Topological state

Topoisomerase enzymes control and modify the topologic states of DNA. The mechanisms of these enzymes involve DNA cleavage and strand passage through the break, followed by religation of the cleaved DNA. Two main forms of topoisomerase exist. The type... 

Norinder, U. and Osterberg, T., Theoretical calculation and prediction of drug transport processes using simple parameters and partial least squares projections to latent structures (PLS) statistics. The use of electro-topological state indices., J. Pharm. 

Kier, L. B., Hall, L. H., Molecular Structure Description The Electro-topological State. Academic Press,... 

Use of E-state Descriptors A method that is still growing is the use of electro-topological state indices (E-state indices) for the prediction of log P. These E-state indices express both topological and electronic valence status of each atom type in a molecule (atom-type E-state indices). In the same way, such indices describe well... 

These values are also known as atom-type E-state indices (Hall and Kier, 1995). In the topological state formalism, hydrogen atoms, which were neglected for many years in the Graph Theory, can also be represented as hydrogen atom-type E-state indices (Maw and Hall, 2000 2001). 

The topological state of the system of rings or uncrossable chains connected into a network coincides with that of the initial state and remains without any... 

To define the characteristic determining the topological state of macromolecules. Such a characteristic is called the topological invariant [6]. It depends on the topological state of chains only and does not depend on the shape of the macromolecule. 

To determine the partition function, Z, i.e. the number of available chain conformations for fixed topological state. 

Thus, it should be stressed that the mathematical topological theory investigates, as a rule, the problems of classification of knots and links, the construction of topological invariants, definitions of topological classes, etc. whereas the fundamental physical problem in the theory of topological properties of polymer chains is the determination of the entropy, S = In Z with the fixed topological state of chains. Both these problems are very difficult, but important. 

The topological state of the chain trajectory on z-plane. In particular, the closed contours on the (-plane correspond only to unentangled closed contours on the z-plane. 

In the course of investigation of polymer dynamics, all topological states of chains are equivalent due to the presence of their free ends and it is not necessary to construct the topological invariant. However, for every instantaneous chain configuration, its topological state is definite and is determined by the topological invariant - the primitive path. 

It would be interesting to find out, using computer simulations, if this quasi-topological state of the linear globular chain is practically independent of the positions of the chain ends. 

Because of the fact that the topological state of the chain part in every crumple is fixed and coincides with the state of the whole chain, which is unknotted, this chain part can be presented as an unknotted ring. Others chain... 

Attempts have been made recently to analyze directly the topological state of chromosomal DNA in extremely thermophilic archaebacteria. A nucleoid-like structure has been isolated from S. acidocaldarius using procedures similar to those previously used to analyze DNA topology of E. coli chromosome [32,33,38,39]. Unfortunately,... 

The electrotopological state 5, of the /th atom in the molecule, called the fl-state index (or electrotopological state index) gives information related to the electronic and topological state of the atom in the molecule and is defined as [Kier and Hall, 1990a Kier and Hall, 1999] ... 

A list of molecular identification numbers is given below. Other important ones are the Hosoya ID number, the -> hyper-Wiener index, the - restricted walk ID number, and the total topological state, defined elsewhere. 

The topological state matrix T [Hall and Kier, 1990] is a square symmetric matrix Ax A, A being the number of -> molecular graph vertices, whose entries are defined as ... 

The diagonal entries f,- correspond to paths of length zero, thus they are simply equal to the vertex degrees. Moreover, for cyclic graphs, there can be more than one path between the vertices v, and vf, hence each topological state matrix element is a sum of the contributions of all paths between the considered vertices. 

From the topological state matrix, a local vertex invariant 5 called the topological state (or vertex topological state), can be calculated as ... 

As the diagonal entries are just the vertex degrees 6, the first term on the right is the - total adjacency index Ay The topological state index is one of the -> molecular ID numbers. 

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