4 research outputs found
Towards a model for protein production rates
In the process of translation, ribosomes read the genetic code on an mRNA and
assemble the corresponding polypeptide chain. The ribosomes perform discrete
directed motion which is well modeled by a totally asymmetric simple exclusion
process (TASEP) with open boundaries. Using Monte Carlo simulations and a
simple mean-field theory, we discuss the effect of one or two ``bottlenecks''
(i.e., slow codons) on the production rate of the final protein. Confirming and
extending previous work by Chou and Lakatos, we find that the location and
spacing of the slow codons can affect the production rate quite dramatically.
In particular, we observe a novel ``edge'' effect, i.e., an interaction of a
single slow codon with the system boundary. We focus in detail on ribosome
density profiles and provide a simple explanation for the length scale which
controls the range of these interactions.Comment: 8 pages, 8 figure
Reconstruction on trees and spin glass transition
Consider an information source generating a symbol at the root of a tree
network whose links correspond to noisy communication channels, and
broadcasting it through the network. We study the problem of reconstructing the
transmitted symbol from the information received at the leaves. In the large
system limit, reconstruction is possible when the channel noise is smaller than
a threshold.
We show that this threshold coincides with the dynamical (replica symmetry
breaking) glass transition for an associated statistical physics problem.
Motivated by this correspondence, we derive a variational principle which
implies new rigorous bounds on the reconstruction threshold. Finally, we apply
a standard numerical procedure used in statistical physics, to predict the
reconstruction thresholds in various channels. In particular, we prove a bound
on the reconstruction problem for the antiferromagnetic ``Potts'' channels,
which implies, in the noiseless limit, new results on random proper colorings
of infinite regular trees.
This relation to the reconstruction problem also offers interesting
perspective for putting on a clean mathematical basis the theory of glasses on
random graphs.Comment: 34 pages, 16 eps figure