Warning: mysql_query(): Unable to save result set in /home/onemol/public_html/wp-includes/wp-db.php on line 1933
Warning: mysql_query(): Unable to save result set in /home/onemol/public_html/wp-includes/wp-db.php on line 1933
Some of our main papers since 2003 are listed below, with commentaries and reprints. Some older papers and classics can be downloaded here too.
.For more papers, follow these links.
David Colquhoun‘s papers are listed below and on the theory papers page.See also David Colquhoun’s profile on Google scholar.
Some may still be on old UCL page (some with reprints) and older papers here.
Some recent papers with commentary and reprints
Michael Epstein, Ben Calderhead, Mark A. Girolami, and Lucia G. Sivilotti (2016) Bayesian Statistical Inference in Ion-Channel Models with Exact Missed Event Correction. Biophysical Journal (2016). http://dx.doi.org/10.1016/j.bpj.2016.04.053 [Download pdf].
This is the first paper to implement a Bayesian analysis of single ion channel records which uses the exact missed event correction (as used in our maximum likelihood program, HJCFIT) [download HJCFIT]. The prior distribution for each parameter (rate constant) is uniform over the physically-plausible range of values. In HJCFIT the parameter estimates are constrained to the same range, so the estimates of rate constants should be identical. In the case of well-defined parameters, the estimates are indeed much the same, and their errors (covariance matrix) are represented well by the covariance matrix found from the Hessian, in HJCFIT. But the posterior distribution of each parameter provides a way to look at the uncertainty in the ill-defined rate constants that occur in over-parameterised problems. The Biophysical Journal commissioned a commentary on this paper, by Frank Ball [download pdf]
Lucia Sivilotti and David Colquhoun (2016) In Praise of Single Channel Kinetics. Journal of General Physiology (2016). DOI: 10.1085/jgp.201611649 [Download pdf]. [open access]
This is a commentary on Mukhtasimova, N., C.J. daCosta, and S.M. Sine. 2016 Improved resolution of single channel dwell times reveals mechanisms of binding, priming, and gating in muscle AChR. J.Gen. Physiol. 148:43–63 (http ://dx .doi .org /10 .1085 /jgp .201611584)
The improved resolution confirms that the channel opening does not arise directly from the resting conformation, but rather from a short-lived pre-open shut conformation. It also confirms that partial agonists have essentially the same opening rate as full agonists, and that the origin of their low efficacy lies in the initial conformation changes, not in the shut-open conformation change. These conclusions are compatible with those of Burzomato et al., (2004) and with Lape et al.. (2008). The major difference from earlier work lies in the postulation of negative cooperativity in the two bindings to the resting conformation, which has not been needed before. This problem is discussed.
Alessandro Marabelli, Remigijus Lape, and Lucia Sivilotti (2015)Mechanism of activation of the prokaryotic channel ELIC by propylamine: A single-channel studyJournal of General Physiology (2015) 145, 23–45
www.jgp.org/cgi/doi/10.1085/jgp.201411234 [Download pdf].
A single channel study of the prokaryotic channel from Erwinia chrysanthemi (ELIC). This channel has a high conductance and its structure is better known than that of the related eukaryotic channels such as the glycine and nicotinic receptors. The results could not be fitted well with the Flipped model, but were well-described by the Primed model.
Rilei Yu, Eliott Hurdiss, Timo Greiner, Remigijus Lape, Lucia Sivilotti and Philip C. Biggin
(2015) Agonist and Antagonist Binding in Human Glycine Receptors
. Biochemistry 53, 6041−6051 (2014). dx.doi.org/10.1021/bi500815f
An investigation of the binding of glycine by molecular dynamics, using a homology model of the human glycine receptor. The results cast new light on the glycine binding site. Simulation of the binding of the antagonist, strychnine, suggests the strychnine binding induces movement to a conformational state that is distinct from the glycine-bound or apo state, not only within the ligand-binding domain but also in the transmembrane domain. This implies that strychnine is not just a passive competitive antagonist, but produces effects of its own.
Zimmermann I, Marabelli A, Bertozzi C, Sivilotti LG, Dutzler R (2012) Inhibition of the Prokaryotic Pentameric Ligand-Gated Ion Channel ELIC by Divalent Cations. PLoS Biol 10(11): e1001429. doi:10.1371/journal.pbio.1001429 [Download pdf]. [Download supplementary info]
An investigation the effect of divalent ions on ELIC, a prokaryotic pentameric homologut if ligand gated ion channels with known structure. Divalent cations inhibit the activation of ELIC by the agonist cysteamine,
reducing both its potency and, at higher concentrations, its maximum response. X-ray crystallography was used to locate the binding site for divalent cations is located at the outer rim of the extracellular domain, at the interface between adjacent subunits, at some distance from the agonist binding region. [#zmbsd12]
- David Colquhoun and Remigijus Lape(2012). Allosteric coupling in ligand-gated ion channels. Journal of General Physiology 140, :599 – 612. [Download pdf].
Our contribution to a series of Perspectives on: Conformational coupling in ion channels. It is argued that the word “allosteric” is too ambiguous to be useful as a description of mechanism. When it is possible to estimate all the rate constants in a specified reaction mechanism, such descriptions become redundant. Topics discussed include microscopic reversibility and the preferred routes from shut to open. [#cl2012]
- Remigijus Lape, Andrew J. R. Plested, Mirko Moroni, David Colquhoun,and Lucia G. Sivilotti (2012). The α1K276E Startle Disease Mutation Reveals Multiple Intermediate States in the Gating of Glycine Receptors Journal of Neuroscience. 32(4), :1336 – 1352. [Download pdf].
In human glycine receptors the α1K276E mutation causes hyperekplexia, a rare inherited disease associated with an exaggerated startle response. It took us quite a long time to work out the mechanistic reason for the loss of function in the mutant receptor. It is interesting to us, because it is the first case we’ve encountered in which our flip model has failed to provide an adequate description of the observations. The “flip” mechanism was introduced in Burzomato et al 2004, for alpha1-containing glycine receptors and found also to fit nicotinic acetylcholine receptors by Lape et al., 2008, who also showed that it provided an elegant description of partial agonism. It was obvious from the start that the flip model would not describe channels which open spontaneously and that a generalisation of it, like the “primed” model, would be needed (Muhktasimova et al., Nature 459, 451, 2009). In the case of the α1K276E the results were too complicated to be fitted by the flip model, but the more general primed model fitted well.
- Paraskevi Krashia, Remigijus Lape, Francesco Lodesani, David Colquhoun, and Lucia G. Sivilotti (2011). The long activations of alpha2 glycine channels can be described by a mechanism with reaction intermediates (“flip”) Journal of General Physiology. 137, 197 – 216. [Download reprint].
Our flip model survives another test. The “flip” mechanism was introduced in Burzomato et al 2004, for alpha1-containing glycine receptors and found also to fit nicotinic acetylcholine receptors by Lape et al., 2008, who also showed that it provided an elegant description of partial agonism. This paper is about a very different glycine receptor, the homomeric alpha2 receptor. At first the flip model did not seem to describe the results, but after we realised that the very long groups of openings seen at low concentrations of glycine were actually single very long activations of the channel, everything fell in to place. The flip model provides also an elegant mechanistic description of the very long shut times between activations. [#krashia2011]
- Mirko Moroni, Istvan Biro, Michele Giugliano, Ranjit Vijayan, Philip C. Biggin and Lucia G. Sivilotti (2011). Chloride ions in the pore of glycine and GABA channels shape the time course and voltage dependence of agonist currents Journal of Neuroscience. 31, 14095 – 14106. [Download reprint].
We show that glycine and GABA receptors “sense” chloride concentrations because of interactions between the M2 pore-lining domain and the permeating ions. This interaction is complex and must involve a site with asymmetrical access from the two sides of the membrane, because high extracellular chloride can slow deactivation, but only if intracellular chloride is low (4 mM). The sensitivity of channel gating to chloride is abolished if the channel is mutated to become cation selective. The appropriate interaction between permeating ions and channel pore is also necessary to maintain the channel voltage sensitivity of gating. [#moroni2011]
- Sivilotti LG (2010). What single channel analysis tells us of the activation mechanism of ligand-gated channels: the case of the glycine receptor. J Physiol 2010; 588:45-58. [download reprint]
- Remigijus Lape, Paraskevi Krashia, David Colquhoun and Lucia G. Sivilotti (2009) Agonist and blocking actions of choline
and tetramethylammonium on human muscle acetylcholine receptors.Journal of Physiology. 587, 5045 – 5072. [download reprint].
Choline has been widely used as a very weak agonist iun studies of gain-of-function mutants. It is very hard to study because it blocks ion channels at concentrations lower than those needed to activate the channel, so it has taken a while to get enough results, The single channel results can be fitted on the hypothesis that choline is actually a full agonist and its reposnse is limited bu channel block rather than partial agonism. However concentration jump experiments (as well as the feeling that it is likely to be quailitatively like TMA) favour the alternative idea that choline is a very weak agonist because it is very inefficient at producing the intermediate pre-open ‘flipped’ conformation of the receptor. Once flipped, the channel can open and shut with similar rates to those found with acetylcholine and TMA. This interpretation is consistent with our earlier work in Burzomato et al 2004), and in Lape et al., 2008.
- Remigijus Lape, David Colquhoun & Lucia Sivilotti (2008) On the nature of partial agonism in the nicotinic receptor superfamily (2008).Nature. 454, 722 – 728. [Download reprint, or zip file with movie]
This paper is the culmination of three years’ work. For 50 years, ever since del Castillo & Katz (1957), it has been assumed that partial agonists will be deficient in producing the open-shut reaction. In this paper we find, for both glycine and nicotinic receptors, that opening and shutting of the channel is very much the same for partial and full agonists. The deficiency in partial agonists lies earlier, in the production of the pre-open ‘flip’ state (first identified in Burzomato et al 2004).
See also items about this paper on UCL News, the News and Views in Nature and Making the paper in Nature. [#lcs2008]
- Pitt, S, Sivilotti, LG & Beato, M. (2008) High intracellular chloride slows the decay of glycinergic currents.J.Neuroscience 28, 11454-67. [download reprint].
Synaptic-like currents produced by concentration-jumps of glycine onto outside-out patches were at least 3-fold slower than expected from the results of our kinetic model fitted to cell-attached data. This discrepancy is due to different recording solutions for the two configurations and not to a difference between native and recombinant channels. High symmetrical chloride is often used especially in neurons to enhance recorded inhibitory synaptic currents, but it distorts them by making them much slower. By recording synaptic currents from motoneurones before and after raising their intracellular chloride, we show that this effect is important also in slice recordings. We have since shown that a similar phenomenon occurs for GABAA channels
- Beato, M. & Sivilotti, L.G. (2007) Single-channels properties of glycine receptors of juvenile rat spinal motoneurones in vitro. J.Physiol, 580, 497-506. [download reprint]
The conductance of these native glycine channels in cell-attached patches shows that they are likely to be heteromers. In addition to that, native channels have kinetic properties similar to those of recombinant a1b channels: their fast and effective gating can be described by the ‘flip ’mechanism of Burzomato et al., 2004.
- Plested, A., Groot-Kormelink, P., Colquhoun, D. & Sivilotti, L.G. (2007) Single channel study of the spasmodic mutation α1 A52S in recombinant rat glycine receptors. J.Physiol., 581, 51-73. see accompanying Perspective by J.H. Steinbach, J.Physiol., 581,3 [download reprint] [download perspective]
Inherited defects in glycine receptors produce hyperekplexia, or startle disease. A mutant mouse, spasmodic, that has a startle phenotype, has a point mutation (A52S) in the glycine receptor α1 subunit. The results could be fitted with our flip mechanism (Burzomato et al. 2004). The reduction in affinity for the flipped conformation accounts for the reduction in apparent cooperativity seen in the mutant receptor (without having to postulate interaction between the binding sites) and it accounts for the decreased potency of glycine on mutant receptors. This mechanism also predicts accurately the faster decay of synaptic currents that is observed in spasmodic mice. [#A52S-2007]
- Beato, M., Burzomato, V. & Sivilotti, L.G. (2007) The kinetics of inhibition of rat recombinant heteromeric α1β glycine receptors by the low affinity antagonist SR-95531. J.Physiol, 580: 171-179. [download reprint]
- Colquhoun, D (2007) Why the Schild method is better than Schild realised Trends in Pharmacological Sciences, 28, 608 – 614.[download reprint].
The Schild method allows genuine physical equilibrium constants for competitive antagonists to be obtained from experiments in which complex responses are measured. This paper extends work done in 1973 (here), and gives conditions under which valid results can be obtained. The Schild method may still be valid with multiple agonist binding sites, even when agonist binding sites interact and/or are not identical. [#schild2007]
- Groot-Kormelink, P., Broadbent, S, Beato, M. & Sivilotti, L.G. (2006) Constraining the expression of nicotinic acetylcholine receptors using pentameric constructs. Mol. Pharm., 69, 558-63; see Perspective in Mol Pharm. 69, 407-10. [download reprint] [download Perspective]
An alternative approach that is more effective in constraining receptor composition than the tandem + monomer formula is to produce pentameric constructs. This paper shows a first characterization of their properties.
- Broadbent, S., Groot-Kormelink, P., Krashia, P., Harkness, P.,Millar, N., Beato, M. & Sivilotti, L.G.(2006) Incorporation of the beta3 subunit has a dominant negative effect on the function of recombinant central-type neuronal nicotinic receptors. Mol Pharm, 70, 1350-7. [download reprint]
- Schorge, S., Elenes, S. & Colquhoun, D. (2005). Maximum likelihood fitting of single channel NMDA activity with a mechanism composed of independent dimers of subunits Journal of Physiology 569, 395 – 418. [Download reprint 5.9Mb]
Our best shot at kinetic analysis of an NMDA receptor.We find an opening rate for the channel that is much faster than that found by other labs, probably because our analysis methods can detect fast shut times (see Fig. 11). [#ss2005]
- Burzomato, V., Beato, M., Groot-Kormelink, P., Colquhoun, D. & Sivilotti, L.G. (2004) Single-channel behavior of heteromeric alpha1beta glycine receptors: An attempt to detect a conformational change before the channel opens J.Neuroscience, 24, 10924-10940. [download reprint]
In heteromeric glycine channels (found in adult synapses), the three glycine binding sites appear to interact, i.e. there is a progressive increase in the channel affinity for glycine as more molecules bind. This apparent interaction may be explained by a conformational change that takes place upon binding, but while the channel is still closed (‘flip’ mechanism). This is the first time that a reaction intermediate has been identified and it represents the first qualitative advance in reaction mechanisms since the classic work of Castillo & Katz, over 50 years ago. The basic idea has now been confirmed in the USA (Muhktasimova et al, Nature 459, 451, 2009). It was exploited by us to reinterpret the action of partial agonists (see Lape et al. 2008). [#vb2004]
- Colquhoun, D. ( 2003) Challenging the tyranny of impact factors Nature 423, 479.
[Get PDF] [#impact2003]
- Professor Sir Bernard Katz. Biophysicist who arrived in England with £4 and went on to win a Nobel Prize (Obituary) Independent 26 April 2003
- Professor Sir Bernard Katz. A longer account of his life from Physiology News (Autumn 2003, number 52, pp 34–38) [Get PDF]
Inside front cover (portrait) [Get PDF]
Inside back cover (scenes from BK’s life) [Get PDF]
- Colquhoun, D., Hatton, C., & Hawkes, A. G. ( 2003) The quality of maximum likelihood estimation of ion channel rate constants . Journal of Physiology (London) 547, 699–728. [Get PDF]
A study of the ability of the HJCFIT method to extract rate constants for a reaction mechanism from a sequence of open and shut times. our analysis was applied to a large number of ‘experiments’ that were generated by simulation, so the true values for the rate constants were known. Sampling distributions are shown for the fitted parameters. HJCFIT is the only fitting method that has been tested in this way. [#chh2003]
- Hatton, C., Shelley, C., Brydson, M., Beeson, D., & Colquhoun, D. ( 2003) Properties of the human muscle nicotinic receptor, and of the slow–channel syndrome mutant eL221F, inferred from maximum likelihood fits. Journal of Physiology (London) 547, 729-760. [Get PDF]
Application of the HJCFIT method to wild type nicotinic receptors, and to a disease–causing mutant. [#hsbbc2003]
- Colquhoun, D., Unwin, N., Shelley, C., Hatton, C. J., & Sivilotti, L. ( 2003) Nicotinic Acetylcholine Receptors. Abrahams, D. 6th Edition, Vol 2: Drug Discovery and Drug Development, Chapter 11, 357–405. New York, John Wiley. Burger’s Medicinal Chemistry.
A review of the relationship between structure and function in nicotinic receptors. [#cushs03]
- Schorge, S. & Colquhoun, D. (2003). Studies of NMDA receptor function and stoichiometry with truncated and tandem subunits. Journal of Neuroscience 23, 1151–1158 [Get PDF]
A study with tandem constructs. The results suggest that the order of the subunits in NMDA receptor is NR1–NR1–NR2–NR2, perhaps because it is a dimer made of one NR1 dimer and and NR2 dimer. [#sc03]
Some of the basic principles were laid out in a 1998 review
Colquhoun, D. (1998). Binding, gating, affinity and efficacy. The interpretation of structure–activity relationships for agonists and of the effects of mutating receptors British Journal of Pharmacology , 125,923–948. [Get PDF]
A review that attempts to bring together the classical pharmacological ideas of ‘affinity’ and ‘efficacy’, with the ‘binding–gating’ problem that arises whenever binding of a ligand causes a conformation change in a protein . [#bjp1998]
Some classical papers
Hill,A.V. (1909) The mode of action of nicotine and curari determined by the form of the contraction curve and the method of temperature coefficients. J. Physiol. (Lond), 39, 361-373. [Get pdf (0.58 Mb)]
This is A.V. Hill’s first paper. It describes the Langmuir equation (both rates and equilibrium) some time before Langmuir (1918) did so. [#Hill1909]
Haldane, J.B.S. (1930) Enzymes, Longmans, Green and Co.London. [Get pdf (0.31.Mb)]
This is the section of Haldane’s book that describes mechanisms: Michaelis-Menten and Briggs-Haldane, and in particular the case of competitive inhibition (see pp 46-47 of book, pp 20-21 of pdf file). [#jbsh1938]
Older papers from DC lab
The JSTOR web site now has in pdf format, in its General Science Collection, the entire contents of the Royal Society journals back to the 17th century, Proceedings of the National Academy of Sciences, and of Science. The pdf files can be downloaded by any site that subscribes to JSTOR.
Older papers from the Journal of Physiology are now available from the Pubmed central archive, For example
Colquhoun, D. & Sakmann, B. (1985). Fast events in single-channel currents activated by acetylcholine and its analogues at the frog muscle end-plate. Journal of Physiology ( London ) 369 , 501-557. [Get pdf)]
See also the ‘classical perspective on this paper, written in 2007 (here). [#cs85]
Gardner, P., Ogden, D.C. and Colquhoun, D. (1984) Conductances of single ion channels opened by nicotinic agonists are indistinguishable. Nature, 309, 160 – 162. [Get PDF)]
This paper used single channel measurements to show that all the agonists were tested produced openings of virtually the same amplitude. It corrected a 1975 paper which had come to the opposite conclusion using noise analysis. This showed that the reason that some agonists are partial is not because they open channels of lower conductance than full agonists. The use of single channels made the measurements very simple, so it’s doubtful if this would have appeared in Nature if it were not for the fact that it corrected our earlier report. This was so obvious that when I walked into the common room in in Göttingen, shortly after it came out, someone said “How did you get that into Nature, are you sleeping with Maxine Clarke?”. [#goc84]
Colquhoun, D. & Hawkes, A.G. (1982) On the stochastic properties of bursts of single ion channel openings and of clusters of bursts. Philosophical Transactions of the Royal Society London B 300, 1-59. [Get PDF (2.6 Mb)]
This is the paper that describes the notation used in all subsequent papers, and uses it to obtain distributions of open and shut times, of burst properties, and the properties of clusters of bursts (it supersedes a theoretical paper written a year earlier, in 1981, which used a much clumsier notation). The equations derived here are elegant closed forms, but make no allowance for missed events. That did not become possible until 1990 – 1992. [#ch02]
Colquhoun, D. & Sakmann, B.(1981) Fluctuations in the microsecond time range of the current through single acetylcholine receptor ion channels. Nature 294, 464 – 466. [Get PDF]
This is our first experimental single ion channel paper. It gives our first rough values for affinity and efficacy and it’s also the first description of the existence of a component of short openings which we attributed, tentatively, to brief openings of mono-liganded receptors. [#ch81]
Colquhoun, D. (1981). How fast do drugs work? Trends in Pharmacological Sciences 8, 212 – 217 [Get pdf]
This old paper is still sometimes found useful by students. It was written as an introduction to ideas about measuring the rates of reactions, as opposed to equilibrium constants. It therefore deals with macroscopic responses, noise analysis and single channels in an elementary way.
Colquhoun, D., Dreyer, F., & Sheridan, R. E. (1979). The actions of tubocurarine at the frog neuromuscular junction. Journal of Physiology (London) 293, 247-284. [Get PDF)]
This paper describes the very long lasting channel blockages’ that can be produced by (+)-tubocurarine (in addition to its competitive action). Such long blockages would be hard to identify on single channel records so even if we had been able to measure them in 1977 -78, the voltage-jump method used here might still have been the best. [#cds79]
Colquhoun, D. & Hawkes, A. G. (1977). Relaxation and fluctuations of membrane currents that flow through drug-operated channels. Proceedings of the Royal Society London B 199, 231-262.
[Get pdf 2.6 Mb]
This 1977 paper is the first of many papers written with Alan Hawkes. Its origin dates back to 1972 when I wrote to Alan Hawkes to ask how the noise analysis, recently published by Katz & Miledi, could be generalised to any reaction mechanism. The theory predicted that the predominant time constant from noise analysis would be longer than the mean channel open time, for any realistic values of the rate constants. The physical meaning of this eluded us at first, but after being pressed by Bernard Katz to explain the result, we realised that it was a result of channel openings being predicted to not to occur singly, but in bursts. By the time the paper came out, Neher & Sakmann’s 1976 paper had appeared and we were soon able to test the prediction. [#ch77]
Colquhoun, D., Dionne, V. E., Steinbach, J. H. & Stevens, C. F. (1975). Conductance of channels opened by acetylcholine-like drugs in muscle end-plate. Nature 253, 204-206. [Get pdf]
In this paper we tested the hyopthesis that partial agonists produce a smaller maximum response than full antagonists because they open channels with lower conductance than full agonists. It was before the days when single channel measurements were possible so we used noise analysis. We found that partial agonists opened channels with smaller conductance than those elicited by full agonists. When we tested this again with single channel measurements in 1984, this result was found to be wrong. Despite some careful calculations, the quality of the two-electrode voltage clamp at the frog endplate must have been lower than we thought. The partial agonist tended to have higher frequency components than full agonsits and some of the area under the power spectrum must have been lost. [#cdss75]
Colquhoun, D.(1970). How long does a molecule stay on the receptor? Explanation of a paradox. British Journal of Pharmacology 39, 215P [Get PDF]
This is the abstract of a talk given at the 1969 meeting of the British Pharmacological Society. At the time I had just discovered, via Alan Hawkes, the waiting time paradox. This resolved, at a stroke, many of the problems that I’d been having in thinking about what happened at the level of a single drug-receptor complex.
Colquhoun, D. (1969). A comparison of estimators for a two-parameter hyperbola. Journal of Royal Statistical Society C 18, 130-140. [Get PDF (887 kb)] ]
Another historical item: a study of the quality of estimates for a simple Langmuir equation by different methods of fitting, showing the best method is generally least squares. This was one of my first attempts at programming a real computer. The simulations were run on an Elliott 803, using Algol, on punched paper tape.
Colquhoun, D. (1968). The rate of equilibration in a competitive n drug system and the auto-inhibitory equations of enzyme kinetics: some properties of simple models for passive sensitization. Proceedings of the Royal Society. B. 170, 135-154 [Get PDF (2460 kb)] ]
This was DC’s first published work to use matrix notation, for macroscopic (not single channel) kinetics. It provided a general way to look at the rate of approach to equilibrium in systems with n competing ligands. The results were applied to several models for passive sensitisation that were of interest at the time. Curve-fitting programs were written in Algol, for the University of London Atlas computer
Two older papers from books
These two papers have been scanned (because the books in which they appeared are now hard to find).
Colquhoun, D. (1973). The relation between classical and cooperative models for drug action. In Drug Receptors, ed. Rang, H. P., pp. 149-182. Macmillan Press, London. [Get pdf file: 4.04 Mb]
This paper attempted to reconcile the emerging knowledge of cooperativity in ion channel receptors with the more classical views. It showed that the Schild approach for competitive antagonsists was indeed valid for a wide range of receptor mechanisms, but that agonists could give results that were incompatible with Stephenson’s ideas. But it failed to grasp completely the fatal error in the classical approach, The approach to the Schild plot was updated and generalised in 2007. [#dc73]
Colquhoun, D. (1987). Affinity, efficacy and receptor classification: is the classical theory still useful? In Perspectives on hormone receptor classification, ed. Black, J. W., pp. 103-114. Alan R. Liss Inc., New York. [get pdf file]
This paper explains why Stephenson’s quantitative formulation contained an error, and how this error implied that none of the published methods for experimental determination of ‘affinity’ and ‘efficacy’ could actually achieve the separation of these quantities that had been claimed for them. [#dc87]