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Joint distributions of apparent open and shut times of single-ion channels and maximum likelihood fitting of mechanisms

1996; Royal Society; Volume: 354; Issue: 1718 Linguagem: Inglês

10.1098/rsta.1996.0115

1471-2962

David Colquhoun, Alan G. Hawkes, K. Srodzinski,

stochastic dynamics and bifurcation

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Colquhoun David , Hawkes A. G. and Srodzinski K. 1996Joint distributions of apparent open and shut times of single-ion channels and maximum likelihood fitting of mechanismsPhil. Trans. R. Soc. A.3542555–2590http://doi.org/10.1098/rsta.1996.0115SectionRestricted accessArticleJoint distributions of apparent open and shut times of single-ion channels and maximum likelihood fitting of mechanisms David Colquhoun Google Scholar Find this author on PubMed Search for more papers by this author , A. G. Hawkes Google Scholar Find this author on PubMed Search for more papers by this author and K. Srodzinski Google Scholar Find this author on PubMed Search for more papers by this author David Colquhoun Google Scholar Find this author on PubMed , A. G. Hawkes Google Scholar Find this author on PubMed and K. Srodzinski Google Scholar Find this author on PubMed Published:15 November 1996https://doi.org/10.1098/rsta.1996.0115AbstractThe openings and shuttings of individual ion channel molecules can be modelled in terms of an underlying Markov process with discrete states in continuous time. In practice, some of the open times, and/or shut times, are too short to be detected reliably, making the durations of some of these intervals appear to be longer than they really are. Under certain assumptions about how this happens, the probability densities of these apparent times have previously been obtained. It has been shown that the ability to distinguish between alternative postulated reaction mechanisms can be greatly improved by considering bivariate distributions. In this paper we obtain joint distributions, and hence conditional distributions, of adjacent apparent open and shut times. Numerical examples illustrate what insight these conditional distributions may provide about the underlying mechanism. Bivariate distributions are readily generalized to multivariate distributions which enable the likelihood for an entire single-channel recording to be computed, and hence efficient maximum likelihood estimates for the mechanism's rate constants can be obtained. Numerical examples of such fitting are given.FootnotesThis text was harvested from a scanned image of the original document using optical character recognition (OCR) software. As such, it may contain errors. Please contact the Royal Society if you find an error you would like to see corrected. Mathematical notations produced through Infty OCR. 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Patel L, Gustafsson N, Lin Y, Ober R, Henriques R and Cohen E A hidden Markov model approach to characterizing the photo-switching behavior of fluorophores, The Annals of Applied Statistics, 10.1214/19-AOAS1240, 13:3 Siekmann I, Cao P, Sneyd J and Crampin E (2019) Data-Driven Modelling of the Inositol Trisphosphate Receptor ( $$\text {IP}_3\text {R}$$ ) and its Role in Calcium-Induced Calcium Release (CICR) Computational Glioscience, 10.1007/978-3-030-00817-8_2, (39-68), . Salari A, Navarro M, Milescu M and Milescu L (2018) Estimating kinetic mechanisms with prior knowledge I: Linear parameter constraints, Journal of General Physiology, 10.1085/jgp.201711911, 150:2, (323-338), Online publication date: 5-Feb-2018. Gibb A, Ogden K, McDaniel M, Vance K, Kell S, Butch C, Burger P, Liotta D and Traynelis S (2018) A structurally derived model of subunit-dependent NMDA receptor function, The Journal of Physiology, 10.1113/JP276093, 596:17, (4057-4089), Online publication date: 1-Sep-2018. Pein F, Tecuapetla-Gomez I, Schutte O, Steinem C and Munk A Fully Automatic Multiresolution Idealization for Filtered Ion Channel Recordings: Flickering Event Detection, IEEE Transactions on NanoBioscience, 10.1109/TNB.2018.2845126, 17:3, (300-320) Colquhoun D (2017) The reproducibility of research and the misinterpretation of p-values, Royal Society Open Science, 4:12, Online publication date: 1-Dec-2017.Siekmann I, Fackrell M, Crampin E and Taylor P (2016) Modelling modal gating of ion channels with hierarchical Markov models, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472:2192, Online publication date: 1-Aug-2016. Tveito A and Lines G (2016) Background: Problem and Methods Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models, 10.1007/978-3-319-30030-6_1, (1-22), . Pirchi M, Tsukanov R, Khamis R, Tomov T, Berger Y, Khara D, Volkov H, Haran G and Nir E (2016) Photon-by-Photon Hidden Markov Model Analysis for Microsecond Single-Molecule FRET Kinetics, The Journal of Physical Chemistry B, 10.1021/acs.jpcb.6b10726, 120:51, (13065-13075), Online publication date: 29-Dec-2016. Ball F (2016) MCMC for Ion-Channel Sojourn-Time Data: A Good Proposal, Biophysical Journal, 10.1016/j.bpj.2016.02.042, 111:2, (267-268), Online publication date: 1-Jul-2016. Epstein M, Calderhead B, Girolami M and Sivilotti L (2016) Bayesian Statistical Inference in Ion-Channel Models with Exact Missed Event Correction, Biophysical Journal, 10.1016/j.bpj.2016.04.053, 111:2, (333-348), Online publication date: 1-Jul-2016. Varin C, Cattelan M and Firth D (2015) Statistical modelling of citation exchange between statistics journals, Journal of the Royal Statistical Society: Series A (Statistics in Society), 10.1111/rssa.12124, 179:1, (1-63), Online publication date: 1-Jan-2016. Cummings K, Iacobucci G and Popescu G (2016) Extracting Rate Constants for NMDA Receptor Gating from One-Channel Current Recordings Ionotropic Glutamate Receptor Technologies, 10.1007/978-1-4939-2812-5_18, (273-299), . Sivilotti L and Colquhoun D (2016) In praise of single channel kinetics, Journal of General Physiology, 10.1085/jgp.201611649, 148:2, (79-88), Online publication date: 1-Aug-2016. Marabelli A, Lape R and Sivilotti L (2014) Mechanism of activation of the prokaryotic channel ELIC by propylamine: A single-channel study, Journal of General Physiology, 10.1085/jgp.201411234, 145:1, (23-45), Online publication date: 1-Jan-2015. Shelley C (2015) Single‐Channel Analysis of Glutamate Receptors, Current Protocols in Pharmacology, 10.1002/0471141755.ph1117s68, 68:1, Online publication date: 1-Mar-2015. Rollins G, Shin J, Bustamante C and Pressé S (2014) Stochastic approach to the molecular counting problem in superresolution microscopy, Proceedings of the National Academy of Sciences, 10.1073/pnas.1408071112, 112:2, Online publication date: 13-Jan-2015. Sachs F and Flomenbom O (2015) How to get more from less, Physics of Life Reviews, 10.1016/j.plrev.2015.03.006, 13, (150-152), Online publication date: 1-Jun-2015. Siekmann I, Sneyd J and Crampin E (2014) Statistical analysis of modal gating in ion channels, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470:2166, Online publication date: 8-Jun-2014. Chung H and Gopich I (2014) Fast single-molecule FRET spectroscopy: theory and experiment, Physical Chemistry Chemical Physics, 10.1039/C4CP02489C, 16:35, (18644) Qin F (2014) Principles of Single-Channel Kinetic Analysis Patch-Clamp Methods and Protocols, 10.1007/978-1-4939-1096-0_23, (371-399), . Marabelli A, Moroni M, Lape R and Sivilotti L (2013) The kinetic properties of the α3 rat glycine receptor make it suitable for mediating fast synaptic inhibition, The Journal of Physiology, 10.1113/jphysiol.2013.252189, 591:13, (3289-3308), Online publication date: 1-Jul-2013. Calderhead B, Epstein M, Sivilotti L and Girolami M (2013) Bayesian Approaches for Mechanistic Ion Channel Modeling In Silico Systems Biology, 10.1007/978-1-62703-450-0_13, (247-272), . Hawkes A, Cui L and Du S (2013) Occupancy Times for Markov and Semi-Markov Models in Systems Reliability Applied Reliability Engineering and Risk Analysis, 10.1002/9781118701881.ch16, (218-230) FLOMENBOM O (2014) MATHEMATICAL TREATMENTS THAT SOLVE SINGLE MOLECULES, Biophysical Reviews and Letters, 10.1142/S1793048013300016, 08:03n04, (109-136), Online publication date: 1-Dec-2013. Gopich I (2012) Likelihood functions for the analysis of single-molecule binned photon sequences, Chemical Physics, 10.1016/j.chemphys.2011.06.006, 396, (53-60), Online publication date: 1-Mar-2012. Siekmann I, Wagner L, Yule D, Crampin E and Sneyd J (2012) A Kinetic Model for Type I and II IP3R Accounting for Mode Changes, Biophysical Journal, 10.1016/j.bpj.2012.07.016, 103:4, (658-668), Online publication date: 1-Aug-2012. Krashia P, Lape R, Lodesani F, Colquhoun D and Sivilotti L (2011) The long activations of α2 glycine channels can be described by a mechanism with reaction intermediates ("flip"), Journal of General Physiology, 10.1085/jgp.201010521, 137:2, (197-216), Online publication date: 1-Feb-2011. Siekmann I, Wagner L, Yule D, Fox C, Bryant D, Crampin E and Sneyd J (2011) MCMC Estimation of Markov Models for Ion Channels, Biophysical Journal, 10.1016/j.bpj.2011.02.059, 100:8, (1919-1929), Online publication date: 1-Apr-2011. Gopich I and Szabo A (2009) Decoding the Pattern of Photon Colors in Single-Molecule FRET, The Journal of Physical Chemistry B, 10.1021/jp903671p, 113:31, (10965-10973), Online publication date: 6-Aug-2009. Gin E, Falcke M, Wagner L, Yule D and Sneyd J (2009) Markov chain Monte Carlo fitting of single-channel data from inositol trisphosphate receptors, Journal of Theoretical Biology, 10.1016/j.jtbi.2008.12.020, 257:3, (460-474), Online publication date: 1-Apr-2009. Schroeder I and Hansen U (2009) Using a five-state model for fitting amplitude histograms from MaxiK channels: β-distributions reveal more than expected, European Biophysics Journal, 10.1007/s00249-009-0515-0, 38:8, (1101-1114), Online publication date: 1-Oct-2009. Colquhoun D, Lape R and Sivilotti L (2009) Single Ion Channels Single Molecule Biology, 10.1016/B978-0-12-374227-8.00008-0, (223-251), . Lape R, Krashia P, Colquhoun D and Sivilotti L (2009) Agonist and blocking actions of choline and tetramethylammonium on human muscle acetylcholine receptors, The Journal of Physiology, 10.1113/jphysiol.2009.176305, 587:21, (5045-5072), Online publication date: 1-Nov-2009. Bartos M, Corradi J and Bouzat C (2009) Structural Basis of Activation of Cys-Loop Receptors: the Extracellular–Transmembrane Interface as a Coupling Region, Molecular Neurobiology, 10.1007/s12035-009-8084-x, 40:3, (236-252), Online publication date: 1-Dec-2009. Milescu L, Yamanishi T, Ptak K, Mogri M and Smith J (2008) Real-Time Kinetic Modeling of Voltage-Gated Ion Channels Using Dynamic Clamp, Biophysical Journal, 10.1529/biophysj.107.118190, 95:1, (66-87), Online publication date: 1-Jul-2008. Flomenbom O and Silbey R (2008) Toolbox for analyzing finite two-state trajectories, Physical Review E, 10.1103/PhysRevE.78.066105, 78:6 Shelley C and Magleby K (2008) Linking Exponential Components to Kinetic States in Markov Models for Single-Channel Gating, Journal of General Physiology, 10.1085/jgp.200810008, 132:2, (295-312), Online publication date: 1-Aug-2008. Danelon C, Grandl J, Hovius R and Vogel H (2007) Modulation of proton-induced current fluctuations in the human nicotinic acetylcholine receptor channel, Biochimica et Biophysica Acta (BBA) - Biomembranes, 10.1016/j.bbamem.2006.07.015, 1768:1, (76-89), Online publication date: 1-Jan-2007. Qin F (2007) Principles of Single-Channel Kinetic Analysis Patch-Clamp Methods and Protocols, 10.1007/978-1-59745-529-9_17, (253-286), . Beato M and Sivilotti L (2007) Single-channel properties of glycine receptors of juvenile rat spinal motoneurones in vitro , The Journal of Physiology, 10.1113/jphysiol.2006.125740, 580:2, (497-506), Online publication date: 15-Apr-2007. Plested A, Groot-Kormelink P, Colquhoun D and Sivilotti L (2007) Single-channel study of the spasmodic mutation α1A52S in recombinant rat glycine receptors, The Journal of Physiology, 10.1113/jphysiol.2006.126920, 581:1, (51-73), Online publication date: 15-May-2007. Wyllie D (2007) Single-Channel Recording Patch-Clamp Analysis, 10.1007/978-1-59745-492-6_3, (69-119), . The Y and Timmer J (2005) Analysis of single ion channel data incorporating time-interval omission and sampling, Journal of The Royal Society Interface, 3:6, (87-97), Online publication date: 22-Feb-2006. Colquhoun D (2009) Agonist-activated ion channels, British Journal of Pharmacology, 10.1038/sj.bjp.0706502, 147:S1, (S17-S26), Online publication date: 1-Jan-2006. Milescu L, Yildiz A, Selvin P and Sachs F (2006) Maximum Likelihood Estimation of Molecular Motor Kinetics from Staircase Dwell-Time Sequences, Biophysical Journal, 10.1529/biophysj.105.079541, 91:4, (1156-1168), Online publication date: 1-Aug-2006. The Y, Fernandes J, Popa M, Alekov A, Timmer J and Lerche H (2006) Modeling of Single Noninactivating Na+ Channels: Evidence for Two Open and Several Fast Inactivated States, Biophysical Journal, 10.1529/biophysj.105.073072, 90:10, (3511-3522), Online publication date: 1-May-2006. Csanády L (2006) Statistical Evaluation of Ion-Channel Gating Models Based on Distributions of Log-Likelihood Ratios, Biophysical Journal, 10.1529/biophysj.105.075135, 90:10, (3523-3545), Online publication date: 1-May-2006. Colquhoun D (2006) The quantitative analysis of drug–receptor interactions: a short history, Trends in Pharmacological Sciences, 10.1016/j.tips.2006.01.008, 27:3, (149-157), Online publication date: 1-Mar-2006. Schorge S, Elenes S and Colquhoun D (2005) Maximum likelihood fitting of single channel NMDA activity with a mechanism composed of independent dimers of subunits, The Journal of Physiology, 10.1113/jphysiol.2005.095349, 569:2, (395-418), Online publication date: 1-Dec-2005. Schröder I, Harlfinger P, Huth T and Hansen U (2005) A Subsequent Fit of Time Series and Amplitude Histogram of Patch-Clamp Records Reveals Rate Constants up to 1 per Microsecond, Journal of Membrane Biology, 10.1007/s00232-005-0734-y, 203:2, (83-99), Online publication date: 1-Jan-2005. Shelley C and Colquhoun D (2005) A human congenital myasthenia-causing mutation (ɛL78P) of the muscle nicotinic acetylcholine receptor with unusual single channel properties, The Journal of Physiology, 10.1113/jphysiol.2004.081497, 564:2, (377-396), Online publication date: 1-Apr-2005. Flomenbom O and Klafter J (2005) On the relationships between kinetic schemes and two-state single molecule trajectories, The Journal of Chemical Physics, 10.1063/1.1979489, 123:6, (064903), Online publication date: 8-Aug-2005. Liao J, Jeong Y, Kim D, Patel S and Oster G (2005) Mechanochemistry of T7 DNA Helicase, Journal of Molecular Biology, 10.1016/j.jmb.2005.04.051, 350:3, (452-475), Online publication date: 1-Jul-2005. Milescu L, Akk G and Sachs F (2005) Maximum Likelihood Estimation of Ion Channel Kinetics from Macroscopic Currents, Biophysical Journal, 10.1529/biophysj.104.053256, 88:4, (2494-2515), Online publication date: 1-Apr-2005. Flomenbom O, Klafter J and Szabo A (2005) What Can One Learn from Two-State Single-Molecule Trajectories?, Biophysical Journal, 10.1529/biophysj.104.055905, 88:6, (3780-3783), Online publication date: 1-Jun-2005. Qin F and Li L (2004) Model-Based Fitting of Single-Channel Dwell-Time Distributions, Biophysical Journal, 10.1529/biophysj.103.037531, 87:3, (1657-1671), Online publication date: 1-Sep-2004. Colquhoun D, Shelley C, Hatton C, Unwin N and Sivilotti L (2003) Nicotinic Acetylcholine Receptors Burger's Medicinal Chemistry and Drug Discovery, 10.1002/0471266949.bmc030, (357-405), Online publication date: 21-Feb-2003. Baran I (2003) Integrated Luminal and Cytosolic Aspects of the Calcium Release Control, Biophysical Journal, 10.1016/S0006-3495(03)74960-1, 84:3, (1470-1485), Online publication date: 1-Mar-2003. Colquhoun D, Hatton C and Hawkes A (2003) The quality of maximum likelihood estimates of ion channel rate constants, The Journal of Physiology, 10.1111/j.1469-7793.2003.00699.x, 547:3, (699-728), Online publication date: 1-Mar-2003. Hatton C, Shelley C, Brydson M, Beeson D and Colquhoun D (2003) Properties of the human muscle nicotinic receptor, and of the slow-channel myasthenic syndrome mutant epsilonL221F, inferred from maximum likelihood fits, The Journal of Physiology, 10.1111/j..2003.t01-1-00729.x, 547:3, (729-760), Online publication date: 1-Mar-2003. Beato M, Groot-Kormelink P, Colquhoun D and Sivilotti L (2002) Openings of the Rat Recombinant α1 Homomeric Glycine Receptor as a Function of the Number of Agonist Molecules Bound, Journal of General Physiology, 10.1085/jgp.20028530, 119:5, (443-466), Online publication date: 1-May-2002. WAGNER M and TIMMER J (2001) Model Selection in Non-nested Hidden Markov Models for Ion Channel Gating, Journal of Theoretical Biology, 10.1006/jtbi.2000.2230, 208:4, (439-450), Online publication date: 1-Feb-2001. Farokhi A, Keunecke M and Hansen U (2000) The Anomalous Mole Fraction Effect in Chara: Gating at the Edge of Temporal Resolution, Biophysical Journal, 10.1016/S0006-3495(00)76542-8, 79:6, (3072-3082), Online publication date: 1-Dec-2000. Wagner M and Timmer J (2000) The Effects of Non-Identifiability on Testing for Detailed Balance in Aggregated Markov Models for Ion-Channel Gating, Biophysical Journal, 10.1016/S0006-3495(00)76529-5, 79:6, (2918-2924), Online publication date: 1-Dec-2000. Béhé P, Colquhoun D and Wyllie D (1999) Activation of Single AMPA- and NMDA-Type Glutamate-Receptor Channels Ionotropic Glutamate Receptors in the CNS, 10.1007/978-3-662-08022-1_5, (175-218), . Qin F, Auerbach A and Sachs F (1997) Maximum likelihood estimation of aggregated Markov processes, Proceedings of the Royal Society of London. Series B: Biological Sciences, 264:1380, (375-383), Online publication date: 22-Mar-1997.Colquhoun D, Hawkes A, Merlushkin A and Edmonds B (1997) Properties of single ion channel currents elicted by a pulse of agonist concentration or voltage, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 355:1730, (1743-1786), Online publication date: 15-Sep-1997. Tewari S, Zhou Y, Otto B, Dash R, Kwok W and Beard D (2015) Markov chain Monte Carlo based analysis of post-translationally modified VDAC gating kinetics, Frontiers in Physiology, 10.3389/fphys.2014.00513, 5 Hawkes A (2014) Ion Channel Modeling Wiley StatsRef: Statistics Reference Online, 10.1002/9781118445112.stat05070 Hawkes A (2005) Ion Channel Modeling Encyclopedia of Biostatistics, 10.1002/0470011815.b2a07031 Ball S, Celik N, Sayari E, Abdul Kadir L, O'Brien F, Barrett-Jolley R and V E S (2022) DeepGANnel: Synthesis of fully annotated single molecule patch-clamp data using generative adversarial networks, PLOS ONE, 10.1371/journal.pone.0267452, 17:5, (e0267452) This Issue15 November 1996Volume 354Issue 1718 Article InformationDOI:https://doi.org/10.1098/rsta.1996.0115Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Manuscript received07/12/1995Manuscript accepted30/04/1996Published online01/01/1997Published in print15/11/1996 License:Scanned images copyright © 2017, Royal Society Citations and impact