482 research outputs found
Efficient Stochastic Simulations of Complex Reaction Networks on Surfaces
Surfaces serve as highly efficient catalysts for a vast variety of chemical
reactions. Typically, such surface reactions involve billions of molecules
which diffuse and react over macroscopic areas. Therefore, stochastic
fluctuations are negligible and the reaction rates can be evaluated using rate
equations, which are based on the mean-field approximation. However, in case
that the surface is partitioned into a large number of disconnected microscopic
domains, the number of reactants in each domain becomes small and it strongly
fluctuates. This is, in fact, the situation in the interstellar medium, where
some crucial reactions take place on the surfaces of microscopic dust grains.
In this case rate equations fail and the simulation of surface reactions
requires stochastic methods such as the master equation. However, in the case
of complex reaction networks, the master equation becomes infeasible because
the number of equations proliferates exponentially. To solve this problem, we
introduce a stochastic method based on moment equations. In this method the
number of equations is dramatically reduced to just one equation for each
reactive species and one equation for each reaction. Moreover, the equations
can be easily constructed using a diagrammatic approach. We demonstrate the
method for a set of astrophysically relevant networks of increasing complexity.
It is expected to be applicable in many other contexts in which problems that
exhibit analogous structure appear, such as surface catalysis in nanoscale
systems, aerosol chemistry in stratospheric clouds and genetic networks in
cells
An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci
A model of mutation rate evolution for multiple loci under arbitrary
selection is analyzed. Results are obtained using techniques from Karlin (1982)
that overcome the weak selection constraints needed for tractability in prior
studies of multilocus event models. A multivariate form of the reduction
principle is found: reduction results at individual loci combine topologically
to produce a surface of mutation rate alterations that are neutral for a new
modifier allele. New mutation rates survive if and only if they fall below this
surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994)
for a multilocus recombination modifier. Increases in mutation rates at some
loci may evolve if compensated for by decreases at other loci. The strength of
selection on the modifier scales in proportion to the number of germline cell
divisions, and increases with the number of loci affected. Loci that do not
make a difference to marginal fitnesses at equilibrium are not subject to the
reduction principle, and under fine tuning of mutation rates would be expected
to have higher mutation rates than loci in mutation-selection balance. Other
results include the nonexistence of 'viability analogous, Hardy-Weinberg'
modifier polymorphisms under multiplicative mutation, and the sufficiency of
average transmission rates to encapsulate the effect of modifier polymorphisms
on the transmission of loci under selection. A conjecture is offered regarding
situations, like recombination in the presence of mutation, that exhibit
departures from the reduction principle. Constraints for tractability are:
tight linkage of all loci, initial fixation at the modifier locus, and mutation
distributions comprising transition probabilities of reversible Markov chains.Comment: v3: Final corrections. v2: Revised title, reworked and expanded
introductory and discussion sections, added corollaries, new results on
modifier polymorphisms, minor corrections. 49 pages, 64 reference
Translocation of structured polynucleotides through nanopores
We investigate theoretically the translocation of structured RNA/DNA
molecules through narrow pores which allow single but not double strands to
pass. The unzipping of basepaired regions within the molecules presents
significant kinetic barriers for the translocation process. We show that this
circumstance may be exploited to determine the full basepairing pattern of
polynucleotides, including RNA pseudoknots. The crucial requirement is that the
translocation dynamics (i.e., the length of the translocated molecular segment)
needs to be recorded as a function of time with a spatial resolution of a few
nucleotides. This could be achieved, for instance, by applying a mechanical
driving force for translocation and recording force-extension curves (FEC's)
with a device such as an atomic force microscope or optical tweezers. Our
analysis suggests that with this added spatial resolution, nanopores could be
transformed into a powerful experimental tool to study the folding of nucleic
acids.Comment: 9 pages, 5 figure
Predicting Gene Expression Level from Relative Codon Usage Bias: An Application to Escherichia coli Genome
We present an expression measure of a gene, devised to predict the level of gene expression from relative codon bias (RCB). There are a number of measures currently in use that quantify codon usage in genes. Based on the hypothesis that gene expressivity and codon composition is strongly correlated, RCB has been defined to provide an intuitively meaningful measure of an extent of the codon preference in a gene. We outline a simple approach to assess the strength of RCB (RCBS) in genes as a guide to their likely expression levels and illustrate this with an analysis of Escherichia coli (E. coli) genome. Our efforts to quantitatively predict gene expression levels in E. coli met with a high level of success. Surprisingly, we observe a strong correlation between RCBS and protein length indicating natural selection in favour of the shorter genes to be expressed at higher level. The agreement of our result with high protein abundances, microarray data and radioactive data demonstrates that the genomic expression profile available in our method can be applied in a meaningful way to the study of cell physiology and also for more detailed studies of particular genes of interest
Fractional Operators, Dirichlet Averages, and Splines
Fractional differential and integral operators, Dirichlet averages, and
splines of complex order are three seemingly distinct mathematical subject
areas addressing different questions and employing different methodologies. It
is the purpose of this paper to show that there are deep and interesting
relationships between these three areas. First a brief introduction to
fractional differential and integral operators defined on Lizorkin spaces is
presented and some of their main properties exhibited. This particular approach
has the advantage that several definitions of fractional derivatives and
integrals coincide. We then introduce Dirichlet averages and extend their
definition to an infinite-dimensional setting that is needed to exhibit the
relationships to splines of complex order. Finally, we focus on splines of
complex order and, in particular, on cardinal B-splines of complex order. The
fundamental connections to fractional derivatives and integrals as well as
Dirichlet averages are presented
On the Three-dimensional Central Moment Lattice Boltzmann Method
A three-dimensional (3D) lattice Boltzmann method based on central moments is
derived. Two main elements are the local attractors in the collision term and
the source terms representing the effect of external and/or self-consistent
internal forces. For suitable choices of the orthogonal moment basis for the
three-dimensional, twenty seven velocity (D3Q27), and, its subset, fifteen
velocity (D3Q15) lattice models, attractors are expressed in terms of
factorization of lower order moments as suggested in an earlier work; the
corresponding source terms are specified to correctly influence lower order
hydrodynamic fields, while avoiding aliasing effects for higher order moments.
These are achieved by successively matching the corresponding continuous and
discrete central moments at various orders, with the final expressions written
in terms of raw moments via a transformation based on the binomial theorem.
Furthermore, to alleviate the discrete effects with the source terms, they are
treated to be temporally semi-implicit and second-order, with the implicitness
subsequently removed by means of a transformation. As a result, the approach is
frame-invariant by construction and its emergent dynamics describing fully 3D
fluid motion in the presence of force fields is Galilean invariant. Numerical
experiments for a set of benchmark problems demonstrate its accuracy.Comment: 55 pages, 8 figure
Cloning and sequence analysis of cDNAs encoding the cytosolic precursors of subunits GapA and GapB of chloroplast glyceraldehyde-3-phosphate dehydrogenase from pea and spinach
Chloroplast glyceraldehyde-3-phosphate dehydrogenase (GAPDH) is composed of two different subunits, GapA and GapB. cDNA clones containing the entire coding sequences of the cytosolic precursors for GapA from pea and for GapB from pea and spinach have been identified, sequenced and the derived amino acid sequences have been compared to the corresponding sequences from tobacco, maize and mustard. These comparisons show that GapB differs from GapA in about 20% of its amino acid residues and by the presence of a flexible and negatively charged C-terminal extension, possibly responsible for the observed association of the enzyme with chloroplast envelopes in vitro. This C-terminal extension (29 or 30 residues) may be susceptible to proteolytic cleavage thereby leading to a conversion of chloroplast GAPDH isoenzyme I into isoenzyme II. Evolutionary rate comparisons at the amino acid sequence level show that chloroplast GapA and GapB evolve roughly two-fold slower than their cytosolic counterpart GapC. GapA and GapB transit peptides evolve about 10 times faster than the corresponding mature subunits. They are relatively long (68 and 83 residues for pea GapA and spinach GapB respectively) and share a similar amino acid framework with other chloroplast transit peptides
Pendampingan Masyarakat Desa dalam Membangun Kesadaran Mendaftarkan Tanah Hak Milik (Penyuluhan Hukum di Desa Buntulia Utara Kec. Buntulia Kab. Pohuwato)
The problem of land ownership in Buntulia Village is influenced by the lack of knowledge and awareness of the community about land ownership rights because of the total population of 549 families, 463 people have not registered their own land. This of course raises a fairly basic problem by the village government to be resolved. Therefore, in this downstreaming, the service team provides understanding and legal knowledge to the community about the importance of registering property rights and providing assistance to the community together with the Land Agency through the Border Marks Post Community Movement (GEMA PATAS) in order to increase community participation in installing boundary markings, making it easier for BPN officers to take measurements, as well as being able to accelerate the government program on Complete Systematic Land Registration. Thus the community could see the importance of legalizing property rights to the land in order to avoid disputes and thereby give legal certainty to the parties
Mutation, selection, and ancestry in branching models: a variational approach
We consider the evolution of populations under the joint action of mutation
and differential reproduction, or selection. The population is modelled as a
finite-type Markov branching process in continuous time, and the associated
genealogical tree is viewed both in the forward and the backward direction of
time. The stationary type distribution of the reversed process, the so-called
ancestral distribution, turns out as a key for the study of mutation-selection
balance. This balance can be expressed in the form of a variational principle
that quantifies the respective roles of reproduction and mutation for any
possible type distribution. It shows that the mean growth rate of the
population results from a competition for a maximal long-term growth rate, as
given by the difference between the current mean reproduction rate, and an
asymptotic decay rate related to the mutation process; this tradeoff is won by
the ancestral distribution.
Our main application is the quasispecies model of sequence evolution with
mutation coupled to reproduction but independent across sites, and a fitness
function that is invariant under permutation of sites. Here, the variational
principle is worked out in detail and yields a simple, explicit result.Comment: 45 pages,8 figure
Single Molecule Statistics and the Polynucleotide Unzipping Transition
We present an extensive theoretical investigation of the mechanical unzipping
of double-stranded DNA under the influence of an applied force. In the limit of
long polymers, there is a thermodynamic unzipping transition at a critical
force value of order 10 pN, with different critical behavior for homopolymers
and for random heteropolymers. We extend results on the disorder-averaged
behavior of DNA's with random sequences to the more experimentally accessible
problem of unzipping a single DNA molecule. As the applied force approaches the
critical value, the double-stranded DNA unravels in a series of discrete,
sequence-dependent steps that allow it to reach successively deeper energy
minima. Plots of extension versus force thus take the striking form of a series
of plateaus separated by sharp jumps. Similar qualitative features should
reappear in micromanipulation experiments on proteins and on folded RNA
molecules. Despite their unusual form, the extension versus force curves for
single molecules still reveal remnants of the disorder-averaged critical
behavior. Above the transition, the dynamics of the unzipping fork is related
to that of a particle diffusing in a random force field; anomalous,
disorder-dominated behavior is expected until the applied force exceeds the
critical value for unzipping by roughly 5 pN.Comment: 40 pages, 18 figure
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