8885ac05157-1898/12/038:55 AM Page161mac78mac78:385p Protein function 161 1.0 1.0 00.5 0.5 (arbitrary units) (b) pO2(kPa) FIGURE 5-4 Graphical representations of ligand binding. The frac- or Kd. The curve has a horizontal asymptote at 0=1 and a vertical tion of ligand-binding sites occupied, e, is plotted against the con- asymptote (not shown)at [L]=-1/Ka (b)A curve describing the bind centration of free ligand. Both curves are rectangular hyperbolas. ing of oxygen to myoglobin. The partial pressure of O2 in the air above (a)A hypothetical binding curve for a ligand L. The [L] at which half the solution is expressed in kilopascals(kPa). Oxygen binds tightly to of the available ligand-binding sites are occupied is equivalent to 1/K. myoglobin, with a Pso of only 0.26 kPa a lower value of Kd corresponds to a higher affinity of As for any ligand, Ka is equal to the [oa] at which half igand for the protein. The mathematics can be reduced of the available ligand-binding sites are occupied, or to simple statements: Kd is equivalent to the molar con- [O.s. Equation 5-9 thus becomes centration of ligand at which half of the available ligand binding sites are occupied. At this point, the protein is (5-10) said to have reached half-saturation with respect to lig. nd binding. The more tightly a protein binds a ligand, In experiments using oxygen as a ligand, it is the par the lower the concentration of ligand required for half tial pressure of oxygen in the gas phase above the the binding sites to be occupied, and thus the lower the solution, pO,, that is varied, because this is easier to value of Kd. Some representative dissociation constants measure than the concentration of oxygen dissolved in are given in Table 5-1 the solution The concentration of a volatile substance The binding of oxygen to myoglobin follows the pat in solution is always proportional to the local partial terns discussed above. However, because oxygen is a pressure of the gas. So, if we define the partial pressure gas, we must make some minor adjustments to the equa- of oxygen at [ojO.s as Pso, substitution in Equation 5-10 tions so that laboratory experiments can be carried out gives more conveniently. We first substitute the concentration 02 of dissolved oxygen for L in Equation 5-8 to give (5-11) a binding curve for myoglobin that relates e to pOe is shown in Figure 5-4b TABLE 5-1 Some Protein Dissociation Constants Prote Ligand Kd(M) Avidin(egg white Biotin 1×10 Insulin receptor(human) Insulin 1×10 gp41(HIV-1 surface protein) 4 Nickel-binding protein(E. co) 1×10-7 3×10-6 rticular solution cond tions under which it was measured. Ke values for a protein-ligand interaction I be altered, sometimes by several orders of magnitude, by changes in the solutions salt concentration, pH, or other variables. ' interaction of avidin with biotin, an enzyme cofactor, is among the strongest noncovalent biochemical interactions known. "This immunoglobulin w and the K repo should not be considered characteristic of all immunoglobulins Calmodulin has four binding sites for calum. The values shown reflect the highest- and lowest-affinity bind ng sites observed in one set of measurements.a lower value of Kd corresponds to a higher affinity of ligand for the protein. The mathematics can be reduced to simple statements: Kd is equivalent to the molar con￾centration of ligand at which half of the available ligand￾binding sites are occupied. At this point, the protein is said to have reached half-saturation with respect to lig￾and binding. The more tightly a protein binds a ligand, the lower the concentration of ligand required for half the binding sites to be occupied, and thus the lower the value of Kd. Some representative dissociation constants are given in Table 5–1. The binding of oxygen to myoglobin follows the pat￾terns discussed above. However, because oxygen is a gas, we must make some minor adjustments to the equa￾tions so that laboratory experiments can be carried out more conveniently. We first substitute the concentration of dissolved oxygen for [L] in Equation 5–8 to give [O2 [ ] O
2] Kd (5–9) As for any ligand, Kd is equal to the [O2] at which half of the available ligand-binding sites are occupied, or [O2]0.5. Equation 5–9 thus becomes [O2]
[O [ 2 O ]  2]0.5 (5–10) In experiments using oxygen as a ligand, it is the par￾tial pressure of oxygen in the gas phase above the solution, pO2, that is varied, because this is easier to measure than the concentration of oxygen dissolved in the solution. The concentration of a volatile substance in solution is always proportional to the local partial pressure of the gas. So, if we define the partial pressure of oxygen at [O2]0.5 as P50, substitution in Equation 5–10 gives pO2 pO
2 P50 (5–11) A binding curve for myoglobin that relates to pO2 is shown in Figure 5–4b. Chapter 5 Protein Function 161 1.0 0.5 0 v P50 5 10 (b) pO2 (kPa) 1.0 0.5 0 v 5 (a) Kd 10 [L] (arbitrary units) FIGURE 5–4 Graphical representations of ligand binding. The frac￾tion of ligand-binding sites occupied, , is plotted against the con￾centration of free ligand. Both curves are rectangular hyperbolas. (a) A hypothetical binding curve for a ligand L. The [L] at which half of the available ligand-binding sites are occupied is equivalent to 1/Ka, or Kd. The curve has a horizontal asymptote at 1 and a vertical asymptote (not shown) at [L] 1/Ka. (b) A curve describing the bind￾ing of oxygen to myoglobin. The partial pressure of O2 in the air above the solution is expressed in kilopascals (kPa). Oxygen binds tightly to myoglobin, with a P50 of only 0.26 kPa. TABLE 5–1 Some Protein Dissociation Constants Protein Ligand Kd (M)* Avidin (egg white)† Biotin 1  1015 Insulin receptor (human) Insulin 1  1010 Anti-HIV immunoglobulin (human)‡ gp41 (HIV-1 surface protein) 4  1010 Nickel-binding protein (E. coli) Ni2
1  107 Calmodulin (rat)§ Ca2
3  106 2  105 *A reported dissociation constant is valid only for the particular solution conditions under which it was measured. Kd values for a protein-ligand interaction can be altered, sometimes by several orders of magnitude, by changes in the solution’s salt concentration, pH, or other variables. † Interaction of avidin with biotin, an enzyme cofactor, is among the strongest noncovalent biochemical interactions known. ‡ This immunoglobulin was isolated as part of an effort to develop a vaccine against HIV. Immunoglobulins (described later in the chapter) are highly variable, and the Kd reported here should not be considered characteristic of all immunoglobulins. § Calmodulin has four binding sites for calcium. The values shown reflect the highest- and lowest-affinity binding sites observed in one set of measurements. 8885d_c05_157-189 8/12/03 8:55 AM Page 161 mac78 mac78:385_REB: