Topological Domain Biology Definition

When used in higher dimensions than one the term topological gradient is also used to name the first order term of the topological asymptotic expansion dealing only with infinitesimal singular domain perturbations.

Topological domain biology definition. In this case there are obviously no dna ends at all since both dna strands are covalently closed. Boundaries at both side of the these domains are conserved between different mammalian cell types and even across species and are highly enriched with ccctc binding factor and cohesin binding s. Combinatorial binding of architectural proteins shapes topological domain structure. Topological domains are annotated according to a controlled vocabulary the elements of which are listed below.

The deformations that are considered in topology are homeomorphisms and homotopies. Although eukaryotic chromosomes are linear overall they consist of large dna loops firmly attached to the nuclear matrix. We propose that differences. By definition the formation of a topological domain requires topologically constrained dna.

Once i ve done that i have a topological space. 1 consequently dna within a topological domain can be subjected to. Study or analysis of configuration of parts or elements. That is what properties do objects have when you re allowed to stretch and bend them but not allow them to break or pass through themselves.

Basic examples of top. Topology is the study of flexible geometries. The constraint might result from a pair of physical clamps attaching the dna at specialized sites or from restrained rotation of one strand of the double helix around the other in the viscous cellular environment. Model illustrating the relationship between protein occupancy at apbss and observed heterogeneity in tad border strengths.

A topologically associating domain is a self interacting genomic region meaning that dna sequences within a tad physically interact with each other more frequently than with sequences outside the tad. I can create a different topological space with the same underlying set by equipping mathbb r with a different topology and that s what i ve done above. A topological space is a set endowed with a structure called a topology which allows defining continuous deformation of subspaces and more generally all kinds of continuity. A property that is invariant under such deformations is a topological property.

Now that i have these two topological spaces i can start talking about continuous maps from one of them to the other. Topology is used in various scientific fields. Thus it may be perceived differently depending on the way a field applies it. It has applications in shape optimization topology optimization image processing and.

A canonical example of a topological domain is circular dna which is typical of bacteria mitochondria chloroplasts many viruses etc. Topologically they re the same object. We uncover a spectrum of architectural protein co localization ranging from low blue to high red which scales with the strength of tad border formation. A dna segment constrained so that the free rotation of its ends is impossible is called a topological domain figure 2.

The topological derivative is conceptually a derivative of a shape functional with respect to infinitesimal changes in its topology such as adding an infinitesimal hole or crack.