What is it about?

Getting High on Single Molecule Biophysics: We first provide solutions to the problems : - how bulk egodicity behaves for subpopulations of biomacromolecules and - in what ways and how much the interaction network of single molecules can be rendered nonergodic by ensemble averaging during the measurement.

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Why is it important?

Here, we present an approach on how to decide from a subset of single-molecule measurements how heterogeneous the studied system is in time. Specifically, we present an approach to distinguish between ergodic and non-ergodic behavior. We have proposed a change of the molecular behavior when single molecules are trapped in interactions with their neighboring ligands and reaction partner(s), respectively or/and by conformational changes in a crowded environment. Spatial and temporal conditions are decoupled. Assuming that the number of single-molecule tracks  out of an infinite set of possible outcomes in a non-ergodic system can be ordered, we introduce the following averaging over non-ergodic single-molecule tracks: The averaging is carried out by minimizing the variation between the sum of the temporal averaged MSD data with respect to the logarithmic scaling behavior of the subpopulation. This yields the least possible variation over non-ergodic single-molecule tracks. Eqn. (12) represents nothing more than a minimization of the squares of the errors, e.g. measurement errors. It turns out that the optimal number of tracks is a small number taken from an infinite set of possible values . The most striking feature of performing ensemble averaging in sparse subpopulations of single molecules, however, is a mean value of the solid green line in Fig. (3) that is the same mean value obtained in an ergodic system. Hence, broken ergodicity and unbroken ergodicity are not anymore distinguishable. In addition, when averaging procedures are carried out without knowing whether the underlying molecular system behaves in ergodic or non-ergodic ways, each measurement can be related to an ergodic or a non-ergodic behavior unless one is able to show the single-molecule fingerprint of nonergodicity. https://lnkd.in/dSkTKR6 Zeno.


Quiz question on the 'SINGLE-MOLECULE DEMON' (single-molecule ratchet) in IMAGING/MICROSCOPY/SUPER-RESOLUTION MICROSCOPY (NANOSCOPY) and SPECTROSCOPY of Dilute Liquids and Live Cells that is The 'SINGLE-MOLECULE DEMON' (single-molecule ratchet) in Single-Molecule Localization Microscopy/Nanoscopy (Super-Resolution Microscopy)/Spectroscopy and Single-Molecule Laser Scanning Microscopy or Single-Molecule Image Analysis in liquids or live cells without immobilization on artificial or biological surfaces or without significant hydrodynamic flow: Is there a 'perpetuum mobile' (perpetual motion) for the freely diffusing individual molecules (one and the same molecules, selfsame molecules, single molecules) in liquids or live cells? In other words, is there an experiment that would violate the "temporal resolution of single molecules without immobilization on artificial or biological membranes/surfaces or without significant hydrodynamic flow"? This hypothetical phenomenon, which would apparently violate the 1st or 2nd law of thermodynamics, has not yet been experimentally confirmed. Many of the ideas about molecular motors and machines that were originally pure thought experiments are now being achieved by the synthetic capabilities of modern chemistry; Kay et al. [1] presented old and current ideas and discussed the technical problems and physical principles. [1] Euan R Kay, David A Leigh, Francesco Zerbetto: Synthetic molecular motors and mechanical machines. Angew Chem Int Ed Engl. 2007; 46 (1-2):72-191 https://www.growkudos.com/publications/10.2174%252F138920107782109930/reader https://www.linkedin.com/pulse/how-get-high-single-molecule-biophysics-biochemistry-data-zeno?trk=public_profile_article_view The advantages of the physical 'Theory of Single-Molecule Biophysics & Biochemistry Based On Individually Diffusing Molecules in Dilute Liquids and Live Cells' are evident. The thermodynamic Single-Molecule DEMON: How to avoid him in the measurements of dilute liquids and live cells without immobilization or flow: https://www.linkedin.com/pulse/thermodynamic-single-molecule-demon-zeno-földes-papp/?trk=public_profile_article_view

Professor Zeno Földes-Papp [Biochemist, Gerontologist (Biochemiker, Geriater)]: Single-Molecule Biophysics & Biochemistry Based On the Stochastic Nature of Diffusion. -- I hope that my humble scientific work will be well received by the communities of single-molecule imaging and spectroscopy and by all users of these technologies as well as biotechnologies in the various and different disciplines:
Head of Geriatric Medicine (Medical Director of the Geriatric Service: Sektionsleitung Geriatrie) at Asklepios Klinikum Lindau (Bodensee), Bavaria, Germany

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This page is a summary of: Fluorescence Molecule Counting for Single-Molecule Studies in Crowded Environment of Living Cells without and with Broken Ergodicity, Current Pharmaceutical Biotechnology, May 2011, Bentham Science Publishers, DOI: 10.2174/138920111795470949.
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