Kinetic topology

The kinetic topology provides an opportunity of choosing an optimal inhibitor by estimating k-> for the minimal consumption of inhibitor at efficient chain termination. This can be illustrated with reference to oxidation by mechanism VI. Taking into account the initiation reaction, the consumption of an inhibitor can be described by the expressions... 

To solve this task a kinetic mosaic approach (the method of kinetic topology ) was offered by E.T. Denisov (see Chapter 2). Conceptually, such an approach represents the analysis of more simple, sufficiently autonomous reaction schemes that may be solved analytically. Later, using these data one can compile the overall picture on the behavour of an inhibited reaction. A more detailed solution of such a problem may be represented as follows [13,14] ... 

The above-listed stages in solving the problem on the efficient antioxidant selection in the framework of the kinetic topology may be represented in the form of a fundamental logic diagram (Figure 7.2). 

Figure 7.2. Outline of the procedures to identify an efficient antioxidant, applying the kinetic topology method.

For these sequences the value of Gj, is less than a certain small value g. For such sequences the folding occurs directly from the ensemble of unfolded states to the NBA. The free energy surface is dominated by the NBA (or a funnel) and the volume associated with NBA is very large. The partition factor <6 is near unify so that these sequences reach the native state by two-state kinetics. The amplitudes in (C2.5.7) are nearly zero. There are no intennediates in the pathways from the denatured state to the native state. Fast folders reach the native state by a nucleation-collapse mechanism which means that once a certain number of contacts (folding nuclei) are fonned then the native state is reached very rapidly [25, 26]. The time scale for reaching the native state for fast folders (which are nonnally associated with those sequences for which topological fmstration is minimal) is found to be... 

OM Becker, M Karplus. The topology of multidimensional potential energy surfaces Theory and application to peptide stiaicture and kinetics. I Chem Phys 106 1495-1517, 1997. 

For dynamical studies of diffusion, conformational and transport behavior under shear stress, or kinetics of relaxation, one resorts to dynamic models [54,58,65] in which the topological connectivity of the chains is maintained during the simulation. 

There are cases where non-regular lattices may be of advantage [36,37]. The computational effort, however, is substantially larger, which makes the models less flexible concerning changes of boundary conditions or topological constraints. Another direction, which may be promising in the future, is the use of hybrid models, where for example local attachment kinetics are treated on a microscopic atomistic scale, while the transport properties are treated by macroscopic partial differential equations [5,6]. 

Hikosaka presented a chain sliding diffusion theory and formulated the topological nature in nucleation theory [14,15]. We will define chain sliding diffusion as self-diffusion of a polymer chain molecule along its chain axis in some anisotropic potential field as seen within a nucleus, a crystal or the interface between the crystalline and the isotropic phases . The terminology of diffusion derives from the effect of chain sliding diffusion, which could be successfully formulated as a diffusion coefficient in our kinetic theory. 

We have shown that only Io(oc D) depends on ve, while C(a AG ) does not depend on ve. This means that the topological nature of nucleation is reflected only on the kinetic factor (D) and not on the thermodynamic factor (AG ) as... 

The mechanisms by which an inhibitor adds to an oxidized hydrocarbon exerts its influence may differ depending on the reaction conditions. If the rate constants of the elementary reactions of RH, InH, R02 , In, ROOH, and 02 are known, the kinetics of the inhibited oxidation of RH can mathematically be described for any conditions. However, such an approach fails to answer questions how the mechanism of inhibited oxidation is related to the structure and reactivity of InH, RH, and R02 or what inhibitor appears the most efficient under the given conditions, and so on. At the same time, these questions can easily be clarified in terms of a topological approach whose basic ideas are the following [43-45,70-72] ... 

---