Relaxation techniques in biochemistry

Because many biochemical reactions are fast, we need to know how to measure their rates. Rapid mixing and stopped-flow techniques In the laboratory 6.1) are ideal for studying events on a millisecond timescale, such as some 

FIgi 7.3 The relaxation to the new equilibrium composition when a reaction initially at equilibrium at a temperature Ti is subjected to a sudden change of temperature, which takes it to T2. 

When a sudden temperature increase is applied to a simple A B equihhrimn that is first order in each direction, we show in the following Justification that the composition relaxes exponentially to the new equilibrium composition  

When the temperature of a system at equihhrium is increased suddenly, the rate constants change from their earher values to the new values fc, and fcj characteristic of that temperature, but the concentrations of A and B remain for an instant at their old equilibrium values. As the system is no longer at equihhrium, it readjusts to the new equihhrium concentrations at a rate that depends on the new rate constants. We write the deviation of [A] from its new equihhrium value as x, so [A] = [A]eq + x and [B] = [B]eq — x. The net rate of change of the concentration of A is 

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