This behavior where the binding of one molecule

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This behavior, where the binding of one molecule influences the binding of successive molecules of the same kind, is referred to as a homotropic allosteric * Many authors use the symbcl P so (corresponding to 50% saturation) for P'/2.
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(A) 100 cr> 80 C 0 .1ij 60 :; os (f) "g 40 0 20 ............ ......... ...•• ····~~~-cooperative / .... f'- - - - - - - .................. :: .. :.:.;.: ... = ... = ... _-- 175 (B) log_8- 1 - 8 __ ~ __ ~'--_ 0 __ +_/_/I'CC 1 _ O _ 9 _ P _(_O_2) ... lor log P 1 (02) / 2 //'" high affinity '1 form ! slope n max (C) d[l09~] n = d[log P(02)] Figure 4.4 Cooperative and non-cooperative binding of dioxygen: 9 (A) Binding curves; (B) Hill plot of binding curves; (C) First derivative (slope) of the Hill plots.
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176 saturated unsaturated weight = 1 1 or 3 molecules of 02 bound weight = 4 2 molecules of 02 bound weight = 6 Figure 4.5 Diagram of tetrameric hemoglobin, showing statistical weights of different saturations (see text). interaction. A heterotropic allosteric interaction occurs when the interaction with the protein of a second unlike molecule, for instance, an organic polyphosphate for human hemoglobins, influences the binding of the first molecule (e.g., diox- ygen). Such molecules are often termed allosteric effectors. A commonly ob- served heterotropic allosteric interaction is the Bohr effect, named after the biol- ogist Christian Bohr, father of physicist Niels Bohr. This effect, which relates the change in partial pressure of O 2 to a change in pH at constant saturation of binding sites (0), is related thermodynamically to the Haldane effect, which relates the number of protons released (# H +) with a change in 0 at constant pH (Equation 4.13). A very large Bohr effect, where O 2 affinity decreases sharply with pH, is often called the Root effect. 25a It is physiologically important for
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I. INTRODUCTION: BIOLOGICAL DIOXYGEN TRANSPORT SYSTEMS 177 fish such as trout, probably in maintaining buoyancy, but its molecular basis in trout hemoglobin IV remains to be discovered. 25b (4.13) The degree of cooperativity can be characterized in a number of ways. By means of a Hill plot of log (O/(l - 0)) versus log (P(02)), the limiting slopes (which should be unity) at high O 2 pressure and low O 2 pressure may be extrapolated as shown in Figure 4.4B to log «(}/(l 0)) = 0, where 0 = 0.5. Two limiting values for PI/ 2 (02) are obtained, one characterizing the regime of high partial pressure of dioxygen, where the O 2 affinity is high (for the case illustrated of positive cooperativity). The other PI/2(02) value characterizes the regime of low partial pressure of dioxygen, where affinity is relatively low. This difference in affinities can be converted into a difference between the free-energy change upon O 2 binding in the low-affinity state (K/ ) and the high-affinity state (K/) [the designations T and R will be described in subsection d]: - RTIn (K/ /K/). (4.14) 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 or O/(l - 0) log (O/(l - 0)) K p pn(02) -log (P 1/2(0 2 )) + n log (P(02))' (4.15) The Hill coefficient (n) is an empirical coefficient that has a value of unity for non-cooperative binding, where Equation (4.15) reduces to the Langmuir iso- therm, Equation (4.12). Any number greater than unity indicates positive coop-
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