Hill equation/plot

Linked-function mechanisms for cooperative binding interaction of metabolites and/or drugs, based on the presence of two or more different conformational states of the protein or receptor. See Adair Equation Cooperative Ligand Binding Hemoglobin Hill Equation Plot Koshland-Nemethy-Filmer Model Monod-Wyman-Changeux Model Negative Cooperativity Positive Cooperativity... 

HILL EQUATION PLOT ALLOSE KINASE ALLOSTERY... 

ADAIR EQUATION COOPERATIVE LIGAND BINDING HILL EQUATION PLOT KOSHLAND-NEMETHY-EILMER MODEL MONOD-WYMAN-CHANCEUX MODEL NEGATIVE COOPERATIVITY POSITIVE COOPERATIVITY HEMOGLOBIN ALLOTOPIC EFFECT Allowed electronic transitions,... 

Theoretical curves, (a) Using the Hill equation, plot an oxygenbinding curve for a hypothetical two-subunit Iiemoglobin with n = 1,8 and P ) 10 torr. (b) Repeal by using the concerted model with n — 2, L = 1000, c = 0.01, and — 1 torr. 

The linear form of this equation is denoted hy the Lineweaver-Burk or double reciprocal plot, which is derived from the Michaelis-Menten and Hill equation and is denoted as ... 

HILL EQUATION AND PLOT COOPERATMTY ALLOSTERISM HYSTERESIS... 

LINKED FUNCTIONS SCATCHARD PLOT HILL EQUATION AND PLOT Ligand binding,... 

SCATCHARD PLOT KLOTZ PLOT ALLOSTERISM COOPERATIVITY HILL EQUATION AND PLOT WOMACK-COLOWICK DIALYSIS METHOD... 

Figure 8. Two routes to ultrasensitivity. A, Cooperativity generates an ultrasensitive dose-response curve. Plots were generated for the Hill equation, y = x / ( C + x"), for C = 20 for n = 1, 2 and 3. B, An exponential function also generates an ultrasensitive dose-response curve. Plot was generated for the equation y = e / (e + e ) for C = 20.

It was noted earlier that Michaelis-Menten kinetics and its linear transformations are not valid for allosteric enzymes. Instead, the Hill equation, an equation originally empirically developed to describe the cooperative binding of Oz to hemoglobin (Chapter 7), is used. The expression describing such a straight-line plot is... 

Be able to derive and use the Hill equation and know the meaning of the Hill coefficient P and the Hill plot. 

This result is in a qualitative agreement with the experimental t-plot of Ar adsorption at 87 K on MCM 41 samples (see Figure 2(b)) using the data given in reference [13], As for simulation data, we assume that the density of the adsorbate equals that of the 3D-liquid and we have determined the thickness of the adsorbed film as the ratio of the adsorbed volume with the surface of the sample. Assuming pores of MCM 41 are cylinders, the specific surface S of each sample was determined via the relation between the porous volume V (given by the adsorbed amount after capillary condensation) and the diameter d of the pores S = 4V/d. Comparison of the different t-curves indicates that there is a pore size (5.1 nm) above which no confinement effect occurs on multilayer adsorption. Below this value, the thickness of the adsorbed film increases as the pore diameter decreases, t-curves are often analysed with the Frenkel-Halsey-Hill equation [14] /n... 

Figure 13.3a shows a plot of the rate of packaging as a function of the ATP concentration under a constant force of 5pN. This data is well described by the characteristic Michaelis-Menten behavior with a Pmax 100 bp s and a Km 30 gM. Interestingly, the fit, done to a Michaelis-Menten-Hill equation reveals a Hill coefficient n I, indicating that the binding of the ATP to the motor is not cooperative. These same studies revealed that ADP is a competitive inhibitor of the motor and that phosphate release should be a nearly irreversible step [55], as its concentration in solution can be varied three orders of magnitude without affecting the rate of the motor. 

THE HILL PLOT-LOGARITHMIC FORM OF THE HILL EQUATION... 

Equation (7.8) is known as the Hill equation. A plot of log(T/l — Y) versus log P02 yields a straight line with a slope of 1 (the Hill coefficient) (Figure 7-10). Thus, a value... 

The plot of log[Y/(l - Y)] versus log[L] is linear (Fig. 9.3) with a slope of n. The all-or-none binding assumes extreme cooperativity in ligand binding. Under such conditions n should equal the number of sites within the protein. Few proteins exhibit extreme cooperativity. Therefore, the value for n is usually less than the number of sites but, when positive cooperativity occurs, n is greater than 1. In the case of negative cooperativity n is less than 1. An n value of 1 reduces the fractional saturation for the Hill equation (Equation 9.7) to that of simple ligand binding (Equation 9.4). 

A second way to characterize cooperativity involves fitting the oxygen-binding data at intermediate saturation (0.2 < 0 < 0.8)—that is, about the inflection point in a Hill plot—to the Hill equation... 

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