BIOCHEMISTRY - L. Stryer - 1984

VOLUME 1

PART I. CONFORMATION AND DYNAMICS

CHAPTER 4. HEMOGLOBIN: AN ALLOSTERIC PROTEIN

4.2. Cooperativity of Oxygen Binding by Hemoglobin

The ratio of oxygen-occupied binding sites to the total number of sites represents the fraction of saturation, or simply the oxygen saturation of Hemoglobin, and is denoted by Y. The value of Y ranges from 0 (all sites empty) to 1 (all sites fully occupied). The graph of Y versus the partial pressure of oxygen, pO₂, is called the oxygen dissociation curve. The oxygen dissociation curves for hemoglobin and Myoglobin differ in two respects (Figs. 4.2 and 4.3). First, at any given pO₂, the saturation Y is higher for myoglobin than for hemoglobin. In other words, myoglobin has a higher affinity for O₂ than hemoglobin does. Oxygen affinity is characterized by the P₅₀ value, which is numerically equal to the oxygen partial pressure at which 50% of the binding sites are saturated (i.e., Y = 0.5). For myoglobin, P₅₀ is typically 1 torr, whereas for hemoglobin it is 26 torr.

Class="center">Fig. 4.2. Oxygen dissociation curves for Myoglobin and hemoglobin. The saturation of oxygen-binding sites is shown as a function of the partial pressure of oxygen in the surrounding solution.

Fig. 4.3. Oxygen dissociation curve for hemoglobin. The abscissa indicates pO₂ values characteristic of capillaries in active Muscle and of lung alveoli. Note that P50 for hemoglobin under physiological conditions lies between these two values.

Torr is a unit of pressure numerically equal to the pressure exerted by a mercury Column 1 mm high at 0°C under standard gravitational acceleration (1 mm Hg). It is named after Evangelista Torricelli (1608–1647), the inventor of the mercury barometer.

The second difference is that the oxygen dissociation curve is hyperbolic for myoglobin, whereas it is sigmoidal for hemoglobin. As discussed below, the sigmoidal shape of the curve is ideally suited to The Physiological Role of Hemoglobin as an oxygen carrier in the Blood. At THE MOLECULAR LEVEL, sigmoidal behavior means that oxygen binding by hemoglobin is cooperative—that is, the binding of oxygen to one heme facilitates its binding to the remaining ones.

Let us examine the oxygen dissociation curves quantitatively, starting with myoglobin as the simpler case. The binding of oxygen to myoglobin (Mb) is described

by the following equation:

MbO₂ ⇄ Mb + O₂. (1)

The Equilibrium Constant for the dissociation of oxymyoglobin is expressed as

where [MbO₂] is the concentration of oxymyoglobin, [Mb] is the concentration of deoxymyoglobin, and [O₂] is the concentration of free oxygen, all expressed in moles per liter. The fractional saturation Y is defined as

Substituting into equation (3) using the equality (2), we obtain

Since O₂ is a gas, it is more convenient to express its concentration in terms of pO₂, the partial pressure of oxygen (in torr) in the atmosphere surrounding the solution. Equation (4) then takes the following form:

Equation (5) is graphically represented by a hyperbola. Indeed, the oxygen dissociation curve calculated from equation (5) with a P₅₀ of 1 torr agrees well with the experimental curve obtained for myoglobin.

In contrast, the oxygen dissociation curve for hemoglobin is sigmoidal and does not match any curve described by equation (5). This indicates Cooperative binding of O₂ by the hemoglobin molecule. Let us consider the extreme case where only deoxyhemoglobin and hemoglobin (Hb) with 4 bound O₂ molecules are present:

Нb(O₂)₄ ⇄ Нb + 4O₂. (6)

The equilibrium constant for this hypothetical reaction is expressed as

(7)

and further

(8)

Graphically, equation (8) is represented by a sigmoidal curve (Fig. 4.4). It should be noted, however, that the calculated curve rises more steeply than the experimentally obtained curve. In other words, the process mechanism described by equation (6) is an extreme case.

Fig. 4.4. The hemoglobin-oxygen saturation curve lies between the dissociation curves calculated for n = 1 (noncooperative binding) and n = 4 (fully cooperative binding)

How, then, can we characterize the binding process with an intermediate degree of cooperativity? In 1913, Archibald Hill demonstrated that the curve plotted from data on oxygen binding by hemoglobin is described by an equation corresponding to the hypothetical process:

Нb(O₂) n ⇄ Нb + nO₂. (9)

The saturation Y in this case will be

(10)

After rearrangement, we obtain

(11)

The last equation shows that the ratio of oxyhemoglobin (Y) to deoxyhemoglobin (1 — Y) is equal to the ratio of pO₂ to P₅₀ raised to the n-th power. Taking the logarithm of this equation, we get:

(12)

It should be emphasized that the dependence of lg [Y/(1 — Y)] on lg pO₂ forms a straight line with a slope of n. Such a plot is called a Hill plot, and the slope value n at the oxygen half-saturation point (Y = 0.5) represents the Hill coefficient.

Myoglobin yields a linear Hill plot with n = 1.0, whereas hemoglobin has n = 2.8 (Fig. 4.5). A slope of 1.0 indicates that oxygen molecules bind to myoglobin independently of one another, as described in equation (1). On the other hand, a Hill coefficient of 2.8 points to Cooperative oxygen binding by hemoglobin. The binding of O₂ to one heme facilitates the attachment of oxygen to the other Hemes of the same tetramer, and conversely, the release of oxygen from one heme facilitates its release from the rest. In other words, there is interaction among the hemes within the hemoglobin molecule. The cooperativity of oxygen binding by hemoglobin is sometimes referred to as heme-heme interaction. We will discuss its mechanism below.

Fig. 4.5. Hill plots for oxygen binding by myoglobin and hemoglobin. A slope of 2.8 for hemoglobin indicates cooperative oxygen binding; myoglobin, by contrast, binds oxygen noncooperatively, as evidenced by a curve slope of 1.0