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Peixuan Guo - One of the best experts on this subject based on the ideXlab platform.
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A simple mathematical formula for stoichiometry quantification of viral and nanobioLogical assemblage using slopes of Log/Log Plot curves
Journal of Virological Methods, 2004Co-Authors: Dan Shu, Lisa Huang, Peixuan GuoAbstract:In nanotechnoLogy, biomolecular assemblies serve not only as model systems for the construction of nanodevices, but they can also be used directly as templates for the formation of nanostructures. BioLogical nano-building blocks can either be isolated as complete functional units from living cells or viruses (bioLogical “Top down” approach) or formed by biomolecular assembly from recombinant or synthetic components (“Bottom up” approach). In both cases, rational design of nanostructures requires knowledge of the stoichiometry of the bioLogical structures, which frequently occur as multimers, i.e., the morphoLogical complex is composed of multiple copies of one or more macromolecules. In this paper, a method is described for the stoichiometric quantification of molecules in bio-nanostructures. The method is based on using dilution factors and relative concentrations rather than absolute quantities, which are often difficult to determine, especially in short-lived assembly intermediates. The approach exploits the fact that the larger the stoichiometry of the component is, the more dramatic is the influence of the dilution factor (decrease in concentration) on the reaction. We established and used the method to determine the stoichiometry of components of bacterial virus phi29. The Log of dilution factors was Plotted against the Log of reaction yield. The stoichiometry Z was determined with the equation Z=−1.58+2.4193T−0.001746T2 [T ∈ (0,1000), or ∠α ∈ (0°, 89.9°)], where T is the slope of the curve (tangent of ∠α, which is the angle between the x-axis and the concentration dependent curve). Z can also be determined from a standard table given in this report. With the bacteriophage phi29 in vitro assembly system, up to 5×108 infectious virions per ml can be assembled from 11 purified components, giving our method a sensitivity of nine orders of magnitude. We confirmed the stoichiometries of phi29 components that were determined previously with microscopic approaches. The described method also responded to programmed stoichiometry changes, which were generated by assembling the phi29 DNA packaging motor from modified pRNA (DNA-packaging RNA) molecules forming a trimer of dimers or a dimer of trimers, instead of the wild-type hexamer.
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a simple mathematical formula for stoichiometry quantification of viral and nanobioLogical assemblage using slopes of Log Log Plot curves
Journal of Virological Methods, 2004Co-Authors: Dan Shu, Lisa Huang, Peixuan GuoAbstract:In nanotechnoLogy, biomolecular assemblies serve not only as model systems for the construction of nanodevices, but they can also be used directly as templates for the formation of nanostructures. BioLogical nano-building blocks can either be isolated as complete functional units from living cells or viruses (bioLogical “Top down” approach) or formed by biomolecular assembly from recombinant or synthetic components (“Bottom up” approach). In both cases, rational design of nanostructures requires knowledge of the stoichiometry of the bioLogical structures, which frequently occur as multimers, i.e., the morphoLogical complex is composed of multiple copies of one or more macromolecules. In this paper, a method is described for the stoichiometric quantification of molecules in bio-nanostructures. The method is based on using dilution factors and relative concentrations rather than absolute quantities, which are often difficult to determine, especially in short-lived assembly intermediates. The approach exploits the fact that the larger the stoichiometry of the component is, the more dramatic is the influence of the dilution factor (decrease in concentration) on the reaction. We established and used the method to determine the stoichiometry of components of bacterial virus phi29. The Log of dilution factors was Plotted against the Log of reaction yield. The stoichiometry Z was determined with the equation Z=−1.58+2.4193T−0.001746T2 [T ∈ (0,1000), or ∠α ∈ (0°, 89.9°)], where T is the slope of the curve (tangent of ∠α, which is the angle between the x-axis and the concentration dependent curve). Z can also be determined from a standard table given in this report. With the bacteriophage phi29 in vitro assembly system, up to 5×108 infectious virions per ml can be assembled from 11 purified components, giving our method a sensitivity of nine orders of magnitude. We confirmed the stoichiometries of phi29 components that were determined previously with microscopic approaches. The described method also responded to programmed stoichiometry changes, which were generated by assembling the phi29 DNA packaging motor from modified pRNA (DNA-packaging RNA) molecules forming a trimer of dimers or a dimer of trimers, instead of the wild-type hexamer.
Chen Hong-yuan - One of the best experts on this subject based on the ideXlab platform.
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The i-E Equations of Steady-state Voltammograms at Microdisk Electrodes
1993Co-Authors: Chen Hong-yuanAbstract:Based on the theories of conventional electrodes, as well as the properties of microdisk electrode, the i-E equations for chronoamperometry at disk microelectrode for reversible, quasi-reversible and irreversible systems are derived. Steady-state voltammograms for the oxidation of [Fe(CN)6]4- , Fe2+ and ascorbic acid were measured at a series of microdisk electrodes with different radii. The conventional Log-Plot shows that oxidations of [Fe(CN)6]4- and ascorbic acid are reversible and totally irreversible, respectively, but the oxidation of Fe2+ is reversible at larger radius microdisk electrodes and quasi-reversible at smaller radius microdisk electrodes. The application of the Log-Plot to the voltammograms yielded a straight line, its slope allows us to evaluate the charge transfer coefficient and the intercept gives values of the electron transfer rate constant.
Dan Shu - One of the best experts on this subject based on the ideXlab platform.
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A simple mathematical formula for stoichiometry quantification of viral and nanobioLogical assemblage using slopes of Log/Log Plot curves
Journal of Virological Methods, 2004Co-Authors: Dan Shu, Lisa Huang, Peixuan GuoAbstract:In nanotechnoLogy, biomolecular assemblies serve not only as model systems for the construction of nanodevices, but they can also be used directly as templates for the formation of nanostructures. BioLogical nano-building blocks can either be isolated as complete functional units from living cells or viruses (bioLogical “Top down” approach) or formed by biomolecular assembly from recombinant or synthetic components (“Bottom up” approach). In both cases, rational design of nanostructures requires knowledge of the stoichiometry of the bioLogical structures, which frequently occur as multimers, i.e., the morphoLogical complex is composed of multiple copies of one or more macromolecules. In this paper, a method is described for the stoichiometric quantification of molecules in bio-nanostructures. The method is based on using dilution factors and relative concentrations rather than absolute quantities, which are often difficult to determine, especially in short-lived assembly intermediates. The approach exploits the fact that the larger the stoichiometry of the component is, the more dramatic is the influence of the dilution factor (decrease in concentration) on the reaction. We established and used the method to determine the stoichiometry of components of bacterial virus phi29. The Log of dilution factors was Plotted against the Log of reaction yield. The stoichiometry Z was determined with the equation Z=−1.58+2.4193T−0.001746T2 [T ∈ (0,1000), or ∠α ∈ (0°, 89.9°)], where T is the slope of the curve (tangent of ∠α, which is the angle between the x-axis and the concentration dependent curve). Z can also be determined from a standard table given in this report. With the bacteriophage phi29 in vitro assembly system, up to 5×108 infectious virions per ml can be assembled from 11 purified components, giving our method a sensitivity of nine orders of magnitude. We confirmed the stoichiometries of phi29 components that were determined previously with microscopic approaches. The described method also responded to programmed stoichiometry changes, which were generated by assembling the phi29 DNA packaging motor from modified pRNA (DNA-packaging RNA) molecules forming a trimer of dimers or a dimer of trimers, instead of the wild-type hexamer.
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a simple mathematical formula for stoichiometry quantification of viral and nanobioLogical assemblage using slopes of Log Log Plot curves
Journal of Virological Methods, 2004Co-Authors: Dan Shu, Lisa Huang, Peixuan GuoAbstract:In nanotechnoLogy, biomolecular assemblies serve not only as model systems for the construction of nanodevices, but they can also be used directly as templates for the formation of nanostructures. BioLogical nano-building blocks can either be isolated as complete functional units from living cells or viruses (bioLogical “Top down” approach) or formed by biomolecular assembly from recombinant or synthetic components (“Bottom up” approach). In both cases, rational design of nanostructures requires knowledge of the stoichiometry of the bioLogical structures, which frequently occur as multimers, i.e., the morphoLogical complex is composed of multiple copies of one or more macromolecules. In this paper, a method is described for the stoichiometric quantification of molecules in bio-nanostructures. The method is based on using dilution factors and relative concentrations rather than absolute quantities, which are often difficult to determine, especially in short-lived assembly intermediates. The approach exploits the fact that the larger the stoichiometry of the component is, the more dramatic is the influence of the dilution factor (decrease in concentration) on the reaction. We established and used the method to determine the stoichiometry of components of bacterial virus phi29. The Log of dilution factors was Plotted against the Log of reaction yield. The stoichiometry Z was determined with the equation Z=−1.58+2.4193T−0.001746T2 [T ∈ (0,1000), or ∠α ∈ (0°, 89.9°)], where T is the slope of the curve (tangent of ∠α, which is the angle between the x-axis and the concentration dependent curve). Z can also be determined from a standard table given in this report. With the bacteriophage phi29 in vitro assembly system, up to 5×108 infectious virions per ml can be assembled from 11 purified components, giving our method a sensitivity of nine orders of magnitude. We confirmed the stoichiometries of phi29 components that were determined previously with microscopic approaches. The described method also responded to programmed stoichiometry changes, which were generated by assembling the phi29 DNA packaging motor from modified pRNA (DNA-packaging RNA) molecules forming a trimer of dimers or a dimer of trimers, instead of the wild-type hexamer.
Marcel Ausloos - One of the best experts on this subject based on the ideXlab platform.
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Toward fits to scaling-like data, but with inflection points & generalized Lavalette function
2014Co-Authors: Marcel AusloosAbstract:Experimental and empirical data are often analyzed on Log-Log Plots in order to find some scaling argument for the observed/examined phenomenon at hands, in particular for rank-size rule research, but also in critical phenomena in thermodynamics, and in fractal geometry. The fit to a straight line on such Plots is not always satisfactory. Deviations occur at low, intermediate and high regimes along the Log(x)-axis. Several improvements of the mere power law fit are discussed, in particular through a Mandelbrot trick at low rank and a Lavalette power law cut-off at high rank. In so doing, the number of free parameters increases. Their meaning is discussed, up to the 5 parameter free super-generalized Lavalette law and the 7-parameter free hyper-generalized Lavalette law. It is emphasized that the interest of the basic 2-parameter free Lavalette law and the subsequent generalizations resides in its ”noid” (or sigmoid, depending on the sign of the exponents) form on a semi-Log Plot; something incapable to be found in other empirical law, like the Zipf-Pareto-Mandelbrot law. It remained for completeness to invent a simple law showing an inflection point on a Log-Log Plot. Such a law can result from a transformation of the Lavalette law through x → Log(x), but this meaning is theoretically unclear. However, a simple linear combination of two basic Lavalette law is shown to provide the requested feature. Generalizations taking 1 ar X iv :1 40 4. 36 05 v1 [ ph ys ic s. da ta -a n] 1 1 A pr 2 01 4 into account two super-generalized or hyper-generalized Lavalette laws are suggested, but need to be fully considered at fit time on appropriate data.
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Toward fits to scaling-like data, but with inflection points & generalized Lavalette function
arXiv: Data Analysis Statistics and Probability, 2014Co-Authors: Marcel AusloosAbstract:Experimental and empirical data are often analyzed on Log-Log Plots in order to find some scaling argument for the observed/examined phenomenon at hands, in particular for rank-size rule research, but also in critical phenomena in thermodynamics, and in fractal geometry. The fit to a straight line on such Plots is not always satisfactory. Deviations occur at low, intermediate and high regimes along the Log($x$)-axis. Several improvements of the mere power law fit are discussed, in particular through a Mandelbrot trick at low rank and a Lavalette power law cut-off at high rank. In so doing, the number of free parameters increases. Their meaning is discussed, up to the 5 parameter free super-generalized Lavalette law and the 7-parameter free hyper-generalized Lavalette law. It is emphasized that the interest of the basic 2-parameter free Lavalette law and the subsequent generalizations resides in its "noid" (or sigmoid, depending on the sign of the exponents) form on a semi-Log Plot; something incapable to be found in other empirical law, like the Zipf-Pareto-Mandelbrot law. It remained for completeness to invent a simple law showing an inflection point on a \underline{Log-Log Plot}. Such a law can result from a transformation of the Lavalette law through $x$ $\rightarrow$ Log($x$), but this meaning is theoretically unclear. However, a simple linear combination of two basic Lavalette law is shown to provide the requested feature. Generalizations taking into account two super-generalized or hyper-generalized Lavalette laws are suggested, but need to be fully considered at fit time on appropriate data.
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generalized m k zipf law for fractional brownian motion like time series with or without effect of an additional linear trend
International Journal of Modern Physics C, 2003Co-Authors: Philippe Bronlet, Marcel AusloosAbstract:We have translated fractional Brownian motion (FBM) signals into a text based on two "letters", as if the signal fluctuations correspond to a constant stepsize random walk. We have applied the Zipf method to extract the ζ′ exponent relating the word frequency and its rank on a Log–Log Plot. We have studied the variation of the Zipf exponent(s) giving the relationship between the frequency of occurrence of words of lengthm
Lisa Huang - One of the best experts on this subject based on the ideXlab platform.
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A simple mathematical formula for stoichiometry quantification of viral and nanobioLogical assemblage using slopes of Log/Log Plot curves
Journal of Virological Methods, 2004Co-Authors: Dan Shu, Lisa Huang, Peixuan GuoAbstract:In nanotechnoLogy, biomolecular assemblies serve not only as model systems for the construction of nanodevices, but they can also be used directly as templates for the formation of nanostructures. BioLogical nano-building blocks can either be isolated as complete functional units from living cells or viruses (bioLogical “Top down” approach) or formed by biomolecular assembly from recombinant or synthetic components (“Bottom up” approach). In both cases, rational design of nanostructures requires knowledge of the stoichiometry of the bioLogical structures, which frequently occur as multimers, i.e., the morphoLogical complex is composed of multiple copies of one or more macromolecules. In this paper, a method is described for the stoichiometric quantification of molecules in bio-nanostructures. The method is based on using dilution factors and relative concentrations rather than absolute quantities, which are often difficult to determine, especially in short-lived assembly intermediates. The approach exploits the fact that the larger the stoichiometry of the component is, the more dramatic is the influence of the dilution factor (decrease in concentration) on the reaction. We established and used the method to determine the stoichiometry of components of bacterial virus phi29. The Log of dilution factors was Plotted against the Log of reaction yield. The stoichiometry Z was determined with the equation Z=−1.58+2.4193T−0.001746T2 [T ∈ (0,1000), or ∠α ∈ (0°, 89.9°)], where T is the slope of the curve (tangent of ∠α, which is the angle between the x-axis and the concentration dependent curve). Z can also be determined from a standard table given in this report. With the bacteriophage phi29 in vitro assembly system, up to 5×108 infectious virions per ml can be assembled from 11 purified components, giving our method a sensitivity of nine orders of magnitude. We confirmed the stoichiometries of phi29 components that were determined previously with microscopic approaches. The described method also responded to programmed stoichiometry changes, which were generated by assembling the phi29 DNA packaging motor from modified pRNA (DNA-packaging RNA) molecules forming a trimer of dimers or a dimer of trimers, instead of the wild-type hexamer.
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a simple mathematical formula for stoichiometry quantification of viral and nanobioLogical assemblage using slopes of Log Log Plot curves
Journal of Virological Methods, 2004Co-Authors: Dan Shu, Lisa Huang, Peixuan GuoAbstract:In nanotechnoLogy, biomolecular assemblies serve not only as model systems for the construction of nanodevices, but they can also be used directly as templates for the formation of nanostructures. BioLogical nano-building blocks can either be isolated as complete functional units from living cells or viruses (bioLogical “Top down” approach) or formed by biomolecular assembly from recombinant or synthetic components (“Bottom up” approach). In both cases, rational design of nanostructures requires knowledge of the stoichiometry of the bioLogical structures, which frequently occur as multimers, i.e., the morphoLogical complex is composed of multiple copies of one or more macromolecules. In this paper, a method is described for the stoichiometric quantification of molecules in bio-nanostructures. The method is based on using dilution factors and relative concentrations rather than absolute quantities, which are often difficult to determine, especially in short-lived assembly intermediates. The approach exploits the fact that the larger the stoichiometry of the component is, the more dramatic is the influence of the dilution factor (decrease in concentration) on the reaction. We established and used the method to determine the stoichiometry of components of bacterial virus phi29. The Log of dilution factors was Plotted against the Log of reaction yield. The stoichiometry Z was determined with the equation Z=−1.58+2.4193T−0.001746T2 [T ∈ (0,1000), or ∠α ∈ (0°, 89.9°)], where T is the slope of the curve (tangent of ∠α, which is the angle between the x-axis and the concentration dependent curve). Z can also be determined from a standard table given in this report. With the bacteriophage phi29 in vitro assembly system, up to 5×108 infectious virions per ml can be assembled from 11 purified components, giving our method a sensitivity of nine orders of magnitude. We confirmed the stoichiometries of phi29 components that were determined previously with microscopic approaches. The described method also responded to programmed stoichiometry changes, which were generated by assembling the phi29 DNA packaging motor from modified pRNA (DNA-packaging RNA) molecules forming a trimer of dimers or a dimer of trimers, instead of the wild-type hexamer.
