42,527 research outputs found
Implementation of the Combined--Nonlinear Condensation Transformation
We discuss several applications of the recently proposed combined
nonlinear-condensation transformation (CNCT) for the evaluation of slowly
convergent, nonalternating series. These include certain statistical
distributions which are of importance in linguistics, statistical-mechanics
theory, and biophysics (statistical analysis of DNA sequences). We also discuss
applications of the transformation in experimental mathematics, and we briefly
expand on further applications in theoretical physics. Finally, we discuss a
related Mathematica program for the computation of Lerch's transcendent.Comment: 23 pages, 1 table, 1 figure (Comput. Phys. Commun., in press
Stochastic modelling, Bayesian inference, and new in vivo measurements elucidate the debated mtDNA bottleneck mechanism
Dangerous damage to mitochondrial DNA (mtDNA) can be ameliorated during
mammalian development through a highly debated mechanism called the mtDNA
bottleneck. Uncertainty surrounding this process limits our ability to address
inherited mtDNA diseases. We produce a new, physically motivated, generalisable
theoretical model for mtDNA populations during development, allowing the first
statistical comparison of proposed bottleneck mechanisms. Using approximate
Bayesian computation and mouse data, we find most statistical support for a
combination of binomial partitioning of mtDNAs at cell divisions and random
mtDNA turnover, meaning that the debated exact magnitude of mtDNA copy number
depletion is flexible. New experimental measurements from a wild-derived mtDNA
pairing in mice confirm the theoretical predictions of this model. We
analytically solve a mathematical description of this mechanism, computing
probabilities of mtDNA disease onset, efficacy of clinical sampling strategies,
and effects of potential dynamic interventions, thus developing a quantitative
and experimentally-supported stochastic theory of the bottleneck.Comment: Main text: 14 pages, 5 figures; Supplement: 17 pages, 4 figures;
Total: 31 pages, 9 figure
DNA Computing by Self-Assembly
Information and algorithms appear to be central to biological organization
and processes, from the storage and reproduction of genetic information to
the control of developmental processes to the sophisticated computations
performed by the nervous system. Much as human technology uses electronic
microprocessors to control electromechanical devices, biological
organisms use biochemical circuits to control molecular and chemical events.
The engineering and programming of biochemical circuits, in vivo and in
vitro, would transform industries that use chemical and nanostructured
materials. Although the construction of biochemical circuits has been
explored theoretically since the birth of molecular biology, our practical
experience with the capabilities and possible programming of biochemical
algorithms is still very young
Exact theory of kinkable elastic polymers
The importance of nonlinearities in material constitutive relations has long
been appreciated in the continuum mechanics of macroscopic rods. Although the
moment (torque) response to bending is almost universally linear for small
deflection angles, many rod systems exhibit a high-curvature softening. The
signature behavior of these rod systems is a kinking transition in which the
bending is localized. Recent DNA cyclization experiments by Cloutier and Widom
have offered evidence that the linear-elastic bending theory fails to describe
the high-curvature mechanics of DNA. Motivated by this recent experimental
work, we develop a simple and exact theory of the statistical mechanics of
linear-elastic polymer chains that can undergo a kinking transition. We
characterize the kinking behavior with a single parameter and show that the
resulting theory reproduces both the low-curvature linear-elastic behavior
which is already well described by the Wormlike Chain model, as well as the
high-curvature softening observed in recent cyclization experiments.Comment: Revised for PRE. 40 pages, 12 figure
Elastic Rod Model of a Supercoiled DNA Molecule
We study the elastic behaviour of a supercoiled DNA molecule. The simplest
model is that of a rod like chain, involving two elastic constants, the bending
and the twist rigidities. We show that this model is singular and needs a small
distance cut-off, which is a natural length scale giving the limit of validity
of the model, of the order of the double helix pitch. The rod like chain in
presence of the cutoff is able to reproduce quantitatively the experimentally
observed effects of supercoiling on the elongation-force characteristics, in
the small supercoiling regime. An exact solution of the model, using both
transfer matrix techniques and its mapping to a quantum mechanics problem,
allows to extract, from the experimental data,the value of the twist rigidity.
We also analyse the variation of the torque and the writhe to twist ratio
versus supercoiling, showing analytically the existence of a rather sharp
crossover regime which can be related to the excitation of plectonemic-like
structures. Finally we study the extension fluctuations of a stretched and
supercoiled DNA molecule, both at fixed torque and at fixed supercoiling angle,
and we compare the theoretical predictions to some preliminary experimental
data.Comment: 29 pages Revtex 5 figure
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