Double Exponential Time Research Articles

Guarded fixed point logics and the monadic theory of countable trees

Different variants of guarded logics (a powerful generalization of modal logics) are surveyed and an elementary proof for the decidability of guarded fixed point logics is presented. In a joint paper with Igor Walukiewicz, we proved that the satisfiability problems for guarded fixed point logics are decidable and complete for deterministic double exponential time (E. Grädel and I. Walukiewicz, Proc. 14th IEEE Symp. on Logic in Computer Science, 1999, pp. 45–54). That proof relies on alternating automata on trees and on a forgetful determinacy theorem for games on graphs with unbounded branching. The exposition given here emphasizes the tree model property of guarded logics: every satisfiable sentence has a model of bounded tree width. Based on the tree model property, we show that the satisfiability problem for guarded fixed point formulae can be reduced to the monadic theory of countable trees (S ωS), or to the μ-calculus with backwards modalities.

Properties of voltage dependent potassium currents in acutely isolated rat oculomotor neurons.

Voltage-dependent potassium currents in oculomotor neurons (OMNs) were studied with whole-cell patch clamp recordings. Fast inactivating outward currents (I(fast)) had half activation voltage (Vh) of -37.1 mV with slope factor (Vc) of 10.9 mV. I(fast) had half inactivation voltage (Vh) of -66.5 mV and Vc of 11.4 mV. I(fast) decayed with a time constant(tau) of 5.1 ms at +10 mV. I(fast) were sensitive to 4-aminopyridine, showing 50% inhibitory concentration (IC(50)) of 0.97 mM. Slowly inactivating outward currents (I(slow)) had two components. The low-concentration-TEA-sensitive currents had Vh of -3.7 mV with Vc of 9.7 mV in activation and had Vh of -54.7 mV with Vc of 23.8 mV in inactivation. The persistent currents had Vh of 7.4 mV and Vc of 11.8 mV in activation and Vh of -54.4 mV and Vc of 21.2 mV in inactivation. Decay of I(slow) (+10 mV) followed a double exponential time course (tau 215, 1165.6 ms). Low-concentration-TEA-sensitive currents were blocked completely by tetraethylammonium (TEA) of 3 mM with an IC(50) of 1.52 mM. Higher concentrations (3-20 mM) of TEA blocked the persistent currents, with an IC(50) of 6.9 mM.

Temperature dependence of human muscle ClC-1 chloride channel.

1. In the present work we investigated the dependence on temperature of the ionic conductance and gating of human muscle ClC-1 chloride channels, transiently expressed in human embryonic kidney (HEK 293) cells. 2. At normal pH, ClC-1 currents deactivated at negative potentials with a double-exponential time course. The time constants of the exponential components, corresponding to the relaxations of the fast and slow gates, were temperature dependent with Q(10) values of approximately 3 and approximately 4, respectively. Current amplitude increased with increasing temperature with a Q(10) of approximately 1.6. 3. The voltage dependence of the two gating processes was shifted towards more positive potentials with increasing temperature. The half-saturation voltage (V(1/2)) of the steady-state open probability (P(o)) was shifted by approximately 23 and approximately 34 mV per 10 degrees C increase in temperature, for the fast and slow gate, respectively. 4. At low pH, the voltage dependence of ClC-1 was reversed and currents were activated by hyperpolarisation with a single-exponential time course. This type of gating in ClC-1 resembled the slow gating of the Torpedo ClC-0 homologue, but differed with respect to its kinetics and temperature dependence, with a Q(10) of gating relaxations at negative potentials of approximately 5. The Arrhenius plot of ClC-1 conductance at low pH had a clear break point at approximately 25 degrees C, with higher Q(10) values at lower temperatures. 5. The temperature sensitivity of relaxation and open probability of the slow gate, which in both ClC-0 and ClC-1 controls two pores simultaneously, implies that the slow gating of ClC-1 is mechanistically different from that of ClC-0.

Spermine mediates inward rectification in potassium channels of turtle retinal Müller cells.

Retinal Müller cells are highly permeable to potassium as a consequence of their intrinsic membrane properties. Therefore these cells are able to play an important role in maintaining potassium homeostasis in the vertebrate retina during light-induced neuronal activity. Polyamines and other factors present in Müller cells have the potential to modulate the rectifying properties of potassium channels and alter the Müller cells capacity to siphon potassium from the extracellular space. In this study, the properties of potassium currents in turtle Müller cells were investigated using whole cell voltage-clamp recordings from isolated cells. Overall, the currents were inwardly rectifying. Depolarization elicited an outward current characterized by a fast transient that slowly recovered to a steady level along a double exponential time course. On hyperpolarization the evoked inward current was characterized by an instantaneous onset (or step) followed by a slowly developing sustained inward current. The kinetics of the time-dependent components (block of the transient outward current and slowly developing inward current) were dependent on holding potential and changes in the intracellular levels of magnesium ions and polyamines. In contrast, the instantaneous inward and the sustained outward currents were ohmic in character and remained relatively unaltered with changes in holding potential and concentration of applied spermine (0.5--2 mM). Our data suggest that cellular regulation in vivo of polyamine levels can differentially alter specific aspects of potassium siphoning by Müller cells in the turtle retina by modulating potassium channel function.

Fast activation of a time-dependent outward current in protoplasts derived from coats of developing Phaseolus vulgaris seeds.

An outward current that appeared to activate instantaneously in response to depolarising voltage pulses at low sampling frequencies predominated in the plasma membrane of ground-parenchyma protoplasts derived from coats of developing Phaseolus vulgaris L. (cv. Redland Pioneer) seeds. However, the outward current showed time-dependent activation when higher sampling frequencies were used to measure the current. Activation of the current was best described as a double-exponential time course with the fast and slow time constants being 1 and 20 ms, respectively. The current also exhibited a rapid deactivation that followed a double-exponential time course with time constants of approximately 2 and 30 ms, respectively. "Tail-current" analysis allowed us to show that this current exhibited a low selectivity between K- and Cl- (PK:Cl = 1.8). Such a fast-activating current may account for some of the reports of time-independent, instantaneous currents that have been observed in plasma membranes of plant cells digitised at low sampling frequencies. Therefore, when "instantaneous" currents appear it is advisable to characterise these currents using higher sampling frequencies with correspondingly higher filtering frequency cut-offs.

EXPtime tableaux for [formula omitted

The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semi-structured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPtime-complete. Second, experiments in automated reasoning have substantially broadened the meaning of “practical tractability”. Instances of realistic size for Pspace-complete problems are now within reach for implemented systems. Still, there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems. Indeed, the algorithms based on tree-automata, which are used to prove EXPtime-completeness, require exponential time and space even in simple cases. On the other hand, current algorithms based on tableau methods can take advantage of such cases, but require double exponential time in the worst case. We propose a tableau calculus for the description logic ALC for checking the satisfiability of a concept with respect to a TBox with general axioms, and transform it into the first simple tableau-based decision procedure working in single exponential time. To guarantee the ease of implementation, we also discuss the effects that optimizations (propositional backjumping, simplification, semantic branching, etc.) might have on our complexity result, and introduce a few optimizations ourselves.

Alterations in Outward K+ Currents on Removal of External Ca2+ in Human Atrial Myocytes

External divalent cations are known to play an important role in the function of voltage-gated ion channels. The purpose of this study was to examine the sensitivity of the voltage-gated K+ currents of human atrial myocytes to external Ca2+ ions. Myocytes were isolated by collagenase digestion of atrial appendages taken from patients undergoing coronary artery-bypass surgery. Currents were recorded from single isolated myocytes at 37°C using the whole-cell patch-clamp technique. With 0.5 mM external Ca2+, voltage pulses positive to −20 mV (holding potential = −60 mV) activated outward currents which very rapidly reached a peak (Ipeak) and subsequently inactivated (τ = 7.5 ± 0.7 msec at +60 mV) to a sustained level, demonstrating the contribution of both rapidly inactivating transient (Ito1) and non-inactivating sustained (Iso) outward currents. The Ito1 component of Ipeak, but not Iso, showed voltage-dependent inactivation using 100 msec prepulses (V1/2 = −35.2 ± 0.5 mV). The K+ channel blocker, 4-aminopyridine (4-AP, 2 mM), inhibited Ito1 by ∼76% and reduced Iso by ∼33%. Removal of external Ca2+ had several effects: (i) Ipeak was reduced in a manner consistent with an ∼13 mV shift to negative voltages in the voltage-dependent inactivation of Ito1. (ii) Iso was increased over the entire voltage range and this was associated with an increase in a non-inactivating 4-AP-sensitive current. (iii) In 79% cells (11/14), a slowly inactivating component was revealed such that the time-dependent inactivation was described by a double exponential time course (τ1 = 7.0 ± 0.7, τ2 = 90 ± 21 msec at +60 mV) with no effect on the fast time constant. Removal of external Ca2+ was associated with an additional component to the voltage-dependent inactivation of Ipeak and Iso (V1/2 = −20.5 ± 1.5 mV). The slowly inactivating component was seen only in the absence of external Ca2+ ions and was insensitive to 4-AP (2 mM). Experiments with Cs+-rich pipette solutions suggested that the Ca2+-sensitive currents were carried predominantly by K+ ions. External Ca2+ ions are important to voltage-gated K+ channel function in human atrial myocytes and removal of external Ca2+ ions affects Ito1 and 4-AP-sensitive Iso in distinct ways.

Activity-dependent extracellular K+ accumulation in rat optic nerve: the role of glial and axonal Na+ pumps.

1. We measured activity-dependent changes in [K+]o with K(+)-selective microelectrodes in adult rat optic nerve, a CNS white matter tract, to investigate the factors responsible for post-stimulus recovery of [K+]o. 2. Post-stimulus recovery of [K+]o followed a double-exponential time course with an initial, fast time constant, tau fast, of 0.9 +/- 0.2 s (mean +/- S.D.) and a later, slow time constant, tau slow, of 4.2 +/- 1 s following a 1 s, 100 Hz stimulus. tau fast, but not tau slow, decreased with increasing activity-dependent rises in [K+]o. tau slow, but not tau fast, increased with increasing stimulus duration. 3. Post-stimulus recovery of [K+]o was temperature sensitive. The apparent temperature coefficients (Q10, 27-37 degrees C) for the fast and slow components following a 1 s, 100 Hz stimulus were 1.7 and 2.6, respectively. 4. Post-stimulus recovery of [K+]o was sensitive to Na+ pump inhibition with 50 microM strophanthidin. Following a 1 s, 100 Hz stimulus, 50 microM strophanthidin increased tau fast and tau slow by 81 and 464%, respectively. Strophanthidin reduced the temperature sensitivity of post-stimulus recovery of [K+]o. 5. Post-stimulus recovery of [K+]o was minimally affected by the K+ channel blocker Ba2+ (0.2 mM). Following a 10 s, 100 Hz stimulus, 0.2 mM Ba2+ increased tau fast and tau slow by 24 and 18%, respectively. 6. Stimulated increases in [K+]o were followed by undershoots of [K+]o. Post-stimulus undershoot amplitude increased with stimulus duration but was independent of the peak preceding [K+]o increase. 7. These observations imply that two distinct processes contribute to post-stimulus recovery of [K+]o in central white matter. The results are compatible with a model of K+ removal that attributes the fast, initial phase of K+ removal to K+ uptake by glial Na+ pumps and the slower, sustained decline to K+ uptake via axonal Na+ pumps.

Two types of pharmacologically distinct Ca(2+) currents with voltage-dependent similarities in zona fasciculata cells isolated from bovine adrenal gland.

Voltage-activated Ca(2+) currents, in zona fasciculata cells isolated from calf adrenal gland, were characterized using perforated patch-clamp recording. In control solution (Ca(2+): 2.5 mm) a transient inward current was followed, in 40% of the cells, by a sustained one. In 20 mm Ba(2+), 61% of the cells displayed an inward current, which consisted of transient and sustained components. The other cells produced either a sustained or a transient inward current. These different patterns were dependent upon time in culture. Current-voltage relationships show that both the transient and sustained components activated, peaked and reversed at similar potentials: -40, 0 and +60 mV, respectively. The two components, fully inactivated at -10 mV, were separated by double-pulse protocols from different holding potentials where the transient component could be inactivated or reactivated. The decaying phase of the sustained component was fitted by a double exponential (time constants: 1.9 and 20 sec at +10 mV); that of the transient component was fitted by a single exponential (time constant: 19 msec at +10 mV). Steady-state activation and inactivation curves of the two components were superimposed. Their half activation and inactivation potentials were similar, about -15 and -34 mV, respectively. The sustained component was larger in Ba(2+) than in Sr(2+) and Ca(2+). Ni(2+) (20 microm) selectively blocked the transient component while Cd(2+) (10 microm) selectively blocked the sustained one. (+/-)Bay K 8644 (0.5 microm) increased the sustained component and nitrendipine (0.5-1 microm) blocked it selectively. The sustained component was inhibited by calciseptine (1 microm). Both components were unaffected by omega-conotoxin GVIA and MVIIC (0.5 microm). These results show that two distinct populations of Ca(2+) channels coexist in this cell type. Although the voltage dependence of their activation and inactivation are comparable, these two components of the inward current are similar to T- and L-type currents described in other cells.

On the Restraining Power of Guards

AbstractGuarded fragments of first-order logic were recently introduced by Andréka, van Benthem and Németi; they consist of relational first-order formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful model-theoretic properties and especially because they are decidable classes that avoid the usual syntactic restrictions (on the arity of relation symbols, the quantifier pattern or the number of variables) of almost all other known decidable fragments of first-order logic.Here, we investigate the computational complexity of these fragments. We prove that the satisfiability problems for the guarded fragment (GF) and the loosely guarded fragment (LGF) of first-order logic are complete for deterministic double exponential time. For the subfragments that have only a bounded number of variables or only relation symbols of bounded arity, satisfiability is Exptime-complete. We further establish a tree model property for both the guarded fragment and the loosely guarded fragment, and give a proof of the finite model property of the guarded fragment.It is also shown that some natural, modest extensions of the guarded fragments are undecidable.

Complexity of products of modal logics

A relatively new way of combining modal logics is to consider their products. The main application of these product logics lies in the description of parallel computing processes. Axiomatics and decidability of the validity problem have been rather extensively investigated and many logics behave well in these respects. In this paper we look at the product construction from a computational complexity point of view. We show that in many cases there is a drastic increase in complexity, e.g., all products containing the finite S5×S5 products as models have an nexptime-hard satisfaction problem. Products with a functional modality however do not lead to an increase in complexity. For the products K× S5 and S5× S5, we provide a matching upper bound. Combining (modal) logics is a very active area, witness e.g., [4] and the book [1]. A rather special way of combining two modal logics is to consider their products. This approach started with [20], and has recently been developed in great detail in [5]. In temporal logic, products of two logics have been used to describe the temporal logic of intervals (cf. the “product treatment” of the system HS from [8] in [15]: Chapter 4 and the references therein). Almost all products of temporal logics are undecidable, sometimes the validities are not even recursively enumerable [8, 22]. Products of modal (and modal and temporal) logics have applications in the theory of parallel computing [18]. Here we are concerned with the general mathematical theory of products of modal logics, in particular the complexity of several natural decision problems, like the validity problem. With respect to (Hilbert style) axiomatizability a lot of general results are obtained in [5], cf e.g., Theorem 5.7. That paper also contains decidability results for a large number of cases. The general trend for these results is that they are rather hard to prove, but become a lot easier if one of the logics is S5, though even then the filtration arguments are rather involved, and lead to models whose size is in general double exponential in the length of the formula which is to be satisfied. The upper bounds we obtain from these proofs are very bad, in the general case (when none of the logics is S5), the decision-algorithm is non-elementary, and when one of the logics is S5 we only obtain a non-deterministic double exponential time upper bound for the satisfaction problem. Questions concerning computational complexity, have hitherto not been addressed, and we will make a start here. The overall trend is that these logics have a very bad complexity for the satisfaction problem: in many simple cases it is nexptime-hard. Also, even if the satisfaction problem is decidable, the problem whether for a formula φ there exists a model The author is supported by UK EPSRC grant No. GR/K54946.

The kinetics of exocytosis and endocytosis in the synaptic terminal of goldfish retinal bipolar cells.

1. The kinetics of exocytosis and endocytosis were studied in the giant synaptic terminal of depolarizing bipolar cells from the goldfish retina. Two techniques were applied: capacitance measurements of changes in membrane surface area, and fluorescence measurements of exocytosis using the membrane dye FM1-43. 2. Three phases of exocytosis occurred during maintained depolarization to 0 mV. The first component was complete within about 10 ms and involved a pool of 1200-1800 vesicles (with a total membrane area equivalent to about 1.6 % of the surface of the terminal). The second component of exocytosis involved the release of about 4400 vesicles over 1 s. The third component of exocytosis was stimulated continuously at a rate of about 1000 vesicles s-1. 3. After short depolarizations (< 200 ms), neither the FM1-43 signal nor the capacitance signal continued to rise, indicating that exocytosis stopped rapidly after closure of Ca2+ channels. The fall in capacitance could therefore be used to monitor endocytosis independently of exocytosis. The capacitance measured after brief stimuli began to fall immediately, recovering to the pre-stimulus baseline with a rate constant of 0.8 s-1. 4. The amount of exocytosis measured using the capacitance and FM1-43 techniques was similar during the first 200 ms of depolarization, suggesting that the most rapidly released vesicles could be detected by either method. 5. After a few seconds of continuous stimulation, the net increase in membrane surface area reached a plateau at about 5 %, even though continuous exocytosis occurred at a rate of 0.9 % s-1. Under these conditions of balanced exocytosis and endocytosis, the rate constant of endocytosis was about 0.2 s-1. The average rate of endocytosis during maintained depolarization was therefore considerably slower than the rate observed after a brief stimulus. 6. After longer depolarizations (> 500 ms), both the capacitance and FM1-43 signals continued to rise for periods of seconds after closure of Ca2+ channels. The continuation of exocytosis was correlated with a persistent increase in [Ca2+]i in the synaptic terminal, as indicated by the activation of a Ca2+-dependent conductance and measurements of [Ca2+]i using the fluorescent indicator furaptra. 7. The delayed fall in membrane capacitance after longer depolarizations occurred along a double exponential time course indicating the existence of two endocytic processes: fast endocytosis, with a rate constant of 0.8 s-1, and slow endocytosis, with a rate constant of 0.1 s-1. 8. Increasing the duration of depolarization caused an increase in the fraction of membrane recovered by slow endocytosis. After a 100 ms stimulus, all the membrane was recycled by fast endocytosis, but after a 5 s depolarization, about 50 % of the membrane was recycled by slow endocytosis. 9. These results demonstrate the existence of fast and slow endocytic mechanisms at a synapse and support the idea that prolonged stimulation leads to an increase in the amount of membrane retrieved by the slower route. The rise in cytoplasmic Ca2+ that occurred during longer depolarizations was correlated with stimulation of continuous exocytosis and inhibition of fast endocytosis. The results also confirm that transient and continuous components of exocytosis coexist in the synaptic terminal of depolarizing bipolar cells.

The Complexity of Tree Automata and Logics of Programs

The complexity of testing nonemptiness of finite state automata on infinite trees is investigated. It is shown that for tree automata with the pairs (or complemented pairs) acceptance condition having m states and n pairs, nonemptiness can be tested in deterministic time (mn)O(n) ; however, it is shown that the problem is in general NP-complete (or co-NP-complete, respectively). The new nonemptiness algorithm yields exponentially improved, essentially tight upper bounds for numerous important modal logics of programs, interpreted with the usual semantics over structures generated by binary relations. For example, it follows that satisfiability for the full branching time logic CTL* can be tested in deterministic double exponential time. Another consequence is that satisfiability for propositional dynamic logic (PDL) with a repetition construct (PDL-delta) and for the propositional Mu-calculus ($L\mu$) can be tested in deterministic single exponential time.

Abstracts of literature

Abstracts of literature

Characteristics of two slow inactivation mechanisms and their influence on the sodium channel activity of frog ventricular myocytes.

Inactivation of the fast Na+ current of heart muscle occurs in two kinetically distinct phases: a fast process operating on a millisecond time scale and a considerably slower process, the kinetic properties of which have not been explored fully. In this study, we analysed the slow inactivation process in isolated frog ventricular myocytes using the whole-cell variation of the patch-clamp method. Slow inactivation of the Na+ current followed a double-exponential time course, corresponding to slow and ultraslow components of Na+ channel inactivation. The individual time constants were 2-7 s (slow component) and 40-560 s (ultraslow component). Recovery from these slow inactivation processes also followed a double-exponential time course, but was characterized by significantly briefer time constants than those for the inactivation process. The relationship between transmembrane potential and steady-state slow or ultraslow inactivation was well described by the Boltzmann equation. The membrane potential at which half the Na+ channels are inactivated (V1/2) and the slope factor were estimated to be -48.1 and 13.6 mV, respectively, for the slow component alone. Under conditions in which the slow and ultraslow inactivation components were both present, these parameters were -53.1 and 8.7 mV respectively. When the fast and the two slow inactivation processes occurred concomitantly, the resultant steady-state inactivation curves were shifted to more negative potentials and the slope factor was decreased. Treatment with 1 mM Cd2+ externally did not affect the time course of slow inactivation, but produced a 3-7 mV depolarizing shift in its steady-state voltage dependency by virtue of cadmium's known effect on the cell surface potential. This study has thus identified two components of slow Na+ inactivation in heart muscle, operating on a time scale of seconds (slow inactivation) and minutes (ultraslow inactivation).

Reversal of cerebral vasospasm using an intrathecally administered nitric oxide donor.

Intrathecal bolus administration of (Z)-1-[N-(2-aminoethyl)-N-(2-ammonioethyl)aminio]diazen++ +-1-ium-1,2-diolate (DETA/NO), a long half-life diazeniumdiolate-class nitric oxide (NO) donor, was evaluated for safety and efficacy in the treatment of delayed cerebral vasospasm in a canine model of subarachnoid hemorrhage (SAH). The baseline basilar artery (BA) diameter of 25 dogs was measured with the aid of angiography on Day 0. Vasospasm was then induced by intracisternal injection of autologous arterial blood on Days 0 and 2. Repeated arteriography on Day 7 revealed an average BA diameter of 58% of baseline. Each dog was then randomized to one of four groups: a pathology control group (SAH only, four animals); a treatment control group (SAH plus 2 micromol of the inactive drug carrier DETA, eight animals); a low-dose treatment group (SAH plus 0.2 micromol DETA/NO, six animals); or a high-dose treatment group (SAH plus 2 micromol DETA/NO, six animals). The drugs were administered in a 2-ml intrathecal bolus via the cisterna magna. Arterial caliber was monitored by angiography over the subsequent 4 hours. A 2-micromol dose of the drug was then given and serial arteriography continued for an additional hour to screen for tachyphylaxis. Intracranial pressure and respiratory and hemodynamic parameters were continuously monitored. Histopathological analyses of the animals' brains were performed after the dogs were killed on Day 8. The drug DETA/NO produced reversal of vasospasm in a dose-dependent fashion that roughly followed a double exponential time course. Doses of 2 micromol DETA/NO resulted in restoration of the angiographically monitored BA diameter to the prevasospasm size at 1.5 hours posttreatment, and this was sustained at 88% of baseline at 4 hours (p < 0.01, independent samples t-test). By contrast, the treatment control group remained on average at 54% of baseline diameter. The low-dose treatment group achieved only partial and more transitory relaxation. Histopathological analyses showed findings consistent with chronic SAH but did not demonstrate any toxicity associated with the NO donor. No adverse physiological changes were seen. This study indicates that long-acting NO donors are potentially useful as agents to restore circulation in patients suffering from cerebral vasospasm.

Electrophysiological characterization of voltage-gated Na+ current expressed in the highly metastatic Mat-LyLu cell line of rat prostate cancer.

Voltage-gated Na+ channels, classically associated with impulse conduction in excitable tissues, are also found in a variety of epithelial cell types where their possible functions are not known so well. We have previously reported expression of a voltage-gated Na+ channel specifically in the highly metastatic Mat-LyLu rat prostate cancer cell line; blockage of the current with tetrodotoxin (TTX) significantly reduced the invasiveness of the cells in vitro, suggesting that the channel may have a functional role in metastasis. The aim of the present study was to characterize this current using the whole-cell patch clamp recording technique, and compare it to Na+ currents found in various other tissues. The inward current of the Mat-LyLu cells was abolished completely, but reversibly, in Na+-free solution, confirming that Na+ was indeed the permeant ion. Activation occurred at -40 mV and currents reached a maximal amplitude at around 6 mV. Boltzmann fits to current activation and steady-state inactivation revealed that the currents were half activated at about -15 mV and half inactivated at -80 mV. Both current inactivation and recovery from inactivation followed a double-exponential time course with fast and slow components. The Na+ currents were highly sensitive to block by TTX (IC50 approximately 18 nM), whilst 1 microM mu-conotoxin GIIIA mostly had no effect. 100 microM Cd2+ also had no effect on the current, whilst 2.5 mM Cd2+, Mn2+, and Co2+ each caused a depolarizing shift in activation and a reduction in peak conductance of around 20%. In conclusion, the Na+ channel expressed in the highly metastatic Mat-LyLu cell line appeared to have electrophysiological and pharmacological properties of TTX-sensitive channels. Further work is needed, however, to elucidate the exact nature of the channel protein and the mechanism(s) of its involvement in cellular invasiveness.

Functional and pharmacological differences between recombinant N-methyl-D-aspartate receptors.

N-methyl-D-aspartic acid (NMDA) receptors transiently transfected into mammalian HEK-293 cells were characterized with subunit-specific antibodies and electrophysiological recordings. Deactivation time course recorded in response to fast-glutamate pulses were studied in isolated and lifted cells, as well as in outside-out membrane patches excised from cells expressing recombinant NR1 subunits in combination with the NR2A, NR2B, NR2C, or NR2D NMDA receptor subunits. Transfected cells were preidentified by the fluorescence emitted from the coexpressed Aequorea victoria jellyfish Green Lantern protein. Currents generated by NR1/NR2A channels displayed double exponential deactivation time course being faster than that in NR1/NR2B or NR1/NR2C channels. However, a large decay variability was observed within each cotransfection, suggesting that mechanisms additional to subunit composition may also regulate deactivation time course. NR1/NR2D channels displayed slowly deactivating currents. Channel deactivation was fast and comparable among receptors obtained by cotransfecting five distinct spliced variants of the NR1 subunit, each with the NR2A subunit. Additionally, recovery from desensitization was slower for NR1/NR2B than for NR1/NR2A channels. The average deactivation time course of responses to brief L-glutamate applications in cells where NR1/NR2A/NR2B cDNAs were cotransfected at variable ratio was intermediate between those of the NR1/NR2A and NR1/NR2B channels. Although immunocytochemical evidence indicates that the majority of cells are cotransfected by all plasmids in triple transfection, our experimental condition did not allow for a tight control of the expression of NMDA receptor subunits. This produced the result that many cells were characterized by deactivation time course and haloperidol sensitivities of separate NR1/NR2A and NR1/NR2B subunit heteromers. We also speculate on the possible formation of channels resulting from the coassembly in the same receptor of NR1/NR2A/NR2B subunits from a minority of cells that gave responses to brief application of L-glutamate characterized by slow deactivation time course and decreased haloperidol sensitivity.

Verapamil block of the delayed rectifier K current in chick embryo dorsal root ganglion neurons.

We have used the patch-clamp method in the whole-cell configuration to investigate the mechanism of block of the delayed rectifier K current (IDRK) by verapamil in embryonic chick dorsal root ganglion (DRG) neurons. Verapamil induced a dose-dependent decay of the current, without altering its activation kinetics. This observation, together with the good description of IDRK time course at various blocker concentrations with the computer simulation of a three-state chain model (closed left and right arrow open left and right arrow open-blocked), indicates that verapamil acts as a state-dependent, open-channel blocker. To account for the double-exponential time course of recovery from block, this minimal kinetics scheme was expanded to include a closed-blocked state resulting from channel closure (at hyperpolarized voltages) with verapamil still bound to it. The apparent block and unblock rate constants assessed from verapamil-induced current decay in the presence of external Na were 0.95 +/- 0.05 ms-1mM-1 and 0.0037 +/- 0.0016 ms-1, respectively. When external Na was replaced by K, only the unblock rate constant changed, to 0.02 +/- 0.009 ms-1. Under these ionic conditions it was also observed that the recovery from block was modified from the double-exponential time course in the presence of external Na (tau1 = 160 ms; tau2 = 1600 ms), to a faster single-exponential recovery (tau = 100 ms). We tested the voltage dependence of block by applying stimulation protocols aimed at eliminating bias easily introduced by the shift of the gating equilibrium and by the coupling of channel activation and block. Under these experimental conditions the resulting block rate constant was not measurably voltage dependent.

Rapid Synaptic Transmission in the Avian Ciliary Ganglion Is Mediated by Two Distinct Classes of Nicotinic Receptors

We analyzed the kinetics and pharmacology of EPSCs in two kinds of neurons in the embryonic avian ciliary ganglion. Whole-cell voltage-clamp recordings revealed that the singly innervated ciliary neurons had large-amplitude (1.5-8.0 nA) EPSCs that could be classified according to the kinetics of their falling phases. Most of the neurons responded with an EPSC the falling phase of which followed a double exponential time course with time constants of approximately 1 and 10 msec. The EPSCs of the remaining ciliary neurons followed a single time constant ( approximately 8 msec). Multiple innervated choroid neurons had smaller-amplitude responses (0.2-1.5 nA when all inputs were activated) that appeared to contain only a slowly decaying component (tau = 12 msec). The fast and slow components of EPSC decay seen in most ciliary neurons could be pharmacologically isolated with two toxins against nicotinic acetylcholine receptors (AChRs). The fast component was blocked by 50 nM alpha-bungarotoxin (alpha-BuTx), which binds alpha7-subunit-containing AChRs. The slow component was selectively blocked by 50 nM alpha-conotoxin MII (alpha-CTx-MII), which blocks mammalian AChRs containing an alpha3/beta2 subunit interface. A combination of both alpha-BuTx and alpha-CTx-MII abolished nearly all evoked current. Similar pharmacological results were found for ciliary neurons with monoexponentially decaying EPSCs and for choroid neurons. These results suggest that nerve-evoked transmitter acts on at least two different populations of AChRs on autonomic motor neurons in the ciliary ganglion.