Cooperativity coefficient

Show that this enzyme is indeed allosteric determine its cooperativity coefficient (Hill coefficient). Is the cooperativity positive, or is it negative What is K Is K equal to Km If not, why not When is K = Km ... 

In Eqs. (51) and (52), a is comparable with a cooperative coefficient, representing the basic bonding constant. The values of A, B, a and ft are complied in Table 22. In the range of the chain lengths of these oligocations, the standard free energy change of complex formation decreases by about 0.6 kcal/mol upon the addition of one cationic residue. The difference of/3 (about 1.6 kcal/ mol) between two different types of cations may be due to the variation of the hydrophobidties between benzyl and methyl residues. 

In general, since the equilibrium constants will not be equal, Eq. (10) would not be expected to hold, but to preserve the simple form of the equation, Hill introduced a cooperativity coefficient nn to replace n, giving [95]... 

With regard to the role of nonlinear feedback control, periodic behaviour was illustrated in fig. 11.7 for a repression function characterized by a Hill coefficient of 4 however, a value of 2 or 1 for that cooperativity coefficient can also give rise to sustained oscillations. The cooperativity of repression provides a major source of nonlinearity required for sustained oscillatory behaviour. This is the reason why steep thresholds due to zero-order ultrasensitivity are not required here to generate limit cycle oscillations (see the relatively large values of the reduced Michaelis constants K, used in fig. 11.7), in contrast to the situation encountered for the phosphorylation-dephosphorylation cascade model analysed for the mitotic oscillator. 

A value of unity of n implies no cooperativity in binding. A value greater than unity indicates positive cooperativity, and vice versa. Calculated isotherms illustrate the trends for example, Jones (131,183), using the hypothetical case of a macromolecule with 50 binding sites and an assigned binding constant K of 10 constructed a family of isotherms corresponding to different values of the cooperativity coefficient n. (See Fig. 43.) The correlation between cooperativity and steepness of the isotherms is readily seen. 

Strkcttire inflkence. The specificity of interphase transfer in the micellar-extraction systems is the independent and cooperative influence of the substrate molecular structure - the first-order molecular connectivity indexes) and hydrophobicity (log P - the distribution coefficient value in the water-octanole system) on its distribution between the water and the surfactant-rich phases. The possibility of substrates distribution and their D-values prediction in the cloud point extraction systems using regressions, which consider the log P and values was shown. Here the specificity of the micellar extraction is determined by the appearance of the host-guest phenomenon at molecular level and the high level of stmctural organization of the micellar phase itself. 

On the basis of data obtained the possibility of substrates distribution and their D-values prediction using the regressions which consider the hydrophobicity and stmcture of amines was investigated. The hydrophobicity of amines was estimated by the distribution coefficient value in the water-octanole system (Ig P). The molecular structure of aromatic amines was characterized by the first-order molecular connectivity indexes ( x)- H was shown the independent and cooperative influence of the Ig P and parameters of amines on their distribution. Evidently, this fact demonstrates the host-guest phenomenon which is inherent to the organized media. The obtained in the research data were used for optimization of the conditions of micellar-extraction preconcentrating of metal ions with amines into the NS-rich phase with the following determination by atomic-absorption method. 

From the molecular point of view, the self-diffusion coefficient is more important than the mutual diffusion coefficient, because the different self-diffusion coefficients give a more detailed description of the single chemical species than the mutual diffusion coefficient, which characterizes the system with only one coefficient. Owing to its cooperative nature, a theoretical description of mutual diffusion is expected to be more complex than one of self-diffusion [5]. Besides that, self-diffusion measurements are determinable in pure ionic liquids, while mutual diffusion measurements require mixtures of liquids. 

Figure 12-461, Part 1. Impeller geometry versus flow coefficient, dimensionless to define the flow-handling capability of a specific impeller (wheel) geometry, < = 0/(tt/4)(DA). (Used by permission Fullemann, J., Technical Report Centrifugal Compressors, 1963. Cooper Energy Services, Cooper-Cameron Corporation. All rights reserved.)...

This model also can accommodate dose-response curve having Hill coefficients different from unity. This can occur if the stimulus-response coupling mechanism has inherent cooperativity. A general procedure can be used to change any receptor model into a variable slope operational function. This is done by passing the receptor stimulus through a forcing function. 

The operational model allows simulation of cellular response from receptor activation. In some cases, there may be cooperative effects in the stimulus-response cascades translating activation of receptor to tissue response. This can cause the resulting concentration-response curve to have a Hill coefficient different from unity. In general, there is a standard method for doing this namely, reexpressing the receptor occupancy and/or activation expression (defined by the particular molecular model of receptor function) in terms of the operational model with Hill coefficient not equal to unity. The operational model utilizes the concentration of response-producing receptor as the substrate for a Michaelis-Menten type of reaction, given as... 

By using Hill s coefficient, it is possible to draw a conclusion about the character of the process and to determine ligand concentration in one cooperative unit. 

In spite of its wide application, the mechanisms of this reaction remain obscure. Many diverse arguments have been published since the reaction was first investigated in 1897 (Bl, C5, C9, F7, J6, M5, P9, R2, S5, W2, W4, Yl, Y4). Cooper et al. (C9) introduced this method as a yardstick for the measurement of volumetric mass-transfer coefficients in gas-liquid contacting. Karow et al. (Kl) later concluded that the sulfite oxidation is suitable for fermentation process scale-up studies. Cooper et al. established that the reaction proceeds at a rate independent of sulfite ion concentration over wide concentration ranges. In their work they considered the sulfite oxidation to be of zero order with respect to both sulfite and sulfate concentration. 

Cooper et al. (C9) were the first to determine mass-transfer coefficients by measuring the oxidation rate of sodium sulfite in an aqueous solution catalyzed by cupric ions. Their data were taken for a vaned-disk agitator with 16 blades and for a flat paddle. The ratio of agitator-to-tank diameter was 0.4, and the ratio of paddle to tank diameter was 0.25. The tank was equipped with four baffles, with baffle-width to tank diameter ratio of 0.1. 

In 1960, Yoshida et al. (Y4), working with a geometrically similar system and with the sulfite-oxidation method, confirmed the results reported by Cooper et al. They also showed that the gas film does not offer any resistance to the mass transfer of oxygen from air to the sodium sulfite solution. In addition, they found that the mass-transfer coefficient per unit area was equal for water and for aqueous sodium sulfite. 

A perfect cooperation between phases is the ideal for an optimum behaviour of the composite. A good indication of this cooperation is given, either by the adhesion coefficient A, as defined by the first version of the unfolding model, or by the exponent 2r defined by its second version. 

A linear form of the Hill equation is used to evaluate the cooperative substrate-binding kinetics exhibited by some multimeric enzymes. The slope n, the Hill coefficient, reflects the number, nature, and strength of the interactions of the substrate-binding sites. A... 

The summation for the coefficient of the P2 term likewise includes phase insensitive contributions where I m = Im, but also now one has terms for which I = I 2, which introduce a partial dependence on relative phase shifts— specifically on the cosine of the relative phase shift. Again, this conclusion has long been recognized for example, by an explicit factor cos(ri j — ri i) in one term of the Cooper-Zare formula for the photoelectron (3 parameter in a central potential model [43]. 

The Hill plot is log (B (Bnu>. - B)) vs. log [L], As noted earlier, the slope of the Hill plot (the Hill coefficient, H) is of particular utility. If the equation holds, a straight line of slope = 1 should be obtained. A value greater than 1 may indicate positive cooperativity, and a slope less than 1 either negative cooperativity or commonly the presence of sites with different affinities. The data of Problem 5.1 are also presented as a Hill plot in Figure 5.10. 

In Chapter 1 (Section 1.2.4.3), the Hill equation and the Hill coefficient, nH, are described. Hill coefficients greater than or less than unity are often interpreted as indicating positive or negative cooperativity, respectively, in the relationship between receptor occupancy and response. For example, positive cooperativity could arise due to amplification in a transduction mechanism mediated by G-proteins and changes in cell calcium concentration. 

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