has been utilized to obtain the packet width, energy and loss of memory as a function of the number of kicks. It has also been shown that the free particle wave packet quasienergy spectrum makes a transition from discrete to absolutely continuous atɛ T=2. The behaviour forɛT>2 is quantum mechanically irregular.