Double Exponential Time Research Articles

Temperature dependence of N-methyl- d-aspartate receptor channels and N-methyl- d-aspartate receptor excitatory postsynaptic currents

N-methyl- d-aspartate (NMDA) receptors (NMDARs) are highly expressed in the CNS and mediate the slow component of excitatory transmission. The present study was aimed at characterizing the temperature dependence of the kinetic properties of native NMDARs, with special emphasis on the deactivation of synaptic NMDARs. We used patch-clamp recordings to study synaptic NMDARs at layer II/III pyramidal neurons of the rat cortex, recombinant GluN1/GluN2B receptors expressed in human embryonic kidney (HEK293) cells, and NMDARs in cultured hippocampal neurons. We found that time constants characterizing the deactivation of NMDAR-mediated excitatory postsynaptic currents (EPSCs) were similar to those of the deactivation of responses to a brief application of glutamate recorded under conditions of low NMDAR desensitization (whole-cell recording from cultured hippocampal neurons). In contrast, the deactivation of NMDAR-mediated responses exhibiting a high degree of desensitization (outside-out recording) was substantially faster than that of synaptic NMDA receptors. The time constants characterizing the deactivation of synaptic NMDARs and native NMDARs activated by exogenous glutamate application were only weakly temperature sensitive (Q 10=1.7–2.2), in contrast to those of recombinant GluN1/GluN2B receptors, which are highly temperature sensitive (Q 10=2.7–3.7). Ifenprodil reduced the amplitude of NMDAR-mediated EPSCs by ∼50% but had no effect on the time course of deactivation. Analysis of GluN1/GluN2B responses indicated that the double exponential time course of deactivation reflects mainly agonist dissociation and receptor desensitization. We conclude that the temperature dependences of native and recombinant NMDAR are different; in addition, we contribute to a better understanding of the molecular mechanism that controls the time course of NMDAR-mediated EPSCs.

Ether‐à‐go‐go‐related gene K+ channels contribute to threshold excitability of mouse auditory brainstem neurons

The ionic basis of excitability requires identification and characterisation of expressed channels and their specific roles in native neurons. We have exploited principal neurons of the medial nucleus of the trapezoid body (MNTB) as a model system for examining voltage-gated K(+) channels, because of their known function and simple morphology. Here we show that channels of the ether-à-go-go-related gene family (ERG, Kv11; encoded by kcnh) complement Kv1 channels in regulating neuronal excitability around threshold voltages. Using whole-cell patch clamp from brainstem slices, the selective ERG antagonist E-4031 reduced action potential (AP) threshold and increased firing on depolarisation. In P12 mice, under voltage-clamp with elevated [K(+)](o) (20 mm), a slowly deactivating current was blocked by E-4031 or terfenadine (V(0.5,act) = -58.4 +/- 0.9 mV, V(0.5,inact) = -76.1 +/- 3.6 mV). Deactivation followed a double exponential time course (tau(slow) = 113.8 +/- 6.9 ms, tau(fast) = 33.2 +/- 3.8 ms at -110 mV, tau(fast) 46% peak amplitude). In P25 mice, deactivation was best fitted by a single exponential (tau(fast) = 46.8 +/- 5.8 ms at -110 mV). Quantitative RT-PCR showed that ERG1 and ERG3 were the predominant mRNAs and immunohistochemistry showed expression as somatic plasma membrane puncta on principal neurons. We conclude that ERG currents complement Kv1 currents in limiting AP firing at around threshold; ERG may have a particular role during periods of high activity when [K(+)](o) is elevated. These ERG currents suggest a potential link between auditory hyperexcitability and acoustic startle triggering of cardiac events in familial LQT2.

Polymorphism of PrIr 2Si 2 – In situ XRPD experiments and theoretical calculations

We have confirmed polymorphism of PrIr 2Si 2 and performed the in situ high-temperature X-ray powder diffraction (XRPD) experiments focused on the dynamics of the crystallographic phase transition from the high-temperature CaBe 2Ge 2-type phase to the low-temperature ThCr 2Si 2 phase above 250 °C. A double-exponential time evolution of this phase transformation has been observed at 325 °C. We have also performed density functional calculations to analyze why the low-temperature crystallographic modification becomes the ground state crystal structure. The important role of the c/ a ratio in this process can be argued from results of calculations.

Multiple residues in the p-region and m2 of murine kir 2.1 regulate blockage by external ba.

We have examined the effects of certain mutations of the selectivity filter and of the membrane helix M2 on Ba(2+) blockage of the inward rectifier potassium channel, Kir 2.1. We expressed mutant and wild type murine Kir 2.1 in Chinese hamster ovary (CHO) cells and used the whole cell patch-clamp technique to record K(+) currents in the absence and presence of externally applied Ba(2+). Wild type Kir2.1 was blocked by externally applied Ba(2+) in a voltage and concentration dependent manner. Mutants of Y145 in the selectivity filter showed little change in the kinetics of Ba(2+) blockage. The estimated K(d)(0) was 108 microM for Kir2.1 wild type, 124 microM for a concatameric WT-Y145V dimer, 109 microM for a WT-Y145L dimer, and 267 microM for Y145F. Mutant channels T141A and S165L exhibit a reduced affinity together with a large reduction in the rate of blockage. In S165L, blockage proceeds with a double exponential time course, suggestive of more than one blocking site. The double mutation T141A/S165L dramatically reduced affinity for Ba(2+), also showing two components with very different time courses. Mutants D172K and D172R (lining the central, aqueous cavity of the channel) showed both a decreased affinity to Ba(2+) and a decrease in the on transition rate constant (k(on)). These results imply that residues stabilising the cytoplasmic end of the selectivity filter (T141, S165) and in the central cavity (D172) are major determinants of high affinity Ba(2+) blockage in Kir 2.1.

The time complexity of typechecking tree-walking tree transducers

Tree-walking tree transducers can be typechecked in double exponential time. More generally, compositions of k tree-walking tree transducers can be typechecked in (k + 1)-fold exponential time. Consequently k-pebble tree transducers, which form a model of XML transformations and XML queries, can be typechecked in (k + 2)-fold exponential time. The results hold for both ranked and unranked trees.

Activation of recombinant NR1/NR2C NMDA receptors

The N-methyl-d-aspartate (NMDA) subtype of ionotropic glutamate receptors comprises both NR1 and NR2 subunits, and plays numerous roles in both physiological and pathophysiological processes in the central nervous system (CNS). NR2C-containing NMDA receptors are most abundant in cerebellum, thalamus and olfactory bulb, and are also expressed in oligodendrocytes and hippocampal interneurons. We have used patch clamp recording to explore the activation properties of recombinant NR1/NR2C receptors expressed in HEK293 cells. NR1/NR2C receptors activated by a maximally effective concentration of glutamate and glycine had two main conductance levels of 45 pS and 28 pS when the extracellular Ca(2+) concentration was 0.5 mm and the holding potential was -80 mV. The occurrence of the lower subconductance state was reduced in the absence of extracellular Ca(2+). The distribution of closed durations recorded from patches with a high probability of containing only one active channel were best fitted by five exponential functions; the apparent open duration histogram could be fitted by two exponential functions (n = 10 patches). The apparent mean open time of NR1/NR2C receptors was brief (0.52 +/- 0.04 ms), suggesting that the stability of the open state of the NR1/NR2C receptors is lower than other NR2-containing receptors. NR1/NR2C open probability was exceptionally low, being 0.011 +/- 0.002 in patches containing a single active receptor (n = 8). Fast agonist concentration jumps were performed on outside out patches with multiple NR1/NR2C channels, which activated with a 10-90% rise time of 3.9 +/- 0.4 ms, faster than other NR2-containing receptors. The deactivation time constant after a brief (5-8 ms) application of a maximally effective concentration of agonists was 319 +/- 34 ms. The majority of the patches also showed a modest level of desensitization that could be described by either a single or a double exponential time course with the fastest time constant between 15 and 47 ms. Conceptual models of activation were fitted using the maximum interval likelihood (MIL) method to the sequence of open and closed durations recorded from outside-out patches that contained one active NR1/NR2C channel. NR1/NR2C receptor properties including modest desensitization and low open probability could be described by gating schemes similar to those previously proposed for other NMDA receptor subunit combinations.

Enriched MU-Calculi Module Checking

The model checking problem for open systems has been intensively studied in the literature, for both finite-state (module checking) and infinite-state (pushdown module checking) systems, with respect to Ctl and Ctl*. In this paper, we further investigate this problem with respect to the \mu-calculus enriched with nominals and graded modalities (hybrid graded Mu-calculus), in both the finite-state and infinite-state settings. Using an automata-theoretic approach, we show that hybrid graded \mu-calculus module checking is solvable in exponential time, while hybrid graded \mu-calculus pushdown module checking is solvable in double-exponential time. These results are also tight since they match the known lower bounds for Ctl. We also investigate the module checking problem with respect to the hybrid graded \mu-calculus enriched with inverse programs (Fully enriched \mu-calculus): by showing a reduction from the domino problem, we show its undecidability. We conclude with a short overview of the model checking problem for the Fully enriched Mu-calculus and the fragments obtained by dropping at least one of the additional constructs.

Widely Distributed Residues in Thymosin β4 Are Critical for Actin Binding

We have investigated the contributions of hydrophobic residues, the conserved and variable proline residues, and the conserved lysine residues to the affinity and kinetics of thymosin beta4 (Tbeta4) binding to MgATP-actin monomers. Pro4, Lys18, Lys19, Pro27, Leu28, Pro29, and Ile34 were substituted with alanine residues. Mutagenesis of Pro4 or Pro27 has little effect (<or=3-fold reduction) on the actin binding affinity of Tbeta4. Substitution of Lys18 and Lys19, Leu28, Pro29, or Ile34 weakens the affinity of the actin-Tbeta4 complex >or=10-fold, but the kinetic basis of the lower stability varies among the mutants. Substitution of the conserved lysine residues weakens the affinity by slowing association and accelerating dissociation. Substitution of hydrophobic residue Leu28 or Ile34 weakens the affinity by accelerating dissociation. These results favor a reaction mechanism in which Tbeta4 binds actin monomers following a two-step mechanism in which the formation of a bimolecular complex is followed by isomerization to a strong binding state that is coupled to the formation of widely distributed hydrophobic contacts. The isomerization equilibrium is slowed by mutagenesis of Pro29, as revealed by the double-exponential time course of association. Mutagenesis of Pro4 or Pro27 accelerates binding and dissociation but minimally affects the binding affinity (<or=3-fold reduction), suggesting that cis- trans isomerization of these proline residues contributes to the slow association rate constant of wild-type Tbeta4.

Functional properties of spontaneous IPSCs and glycine receptors in rod amacrine (AII) cells in the rat retina

AII amacrine cells play a crucial role in retinal signal transmission under scotopic conditions. We have used rat retinal slices to investigate the functional properties of inhibitory glycine receptors on AII cells by recording spontaneous IPSCs (spIPSCs) in whole cells and glycine-evoked responses in outside-out patches. Glycinergic spIPSCs displayed fast kinetics with an average 10-90% rise time of approximately 500 mus, and a decay phase best fitted by a double-exponential function with tau(fast) approximately 4.8 ms (97.5% amplitude contribution) and tau(slow) approximately 33 ms. Decay kinetics were voltage dependent. Ultrafast application of brief ( approximately 2-5 ms) pulses of glycine (3 mm) to patches, evoked responses with fast deactivation kinetics best fitted with a double-exponential function with tau(fast) approximately 4.6 ms (85% amplitude contribution) and tau(slow) approximately 17 ms. Double-pulse experiments indicated recovery from desensitization after a 100-ms pulse of glycine with a double-exponential time course (tau(fast) approximately 71 ms and tau(slow) approximately 1713 ms). Non-stationary noise analysis of spIPSCs and patch responses, and directly observed channel gating yielded similar single-channel conductances ( approximately 41 to approximately 47 pS). In addition, single-channel gating occurred at approximately 83 pS. These results suggest that the fast glycinergic spIPSCs in AII cells are probably mediated by alpha1beta heteromeric receptors with a contribution from alpha1 homomeric receptors. We hypothesize that glycinergic synaptic input may target the arboreal dendrites of AII cells, and could serve to shunt excitatory input from rod bipolar cells and transiently uncouple the transcellular current through electrical synapses between AII cells and between AII cells and ON-cone bipolar cells.

Munc13-1 is required for the sustained release of insulin from pancreatic β cells

Munc13-1 is a presynaptic protein that is essential for synaptic vesicle priming. Deletion of Munc13-1/unc13 causes total arrest of synaptic transmission due to a complete loss of fusion-competent synaptic vesicles. The requirement of Munc13-1 for large dense-core vesicles (LDCVs), however, has not been established. In the present study, we use Munc13-1 knockout (KO) and diacylglycerol (DAG) binding-deficient Munc13-1(H567K) mutant knockin (KI) mice to determine the role of Munc13-1 in the secretion of insulin-containing LDCVs from primary cultured pancreatic beta cells. We show that Munc13-1 is required for the sustained insulin release upon prolonged stimulation. The sustained release involves signaling of DAG second messenger, since it is also reduced in KI mice. Insulin secretion in response to glucose stimulation is characterized by a biphasic time course. Our data show that Munc13-1 plays an essential role in the development of the second phase of insulin secretion by priming insulin-containing LDCVs.

Supervisory Control of Discrete Event Systems with CTL* Temporal Logic Specifications

The supervisory control problem of discrete event systems with temporal logic specifications is studied. The full branching time logic of CTL* is used for expressing specifications of discrete event systems. The control problem of CTL* is reduced to the decision problem of CTL*. A small model theorem for the control of CTL* is obtained. It is shown that the control problem of CTL* (resp., CTL) is complete for deterministic double (resp., single) exponential time. A sound and complete supervisor synthesis algorithm for the control of CTL* is provided. Special cases of the control of computation tree logic (CTL) and linear-time temporal logic are also studied.

2-Exp Time lower bounds for propositional dynamic logics with intersection

AbstractIn 1984. Danecki proved that satisfiability in IPDL, i.e., Propositional Dynamic Logic (PDL) extended with an intersection operator on programs, is decidabie in deterministic double exponential time. Since then, the exact complexity of IPDL has remained an open problem: the best known lower bound was the ExpTime one stemming from plain PDL until, in 2004. the first author established ExpSpace-hardness. In this paper, we finally close the gap and prove that IPDL is hard for 2-ExpTime. thus 2-ExpTime-complete. We then sharpen our lower bound, showing that it even applies to IPDL without the test operator interpreted on tree structures.

Presynaptic Na+Channels: Locus, Development, and Recovery from Inactivation at a High-Fidelity Synapse

Na+ channel recovery from inactivation limits the maximal rate of neuronal firing. However, the properties of presynaptic Na+ channels are not well established because of the small size of most CNS boutons. Here we study the Na+ currents of the rat calyx of Held terminal and compare them with those of postsynaptic cells. We find that presynaptic Na+ currents recover from inactivation with a fast, single-exponential time constant (24 degrees C, tau of 1.4-1.8 ms; 35 degrees C, tau of 0.5 ms), and their inactivation rate accelerates twofold during development, which may contribute to the shortening of the action potential as the terminal matures. In contrast, recordings from postsynaptic cells in brainstem slices, and acutely dissociated, reveal that their Na+ currents recover from inactivation with a double-exponential time course (tau(fast) of 1.2-1.6 ms; tau(slow) of 80-125 ms; 24 degrees C). Surprisingly, confocal immunofluorescence revealed that Na+ channels are mostly absent from the calyx terminal but are instead highly concentrated in an unusually long (approximately 20-40 microm) unmyelinated axonal heminode. Outside-out patch recordings confirmed this segregation. Expression of Na(v)1.6 alpha-subunit increased during development, whereas the Na(v)1.2alpha-subunit was not present. Serial EM reconstructions also revealed a long pre-calyx heminode, and biophysical modeling showed that exclusion of Na+ channels from the calyx terminal produces an action potential waveform with a shorter half-width. We propose that the high density and polarized locus of Na+ channels on a long heminode are critical design features that allow the mature calyx of Held terminal to fire reliably at frequencies near 1 kHz.

GABAergic activation of an inwardly rectifying K+ current in mouse cerebellar Purkinje cells

Cerebellar Purkinje cells integrate motor information conveyed by excitatory synaptic inputs from parallel and climbing fibres. Purkinje cells abundantly express B-type G-protein-coupled gamma-aminobutyric acid receptors (GABABR) that are assumed to mediate major responses, including postsynaptic modulation of the synaptic inputs. However, the identity and function of effectors operated by GABABR are not fully elucidated. Here we characterized an inwardly rectifying current activated by baclofen (Ibacl), a GABABR agonist, in cultured mouse Purkinje cells using a ruptured-patch whole-cell technique. Ibacl is operated by GABABR via Gi/o-proteins, as it is not inducible in pertussis-toxin-pretreated cells. Ibacl is carried by K+ because its reversal potential shifts with the equilibrium potential of K+. Ibacl is blocked by 10(-3) M Ba2+ or Cs+, and 10(-8) M tertiapin-Q. Upon the onset and offset of a hyperpolarizing step, Ibacl is activated and deactivated, respectively, with double-exponential time courses (time constants, <1 ms and 30-80 ms). Based on similarities in the above properties, G-protein-coupled inwardly rectifying K+ (GIRK) channels are thought to be responsible for Ibacl. Perforated-patch recordings from cultured Purkinje cells demonstrate that Ibacl hyperpolarizes the resting potential and the peak level achieved by glutamate-evoked potentials initiated in the dendrites. Moreover, cell-attached recordings from Purkinje cells in cerebellar slices demonstrate that Ibacl impedes spontaneous firing. Therefore, Ibacl may reduce the postsynaptic and intrinsic excitability of Purkinje cells under physiological conditions. These findings give a new insight into the role of GABABR signalling in cerebellar information processing.

Molecular Beacon Probes of Photodamage in Thymine and Uracil Oligonucleotides¶

Abstract Molecular beacons (MB) are becoming more common as sequence-selective detectors of nucleic acids. Although they can easily detect single-base mismatches, they have never been used to directly detect DNA or RNA damage. To measure the degree of ultraviolet (UV) light damage in oligonucleotides, we report a novel MB approach for general detection of photoproducts in UV-irradiated rU17 and dT17 oligonucleotides. With monochromatic UV light irradiation at ca 280 nm under anoxic conditions, the oligonucleotide absorption decays with a single-exponential time constant of 123 ± 1 min for rU17 and with double-exponential time constants of 78 ± 0.5 min (99%) and 180 ± 5 min (0.05%) for dT17 oligonucleotides. Under the same conditions, the MB fluorescence decays more quickly, with single-exponential time constants of 19 ± 2 and 26 ± 3 min for rU17 and dT17, respectively. Similar kinetics were observed with broadband UV light irradiation of oligonucleotides. The differences in the UV damage kinetics of dT17 ...

Light dependence of oxygen consumption by blowfly eyes recorded with a magnetic diver balance

We measured the oxygen (O2) consumption of isolated blowfly eyes using a magnetic diver balance, a device for high-resolution volumetric O2 consumption measurements. The light-induced O2 consumption is at most three times the value of the dark consumption, which is 0.6 nl O2 s(-1) eye(-1), and is in good agreement with the estimates based on electrophysiological data. With longer stimuli the increase follows a double exponential time course. The respective time constants are approximately 2 and 20 s and show no dependence on light intensity, whereas the dependence of amplitudes can be fitted by a Hill equation. Decreasing the stimulus duration reveals that the peak in O2 consumption overshoots the time course induced by long stimuli. We suggest this may be a general feature of mitochondrial activation. The dependence of the O2 consumption peak on stimulus duration at high light intensity has a hump with stimulus durations of 10-20 ms, coinciding with the stimulus durations that start to induce the adaptation of the receptor potential.

Molecular Beacon Probes of Photodamage in Thymine and Uracil Oligonucleotides

Molecular beacons (MB) are becoming more common as sequence-selective detectors of nucleic acids. Although they can easily detect single-base mismatches, they have never been used to directly detect DNA or RNA damage. To measure the degree of ultraviolet (UV) light damage in oligonucleotides, we report a novel MB approach for general detection of photoproducts in UV-irradiated rU17 and dT17 oligonucleotides. With monochromatic UV light irradiation at ca 280 nm under anoxic conditions, the oligonucleotide absorption decays with a single-exponential time constant of 123+/-1 min for rU17 and with double-exponential time constants of 78+/-0.5 min (99%) and 180+/-5 min (0.05%) for dT17 oligonucleotides. Under the same conditions, the MB fluorescence decays more quickly, with single-exponential time constants of 19+/-2 and 26+/-3 min for rU17 and dT17, respectively. Similar kinetics were observed with broadband UV light irradiation of oligonucleotides. The differences in the UV damage kinetics of dT17 and rU17 and their detection by absorption and fluorescence techniques will be discussed in the context of differential instabilities introduced in the nucleic acid-MB duplex by the different photoproducts formed.

Time domain analysis of grounding electrodes impulse response

Lightning protection studies require estimation of grounding systems dynamic behavior. This paper presents the results of a new methodology for calculating the lightning response of the basic component of any grounding system, the grounding electrode. Lightning strike is modeled using a double exponential time function. Closed-form mathematical formulae are used to describe current and voltage distribution along the electrode. The effect of soil ionization can be also taken into account. The proposed methodology is validated by comparison of the obtained results with experimental and simulated waveforms found in literature.

In search of an easy witness: exponential time vs. probabilistic polynomial time

Restricting the search space {0,1} n to the set of truth tables of “easy” Boolean functions on log n variables, as well as using some known hardness–randomness tradeoffs, we establish a number of results relating the complexity of exponential-time and probabilistic polynomial-time complexity classes. In particular, we show that NEXP ⊂ P / poly ⇔ NEXP = MA ; this can be interpreted as saying that no derandomization of MA (and, hence, of promise- BPP ) is possible unless NEXP contains a hard Boolean function. We also prove several downward closure results for ZPP , RP , BPP , and MA ; e.g., we show EXP = BPP ⇔ EE = BPE , where EE is the double-exponential time class and BPE is the exponential-time analogue of BPP .

Time Domain Analysis of Grounding Electrodes' Impulse Response

Lightning protection studies require estimation of grounding systems' dynamic behavior. This paper presents the results of a new methodology for calculating the lightning response of the basic component of any grounding system, the grounding electrode. Lightning strike is modeled using a double exponential time function. Closed-form mathematical formulae are used to describe current and voltage distribution along the electrode. The effect of soil ionization can be also taken into account. The proposed methodology is validated by comparison of the obtained results with experimental and simulated waveforms found in literature.