Bayesian inference: The comprehensive approach to analyzing single-molecule experiments

2020 ◽  
Author(s):  
Colin D. Kinz-Thompson ◽  
Korak Kumar Ray ◽  
Ruben L. Gonzalez
Keyword(s):  
Experimental Data ◽  
Probability Theory ◽  
Bayesian Inference ◽  
Single Molecule ◽  
Biophysical Model ◽  
Structural Details ◽  
Self Consistent ◽  
Insight Into ◽  
The Bayesian Approach ◽  
Data Analysis Methods

ABSTRACTBiophysics experiments performed at single-molecule resolution contain exceptional insight into the structural details and dynamic behavior of biological systems. However, extracting this information from the corresponding experimental data unequivocally requires applying a biophysical model. Here, we discuss how to use probability theory to apply these models to single-molecule data. Many current single-molecule data analysis methods apply parts of probability theory, sometimes unknowingly, and thus miss out on the full set of benefits provided by this self-consistent framework. The full application of probability theory involves a process called Bayesian inference that fully accounts for the uncertainties inherent to single-molecule experiments. Additionally, using Bayesian inference provides a scientifically rigorous manner to incorporate information from multiple experiments into a single analysis and to find the best biophysical model for an experiment without the risk of overfitting the data. These benefits make the Bayesian approach ideal for analyzing any type of single-molecule experiment.

scholarly journals Bayesian Inference: The Comprehensive Approach to Analyzing Single-Molecule Experiments

2021 ◽  
Vol 50 (1) ◽  
Author(s):  
Colin D. Kinz-Thompson ◽  
Korak Kumar Ray ◽  
Ruben L. Gonzalez
Keyword(s):  
Probability Theory ◽  
Bayesian Inference ◽  
Single Molecule ◽  
Biophysical Model ◽  
Annual Review ◽  
Publication Date ◽  
Structural Details ◽  
Self Consistent ◽  
Insight Into ◽  
Data Analysis Methods

Biophysics experiments performed at single-molecule resolution provide exceptional insight into the structural details and dynamic behavior of biological systems. However, extracting this information from the corresponding experimental data unequivocally requires applying a biophysical model. In this review, we discuss how to use probability theory to apply these models to single-molecule data. Many current single-molecule data analysis methods apply parts of probability theory, sometimes unknowingly, and thus miss out on the full set of benefits provided by this self-consistent framework. The full application of probability theory involves a process called Bayesian inference that fully accounts for the uncertainties inherent to single-molecule experiments. Additionally, using Bayesian inference provides a scientifically rigorous method of incorporating information from multiple experiments into a single analysis and finding the best biophysical model for an experiment without the risk of overfitting the data. These benefits make the Bayesian approach ideal for analyzing any type of single-molecule experiment. Expected final online publication date for the Annual Review of Biophysics, Volume 50 is May 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

scholarly journals Denoising Single-Molecule FRET Trajectories with Wavelets and Bayesian Inference

2010 ◽  
Vol 98 (1) ◽  
pp. 164-173 ◽  
Author(s):  
J. Nick Taylor ◽  
Dmitrii E. Makarov ◽  
Christy F. Landes
Keyword(s):  
Bayesian Inference ◽  
Single Molecule ◽  
Single Molecule Fret

Recent progress in the freeze-etching technique

1971 ◽  
Vol 261 (837) ◽  
pp. 121-131 ◽  
Keyword(s):  
High Vacuum ◽  
Molecular Size ◽  
Etching Technique ◽  
Structural Distortions ◽  
Shadow Casting ◽  
Structural Details ◽  
Freeze Etching ◽  
The One ◽  
Insight Into ◽  
Made In

The freeze-etching technique must be improved if structures at the molecular size level are to be seen. The limitations of the technique are discussed here together with the progress made in alleviating them. The vitrification of living specimens is limited by the fact that very high freezing rates are needed. The critical freezing rate can be lowered on the one hand by the introduction of antifreeze agents, on the other hand by the application of high hydrostatic pressure. The fracture process may cause structural distortions in the fracture face of the frozen specimen. The ‘double-replica’ method allows one to evaluate such artefacts and provides an insight into the way that membranes split. During etching there exists the danger of contaminating the fracture faces with condensable gases. Because of specimen temperatures below —110 °C, special care has to be taken in eliminating water vapour from the high vacuum. An improvement in coating freeze-etched specimens has resulted from the application of electron guns for evaporation of the highest melting-point metals. If heat transfer from gun to specimen is reduced to a minimum, Pt, Ir, Ta, W and C can be used for shadow casting. Best results are obtained with Pt-C and Ta-W . With the help of decoration effects Pt-C shadow castings give the most information about the fine structural details of the specimen.

scholarly journals On the Trigonometric Descriptions of Colors

2016 ◽  
Vol 8 (3) ◽  
pp. 5
Author(s):  
Jirí Stavek
Keyword(s):  
Experimental Data ◽  
Transverse Energy ◽  
Gravitational Constant ◽  
Isaac Newton ◽  
Type Ia ◽  
New Interpretation ◽  
The Stability ◽  
Mass Evaporation ◽  
Supernovae Type Ia ◽  
Insight Into

<p class="1Body">An attempt is presented for the description of the spectral colors using the standard trigonometric tools in order to extract more information about photons. We have arranged the spectral colors on an arc of the circle with the radius R = 1 and the central angle θ = π/3 when we have defined cos (θ) = λ<sub>380</sub>/λ<sub>760</sub> = 0.5. Several trigonometric operations were applied in order to find the gravity centers for the scotopic, photopic, and mesopic visions. The concept of the center of gravity of colors introduced Isaac Newton. We have postulated properties of the long-lived photons with the new interpretation of the Hubble (Zwicky-Nernst) constant H<sub>0</sub> = 2.748… * 10<sup>-18</sup> kg kg<sup>-1 </sup>s<sup>-1</sup>, the specific mass evaporation rate (SMER) of gravitons from the source mass. The stability of international prototypes of kilogram has been regularly checked. We predict that those standard kilograms due to the evaporation of gravitons lost 8.67 μg kg<sup>-1</sup> century<sup>-1</sup>. The energy of long-lived photons was trigonometrically decomposed into three parts that could be experimentally tested: longitudinal energy, transverse energy and energy of evaporated gravitons. We tested the properties of the long-lived photons with the experimental data published for the best available standard candles: supernovae Type Ia. There was found a surprising match of those experimental data with the model of the long-lived photons. Finally, we have proposed a possible decomposition of the big G (Newtonian gravitational constant) and the small kappa κ (Einsteinian gravitational constant) in order to get a new insight into the mysterious gravitational force and/or the curvature concept.</p>

Single-molecule insight into Wurtz reactions on metal surfaces

2016 ◽  
Vol 18 (4) ◽  
pp. 2730-2735 ◽  
Author(s):  
Qiang Sun ◽  
Liangliang Cai ◽  
Yuanqi Ding ◽  
Honghong Ma ◽  
Chunxue Yuan ◽  
...  
Keyword(s):  
Single Molecule ◽  
Systematic Study ◽  
Metal Surfaces ◽  
Insight Into

We have performed a systematic study of Wurtz reactions on different metal surfaces and compared their different activities.

scholarly journals InferenceMAP: mapping of single-molecule dynamics with Bayesian inference

2015 ◽  
Vol 12 (7) ◽  
pp. 594-595 ◽  
Author(s):  
Mohamed El Beheiry ◽  
Maxime Dahan ◽  
Jean-Baptiste Masson
Keyword(s):  
Bayesian Inference ◽  
Single Molecule ◽  
Single Molecule Dynamics ◽  
Molecule Dynamics

scholarly journals Increasing the time resolution of single-molecule experiments with Bayesian inference

2017 ◽  
Author(s):  
Colin D. Kinz-Thompson ◽  
Ruben L. Gonzalez
Keyword(s):  
Bayesian Inference ◽  
Single Molecule ◽  
Time Resolution ◽  
Rate Constants ◽  
Computational Approach ◽  
Biomolecular Systems ◽  
Time Resolved ◽  
The Given ◽  
Kinetics Of ◽  
Resolution Data

AbstractMany time-resolved, single-molecule biophysics experiments seek to characterize the kinetics of biomolecular systems exhibiting dynamics that challenge the time resolution of the given technique. Here we present a general, computational approach to this problem that employs Bayesian inference to learn the underlying dynamics of such systems, even when they are much faster than the time resolution of the experimental technique being used. By accurately and precisely inferring rate constants, our Bayesian Inference for the Analysis of Sub-temporal-resolution Data (BIASD) approach effectively enables the experimenter to super-resolve the poorly resolved dynamics that are present in their data.

scholarly journals Dynamics of Tpm1.8 domains on actin filaments with single molecule resolution

2020 ◽  
Author(s):  
Ilina Bareja ◽  
Hugo Wioland ◽  
Miro Janco ◽  
Philip R. Nicovich ◽  
Antoine Jégou ◽  
...  
Keyword(s):  
Actin Filament ◽  
Single Molecule ◽  
Actin Filaments ◽  
High Probability ◽  
Actin Binding ◽  
Single Molecule Level ◽  
Filament Dynamics ◽  
Kinetics Of ◽  
Insight Into

ABSTRACTTropomyosins regulate dynamics and functions of the actin cytoskeleton by forming long chains along the two strands of actin filaments that act as gatekeepers for the binding of other actin-binding proteins. The fundamental molecular interactions underlying the binding of tropomyosin to actin are still poorly understood. Using microfluidics and fluorescence microscopy, we observed the binding of fluorescently labelled tropomyosin isoform Tpm1.8 to unlabelled actin filaments in real time. This approach in conjunction with mathematical modeling enabled us to quantify the nucleation, assembly and disassembly kinetics of Tpm1.8 on single filaments and at the single molecule level. Our analysis suggests that Tpm1.8 decorates the two strands of the actin filament independently. Nucleation of a growing tropomyosin domain proceeds with high probability as soon as the first Tpm1.8 molecule is stabilised by the addition of a second molecule, ultimately leading to full decoration of the actin filament. In addition, Tpm1.8 domains are asymmetrical, with enhanced dynamics at the edge oriented towards the barbed end of the actin filament. The complete description of Tpm1.8 kinetics on actin filaments presented here provides molecular insight into actin-tropomyosin filament formation and the role of tropomyosins in regulating actin filament dynamics.

scholarly journals Ramping and phasic dopamine activity accounts for efficient cognitive resource allocation during reinforcement learning

2018 ◽  
Author(s):  
Minryung R. Song ◽  
Sang Wan Lee
Keyword(s):  
Experimental Data ◽  
Resource Allocation ◽  
Reinforcement Learning ◽  
Learning Model ◽  
Temporal Difference ◽  
Value Change ◽  
Cognitive Resource ◽  
A Value ◽  
Insight Into ◽  
And Task

AbstractDopamine activity may transition between two patterns: phasic responses to reward-predicting cues and ramping activity arising when an agent approaches the reward. However, when and why dopamine activity transitions between these modes is not understood. We hypothesize that the transition between ramping and phasic patterns reflects resource allocation which addresses the task dimensionality problem during reinforcement learning (RL). By parsimoniously modifying a standard temporal difference (TD) learning model to accommodate a mixed presentation of both experimental and environmental stimuli, we simulated dopamine transitions and compared it with experimental data from four different studies. The results suggested that dopamine transitions from ramping to phasic patterns as the agent narrows down candidate stimuli for the task; the opposite occurs when the agent needs to re-learn candidate stimuli due to a value change. These results lend insight into how dopamine deals with the tradeoff between cognitive resource and task dimensionality during RL.

scholarly journals The Study of the Theoretical Size and Node Probability of the Loop Cutset in Bayesian Networks

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1079 ◽  
Author(s):  
Jie Wei ◽  
Yufeng Nie ◽  
Wenxian Xie
Keyword(s):  
Probability Theory ◽  
Graph Theory ◽  
Bayesian Inference ◽  
Bayesian Networks ◽  
Numerical Simulations ◽  
Complete Graph ◽  
Upper Bound ◽  
Numerical Algorithms ◽  
Theoretical Research ◽  
Theoretical Results

Pearl’s conditioning method is one of the basic algorithms of Bayesian inference, and the loop cutset is crucial for the implementation of conditioning. There are many numerical algorithms for solving the loop cutset, but theoretical research on the characteristics of the loop cutset is lacking. In this paper, theoretical insights into the size and node probability of the loop cutset are obtained based on graph theory and probability theory. It is proven that when the loop cutset in a p-complete graph has a size of p − 2 , the upper bound of the size can be determined by the number of nodes. Furthermore, the probability that a node belongs to the loop cutset is proven to be positively correlated with its degree. Numerical simulations show that the application of the theoretical results can facilitate the prediction and verification of the loop cutset problem. This work is helpful in evaluating the performance of Bayesian networks.

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