David Colquhoun

Fitting and Statistical Analysis of Single-Channel Records

An improved bi-switch construction is provided having an interrupting device arranged in electrical parallel relation therewith so that the circuit through each of the two switches is made through the interrupting device, and, subsequently, the interrupting device is shorted out in the closed-circuit position of the particular switch being operated. During the opening operation, again the interrupting device is brought into play so that a parallel electrical path is provided in shunt relationship to the particular switch being operated through the interrupting device, the interrupting switch assuming the burden of interrupting the circuit; and subsequently the particular switch being operated provides an isolating gap from the interrupting device. The arrangement is particularly desirable when two three-phase switches have a common leg, or terminal, to which one end of the interrupting device may be electrically attached, so that either switch may be operated with the interrupting device serving as a common means for both switches. An improved overcenter spring mechanism is provided for operating the interrupting device in both the closing direction and also in the opening direction for quick-make and quick-break operations of the interrupting device. In one arrangement, the movable contact member of each switch may comprise a rotatable movable blade, which first makes contact with an auxiliary terminal of the interrupting device, while simultaneously the overcenter spring device of the mechanism for operating the interrupting device is being charged. Further rotational movement of the movable rotatable blade of the particular switch effects, through the overcenter spring device, quick closing of the interrupting device, and further rotation of the movable blade effects a bypassing of the interrupting device, so that in the closed position of the particular switch being operated the interrupting blade effects conduction of all of the current to the main terminals of the particular switch being operated to the exclusion of the interrupting device.

On the Stochastic Properties of Single Ion Channels

It is desirable to be able to predict, from a specified mechanism, the appearance of currents that flow through single ion channels (a) to enable interpretation of experiments in which single channel currents are observed, and (b) to allow physical meaning to be attached to the results observed in kinetic (noise and relaxation) experiments in which the aggregate of many single channel currents is observed. With this object, distributions (and their means) are derived for the length of the sojourn in any specified subset of states (e. g. all shut states). In general these are found to depend not only on the state in which the sojourn starts, but also on the state that immediately follows the sojourn. The methods described allow derivation of the distribution of, for example, (a) the number of openings, and total length of the burst of openings, that may occur during a single occupancy, and (b) the apparent gap between such bursts. The methods are illustrated by their application to two simple theories of agonist action. The Castillo-Katz (non-cooperative) mechanism predicts, for example, that the number of openings per occupancy, and the apparent burst length, are independent of agonist concentration whereas a simple cooperative mechanism predicts that both will increase with agonist concentration.

Relaxation and Fluctuations of Membrane Currents that Flow through Drug-Operated Channels

The theoretical background is presented for (a) the relaxation towards equilibrium of drug-induced membrane currents, and (b) the fluctuations of membrane current about its equilibrium value that originate in the opening and closing of membrane ion channels. General expressions are given that relate the relaxation current, autocovariance function, spectral density function, fluctuation variance and mean open channel lifetime to the rate constants and single channel conductances for any theory of drug action based on the law of mass action. The question of how much can be validly inferred from experimental spectra that appear to have only one component is discussed. The equations are illustrated by their application to some simple theories of drug action that are currently under consideration.

On the nature of partial agonism in the nicotinic receptor superfamily

Partial agonists are ligands that bind to receptors but produce only a small maximum response even at concentrations where all receptors are occupied. In the case of ligand-activated ion channels, it has been supposed since 1957 that partial agonists evoke a small response because they are inefficient at eliciting the change of conformation between shut and open states of the channel. We have investigated partial agonists for two members of the nicotinic superfamily—the muscle nicotinic acetylcholine receptor and the glycine receptor—and find that the open–shut reaction is similar for both full and partial agonists, but the response to partial agonists is limited by an earlier conformation change (‘flipping’) that takes place while the channel is still shut. This has implications for the interpretation of structural studies, and in the future, for the design of partial agonists for therapeutic use.

Single-channel conductances of NMDA receptors expressed from cloned cDNAs: comparison with native receptors

To cast light on the subunit composition of native NMDA-type glutamate receptors, four cloned subunits of the NMDA receptor have been expressed, in pairs, in Xenopus oocytes, and their single-channel properties have been measured. The conductances of the channels, and their characteristic patterns of sublevel transitions, turn out to be useful diagnostic criteria for subunit composition. The NR1—NR2A and NR1-NR2B combinations (which have identical TM2 sequences) are very similar to each other. Both have 50 pS openings and brief 40 pS sublevels (in 1 mM external Ca2+), with similar mean lifetimes and frequencies. They also show close quantitative resemblance to the channels of hippocampal CA1 and dentate gyrus cells and of cerebellar granule cells, except that the NR1—NR2A combination has a lower glycine sensitivity than the native channels. In contrast, the NR1-NR2C combination produces a channel with 36 pS and 19 pS conductances of similar (brief) duration; these closely resemble the 38-18 pS channels that have previously been observed in large cerebellar neurons in culture (together with 50 pS channels).

Single‐channel activations and concentration jumps: comparison of recombinant NR1a/NR2A and NR1a/NR2D NMDA receptors

1 We have expressed recombinant NR1a/NR2A and NR1a/NR2D N‐methyl‐D‐aspartate (NMDA) receptor channels in Xenopus oocytes and made recordings of single‐channel and macroscopic currents in outside‐out membrane patches. For each receptor type we measured (a) the individual single‐channel activations evoked by low glutamate concentrations in steady‐state recordings, and (b) the macroscopic responses elicited by brief concentration jumps with high agonist concentrations, and we explore the relationship between these two sorts of observation. 2 Low concentration (5‐100 nM) steady‐state recordings of NR1a/NR2A and NR1a/NR2D single‐channel activity generated shut‐time distributions that were best fitted with a mixture of five and six exponential components, respectively. Individual activations of either receptor type were resolved as bursts of openings, which we refer to as ‘super‐clusters’. 3 During a single activation, NR1a/NR2A receptors were open for 36 % of the time, but NR1a/NR2D receptors were open for only 4 % of the time. For both, distributions of super‐cluster durations were best fitted with a mixture of six exponential components. Their overall mean durations were 35.8 and 1602 ms, respectively. 4 Steady‐state super‐clusters were aligned on their first openings and averaged. The average was well fitted by a sum of exponentials with time constants taken from fits to super‐cluster length distributions. It is shown that this is what would be expected for a channel that shows simple Markovian behaviour. 5 The current through NR1a/NR2A channels following a concentration jump from zero to 1 mM glutamate for 1 ms was well fitted by three exponential components with time constants of 13 ms (rising phase), 70 ms and 350 ms (decaying phase). Similar concentration jumps on NR1a/NR2D channels were well fitted by two exponentials with means of 45 ms (rising phase) and 4408 ms (decaying phase) components. During prolonged exposure to glutamate, NR1a/NR2A channels desensitized with a time constant of 649 ms, while NR1a/NR2D channels exhibited no apparent desensitization. 6 We show that under certain conditions, the time constants for the macroscopic jump response should be the same as those for the distribution of super‐cluster lengths, though the resolution of the latter is so much greater that it cannot be expected that all the components will be resolvable in a macroscopic current. Good agreement was found for jumps on NR1a/NR2D receptors, and for some jump experiments on NR1a/NR2A. However, the latter were rather variable and some were slower than predicted. Slow decays were associated with patches that had large currents.

Studies of NMDA Receptor Function and Stoichiometry with Truncated and Tandem Subunits

The subunits that compose eukaryotic glutamate ion channel receptors have three transmembrane domains (TMs) and terminate with intracellular tails that are important for controlling channel expression and localization. Truncation of NMDA receptor subunits before the final TM showed that this TM and intracellular tail region are necessary to form functional channels. However, it is shown here that these truncated subunits may be partially rescued by coexpressing the final TM and tail as a separate protein. The whole-cell currents so produced are somewhat lower than with full-length subunits, and they do not show the sag characteristic of currents from channels containing NR1 and NR2A subunits in the continued presence of an agonist. In addition, these truncated subunits were joined to full-length subunits to generate tandems. The functional expression of these tandems confirmed the tetrameric structure of NMDA receptors and also suggested that the subunits making up NMDA receptors are arranged as a dimer of dimers in the receptors with a 1-1-2-2 orientation of the subunits in the channel, and not in an alternating pattern of subunits around the pore. These results may redirect future studies into the mechanism of binding and gating in these receptors toward schemes including dimers, and may also be relevant to studies of glutamate receptor ion channels in general.

An investigation of the false discovery rate and the misinterpretation of p-values

If you use p=0.05 to suggest that you have made a discovery, you will be wrong at least 30% of the time. If, as is often the case, experiments are underpowered, you will be wrong most of the time. This conclusion is demonstrated from several points of view. First, tree diagrams which show the close analogy with the screening test problem. Similar conclusions are drawn by repeated simulations of t-tests. These mimic what is done in real life, which makes the results more persuasive. The simulation method is used also to evaluate the extent to which effect sizes are over-estimated, especially in underpowered experiments. A script is supplied to allow the reader to do simulations themselves, with numbers appropriate for their own work. It is concluded that if you wish to keep your false discovery rate below 5%, you need to use a three-sigma rule, or to insist on p≤0.001. And never use the word ‘significant’.

Identification of Amino Acid Residues of the NR2A Subunit That Control Glutamate Potency in Recombinant NR1/NR2A NMDA Receptors

The NMDA type of ligand-gated glutamate receptor requires the presence of both glutamate and glycine for gating. These receptors are hetero-oligomers of NR1 and NR2 subunits. Previously it was thought that the binding sites for glycine and glutamate were formed by residues on the NR1 subunit. Indeed, it has been shown that the effects of glycine are controlled by residues on the NR1 subunit, and a “Venus flytrap” model for the glycine binding site has been suggested by analogy with bacterial periplasmic amino acid binding proteins. By analysis of 10 mutant NMDA receptors, we now show that residues on the NR2A subunit control glutamate potency in recombinant NR1/NR2A receptors, without affecting glycine potency. Furthermore, we provide evidence that, at least for some mutated residues, the reduced potency of glutamate cannot be explained by alteration of gating but has to be caused primarily by impairing the binding of the agonist to the resting state of the receptor. One NR2A mutant, NR2A(T671A), had anEC50 for glutamate 1000-fold greater than wild type and a 255-fold reduced affinity for APV, yet it had single-channel openings very similar to those of wild type. Therefore we propose that the glutamate binding site is located on NR2 subunits and (taking our data together with previous work) is not on the NR1 subunit. Our data further imply that each NMDA receptor subunit possesses a binding site for an agonist (glutamate or glycine).

The actions of tubocurarine at the frog neuromuscular junction.

1. The action of tubocurarine on voltage‐clamped frog muscle end‐plates has been re‐examined by means (a) equilibrium dose‐ratio measurements, (b) current fluctuation measurements and (c) voltage‐jump relaxation measurements. 2. The equilibrium measurements can be interpreted as implying that tubocurarine has (a) a competitive blocking action, with a dissociation constant of 0.34 microM, which is not dependent on membrane potential, and (b) an additional voltage‐dependent blocking action. 3. In the presence of tubocurarine two kinetic components can be seen. The faster one is similar to, but rather faster than, the normal ion channel closing rate. The other is much slower (1‐‐3 sec), and, in relaxation experiments it is in the opposite direction to the fast relaxation. 4. A number of alternative explanations for the results are discussed. The mechanism that fits them best appears to be a combination of competitive block (or block of shut channels), with a strongly voltage‐dependent block of open ion channels by tubocurarine. Estimates of the rate constants for channel blocking (and their voltage dependence) are derived. From these estimates the dissociation constant for the binding of tubocurarine to open channels appears to be roughly 0.12 microM at ‐‐70 mV and 0.02 microM at ‐‐12 mV. 5. Several potential sources of error in the experiments, and in their interpretation, are discussed. The most serious of these are problems associated with diffusion in the small volume of the synaptic cleft, viz. (a) changes in cleft concentration consequent on changes in binding, and (b) ionophoretic flux of antagonist and agonist into the synaptic cleft.