MCMC Estimation of Markov Models for Ion Channels

Slides:



Advertisements
Similar presentations
X-Ray Absorption Spectroscopy of Dinuclear Metallohydrolases David L. Tierney, Gerhard Schenk Biophysical Journal Volume 107, Issue 6, Pages
Advertisements

Pressure and Temperature Dependence of Growth and Morphology of Escherichia coli: Experiments and Stochastic Model  Pradeep Kumar, Albert Libchaber  Biophysical.
Michael Epstein, Ben Calderhead, Mark A. Girolami, Lucia G. Sivilotti 
Multi-Image Colocalization and Its Statistical Significance
Fiona E. Müllner, Sheyum Syed, Paul R. Selvin, Fred J. Sigworth 
Steady-State Differential Dose Response in Biological Systems
Rapid Assembly of a Multimeric Membrane Protein Pore
Statistical Deconvolution for Superresolution Fluorescence Microscopy
Transcription Stochasticity of Complex Gene Regulation Models
Volume 103, Issue 5, Pages (September 2012)
Volume 98, Issue 11, Pages (June 2010)
Florian Mueller, Tatsuya Morisaki, Davide Mazza, James G. McNally 
Vilmos Zsolnay, Michael Fill, Dirk Gillespie  Biophysical Journal 
Phase Transitions in Biological Systems with Many Components
Joseph M. Johnson, William J. Betz  Biophysical Journal 
Volume 111, Issue 2, Pages (July 2016)
Increasing Sensitivity of Ca2+ Spark Detection in Noisy Images by Application of a Matched-Filter Object Detection Algorithm  Cherrie H.T. Kong, Christian.
Prediction of Thylakoid Lipid Binding Sites on Photosystem II
Keegan E. Hines, John R. Bankston, Richard W. Aldrich 
Modulation of the Gating of Unitary Cardiac L-Type Ca2+ Channels by Conditioning Voltage and Divalent Ions  Ira R. Josephson, Antonio Guia, Edward G.
Agata Witkowska, Reinhard Jahn  Biophysical Journal 
Lorin S. Milescu, Gustav Akk, Frederick Sachs  Biophysical Journal 
Volume 100, Issue 1, Pages (January 2011)
Testing the Fit of a Quantal Model of Neurotransmission
Stationary Gating of GluN1/GluN2B Receptors in Intact Membrane Patches
Volume 111, Issue 12, Pages (December 2016)
Volume 88, Issue 5, Pages L30-L32 (May 2005)
F.G.A. Faas, B. Rieger, L.J. van Vliet, D.I. Cherny 
Kinetic Hysteresis in Collagen Folding
Drift and Behavior of E. coli Cells
Volume 107, Issue 8, Pages (October 2014)
Rapid Assembly of a Multimeric Membrane Protein Pore
A Large-Conductance Anion Channel of the Golgi Complex
Bidirectional Power Stroke by Ncd Kinesin
Saswata Sankar Sarkar, Jayant B. Udgaonkar, Guruswamy Krishnamoorthy 
The I182 Region of Kir6.2 Is Closely Associated with Ligand Binding in KATP Channel Inhibition by ATP  Lehong Li, Jing Wang, Peter Drain  Biophysical.
C.A. Bertrand, D.M. Durand, G.M. Saidel, C. Laboisse, U. Hopfer 
Volume 104, Issue 5, Pages (March 2013)
Richa Dave, Daniel S. Terry, James B. Munro, Scott C. Blanchard 
Using a Single Fluorescent Reporter Gene to Infer Half-Life of Extrinsic Noise and Other Parameters of Gene Expression  Michał Komorowski, Bärbel Finkenstädt,
Extracting Dwell Time Sequences from Processive Molecular Motor Data
Volume 97, Issue 7, Pages (October 2009)
Saswata Sankar Sarkar, Jayant B. Udgaonkar, Guruswamy Krishnamoorthy 
A Kinetic Model for Type I and II IP3R Accounting for Mode Changes
Assessing Exhaustiveness of Stochastic Sampling for Integrative Modeling of Macromolecular Structures  Shruthi Viswanath, Ilan E. Chemmama, Peter Cimermancic,
Effects of Temperature on Heteromeric Kv11.1a/1b and Kv11.3 Channels
L. Stirling Churchman, Henrik Flyvbjerg, James A. Spudich 
Blocking of Single α-Hemolysin Pore by Rhodamine Derivatives
Multiple Folding Pathways of the SH3 Domain
Joseph K. Pickrell  The American Journal of Human Genetics 
Multi-Image Colocalization and Its Statistical Significance
Volume 98, Issue 2, Pages (January 2010)
Volume 90, Issue 10, Pages (May 2006)
Volume 86, Issue 3, Pages (March 2004)
Vilmos Zsolnay, Michael Fill, Dirk Gillespie  Biophysical Journal 
Brownian Dynamics of Subunit Addition-Loss Kinetics and Thermodynamics in Linear Polymer Self-Assembly  Brian T. Castle, David J. Odde  Biophysical Journal 
Steady-State Differential Dose Response in Biological Systems
Yongli Zhang, Junyi Jiao, Aleksander A. Rebane  Biophysical Journal 
Time-Resolved NMR: Extracting the Topology of Complex Enzyme Networks
An Introduction to Infinite HMMs for Single-Molecule Data Analysis
Small-Angle X-Ray Scattering of the Cholesterol Incorporation into Human ApoA1- POPC Discoidal Particles  Søren Roi Midtgaard, Martin Cramer Pedersen,
S. Rüdiger, Ch. Nagaiah, G. Warnecke, J.W. Shuai  Biophysical Journal 
Synapse-Specific Contribution of the Variation of Transmitter Concentration to the Decay of Inhibitory Postsynaptic Currents  Zoltan Nusser, David Naylor,
Volume 114, Issue 6, Pages (March 2018)
Time-Resolved NMR: Extracting the Topology of Complex Enzyme Networks
David Naranjo, Hua Wen, Paul Brehm  Biophysical Journal 
ATP Inhibition and Rectification of a Ca2+-Activated Anion Channel in Sarcoplasmic Reticulum of Skeletal Muscle  Gerard P. Ahern, Derek R. Laver  Biophysical.
Volume 108, Issue 8, Pages (April 2015)
Volume 97, Issue 2, Pages (July 2009)
George D. Dickinson, Ian Parker  Biophysical Journal 
Presentation transcript:

MCMC Estimation of Markov Models for Ion Channels Ivo Siekmann, Larry E. Wagner, David Yule, Colin Fox, David Bryant, Edmund J. Crampin, James Sneyd  Biophysical Journal  Volume 100, Issue 8, Pages 1919-1929 (April 2011) DOI: 10.1016/j.bpj.2011.02.059 Copyright © 2011 Biophysical Society Terms and Conditions

Figure 1 Examples for Markov models. Biophysical Journal 2011 100, 1919-1929DOI: (10.1016/j.bpj.2011.02.059) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 2 Histograms for the algorithm MHG after 50,000 iterations and a burn-in time of 10,000 iterations. MHG was run on a test data set consisting of 40,000 data points generated from model M2 (see Table 1, M2 columns). (Vertical dotted lines) True values of the rate constants. (Asterisks) Means of the histograms and (Arrows) standard deviations. Biophysical Journal 2011 100, 1919-1929DOI: (10.1016/j.bpj.2011.02.059) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 3 Model M2 is fitted to test data of 40,000 data points generated from the simpler model M1 using the MH sampler. The convergence plots (a and b) show that the rates connecting to the extra state O5 wander around whereas the others tend to the correct values (compare this to Table 1, M1 columns). Histograms for q45 and q54 are shown in panel c. The wide-spread multimodal posterior distributions for both rate constants clearly indicate that the state O5 is not supported by the data. Biophysical Journal 2011 100, 1919-1929DOI: (10.1016/j.bpj.2011.02.059) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 4 Model M3 is fitted to test data (40,000 data points) generated from the simpler model M1 using the MH algorithm. The stationary probability of the additional open state O5 quickly tends to zero. This suggests that the sampler detects when a model is too complex for representing a given data set and reacts by switching off transitions to the additional state. Biophysical Journal 2011 100, 1919-1929DOI: (10.1016/j.bpj.2011.02.059) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 5 Rosales' Gibbs sampler and the MH algorithm are compared for a test data set of 100,000 data points. As representative examples, we show histograms for components ρ11 and ρ15 of the matrix exponential Aτ (plotted in red) of model M2 (see Fig. 1) with results from Rosales' Gibbs sampler (plotted in green). (Vertical dotted line) Exact value of the matrix component. Both methods give very similar results for the diagonal of Aτ, as can be seen in panel a, for example. Mean and standard deviations for MH algorithm (purple) and Rosales' Gibbs sampler (green) are similar. The histograms for the off-diagonal elements found by Rosales' method are distributed over a wide range and are therefore much less accurate than the estimates found by MH; compare the two fits for ρ15 in panel b. Biophysical Journal 2011 100, 1919-1929DOI: (10.1016/j.bpj.2011.02.059) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 6 Selected histograms for a MHG run (50,000 iterations) and results of QUB-MIL for a test data set of 40,000 data points. (Dotted vertical line) The true value of a rate constant. (Asterisk) The maximum likelihood estimator found by QuB-MIL. (Upper arrows) Standard deviation found by QuB-MIL; (lower arrows) mean and standard deviations found by MHG. The estimates with relative errors are qˆ32MIL=0.522(−13.0%),qˆ32MHG=0.606(+1%) and qˆ45MIL=0.365(+21.5%),qˆ45MHG=0.359(+19.7%). Biophysical Journal 2011 100, 1919-1929DOI: (10.1016/j.bpj.2011.02.059) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 7 Open histogram for a data set of 1,400,000 data points which was collected from an IP3-type I receptor at a calcium concentration of 200 nmol/L (24). This is shown together with the superimposed open time distributions determined by fits to two different models, one with one open state (M1) and one with two open states (M2) (see Fig. 1, a and b). Although the histogram has only one distinguished peak indicating that one open state is sufficient, it shows that the open time histogram is better approximated for long open events by the model with two open states. Biophysical Journal 2011 100, 1919-1929DOI: (10.1016/j.bpj.2011.02.059) Copyright © 2011 Biophysical Society Terms and Conditions