Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic stability analysis of three-component self-regulatory genetic
  circuit   A self-regulatory genetic circuit, where a protein acts as a positive
regulator of its own production, is known to be a simplest form of biological
network with a positive feedback loop. Although at least three components, DNA,
RNA, and the protein, are required to form such a circuit, the stability
analysis of fixed points of the self-regulatory circuit has been performed only
after reducing the system into to a two-component system consisting of RNA and
protein only, assuming a fast equilibration of the DNA component. Here, the
stability of fixed points of the three-component positive feedback loop is
analyzed by obtaining eigenvalues of full three dimensional Hessian matrix. In
addition to rigorously identifying the stable fixed points and the saddle
points, detailed information can be obtained, such as the number of positive
eigenvalues near a saddle point. In particular, complex eigenvalues is shown to
exist for sufficiently slow binding and unbinding of the auto-regulatory
transcription factor to DNA, leading to oscillatory convergence to the steady
states, a novel feature unseen in the two-dimensional analysis.

31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th