3 If volume decreases, pressure will enhance it.
If reaction rates are expressed incorporating a pressure term, the equation looks like this:
(2.2)
where P is the pressure (atm), T is the absolute temperature (°K), R is the universal gas constant (82 cm3 atm °K−1 mol−1), KD is the rate constant at 1 atm, KP is the rate constant at P atm, and ∆V ‡ is the activation volume of the reaction; the change in system volume occurring during the rate‐limiting step of the reaction, in this case, the activation step.
What is the source of changes in volume in enzymatic reactions? First, consider the total reaction system as the water in which the reactions take place, the enzyme itself, and its substrate or ligand. Those three elements of the system are water–protein–ligand (Hochachka and Somero 1984). Pressure will affect a reaction if there is a volume change in any element of the reaction system during the transition from reactants to products. Though intuitively one might expect that changes in the volume of the enzyme protein during the course of the reaction or production of a higher or lower volume product would be the main source of volume change, most volume changes are actually due to changes in the structure of water. The side‐chains of the enzyme protein’s amino acids are surrounded by a layer of highly organized water, and this water has a higher density (smaller volume) than the bulk water of the system. Enzymatic reactions by their nature alter the organization of water around the molecule.
The alteration can take several forms (Hochachka and Somero 1984). During ligand binding, the highly organized water may be squeezed out into the bulk phase of the system as the two molecules come together, increasing the total volume of the reaction system. Similarly, when two subunits of an enzyme protein come together to form an aggregate, water can be squeezed out into the bulk phase, increasing system volume. Changes in conformation of the enzyme protein during the reaction can also result in volume change. In one case, exposure to the aqueous medium of hydrophobic residues normally packed within the molecule would increase system volume and would respond negatively to increased pressure. In the opposite case, a normally buried hydrophilic amino acid side‐chain exposed to the aqueous medium would allow water to become more densely organized around it, resulting in a decline in volume relative to the bulk water and exhibiting a positive response to increased pressure.
An example from Siebenaller and Somero (1979) of adaptation to pressure in the enzymes of deep‐sea fishes is given in Figure 2.19. In their study, the effects of pressure were tested on the LDHs of deep‐ and shallow‐living marine fishes. LDH catalyzes the final reaction in the glycolytic pathway of intermediary metabolism:
Figure 2.19 The effect of hydrostatic pressure on the apparent Michaelis constant (Km) NADH (upper) and pyruvate (lower) for M4‐LDH's of four deep‐living and three shallow‐living species of marine teleost fishes. Shallow‐dwelling species indicated by dashed lines in both graphs.
Source: Siebenaller and Somero (1979), figure 1 (p. 297) Reproduced with the permission of Springer.
Km values were tested for both NADH and pyruvate at a series of pressures. Not surprisingly, Kms of deeper living fishes were insensitive to pressure. In contrast, shallow‐dwelling species showed a marked elevation of Kms in response to pressure. As was discussed above, for enzymes to satisfy the dual role of efficient catalysts and regulators of cellular metabolism, their Kms must fall within a highly conserved range of values (Hochachka and Somero 1984, 2002). The pressure effects noted in Figure 2.20 would be enough to perturb efficient enzyme function in the shallow‐dwelling species. Later studies by Siebenaller have found that differences in pressure‐sensitive and pressure‐insensitive enzymes in closely related species living at different depths can be caused by a change of as little as one amino acid in enzyme structure (Hochachka and Somero 1984).
The final question to consider with respect to enzyme kinetics is that of trade‐offs in adaptation to pressure. If only one amino acid separates a pressure‐insensitive from a pressure‐sensitive enzyme, why would not insensitivity be selected for in most pelagic species? The answer is that pressure‐insensitive enzymes are less efficient. Table 2.3 shows the relative velocities of LDH’s from fishes living at different depths measured at a common temperature. Clearly, the reaction velocities of enzymes from deeper‐living, pressure‐adapted fishes are very much lower than those from shallower dwelling species.
Figure 2.20 Effects of pressure on gill Na+, K+‐ATPase activities in fishes from different habitats. The deep‐sea fish (cold‐deep) was a species living at depths exceeding 2000 m and temperatures of 2–4 °C (Coryphaenoides armatus – the grenadier); vent fishes (warm‐deep) were two species living near warm hydrothermal vents; shallow‐cold was an eastern Pacific fish found at depths less than 2000 m (Anoplopoma fimbria – the sablefish); shallow‐warm was a species from surface waters near Hawaii (the barracuda Sphyraena).
Source: Gibbs (1997), figure 5 (p. 255). Reproduced with the permission of Academic Press.
Table 2.3 Comparison of lactate dehydrogenase kinetics between two species of deep‐sea fishes, three species of shallow‐living marine fishes, and a terrestrial species. Velocities are compared at a common temperature and pressure (5 °C and 1 atm.).
Source: Reprinted by permission from Springer Nature Customer Service Centre GmbH, Nature, Inefficient lactate dehydrogenases of deep‐sea fish, Somero and Siebenaller (1979), table 1 (p. 101).
| Species (depth, body temp., common name) | ∆H (cal mol−1) | ∆S (cal mol−1 K−1) | ∆G (cal mol−1) | Relative velocity |
|---|---|---|---|---|
| Pagothenia borchgrevinki (surface, −2 °C, ice fish) | 10 467 | −12.7 | 14 000 | 1.00 |
| Sebastolobus alascanus (180–440 m, 4–12 °C, rock fish) | 10 515 | −12.6 | 14 009 | 0.98 |
| Coryphaenoides acrolepis (1460–1840 m, 2–10 °C, rattail fish) | 11 813 | −8.7 |
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