Icamipedia:Site support
From Icamipedia
Headline text
Thermodynamic control and kinetic control are two kinds of controls to determine the product of a chemical reaction.
Based on the transition theory, the reactant in a chemical reaction has to overcome the free energy barrier (the activation energy) to become a product.
Figure 1. An Illustration of transition state in reaction process
The same reactant can generate different final products under different controls, according to relevant reacting conditions.
As illustrated in Figure 2 below, starting from the same reactant R, the chemical reaction can generate two kinds of product P1 and P2, through different transition states TS1 and TS2. The product P1 is faster as it passes through lower energetic barrier TS1; while the product P2 is more stable though it has to pass through higher energetic barrier TS2.
Figure 2. An Illustration of reactions under different controls(revised from [1])
Under thermodynamic control, the reverse reaction is faster than the forward reaction, and the product P2 will be the final product as it is more stable. Under kinetic control, the forward reaction dominates the reacting direction, and the product P1 will be the final product as it has a lower energetic barrier. Thermodynamic control is mainly applicable at high temperature, while kinetic control is suitable at mild or low temperature.
A point mutation in a molecule may change the energetic barrier in reaction, and therefore change the product. Taking D178N in Fatal Familiar Insomnia (FFI) for example:
The mutation D178N is a point mutation in prion protein molecule. The reactant is the monomeric cellular prion protein PrPc, and the product is the multimeric scrapie prion protein PrPsc. The impact of free energy change of a point mutation is no larger than 3.0 kcal/mol.[2]
In the thermodynamic control model (see Figure 3), for both the wild-type and mutant protein, the reaction from PrPc to PrPsc is not hard. The mutant PrPsc is more stable than the wild-type PrPsc, and the energy difference between PrPc and PrPsc for mutant protein is ΔGmut = -1.5-3.0 kcal/mol, and the one for wild-type is 1.5-3.0 kcal/mol. Of course the reaction from PrPc to PrPsc for mutant protein is easier to occur, but as the total ΔΔG is 1.5-6.0 kcal/mol, the product efficiency of wild-type PrPsc is about e^(-3)=5% as mutant PrPsc. This result conflicts with the neuropathologic data, and especially for wild-type, if the reaction is so easy to occur, then prion diseases will spread easily for most people.
On the other hand, in the kinetic control model, for both the wild-type and mutant cases, as the energetic barrier is high for both of them (36-38 kcal/mol and 33-34 kcal/mol), the reaction from PrPc to PrPsc is basically hard to achieve. The high energetic barrier between reactant and transition state simply explain the rareness of existence of PrPsc, and it is consistent with neuropathologic data. Moreover, as the impact of a point mutation (D178N), the energetic barrier for mutant protein is lowered by 1.5-3.0 kcal/mol).
Based on the Maxwell-Boltzmann statistical, the probability ratio of wild-type to mutant form for generating PrPSC, is:
Therefore, the difference of 1.5-3.0 kcal/mol in energetic barrier has resulted in the conversion of wild-type PrPc to PrPsc102 scale fold slower than the mutant ones. Based on the fact that the prodromal period for inherited prion disease is about 30-40 years in people with mutant gene[3], then it will be about 3000-4000 years for people with wild-type gene. This explains that prion disease (specifically FFI here) rarely occurs for people with wild-type gene, while it will occur in 100% probability for people with mutant gene.
Figure 3. An Illustration of free energy change in mutation under thermodynamic control and kinetic control.[3]
(ΔG is the free energy difference between PrPc and PrPsc state, and ΔG+ is the activation energy . The wild-type reaction is shown in continuous line, while the mutant reaction is shown in broken line)
For all other point mutations, the free energy changes can be calculated using this equation:
![\Delta G_{a-b} = - k_{B} T \displaystyle\sum_{k=1}^N ln<exp[-\frac{H(r,p; \lambda_{k+1})- H(r,p; \lambda_{k}) }{k_{B} T}] >_{k}](/images/math/7/4/8/74820ce45dd71fd26accb00fa3636b8f.png)
Where a,b denote two different protein structure, H is the hybird Hamiltonian (H(λ) = H1 + λHa + (1 − λ)Hb), λ is a parameter varies between 0 to 1.
[1] http://library.tedankara.k12.tr/carey/ch10-3-2.html
[2] Cohen, F. E. & Prusiner, S. B. Annu. Rev. Biochem.(1998) 67, 793-819.
[3] Cohen, F. E. J. Mol. Biol. (1999) 293, 313±320
