Generic Schemes for Single-Molecule Kinetics. 3: Self-Consistent Pathway Solutions for Nonrenewal Processes

2018 ◽  
Vol 122 (17) ◽  
pp. 4601-4610 ◽  
Author(s):  
D. Evan Piephoff ◽  
Jianshu Cao
Keyword(s):  
Single Molecule ◽  
Self Consistent

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.

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.

AN ELLIPSOIDAL MOLECULES MODEL OF LIQUID CRYSTAL WITH QUADRUPOLAR INTERACTION: SELF-CONSISTENT FREE ENERGY

1990 ◽  
Vol 04 (09) ◽  
pp. 1589-1609
Author(s):  
M.G. RASETTI ◽  
M.L. RASTELLO
Keyword(s):  
Single Molecule ◽  
Short Range ◽  
Lattice Gas ◽  
Mean Field ◽  
Second Order ◽  
Classical Lattice ◽  
Field Approach ◽  
Self Consistent ◽  
Short Range Correlations ◽  
Second Order Phase Transition

We study the structure of the phase space for a system of N molecules of ellipsoidal symmetry, as a function of concentration and temperature. A classical lattice gas approximation is considered and a single molecule is described by a rigid ellipsoidal core with weak attractive tails along the long axis. The method adopted is a second-order mean-field approach – designed in such a way as to keep into account the fluctuations from equilibrium of the order parameters up to the fourth order – combined with a cumulant-cluster expansion, and improved by keeping track of the short-range correlations. Preliminary numerical calculations show the existence, in the case of zero attractive tail, of a second order phase transition.

The evolution of the Kuiper belt during the formation of the outer planets

1999 ◽  
Vol 173 ◽  
pp. 37-44
Author(s):  
M.D. Melita ◽  
A. Brunini
Keyword(s):  
Kuiper Belt ◽  
Outer Planets ◽  
Self Consistent ◽  
Planetary Bodies ◽  
Mass Depletion

AbstractA self-consistent study of the formation of planetary bodies beyond the orbit of Saturn and the evolution of Kuiper disks is carried out by means of an N-body code where accretion and gravitational encounters are considered. This investigation is focused on the aggregation of massive bodies in the outer planetary region and on the consequences of such process in the corresponding cometary belt. We study the link between the bombardment of massive bodies and mass depletion and eccentricity excitation.

The method of replication affects metal film granularity and resolution

1989 ◽  
Vol 47 ◽  
pp. 708-709
Author(s):  
George C. Ruben
Keyword(s):  
Electron Beam ◽  
High Resolution ◽  
Film Thickness ◽  
Single Molecule ◽  
Metal Film ◽  
Vertical Surface ◽  
High Resolution Imaging ◽  
Controllable Factors ◽  
Resolution Imaging

Single molecule resolution in electron beam sensitive, uncoated, noncrystalline materials has been impossible except in thin Pt-C replicas ≤ 150Å) which are resistant to the electron beam destruction. Previously the granularity of metal film replicas limited their resolution to ≥ 20Å. This paper demonstrates that Pt-C film granularity and resolution are a function of the method of replication and other controllable factors. Low angle 20° rotary , 45° unidirectional and vertical 9.7±1 Å Pt-C films deposited on mica under the same conditions were compared in Fig. 1. Vertical replication had a 5A granularity (Fig. 1c), the highest resolution (table), and coated the whole surface. 45° replication had a 9Å granulartiy (Fig. 1b), a slightly poorer resolution (table) and did not coat the whole surface. 20° rotary replication was unsuitable for high resolution imaging with 20-25Å granularity (Fig. 1a) and resolution 2-3 times poorer (table). Resolution is defined here as the greatest distance for which the metal coat on two opposing faces just grow together, that is, two times the apparent film thickness on a single vertical surface.

Single molecule optical diffraction: A tool for understanding the structure of triple stranded left-hand helical cellulose

1989 ◽  
Vol 47 ◽  
pp. 1024-1025
Author(s):  
George C. Ruben ◽  
William Krakow
Keyword(s):  
Single Molecule ◽  
Helical Structure ◽  
Optical Diffraction ◽  
Maximum Diameter ◽  
Primary Cell Wall ◽  
Cellulose Synthesis ◽  
Left Hand ◽  
Left Handed ◽  
Freeze Dried ◽  
Diffraction Patterns

Tobacco primary cell wall and normal bacterial Acetobacter xylinum cellulose formation produced a 36.8±3Å triple-stranded left-hand helical microfibril in freeze-dried Pt-C replicas and in negatively stained preparations for TEM. As three submicrofibril strands exit the wall of Axylinum , they twist together to form a left-hand helical microfibril. This process is driven by the left-hand helical structure of the submicrofibril and by cellulose synthesis. That is, as the submicrofibril is elongating at the wall, it is also being left-hand twisted and twisted together with two other submicrofibrils. The submicrofibril appears to have the dimensions of a nine (l-4)-ß-D-glucan parallel chain crystalline unit whose long, 23Å, and short, 19Å, diagonals form major and minor left-handed axial surface ridges every 36Å.The computer generated optical diffraction of this model and its corresponding image have been compared. The submicrofibril model was used to construct a microfibril model. This model and corresponding microfibril images have also been optically diffracted and comparedIn this paper we compare two less complex microfibril models. The first model (Fig. 1a) is constructed with cylindrical submicrofibrils. The second model (Fig. 2a) is also constructed with three submicrofibrils but with a single 23 Å diagonal, projecting from a rounded cross section and left-hand helically twisted, with a 36Å repeat, similar to the original model (45°±10° crossover angle). The submicrofibrils cross the microfibril axis at roughly a 45°±10° angle, the same crossover angle observed in microflbril TEM images. These models were constructed so that the maximum diameter of the submicrofibrils was 23Å and the overall microfibril diameters were similar to Pt-C coated image diameters of ∼50Å and not the actual diameter of 36.5Å. The methods for computing optical diffraction patterns have been published before.

Structural dynamics of P-type ATPase ion pumps

2019 ◽  
Vol 47 (5) ◽  
pp. 1247-1257 ◽  
Author(s):  
Mateusz Dyla ◽  
Sara Basse Hansen ◽  
Poul Nissen ◽  
Magnus Kjaergaard
Keyword(s):  
Structural Dynamics ◽  
Single Molecule ◽  
New Technologies ◽  
Atp Hydrolysis ◽  
Resonance Energy Transfer ◽  
Resonance Energy ◽  
Time Resolved ◽  
Dynamics Simulations ◽  
Types Of Information ◽  
P Type

Abstract P-type ATPases transport ions across biological membranes against concentration gradients and are essential for all cells. They use the energy from ATP hydrolysis to propel large intramolecular movements, which drive vectorial transport of ions. Tight coordination of the motions of the pump is required to couple the two spatially distant processes of ion binding and ATP hydrolysis. Here, we review our current understanding of the structural dynamics of P-type ATPases, focusing primarily on Ca2+ pumps. We integrate different types of information that report on structural dynamics, primarily time-resolved fluorescence experiments including single-molecule Förster resonance energy transfer and molecular dynamics simulations, and interpret them in the framework provided by the numerous crystal structures of sarco/endoplasmic reticulum Ca2+-ATPase. We discuss the challenges in characterizing the dynamics of membrane pumps, and the likely impact of new technologies on the field.

Label-free, mass-sensitive single-molecule imaging using interferometric scattering microscopy

2020 ◽  
Author(s):  
Nikolas Hundt
Keyword(s):  
Single Molecule ◽  
Cellular Systems ◽  
Single Molecule Imaging ◽  
Label Free ◽  
Measurement Sensitivity ◽  
Mass Distributions ◽  
Quantitative Measurements ◽  
Contrast Mechanism ◽  
Cellular Components ◽  
Scattering Signal

Abstract Single-molecule imaging has mostly been restricted to the use of fluorescence labelling as a contrast mechanism due to its superior ability to visualise molecules of interest on top of an overwhelming background of other molecules. Recently, interferometric scattering (iSCAT) microscopy has demonstrated the detection and imaging of single biomolecules based on light scattering without the need for fluorescent labels. Significant improvements in measurement sensitivity combined with a dependence of scattering signal on object size have led to the development of mass photometry, a technique that measures the mass of individual molecules and thereby determines mass distributions of biomolecule samples in solution. The experimental simplicity of mass photometry makes it a powerful tool to analyse biomolecular equilibria quantitatively with low sample consumption within minutes. When used for label-free imaging of reconstituted or cellular systems, the strict size-dependence of the iSCAT signal enables quantitative measurements of processes at size scales reaching from single-molecule observations during complex assembly up to mesoscopic dynamics of cellular components and extracellular protrusions. In this review, I would like to introduce the principles of this emerging imaging technology and discuss examples that show how mass-sensitive iSCAT can be used as a strong complement to other routine techniques in biochemistry.

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