Kinetics Experiments

Studying the kinetics of folding or unfolding a protein involves the rapid initiation of the reaction by either removal of the denaturing condition (to initiate folding) or addition of the denaturing condition (unfolding). The most common way in which this is done is by a stopped-flow mixing device, in which a solution of the protein in one solution condition (e.g., neutral buffer with no chemical denaturant) is rapidly mixed with a second solution (e.g., concentrated chemical denaturant or acid). Temperature or pressure can also be used as the perturbing condition. Upward temperature jumps can be initiated by high-powered laser pulses or electrical discharges in the solution. Downward pressure jumps can be initiated by releasing some type of valve after high pressure has been established. Other ways to rapidly initiate a protein folding or unfolding reaction include such things as laser flash-induced chemical reactions, which can dissociate heme-carbon monoxide bonds of heme proteins. The remaining discussion will emphasize stopped-flow mixing reactions, since these are the most widely available approaches.

For small, globular proteins, the kinetics of denaturantinduced or acid-induced unfolding reactions are often found to be described as a mono-exponential process, indicating that there is a single energy barrier between the native and unfolded species. For larger proteins, particularly those with multiple domain structures, one often finds the kinetics to be more complicated. In those cases, the folding or unfolding reaction may be described by more than one exponential decay term. This can be an indication of the existence of multiple, slowly interconverting unfolded states, the existence of multiple energy barriers along the folding/unfolding pathway, the existence of more than one pathway, or the existence of some off-path (or dead-end) species. The challenge in kinetics experiments is to first determine the minimum number of decay terms needed to describe the reaction and to then determine a reaction mechanism consistent with the kinetics data. Often, unique mechanisms cannot be determined and it is the art of the scientist to establish which mechanism is most reasonable for the system being studied. In many cases research will focus on determining the number of intermediates on the folding pathway and in trying to gain structural information about these intermediates.

Whether studying folding or unfolding, the reaction should be described with the following general empirical relationship:

⇒ Equation [13]	S(t)[d] = S∞,[d] +	Σ	ΔSi,[d] · exp (−t /τi )
		i

where S(t)_[d] is a time-dependent change in some generalized signal at denaturing condition described by [d],S∞,_[d], is the signal at equilibrium (infinite time after initiation of reaction) at the denaturing condition, and ΔSi,_[d] is the signal amplitude associated with relaxation time constant, τ_i . If there is only a single step in the process (i = 1), the reaction will be a mono-exponential. With more steps, the reaction becomes bi-, tri-, . . . exponential, and fitting the above equation to the data can be difficult. Even with the number of terms and the corresponding values of τi determined, it is still a challenge to relate the τi and the associated amplitudes to a reaction mechanism. How this can be done is beyond the scope of this entry and we refer readers to References 35 and 36.

To experimentally apply the above equation, it is necessary to monitor some signal that responds to the structural state of the protein, just as is the case in equilibrium studies. For very rapid folding/unfolding reactions, the monitoring method must itself be able to respond more rapidly (with adequate signal to noise) than the chemical reaction. Fluorescence, absorbance, and circular dichroism are fairly rapidly responding optical methods and enjoy widespread use in combination with stopped-flow mixers for this purpose. As indicated in Table II, some of the other methods are not easily adapted for the rapid initiation and continuous monitoring of a reaction’s progress. Obviously, when a reaction occurs on the time scale of minutes to hours, then a hand-mixing experiment can suffice.