Hanes Method

Hanes Method.7 A different rearrangement of the Michaelis-Menten equation yields the form that is used in the Hanes plot  

In the Hanes plot (Fig. 2.8), [S]/v (as v) is plotted against [S], yielding a slope of 1/ max and a y intercept of Km/Vmax following linear regression. The parameter Km is then calculated as the y intercept divided by the slope. 

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Singapore) was obtained for estimates Vmax and Km of free lipase reaction and and K p and for immobilised lipase reaction. Hanes-Woolf and Simplex methods were used for the evaluation of kinetic parameters owing to their strength in error handling when experimental data are subject to random errors.5... 

Methods of plotting data obtained from enzyme catalyzed reactions, (a) Lineweaver-Burk plot, (b) Eadie or Hofstee plot, (c) Hanes plot. 

The Systematic Approach. The systematic approach for deriving rate equations was first devised by Fromm based on certain concepts advanced by Volkenstein and Goldstein. Its underlying principles, however, are more akin to the graphic method of King and Altman. The procedure to be described here is a modified method that includes the contributions from the aforementioned workers and from Wong and Hanes. ... 

See Double-Reciprocal Plot Hanes Plot Direct Linear Plot Dixon Plot Dixon-Webb Plot Eadie-Hofstee Plot Substrate Concentration Range Frieden Protocol Fromm Protocol Point-of-Convergence Method Dal-ziel Phi Relationships Scatchard Plots Hill Plots... 

A linear graphical method for analyzing the initial rate kinetics of enzyme-catalyzed reactions. In the Hanes plot, [A]/v is plotted as a function of [A], where v is the initial rate and [A] is the substrate concentration ". ... 

Also referred to as the Hanes-Hultin plot and the Hanes-Woolf (or, Woolf-Hanes) plot, the method is based on a transformation of the Michaelis-Menten equation i.e., the expression for the Uni Uni mechanism) [A]/v = (i a/ max) + ([A]/Umax) whcrc U ax IS the maximum forward velocity and is the Michaelis constant for A. In the Hanes plot, the slope of the line is numerically equal to Umax, the vertical intercept is equivalent to, ... 

There are well-established methods for obtaining the type of inhibition and the value of the inhibition constants from initial-rate kinetics, often from linearized plots such as lineweaver-Burk, Eadie-Hofstee, or Hanes. As these procedures are covered very well by a range of basic textbooks on biochemistry and kinetics (see the list of Suggested Further Reading ) we will not repeat these procedures here. Instead, we will discuss the situation in which an enzyme reaction is followed over more than just the initial range of conversion. Towards this end, the rate equation,... 

The problems associated with the separation of phosphate esters are the tendency of the spots to diffuse difficulty of reproducing RF values variability of RF values with complexity of the mixture being resolved and distance of solvent travel proper purification and equilibration of the filter paper effect of inorganic ions in natural mixtures and the choice of suitable solvent mixtures for desired separations. The problem of detecting the separated spots is somewhat simpler. In addition to methods applicable to the detection of reducing sugars (e.g., use of aniline salts fructose esters are detected by naphthoresorcinol-acid), methods depending on phosphomolybdate formation are most commonly used. Hanes and Isher-... 

The specific activity of the activated wild-type tyrosinase towards L-tyrosine monooxygenation, as determined by the HPLC method, was 1.69 katal/ kg of protein. A Km of 0.82 mM and a cat of 23.6 s 1 for L-tyrosine mono-oxygenation were calculated from Hanes-Woolf plots. 

ScHAEPITZEL, C., HaNES, J., JeRMUTUS, L., Pluckthun, A. (1999). Ribosome display an in vitro method for selection and evolution of antibodies from libraries. 

Flammobility Limits of Methanol-Air Mixtures The Effect of Water Vapor On, is discussed by K. Dvor A. Reiser in ChemListy 49, 467-72(1955) CA 49, 9927(1955) (A static app suitable for liquid foels is described. Results for water-me(hane-air mixts are ven. A simple correlation method on (he basis of heat balances is attempted)... 

Four graphical methods may be used to establish Km and Vjn ,x values under given experimental conditions, called the Eadie-Hofstee, Hanes, Lineweaver-Burk, and Cornish-Bowden-Eisenthal methods. All four involve the measurement of initial rates of reaction as a function of initial substrate concentration, at constant enzyme concentration. 

A plot of v (as y) against v/[S] (as x) will yield, after linear regression, a y intercept of Emax and a slope of A nl (Fig. 2.7). This plot is the preferred linear regression method for determining Km and V/ln ix, since precision and accuracy are somewhat better than those obtained using the Hanes plot, and much better than those found using the Lineweaver-Burk method. 

Koenigs-Knorr conditions. More recent work Indicates, however, that the silver triflate method of Hanes-sian may well have eclipsed earlier procedures. Thus the coupling of with the 4-deoxydaunosamine derivative 110(1.1 equiv) under the agency of CF3S03Ag provides the corresponding a-glycoslde in 70% yleld. Similarly, reaction of 111 (a-Cl anomer)... 

Another method to obtain estimates for Km and is the rearrangement of the Michaelis-Menten equation to a linear form. The estimation for the initial velocities, Vo, from progress curves is not a particularly reliable method. A better way to estimate Vn is by the integrated Michaelis-Menten equation (Cornish-Bowden, 1975). Nevertheless, the graphical methods are popular among enzymolo-gists. The three most common linear transformations of the Michaelis-Menten equation are the Lineweaver-Burk plot of 1/Vo vs. 1/[S] (sometimes called the double-reciprocal plot), the Eadie-Hofstee plot, i.e. v vs. vo/[S], and the Hanes plot, i.e., [SJ/vo vs. [S] (Fig. 9.3). 

Despite their appealing simplicity, these methods have serious limitations. The Lineweaver-Burk and Hanes plots are unreliable, e.g., the variation of the variance almost certainly results in an incorrect weighting, whereas in the Eadie-Hofstee plot Vo is present in both variables. The direct linear plot of Eisenthal and Cornish-Bowden (1974), for which the Michaelis-Menten equation is rearranged to relate to A , i.e., = Vo -f- Vo A ,/[S] is very simple but... 

The unweighted Lineweaver-Burk and Hanes plots yield different answers even though they analyze the same data set. On the other hand, when we use appropriate global weighting factors, both methods yield identical results, as they should. Need we say more about the importance of proper weight-... 

Fig. 3.5 Spreadsheet for the analysis of the data on the kinetics of nicotinamide mononucleotide adenyl transferase by Atkinson etal, Biochem.J. 80 (1961) 318. The results should be read as, e.g., on line 30 K = 0.4406 0.0906 for the unweighted Lineweaver-Burk method, K = 0.5821 0.0522 for the unweighted Hanes plot, or, on line31, vm = 0.5853 0.1039 for Lineweaver-Burk, vm= 0.6848 0.0383 forHanes.

In the context of the analysis of enzyme kinetics it is sometimes stated that one should always use a non-linear least-squares method for such data, because the usual, unweighted least-squares fits depend on the particular analysis method (Lineweaver-Burk, Hanes, etc.) used. We have seen in section 3.5 that the latter part of this statement is correct. But how about the former ... 

M. Seko, Y. Yamagoshi, K. Miyauchi, M. Fukumoto, I. Watanabe, K. Kimoto, T. Hane and S. Tsushima, Membrane composite for preparation of cation exchange membrane, Jpn. Pat. JP 56-37247 (examined application) Cation exchange membrane, Jpn. Pat. JP 56-18605 (examined application) Preparation method of fluorocarbon cation exchange membrane, Jpn. Pat. JP 56-3 7248 (examined application). 

Another way of converting the Michaelis-Menten equation in the form of eq. (6.17) to give the equation of a straight line is the method of Hanes-Woolf... 

Thus, plotting the reciprocal value of the rate vs 1/c, the values of the constants can be obtained (see 6.1). Several other methods are often used in enzymatic kinetics, like the Eadie-Hoftsee and Hanes-Woolf methods. Similarly, in the case of heterogeneous catalytic reactions, if the rate is given for instance by eq. (10.15) after rearrangement... 

Bourne, E. J. See also. Barker, S. A. Bouveng, H. O., and Lindberg, B., Methods in Structural Polysaccharide Chemistry, 15, 53-89 Brady, Robert F., Jr., Cyclic Acetals of Ketoses, 26, 197-278 Bray, H. G., D-Clucuronic Acid in Metabolism, 8, 251-275 Bray, H. G., and Stacey, M., Blood Group Polysaccharides, 4, 37-55 Brimacombe, j. S. See How, M. J. Butter worth, Roger F and Hanes-siAN, Stephen, Tables of the Properties of Deoxy Sugars and Their Simple Derivatives, 26, 279-296... 

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