210 research outputs found
Maximizing Protein Translation Rate in the Ribosome Flow Model: the Homogeneous Case
Gene translation is the process in which intracellular macro-molecules,
called ribosomes, decode genetic information in the mRNA chain into the
corresponding proteins. Gene translation includes several steps. During the
elongation step, ribosomes move along the mRNA in a sequential manner and link
amino-acids together in the corresponding order to produce the proteins.
The homogeneous ribosome flow model(HRFM) is a deterministic computational
model for translation-elongation under the assumption of constant elongation
rates along the mRNA chain. The HRFM is described by a set of n first-order
nonlinear ordinary differential equations, where n represents the number of
sites along the mRNA chain. The HRFM also includes two positive parameters:
ribosomal initiation rate and the (constant) elongation rate. In this paper, we
show that the steady-state translation rate in the HRFM is a concave function
of its parameters. This means that the problem of determining the parameter
values that maximize the translation rate is relatively simple. Our results may
contribute to a better understanding of the mechanisms and evolution of
translation-elongation. We demonstrate this by using the theoretical results to
estimate the initiation rate in M. musculus embryonic stem cell. The underlying
assumption is that evolution optimized the translation mechanism.
For the infinite-dimensional HRFM, we derive a closed-form solution to the
problem of determining the initiation and transition rates that maximize the
protein translation rate. We show that these expressions provide good
approximations for the optimal values in the n-dimensional HRFM already for
relatively small values of n. These results may have applications for synthetic
biology where an important problem is to re-engineer genomic systems in order
to maximize the protein production rate
On Three Generalizations of Contraction
We introduce three forms of generalized contraction (GC). Roughly speaking,
these are motivated by allowing contraction to take place after small
transients in time and/or amplitude. Indeed, contraction is usually used to
prove asymptotic properties, like convergence to an attractor or entrainment to
a periodic excitation, and allowing initial transients does not affect this
asymptotic behavior.
We provide sufficient conditions for GC, and demonstrate their usefulness
using examples of systems that are not contractive, with respect to any norm,
yet are GC
Co-evolution is Incompatible with the Markov Assumption in Phylogenetics
Markov models are extensively used in the analysis of molecular evolution. A
recent line of research suggests that pairs of proteins with functional and
physical interactions co-evolve with each other. Here, by analyzing hundreds of
orthologous sets of three fungi and their co-evolutionary relations, we
demonstrate that co-evolutionary assumption may violate the Markov assumption.
Our results encourage developing alternative probabilistic models for the cases
of extreme co-evolution
Co-evolutionary networks of genes and cellular processes across fungal species
Two new measures of evolution are used to study co-evolutionary networks of fungal genes and cellular processes; links between co-evolution and co-functionality are revealed
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