Theory of Transient State Kinetics and Dynamics

Systems with a Small Number oe Discrete States 

Since proteins are essentially polymers, they may adopt many, almost iso-energetic and very similar structures called protein substates (Austin et al. 1975 Frauenfelder et al. 1988). At ambient temperatures, proteins switch between their substates hence, they are constantly changing their structure (Parak et al. 1982 Parak 2003). By knowing the coordinates of each of the atoms and their velocity vectors at any instant of time, the dynamics of the structural changes, i.e., the trajectories of the molecule s atoms, can be followed exactly. However, this has been achieved only in computer simulations so far. 

FIGURE 1.2 Two-state diagram (states A and B) to describe chemical kinetics. The reaction coordinate can be considered as the pathway with lowest energy through the multidimensional energy hyper-surface of the reaction. represents the transition state, i.e., the state with highest free energy on the reaction coordinate. The reaction enthalpy and the enthalpy differences between the two states and the transition state are depicted by arrows. Note that for the rate coefficients and the differences, have to be considered. 

The reaction rate (or the velocity), which is defined as the change of concentration of a particular species (or protein state), may also be defined as the nnmber of molecules per unit time crossing the barrier from state A to B. It depends on the height of the barrier, the number of molecules available in state A, and the temperatnre T. The height of the barrier and the temperatnre dependence are parameterized by the rate coefficient, k, defined as 

It should be pointed out at this juncture that a reaction with no enthalpy of activation (AH = 0) can nevertheless have a very small rate coefficient, since the entropy of the transition state can be very small compared to that in the state A or B. Accordingly, S becomes negative. In other words, there is a possibility that only a small loophole or a very narrow path in conformational space exists through which molecules may migrate from state A to 5 or vice versa. 

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