66,151 research outputs found
Simple gene assembly as a rewriting of directed overlap-inclusion graphs
The simple intramolecular model for gene assembly in ciliates consists of three molecular operations, simple Id, simple hi and simple dlad. Mathematical models in terms of signed permutations and signed strings proved limited in capturing some of the combinatorial details of the simple gene assembly process. Brijder and Hoogeboom introduced a new model in terms of overlap-inclusion graphs which could describe two of the three operations of the model and their combinatorial properties. To capture the third operation, we extended their framework to directed overlap-inclusion (DOI) graphs in Azimi et al. (2011) [1]. In this paper we introduce DOI graph-based rewriting rules that capture all three operations of the simple gene assembly model and prove that they are equivalent to the string-based formalization of the model. (C) 2012 Elsevier B.V. All rights reserved
Strategies of Loop Recombination in Ciliates
Gene assembly in ciliates is an extremely involved DNA transformation
process, which transforms a nucleus, the micronucleus, to another functionally
different nucleus, the macronucleus. In this paper we characterize which loop
recombination operations (one of the three types of molecular operations that
accomplish gene assembly) can possibly be applied in the transformation of a
given gene from its micronuclear form to its macronuclear form. We also
characterize in which order these loop recombination operations are applicable.
This is done in the abstract and more general setting of so-called legal
strings.Comment: 22 pages, 14 figure
Self-Replication and Self-Assembly for Manufacturing
It has been argued that a central objective of nanotechnology is to make
products inexpensively, and that self-replication is an effective approach
to very low-cost manufacturing. The research presented here is intended to
be a step towards this vision. We describe a computational simulation of
nanoscale machines floating in a virtual liquid. The machines can bond
together to form strands (chains) that self-replicate and self-assemble
into user-specified meshes. There are four types of machines and the
sequence of machine types in a strand determines the shape of the mesh
they will build. A strand may be in an unfolded state, in which the bonds
are straight, or in a folded state, in which the bond angles depend on the
types of machines. By choosing the sequence of machine types in a strand,
the user can specify a variety of polygonal shapes. A simulation typically
begins with an initial unfolded seed strand in a soup of unbonded machines.
The seed strand replicates by bonding with free machines in the soup. The
child strands fold into the encoded polygonal shape, and then the polygons
drift together and bond to form a mesh. We demonstrate that a variety of
polygonal meshes can be manufactured in the simulation, by simply changing
the sequence of machine types in the seed
Nullity Invariance for Pivot and the Interlace Polynomial
We show that the effect of principal pivot transform on the nullity values of
the principal submatrices of a given (square) matrix is described by the
symmetric difference operator (for sets). We consider its consequences for
graphs, and in particular generalize the recursive relation of the interlace
polynomial and simplify its proof.Comment: small revision of Section 8 w.r.t. v2, 14 pages, 6 figure
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