1
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Götz M, Barth A, Bohr SSR, Börner R, Chen J, Cordes T, Erie DA, Gebhardt C, Hadzic MCAS, Hamilton GL, Hatzakis NS, Hugel T, Kisley L, Lamb DC, de Lannoy C, Mahn C, Dunukara D, de Ridder D, Sanabria H, Schimpf J, Seidel CAM, Sigel RKO, Sletfjerding MB, Thomsen J, Vollmar L, Wanninger S, Weninger KR, Xu P, Schmid S. A blind benchmark of analysis tools to infer kinetic rate constants from single-molecule FRET trajectories. Nat Commun 2022. [PMID: 36104339 DOI: 10.1101/2021.11.23.469671v2.article-info] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/28/2023] Open
Abstract
Single-molecule FRET (smFRET) is a versatile technique to study the dynamics and function of biomolecules since it makes nanoscale movements detectable as fluorescence signals. The powerful ability to infer quantitative kinetic information from smFRET data is, however, complicated by experimental limitations. Diverse analysis tools have been developed to overcome these hurdles but a systematic comparison is lacking. Here, we report the results of a blind benchmark study assessing eleven analysis tools used to infer kinetic rate constants from smFRET trajectories. We test them against simulated and experimental data containing the most prominent difficulties encountered in analyzing smFRET experiments: different noise levels, varied model complexity, non-equilibrium dynamics, and kinetic heterogeneity. Our results highlight the current strengths and limitations in inferring kinetic information from smFRET trajectories. In addition, we formulate concrete recommendations and identify key targets for future developments, aimed to advance our understanding of biomolecular dynamics through quantitative experiment-derived models.
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Affiliation(s)
- Markus Götz
- Centre de Biologie Structurale, CNRS UMR 5048, INSERM U1054, Univ Montpellier, 60 rue de Navacelles, 34090, Montpellier, France.
- PicoQuant GmbH, Rudower Chaussee 29, 12489, Berlin, Germany.
| | - Anders Barth
- Institut für Physikalische Chemie, Lehrstuhl für Molekulare Physikalische Chemie, Heinrich-Heine-Universität, Universitätsstr. 1, 40225, Düsseldorf, Germany
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Van der Maasweg 9, 2629, HZ Delft, The Netherlands
| | - Søren S-R Bohr
- Department of Chemistry & Nano-science Center, University of Copenhagen, 2100, Copenhagen, Denmark
- Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Richard Börner
- Department of Chemistry, University of Zurich, 8057, Zurich, Switzerland
- Laserinstitut Hochschule Mittweida, University of Applied Sciences Mittweida, 09648, Mittweida, Germany
| | - Jixin Chen
- Department of Chemistry and Biochemistry, Ohio University, Athens, OH, USA
| | - Thorben Cordes
- Physical and Synthetic Biology, Faculty of Biology, Ludwig-Maximilians-Universität München, Großhadernerstr. 2-4, 82152, Planegg-Martinsried, Germany
| | - Dorothy A Erie
- Department of Chemistry, University of North Carolina, Chapel Hill, NC, 27599, USA
- Lineberger Comprehensive Cancer Center, University of North Carolina, Chapel Hill, NC, 27599, USA
| | - Christian Gebhardt
- Physical and Synthetic Biology, Faculty of Biology, Ludwig-Maximilians-Universität München, Großhadernerstr. 2-4, 82152, Planegg-Martinsried, Germany
| | | | - George L Hamilton
- Department of Physics and Astronomy, Clemson University, Clemson, SC, 29634, USA
- Department of Biochemistry and Molecular Pharmacology, New York University School of Medicine, New York, NY, 10016, USA
| | - Nikos S Hatzakis
- Department of Chemistry & Nano-science Center, University of Copenhagen, 2100, Copenhagen, Denmark
- Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Thorsten Hugel
- Institute of Physical Chemistry, University of Freiburg, Freiburg, Germany
- Signalling Research Centers BIOSS and CIBSS, University of Freiburg, Freiburg, Germany
| | - Lydia Kisley
- Department of Physics, Case Western Reserve University, Cleveland, OH, USA
- Department of Chemistry, Case Western Reserve University, Cleveland, OH, USA
| | - Don C Lamb
- Department of Chemistry and Center for Nano Science (CeNS), Ludwig Maximilians-Universität München, Butenandtstraße 5-13, 81377, München, Germany
| | - Carlos de Lannoy
- Bioinformatics Group, Wageningen University, Droevendaalsesteeg 1, 6708PB, Wageningen, The Netherlands
| | - Chelsea Mahn
- Department of Physics, North Carolina State University, Raleigh, NC, 27695, USA
| | - Dushani Dunukara
- Department of Physics, Case Western Reserve University, Cleveland, OH, USA
| | - Dick de Ridder
- Bioinformatics Group, Wageningen University, Droevendaalsesteeg 1, 6708PB, Wageningen, The Netherlands
| | - Hugo Sanabria
- Department of Physics and Astronomy, Clemson University, Clemson, SC, 29634, USA
| | - Julia Schimpf
- Institute of Physical Chemistry, University of Freiburg, Freiburg, Germany
- Spemann Graduate School of Biology and Medicine (SGBM), University of Freiburg, Freiburg, Germany
| | - Claus A M Seidel
- Institut für Physikalische Chemie, Lehrstuhl für Molekulare Physikalische Chemie, Heinrich-Heine-Universität, Universitätsstr. 1, 40225, Düsseldorf, Germany
| | - Roland K O Sigel
- Department of Chemistry, University of Zurich, 8057, Zurich, Switzerland
| | - Magnus Berg Sletfjerding
- Department of Chemistry & Nano-science Center, University of Copenhagen, 2100, Copenhagen, Denmark
- Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Johannes Thomsen
- Department of Chemistry & Nano-science Center, University of Copenhagen, 2100, Copenhagen, Denmark
- Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Leonie Vollmar
- Institute of Physical Chemistry, University of Freiburg, Freiburg, Germany
- Spemann Graduate School of Biology and Medicine (SGBM), University of Freiburg, Freiburg, Germany
| | - Simon Wanninger
- Department of Chemistry and Center for Nano Science (CeNS), Ludwig Maximilians-Universität München, Butenandtstraße 5-13, 81377, München, Germany
| | - Keith R Weninger
- Department of Physics, North Carolina State University, Raleigh, NC, 27695, USA
| | - Pengning Xu
- Department of Physics, North Carolina State University, Raleigh, NC, 27695, USA
| | - Sonja Schmid
- NanoDynamicsLab, Laboratory of Biophysics, Wageningen University, Stippeneng 4, 6708WE, Wageningen, The Netherlands.
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2
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Götz M, Barth A, Bohr SSR, Börner R, Chen J, Cordes T, Erie DA, Gebhardt C, Hadzic MCAS, Hamilton GL, Hatzakis NS, Hugel T, Kisley L, Lamb DC, de Lannoy C, Mahn C, Dunukara D, de Ridder D, Sanabria H, Schimpf J, Seidel CAM, Sigel RKO, Sletfjerding MB, Thomsen J, Vollmar L, Wanninger S, Weninger KR, Xu P, Schmid S. A blind benchmark of analysis tools to infer kinetic rate constants from single-molecule FRET trajectories. Nat Commun 2022; 13:5402. [PMID: 36104339 PMCID: PMC9474500 DOI: 10.1038/s41467-022-33023-3] [Citation(s) in RCA: 23] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2022] [Accepted: 08/30/2022] [Indexed: 01/04/2023] Open
Abstract
Single-molecule FRET (smFRET) is a versatile technique to study the dynamics and function of biomolecules since it makes nanoscale movements detectable as fluorescence signals. The powerful ability to infer quantitative kinetic information from smFRET data is, however, complicated by experimental limitations. Diverse analysis tools have been developed to overcome these hurdles but a systematic comparison is lacking. Here, we report the results of a blind benchmark study assessing eleven analysis tools used to infer kinetic rate constants from smFRET trajectories. We test them against simulated and experimental data containing the most prominent difficulties encountered in analyzing smFRET experiments: different noise levels, varied model complexity, non-equilibrium dynamics, and kinetic heterogeneity. Our results highlight the current strengths and limitations in inferring kinetic information from smFRET trajectories. In addition, we formulate concrete recommendations and identify key targets for future developments, aimed to advance our understanding of biomolecular dynamics through quantitative experiment-derived models.
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Affiliation(s)
- Markus Götz
- Centre de Biologie Structurale, CNRS UMR 5048, INSERM U1054, Univ Montpellier, 60 rue de Navacelles, 34090, Montpellier, France.
- PicoQuant GmbH, Rudower Chaussee 29, 12489, Berlin, Germany.
| | - Anders Barth
- Institut für Physikalische Chemie, Lehrstuhl für Molekulare Physikalische Chemie, Heinrich-Heine-Universität, Universitätsstr. 1, 40225, Düsseldorf, Germany
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Van der Maasweg 9, 2629, HZ Delft, The Netherlands
| | - Søren S-R Bohr
- Department of Chemistry & Nano-science Center, University of Copenhagen, 2100, Copenhagen, Denmark
- Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Richard Börner
- Department of Chemistry, University of Zurich, 8057, Zurich, Switzerland
- Laserinstitut Hochschule Mittweida, University of Applied Sciences Mittweida, 09648, Mittweida, Germany
| | - Jixin Chen
- Department of Chemistry and Biochemistry, Ohio University, Athens, OH, USA
| | - Thorben Cordes
- Physical and Synthetic Biology, Faculty of Biology, Ludwig-Maximilians-Universität München, Großhadernerstr. 2-4, 82152, Planegg-Martinsried, Germany
| | - Dorothy A Erie
- Department of Chemistry, University of North Carolina, Chapel Hill, NC, 27599, USA
- Lineberger Comprehensive Cancer Center, University of North Carolina, Chapel Hill, NC, 27599, USA
| | - Christian Gebhardt
- Physical and Synthetic Biology, Faculty of Biology, Ludwig-Maximilians-Universität München, Großhadernerstr. 2-4, 82152, Planegg-Martinsried, Germany
| | | | - George L Hamilton
- Department of Physics and Astronomy, Clemson University, Clemson, SC, 29634, USA
- Department of Biochemistry and Molecular Pharmacology, New York University School of Medicine, New York, NY, 10016, USA
| | - Nikos S Hatzakis
- Department of Chemistry & Nano-science Center, University of Copenhagen, 2100, Copenhagen, Denmark
- Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Thorsten Hugel
- Institute of Physical Chemistry, University of Freiburg, Freiburg, Germany
- Signalling Research Centers BIOSS and CIBSS, University of Freiburg, Freiburg, Germany
| | - Lydia Kisley
- Department of Physics, Case Western Reserve University, Cleveland, OH, USA
- Department of Chemistry, Case Western Reserve University, Cleveland, OH, USA
| | - Don C Lamb
- Department of Chemistry and Center for Nano Science (CeNS), Ludwig Maximilians-Universität München, Butenandtstraße 5-13, 81377, München, Germany
| | - Carlos de Lannoy
- Bioinformatics Group, Wageningen University, Droevendaalsesteeg 1, 6708PB, Wageningen, The Netherlands
| | - Chelsea Mahn
- Department of Physics, North Carolina State University, Raleigh, NC, 27695, USA
| | - Dushani Dunukara
- Department of Physics, Case Western Reserve University, Cleveland, OH, USA
| | - Dick de Ridder
- Bioinformatics Group, Wageningen University, Droevendaalsesteeg 1, 6708PB, Wageningen, The Netherlands
| | - Hugo Sanabria
- Department of Physics and Astronomy, Clemson University, Clemson, SC, 29634, USA
| | - Julia Schimpf
- Institute of Physical Chemistry, University of Freiburg, Freiburg, Germany
- Spemann Graduate School of Biology and Medicine (SGBM), University of Freiburg, Freiburg, Germany
| | - Claus A M Seidel
- Institut für Physikalische Chemie, Lehrstuhl für Molekulare Physikalische Chemie, Heinrich-Heine-Universität, Universitätsstr. 1, 40225, Düsseldorf, Germany
| | - Roland K O Sigel
- Department of Chemistry, University of Zurich, 8057, Zurich, Switzerland
| | - Magnus Berg Sletfjerding
- Department of Chemistry & Nano-science Center, University of Copenhagen, 2100, Copenhagen, Denmark
- Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Johannes Thomsen
- Department of Chemistry & Nano-science Center, University of Copenhagen, 2100, Copenhagen, Denmark
- Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Leonie Vollmar
- Institute of Physical Chemistry, University of Freiburg, Freiburg, Germany
- Spemann Graduate School of Biology and Medicine (SGBM), University of Freiburg, Freiburg, Germany
| | - Simon Wanninger
- Department of Chemistry and Center for Nano Science (CeNS), Ludwig Maximilians-Universität München, Butenandtstraße 5-13, 81377, München, Germany
| | - Keith R Weninger
- Department of Physics, North Carolina State University, Raleigh, NC, 27695, USA
| | - Pengning Xu
- Department of Physics, North Carolina State University, Raleigh, NC, 27695, USA
| | - Sonja Schmid
- NanoDynamicsLab, Laboratory of Biophysics, Wageningen University, Stippeneng 4, 6708WE, Wageningen, The Netherlands.
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3
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Faccin M, Schaub MT, Delvenne JC. State Aggregations in Markov Chains and Block Models of Networks. PHYSICAL REVIEW LETTERS 2021; 127:078301. [PMID: 34459654 DOI: 10.1103/physrevlett.127.078301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Revised: 06/17/2021] [Accepted: 07/15/2021] [Indexed: 06/13/2023]
Abstract
We consider state-aggregation schemes for Markov chains from an information-theoretic perspective. Specifically, we consider aggregating the states of a Markov chain such that the mutual information of the aggregated states separated by T time steps is maximized. We show that for T=1 this recovers the maximum-likelihood estimator of the degree-corrected stochastic block model as a particular case, which enables us to explain certain features of the likelihood landscape of this generative network model from a dynamical lens. We further highlight how we can uncover coherent, long-range dynamical modules for which considering a timescale T≫1 is essential. We demonstrate our results using synthetic flows and real-world ocean currents, where we are able to recover the fundamental features of the surface currents of the oceans.
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Affiliation(s)
- Mauro Faccin
- ICTEAM, Université catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
| | - Michael T Schaub
- Department of Engineering Science, University of Oxford, Oxford OX1 2JD, United Kingdom
- Department of Computer Science, RWTH Aachen University, 52074 Aachen, Germany
| | - Jean-Charles Delvenne
- ICTEAM, Université catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
- CORE, Université catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
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4
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Kilic Z, Sgouralis I, Pressé S. Generalizing HMMs to Continuous Time for Fast Kinetics: Hidden Markov Jump Processes. Biophys J 2021; 120:409-423. [PMID: 33421415 PMCID: PMC7896036 DOI: 10.1016/j.bpj.2020.12.022] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2020] [Revised: 12/25/2020] [Accepted: 12/30/2020] [Indexed: 12/18/2022] Open
Abstract
The hidden Markov model (HMM) is a framework for time series analysis widely applied to single-molecule experiments. Although initially developed for applications outside the natural sciences, the HMM has traditionally been used to interpret signals generated by physical systems, such as single molecules, evolving in a discrete state space observed at discrete time levels dictated by the data acquisition rate. Within the HMM framework, transitions between states are modeled as occurring at the end of each data acquisition period and are described using transition probabilities. Yet, whereas measurements are often performed at discrete time levels in the natural sciences, physical systems evolve in continuous time according to transition rates. It then follows that the modeling assumptions underlying the HMM are justified if the transition rates of a physical process from state to state are small as compared to the data acquisition rate. In other words, HMMs apply to slow kinetics. The problem is, because the transition rates are unknown in principle, it is unclear, a priori, whether the HMM applies to a particular system. For this reason, we must generalize HMMs for physical systems, such as single molecules, because these switch between discrete states in "continuous time". We do so by exploiting recent mathematical tools developed in the context of inferring Markov jump processes and propose the hidden Markov jump process. We explicitly show in what limit the hidden Markov jump process reduces to the HMM. Resolving the discrete time discrepancy of the HMM has clear implications: we no longer need to assume that processes, such as molecular events, must occur on timescales slower than data acquisition and can learn transition rates even if these are on the same timescale or otherwise exceed data acquisition rates.
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Affiliation(s)
- Zeliha Kilic
- Center for Biological Physics, Department of Physics, Arizona State University, Tempe, Arizona
| | - Ioannis Sgouralis
- Department of Mathematics, University of Tennessee, Knoxville, Tennessee
| | - Steve Pressé
- Center for Biological Physics, Department of Physics, Arizona State University, Tempe, Arizona; School of Molecular Sciences, Arizona State University, Tempe, Arizona.
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5
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Elliott TJ, Yang C, Binder FC, Garner AJP, Thompson J, Gu M. Extreme Dimensionality Reduction with Quantum Modeling. PHYSICAL REVIEW LETTERS 2020; 125:260501. [PMID: 33449713 DOI: 10.1103/physrevlett.125.260501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2020] [Accepted: 10/23/2020] [Indexed: 05/23/2023]
Abstract
Effective and efficient forecasting relies on identification of the relevant information contained in past observations-the predictive features-and isolating it from the rest. When the future of a process bears a strong dependence on its behavior far into the past, there are many such features to store, necessitating complex models with extensive memories. Here, we highlight a family of stochastic processes whose minimal classical models must devote unboundedly many bits to tracking the past. For this family, we identify quantum models of equal accuracy that can store all relevant information within a single two-dimensional quantum system (qubit). This represents the ultimate limit of quantum compression and highlights an immense practical advantage of quantum technologies for the forecasting and simulation of complex systems.
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Affiliation(s)
- Thomas J Elliott
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
- Complexity Institute, Nanyang Technological University, Singapore 637335, Singapore
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Chengran Yang
- Complexity Institute, Nanyang Technological University, Singapore 637335, Singapore
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Felix C Binder
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna 1090, Austria
| | - Andrew J P Garner
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna 1090, Austria
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Jayne Thompson
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Mile Gu
- Complexity Institute, Nanyang Technological University, Singapore 637335, Singapore
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
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6
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Thomsen J, Sletfjerding MB, Jensen SB, Stella S, Paul B, Malle MG, Montoya G, Petersen TC, Hatzakis NS. DeepFRET, a software for rapid and automated single-molecule FRET data classification using deep learning. eLife 2020; 9:e60404. [PMID: 33138911 PMCID: PMC7609065 DOI: 10.7554/elife.60404] [Citation(s) in RCA: 39] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2020] [Accepted: 10/02/2020] [Indexed: 12/20/2022] Open
Abstract
Single-molecule Förster Resonance energy transfer (smFRET) is an adaptable method for studying the structure and dynamics of biomolecules. The development of high throughput methodologies and the growth of commercial instrumentation have outpaced the development of rapid, standardized, and automated methodologies to objectively analyze the wealth of produced data. Here we present DeepFRET, an automated, open-source standalone solution based on deep learning, where the only crucial human intervention in transiting from raw microscope images to histograms of biomolecule behavior, is a user-adjustable quality threshold. Integrating standard features of smFRET analysis, DeepFRET consequently outputs the common kinetic information metrics. Its classification accuracy on ground truth data reached >95% outperforming human operators and commonly used threshold, only requiring ~1% of the time. Its precise and rapid operation on real data demonstrates DeepFRET's capacity to objectively quantify biomolecular dynamics and the potential to contribute to benchmarking smFRET for dynamic structural biology.
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Affiliation(s)
- Johannes Thomsen
- Department of Chemistry and Nanoscience Centre, University of CopenhagenCopenhagenDenmark
| | | | - Simon Bo Jensen
- Department of Chemistry and Nanoscience Centre, University of CopenhagenCopenhagenDenmark
| | - Stefano Stella
- Structural Molecular Biology Group, Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of CopenhagenCopenhagenDenmark
| | - Bijoya Paul
- Structural Molecular Biology Group, Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of CopenhagenCopenhagenDenmark
| | - Mette Galsgaard Malle
- Department of Chemistry and Nanoscience Centre, University of CopenhagenCopenhagenDenmark
| | - Guillermo Montoya
- Structural Molecular Biology Group, Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of CopenhagenCopenhagenDenmark
| | | | - Nikos S Hatzakis
- Department of Chemistry and Nanoscience Centre, University of CopenhagenCopenhagenDenmark
- Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of CopenhagenCopenhagenDenmark
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7
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Sgouralis I, Madaan S, Djutanta F, Kha R, Hariadi RF, Pressé S. A Bayesian Nonparametric Approach to Single Molecule Förster Resonance Energy Transfer. J Phys Chem B 2019; 123:675-688. [PMID: 30571128 DOI: 10.1021/acs.jpcb.8b09752] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We develop a Bayesian nonparametric framework to analyze single molecule FRET (smFRET) data. This framework, a variation on infinite hidden Markov models, goes beyond traditional hidden Markov analysis, which already treats photon shot noise, in three critical ways: (1) it learns the number of molecular states present in a smFRET time trace (a hallmark of nonparametric approaches), (2) it accounts, simultaneously and self-consistently, for photophysical features of donor and acceptor fluorophores (blinking kinetics, spectral cross-talk, detector quantum efficiency), and (3) it treats background photons. Point 2 is essential in reducing the tendency of nonparametric approaches to overinterpret noisy single molecule time traces and so to estimate states and transition kinetics robust to photophysical artifacts. As a result, with the proposed framework, we obtain accurate estimates of single molecule properties even when the supplied traces are excessively noisy, subject to photoartifacts, and of short duration. We validate our method using synthetic data sets and demonstrate its applicability to real data sets from single molecule experiments on Holliday junctions labeled with conventional fluorescent dyes.
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Affiliation(s)
- Ioannis Sgouralis
- Center for Biological Physics, Department of Physics , Arizona State University , Tempe , Arizona 85287 , United States
| | - Shreya Madaan
- School of Computing, Informatics, and Decision Systems Engineering , Arizona State University , Tempe , Arizona 85287 , United States
| | - Franky Djutanta
- Biodesign Center for Molecular Design and Biomimetics, Biodesign Institute , Arizona State University , Tempe , Arizona 85287 , United States
| | - Rachael Kha
- School for Engineering of Matter, Transport and Energy , Arizona State University , Tempe , Arizona 85287 , United States
| | - Rizal F Hariadi
- Center for Biological Physics, Department of Physics , Arizona State University , Tempe , Arizona 85287 , United States.,Biodesign Center for Molecular Design and Biomimetics, Biodesign Institute , Arizona State University , Tempe , Arizona 85287 , United States
| | - Steve Pressé
- Center for Biological Physics, Department of Physics , Arizona State University , Tempe , Arizona 85287 , United States.,School of Molecular Sciences , Arizona State University , Tempe , Arizona 85287 , United States
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8
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Schmid S, Hugel T. Efficient use of single molecule time traces to resolve kinetic rates, models and uncertainties. J Chem Phys 2018; 148:123312. [PMID: 29604821 DOI: 10.1063/1.5006604] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Single molecule time traces reveal the time evolution of unsynchronized kinetic systems. Especially single molecule Förster resonance energy transfer (smFRET) provides access to enzymatically important time scales, combined with molecular distance resolution and minimal interference with the sample. Yet the kinetic analysis of smFRET time traces is complicated by experimental shortcomings-such as photo-bleaching and noise. Here we recapitulate the fundamental limits of single molecule fluorescence that render the classic, dwell-time based kinetic analysis unsuitable. In contrast, our Single Molecule Analysis of Complex Kinetic Sequences (SMACKS) considers every data point and combines the information of many short traces in one global kinetic rate model. We demonstrate the potential of SMACKS by resolving the small kinetic effects caused by different ionic strengths in the chaperone protein Hsp90. These results show an unexpected interrelation between conformational dynamics and ATPase activity in Hsp90.
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Affiliation(s)
- Sonja Schmid
- Institute of Physical Chemistry II, University of Freiburg, Albertstr. 23 a, 79104 Freiburg, Germany
| | - Thorsten Hugel
- Institute of Physical Chemistry II, University of Freiburg, Albertstr. 23 a, 79104 Freiburg, Germany
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9
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Hadzic MCAS, Börner R, König SLB, Kowerko D, Sigel RKO. Reliable State Identification and State Transition Detection in Fluorescence Intensity-Based Single-Molecule Förster Resonance Energy-Transfer Data. J Phys Chem B 2018; 122:6134-6147. [PMID: 29737844 DOI: 10.1021/acs.jpcb.7b12483] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Single-molecule Förster resonance energy transfer (smFRET) is a powerful technique to probe biomolecular structure and dynamics. A popular implementation of smFRET consists of recording fluorescence intensity time traces of surface-immobilized, chromophore-tagged molecules. This approach generates large and complex data sets, the analysis of which is to date not standardized. Here, we address a key challenge in smFRET data analysis: the generation of thermodynamic and kinetic models that describe with statistical rigor the behavior of FRET trajectories recorded from surface-tethered biomolecules in terms of the number of FRET states, the corresponding mean FRET values, and the kinetic rates at which they interconvert. For this purpose, we first perform Monte Carlo simulations to generate smFRET trajectories, in which a relevant space of experimental parameters is explored. Then, we provide an account on current strategies to achieve such model selection, as well as a quantitative assessment of their performances. Specifically, we evaluate the performance of each algorithm (change-point analysis, STaSI, HaMMy, vbFRET, and ebFRET) with respect to accuracy, reproducibility, and computing time, which yields a range of algorithm-specific referential benchmarks for various data qualities. Data simulation and analysis were performed with our MATLAB-based multifunctional analysis software for handling smFRET data (MASH-FRET).
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Affiliation(s)
| | | | | | - Danny Kowerko
- Department of Computer Science , Chemnitz University of Technology , 09111 Chemnitz , Germany
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10
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Bayat Mokhtari E, Lawrence JJ, Stone EF. Data Driven Models of Short-Term Synaptic Plasticity. Front Comput Neurosci 2018; 12:32. [PMID: 29872388 PMCID: PMC5972196 DOI: 10.3389/fncom.2018.00032] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2018] [Accepted: 04/27/2018] [Indexed: 11/29/2022] Open
Abstract
Simple models of short term synaptic plasticity that incorporate facilitation and/or depression have been created in abundance for different synapse types and circumstances. The analysis of these models has included computing mutual information between a stochastic input spike train and some sort of representation of the postsynaptic response. While this approach has proven useful in many contexts, for the purpose of determining the type of process underlying a stochastic output train, it ignores the ordering of the responses, leaving an important characterizing feature on the table. In this paper we use a broader class of information measures on output only, and specifically construct hidden Markov models (HMMs) (known as epsilon machines or causal state models) to differentiate between synapse type, and classify the complexity of the process. We find that the machines allow us to differentiate between processes in a way not possible by considering distributions alone. We are also able to understand these differences in terms of the dynamics of the model used to create the output response, bringing the analysis full circle. Hence this technique provides a complimentary description of the synaptic filtering process, and potentially expands the interpretation of future experimental results.
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Affiliation(s)
- Elham Bayat Mokhtari
- Department of Mathematical Sciences, The University of Montana, Missoula, MT, United States
| | - J Josh Lawrence
- Pharmacology and Neuroscience, Texas Tech University Health Sciences Center, Lubbock, TX, United States
| | - Emily F Stone
- Department of Mathematical Sciences, The University of Montana, Missoula, MT, United States
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11
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Tavakoli M, Taylor JN, Li CB, Komatsuzaki T, Pressé S. Single Molecule Data Analysis: An Introduction. ADVANCES IN CHEMICAL PHYSICS 2017. [DOI: 10.1002/9781119324560.ch4] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Meysam Tavakoli
- Physics Department; Indiana University-Purdue University Indianapolis; Indianapolis IN 46202 USA
| | - J. Nicholas Taylor
- Research Institute for Electronic Science; Hokkaido University; Kita 20 Nishi 10 Kita-Ku Sapporo 001-0020 Japan
| | - Chun-Biu Li
- Research Institute for Electronic Science; Hokkaido University; Kita 20 Nishi 10 Kita-Ku Sapporo 001-0020 Japan
- Department of Mathematics; Stockholm University; 106 91 Stockholm Sweden
| | - Tamiki Komatsuzaki
- Research Institute for Electronic Science; Hokkaido University; Kita 20 Nishi 10 Kita-Ku Sapporo 001-0020 Japan
| | - Steve Pressé
- Physics Department; Indiana University-Purdue University Indianapolis; Indianapolis IN 46202 USA
- Department of Chemistry and Chemical Biology; Indiana University-Purdue University Indianapolis; Indianapolis IN 46202 USA
- Department of Cell and Integrative Physiology; Indiana University School of Medicine; Indianapolis IN 46202 USA
- Department of Physics and School of Molecular Sciences; Arizona State University; Tempe AZ 85287 USA
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12
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Aghamohammadi C, Mahoney JR, Crutchfield JP. Extreme Quantum Advantage when Simulating Classical Systems with Long-Range Interaction. Sci Rep 2017; 7:6735. [PMID: 28751746 PMCID: PMC5532296 DOI: 10.1038/s41598-017-04928-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2016] [Accepted: 05/23/2017] [Indexed: 11/12/2022] Open
Abstract
Classical stochastic processes can be generated by quantum simulators instead of the more standard classical ones, such as hidden Markov models. One reason for using quantum simulators has recently come to the fore: they generally require less memory than their classical counterparts. Here, we examine this quantum advantage for strongly coupled spin systems-in particular, the Dyson one-dimensional Ising spin chain with variable interaction length. We find that the advantage scales with both interaction range and temperature, growing without bound as interaction range increases. In particular, simulating Dyson's original spin chain with the most memory-efficient classical algorithm known requires infinite memory, while a quantum simulator requires only finite memory. Thus, quantum systems can very efficiently simulate strongly coupled one-dimensional classical spin systems.
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Affiliation(s)
- Cina Aghamohammadi
- Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, CA, 95616, USA.
| | - John R Mahoney
- Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, CA, 95616, USA.
| | - James P Crutchfield
- Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, CA, 95616, USA.
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13
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Single-Molecule Analysis beyond Dwell Times: Demonstration and Assessment in and out of Equilibrium. Biophys J 2017; 111:1375-1384. [PMID: 27705761 DOI: 10.1016/j.bpj.2016.08.023] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2016] [Revised: 08/01/2016] [Accepted: 08/09/2016] [Indexed: 11/21/2022] Open
Abstract
We present a simple and robust technique for extracting kinetic rate models and thermodynamic quantities from single-molecule time traces. Single-molecule analysis of complex kinetic sequences (SMACKS) is a maximum-likelihood approach that resolves all statistically relevant rates and also their uncertainties. This is achieved by optimizing one global kinetic model based on the complete data set while allowing for experimental variations between individual trajectories. In contrast to dwell-time analysis, which is the current standard method, SMACKS includes every experimental data point, not only dwell times. As a result, it works as well for long trajectories as for an equivalent set of short ones. In addition, the previous systematic overestimation of fast over slow rates is solved. We demonstrate the power of SMACKS on the kinetics of the multidomain protein Hsp90 measured by single-molecule Förster resonance energy transfer. Experiments in and out of equilibrium are analyzed and compared to simulations, shedding new light on the role of Hsp90's ATPase function. SMACKS resolves accurate rate models even if states cause indistinguishable signals. Thereby, it pushes the boundaries of single-molecule kinetics beyond those of current methods.
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14
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Lee A, Tsekouras K, Calderon C, Bustamante C, Pressé S. Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis. Chem Rev 2017; 117:7276-7330. [PMID: 28414216 PMCID: PMC5487374 DOI: 10.1021/acs.chemrev.6b00729] [Citation(s) in RCA: 65] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Super-resolution microscopy provides direct insight into fundamental biological processes occurring at length scales smaller than light's diffraction limit. The analysis of data at such scales has brought statistical and machine learning methods into the mainstream. Here we provide a survey of data analysis methods starting from an overview of basic statistical techniques underlying the analysis of super-resolution and, more broadly, imaging data. We subsequently break down the analysis of super-resolution data into four problems: the localization problem, the counting problem, the linking problem, and what we've termed the interpretation problem.
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Affiliation(s)
- Antony Lee
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, United States
- Jason L. Choy Laboratory of Single-Molecule Biophysics, University of California at Berkeley, Berkeley, California 94720, United States
| | - Konstantinos Tsekouras
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, United States
- Department of Physics, Arizona State University, Tempe, Arizona 85287, United States
| | | | - Carlos Bustamante
- Jason L. Choy Laboratory of Single-Molecule Biophysics, University of California at Berkeley, Berkeley, California 94720, United States
- Biophysics Graduate Group, University of California at Berkeley, Berkeley, California 94720, United States
- Institute for Quantitative Biosciences-QB3, University of California at Berkeley, Berkeley, California 94720, United States
- Department of Molecular and Cell Biology, University of California at Berkeley, Berkeley, California 94720, United States
- Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
- Howard Hughes Medical Institute, University of California at Berkeley, Berkeley, California 94720, United States
- Kavli Energy Nanosciences Institute, University of California at Berkeley, Berkeley, California 94720, United States
| | - Steve Pressé
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, United States
- Department of Chemistry and Chemical Biology, Indiana University–Purdue University Indianapolis, Indianapolis, Indiana 46202, United States
- Department of Cell and Integrative Physiology, Indiana University School of Medicine, Indianapolis, Indiana 46202, United States
- School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287, United States
- Department of Physics, Arizona State University, Tempe, Arizona 85287, United States
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15
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Aghamohammadi C, Crutchfield JP. Minimum memory for generating rare events. Phys Rev E 2017; 95:032101. [PMID: 28415193 DOI: 10.1103/physreve.95.032101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2016] [Indexed: 11/07/2022]
Abstract
We classify the rare events of structured, memoryful stochastic processes and use this to analyze sequential and parallel generators for these events. Given a stochastic process, we introduce a method to construct a process whose typical realizations are a given process' rare events. This leads to an expression for the minimum memory required to generate rare events. We then show that the recently discovered classical-quantum ambiguity of simplicity also occurs when comparing the structure of process fluctuations.
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Affiliation(s)
- Cina Aghamohammadi
- Complexity Sciences Center and Department of Physics, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
| | - James P Crutchfield
- Complexity Sciences Center and Department of Physics, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
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16
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Informational and Causal Architecture of Discrete-Time Renewal Processes. ENTROPY 2015. [DOI: 10.3390/e17074891] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
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17
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Strelioff CC, Crutchfield JP. Bayesian structural inference for hidden processes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042119. [PMID: 24827205 DOI: 10.1103/physreve.89.042119] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2013] [Indexed: 06/03/2023]
Abstract
We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ε-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ε-machines, irrespective of estimated transition probabilities. Properties of ε-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.
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Affiliation(s)
- Christopher C Strelioff
- Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
| | - James P Crutchfield
- Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
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18
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König SLB, Hadzic M, Fiorini E, Börner R, Kowerko D, Blanckenhorn WU, Sigel RKO. BOBA FRET: bootstrap-based analysis of single-molecule FRET data. PLoS One 2013; 8:e84157. [PMID: 24386343 PMCID: PMC3873958 DOI: 10.1371/journal.pone.0084157] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2013] [Accepted: 11/12/2013] [Indexed: 01/18/2023] Open
Abstract
Time-binned single-molecule Förster resonance energy transfer (smFRET) experiments with surface-tethered nucleic acids or proteins permit to follow folding and catalysis of single molecules in real-time. Due to the intrinsically low signal-to-noise ratio (SNR) in smFRET time traces, research over the past years has focused on the development of new methods to extract discrete states (conformations) from noisy data. However, limited observation time typically leads to pronounced cross-sample variability, i.e., single molecules display differences in the relative population of states and the corresponding conversion rates. Quantification of cross-sample variability is necessary to perform statistical testing in order to assess whether changes observed in response to an experimental parameter (metal ion concentration, the presence of a ligand, etc.) are significant. However, such hypothesis testing has been disregarded to date, precluding robust biological interpretation. Here, we address this problem by a bootstrap-based approach to estimate the experimental variability. Simulated time traces are presented to assess the robustness of the algorithm in conjunction with approaches commonly used in thermodynamic and kinetic analysis of time-binned smFRET data. Furthermore, a pair of functionally important sequences derived from the self-cleaving group II intron Sc.ai5γ (d3'EBS1*/IBS1*) is used as a model system. Through statistical hypothesis testing, divalent metal ions are shown to have a statistically significant effect on both thermodynamic and kinetic aspects of their interaction. The Matlab source code used for analysis (bootstrap-based analysis of smFRET data, BOBA FRET), as well as a graphical user interface, is available via http://www.aci.uzh.ch/rna/.
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Affiliation(s)
- Sebastian L. B. König
- Institute of Inorganic Chemistry, University of Zurich, Zurich, Switzerland
- * E-mail: (RKOS); (SLBK)
| | - Mélodie Hadzic
- Institute of Inorganic Chemistry, University of Zurich, Zurich, Switzerland
| | - Erica Fiorini
- Institute of Inorganic Chemistry, University of Zurich, Zurich, Switzerland
| | - Richard Börner
- Institute of Inorganic Chemistry, University of Zurich, Zurich, Switzerland
| | - Danny Kowerko
- Institute of Inorganic Chemistry, University of Zurich, Zurich, Switzerland
| | - Wolf U. Blanckenhorn
- Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland
| | - Roland K. O. Sigel
- Institute of Inorganic Chemistry, University of Zurich, Zurich, Switzerland
- * E-mail: (RKOS); (SLBK)
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20
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Varn DP, Canright GS, Crutchfield JP. ∊-Machine spectral reconstruction theory: a direct method for inferring planar disorder and structure from X-ray diffraction studies. Acta Crystallogr A 2013; 69:197-206. [DOI: 10.1107/s0108767312046582] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2012] [Accepted: 11/11/2012] [Indexed: 11/10/2022] Open
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21
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Wiesner K, Gu M, Rieper E, Vedral V. Information-theoretic lower bound on energy cost of stochastic computation. Proc Math Phys Eng Sci 2012. [DOI: 10.1098/rspa.2012.0173] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Physical systems are often simulated using a stochastic computation where different final states result from identical initial states. Here, we derive the minimum energy cost of simulating a data sequence of a general physical system by stochastic computation. We show that the cost is proportional to the difference between two information-theoretic measures of complexity of the data—the
statistical complexity
and the
predictive information
. We derive the difference as the amount of information erased during the computation. Finally, we illustrate the physics of information by implementing the stochastic computation as a Gedanken experiment with a Szilard-type engine. The results create a new link between thermodynamics, information theory and complexity.
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Affiliation(s)
- Karoline Wiesner
- School of Mathematics, Centre for Complexity Sciences, University of Bristol, University Walk, Bristol BS8 1TW, UK
| | - Mile Gu
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, S15-03-18, Singapore 117543, Republic of Singapore
| | - Elisabeth Rieper
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, S15-03-18, Singapore 117543, Republic of Singapore
| | - Vlatko Vedral
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, S15-03-18, Singapore 117543, Republic of Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117543, Republic of Singapore
- Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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22
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Preus S, Wilhelmsson LM. Advances in quantitative FRET-based methods for studying nucleic acids. Chembiochem 2012; 13:1990-2001. [PMID: 22936620 DOI: 10.1002/cbic.201200400] [Citation(s) in RCA: 98] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2012] [Indexed: 01/02/2023]
Abstract
Förster resonance energy transfer (FRET) is a powerful tool for monitoring molecular distances and interactions at the nanoscale level. The strong dependence of transfer efficiency on probe separation makes FRET perfectly suited for "on/off" experiments. To use FRET to obtain quantitative distances and three-dimensional structures, however, is more challenging. This review summarises recent studies and technological advances that have improved FRET as a quantitative molecular ruler in nucleic acid systems, both at the ensemble and at the single-molecule levels.
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Affiliation(s)
- Søren Preus
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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