Pressure jump

Pressure jump is a technique used in the study of chemical kinetics. It involves making rapid changes to the pressure of an experimental system and observing the return to equilibrium or steady state. This allows the study of the shift in equilibrium of reactions that equilibrate in periods between milliseconds to hours (or longer),^[1] these changes often being observed using absorption spectroscopy, or fluorescence spectroscopy though other spectroscopic techniques such as CD,^[2] FTIR^[3] or NMR^[4] can also be used.

Historically, pressure jumps were limited to one direction. Most commonly fast drops in pressure were achieved by using a quick release valve or a fast burst membrane.^[5] Modern equipment can achieve pressure changes in both directions using either double reservoir arrangements^[6] (good for large changes in pressure) or pistons operated by piezoelectric actuators^[7] (often faster than valve based approaches). Ultra fast pressure drops can be achieved using electrically disintegrated burst membranes.^[8] The ability to automatically repeat measurements and average the results is useful since the reaction amplitudes are often small.

The fractional extent of the reaction (i.e. the percentage change in concentration of a measurable species) depends on the molar volume change (ΔV°) between the reactants and products and the equilibrium position. If K is the equilibrium constant and P is the pressure then the volume change is given by:

$\Delta V^o = -RT \left(\frac{\partial \ln K}{\partial P} \right)_T$

where R is the universal gas constant and T is the absolute temperature. The volume change can thus be understood to be the pressure dependency of the change in Gibbs free energy associated with the reaction.

When a single step in a reaction is perturbed in a pressure jump experiment, the reaction follows a single exponential decay function with the reciprocal time constant (1/τ) equal to the sum of the forward and reverse intrinsic rate constants. In more complex reaction networks, when multiple reaction steps are perturbed, then the reciprocal time constants are given by the eigenvalues of the characteristic rate equations. The ability to observe intermediate steps in a reaction pathway is one of the attractive features of this technology.^[9]

References

1. This contrasts with temperature jump in which cooling curves typically limit the time window to a minute or so.
2. Gruenewald B, Knoche W (1978). "Pressure jump method with detection of optical-rotation and circular-dichroism.". Review of Scientific Instruments 49: 797–801. Bibcode:1978RScI...49..797G. doi:10.1063/1.1135618. PMID 18699196.
3. Schiewek M, Krumova M, Hempel G, Blume A (2007). "Pressure jump relaxation setup with IR detection and millisecond time resolution.". Review of Scientific Instruments 78: 045101. Bibcode:2007RScI...78d5101S. doi:10.1063/1.2719020. PMID 17477687.
4. Heuer U, Krumova M, Hempel G, Schiewek M, Blume A (2010). "NMR probe for pressure-jump experiments up to 250 bars and 3 ms jump time.". Review of Scientific Instruments 81: 105102. Bibcode:2010RScI...81j5102H. doi:10.1063/1.3481164. PMID 21034114.
5. Pörschke D (1982). Methods for studying fast kinetics in biological systems in: Davies DB, Saenger W, Danyluk SS (Eds) Structural Molecular Biology. Plenum Publishing Corp. ISBN 0-306-40982-8.
6. Marchal S, Font J, Ribó M, Vilanova M, Phillips RS, Lange R, Torrent J (2009). "Asymmetric kinetics of protein structural changes.". Accounts of Chemical Research 42: 778–87. doi:10.1021/ar800266r. PMID 19378977.
7. Pearson DS, Holtermann G, Ellison P, Cremo C, Geeves MA (2002). "A novel pressure jump apparatus for the microvolume analysis of protein-ligand and protein-protein interactions: its application to nucleotide binding to skeletal-muscle and smooth-muscle myosin subfragment 1.". Biochemical Journal 366: 643–651. doi:10.1042/BJ20020462. PMC 1222786. PMID 12010120.
8. Dumont C, Emilsson T, Gruebele M (2009). "Reaching the protein folding speed limit with large, sub-microsecond pressure jumps.". Nature Methods 6 (7): 515–9. doi:10.1038/nmeth.1336. PMID 19483692.
9. Malnási-Csizmadia, A; Pearson, D.S.; Kovács, M.; Woolley, R.J.; Geeves, M.A.; Bagshaw, C.R. (2001). "Kinetic Resolution of a Conformational Transition and the ATP Hydrolysis Step Using Relaxation Methods with a Dictyostelium Myosin II Mutant Containing a Single Tryptophan Residue". Biochemistry 40: 12727–12737. doi:10.1021/bi010963q. PMID 11601998.