28 research outputs found
The isotropic-nematic interface in suspensions of hard rods: Mean-field properties and capillary waves
We present a study of the isotropic-nematic interface in a system of hard
spherocylinders. First we compare results from Monte Carlo simulations and
Onsager density functional theory for the interfacial profiles of the
orientational order parameter and the density. Those interfacial properties
that are not affected by capillary waves are in good agreement, despite the
fact that Onsager theory overestimates the coexistence densities. Then we show
results of a Monte Carlo study of the capillary waves of the interface. In
agreement with recent theoretical investigations (Eur.Phys.J. E {\bf 18} 407
(2005)) we find a strongly anistropic capillary wave spectrum. For the
wave-numbers accessed in our simulations, the spectrum is quadratic,
i.e.elasticity does not play a role. We conjecture that this effect is due to
the strong bending rigidity of the director field in suspensions of
spherocylinders.Comment: 8 pages, 10 figure
Isotropic-nematic interfacial tension of hard and soft rods: application of advanced grand canonical biased sampling techniques
Coexistence between the isotropic and the nematic phase in suspensions of
rods is studied using grand canonical Monte Carlo simulations with a bias on
the nematic order parameter. The biasing scheme makes it possible to estimate
the interfacial tension gamma in systems of hard and soft rods. For hard rods
with L/D=15, we obtain gamma ~ 1.4 kB T/L^2, with L the rod length, D the rod
diameter, T the temperature, and kB the Boltzmann constant. This estimate is in
good agreement with theoretical predictions, and the order of magnitude is
consistent with experiments.Comment: 10 pages, 10 figure
Hard colloidal rods near a soft wall: wetting, drying, and symmetry breaking
Within an Onsager-like density functional theory we explore the thermodynamic
and structural properties of an isotropic and nematic fluid of hard needle-like
colloids in contact with a hard substrate coated with a soft short-ranged
attractive or repulsive layer. As a function of the range and the strength of
the soft interactions we find wetting and drying transitions, a pre-drying
line, and a symmetry-breaking transition from uniaxial to biaxial in the
wetting and drying film.Comment: 7 pages, 2 figure
Transfer matrix solution of the Wako-Sait\^o-Mu\~noz-Eaton model augmented by arbitrary short range interactions
The Wako-Sait{\^o}-Mu\~noz-Eaton (WSME) model, initially introduced in the
theory of protein folding, has also been used in modeling the RNA folding and
some epitaxial phenomena. The advantage of this model is that it admits exact
solution in the general inhomogeneous case (Bruscolini and Pelizzola, 2002)
which facilitates the study of realistic systems. However, a shortcoming of the
model is that it accounts only for interactions within continuous stretches of
native bonds or atomic chains while neglecting interstretch (interchain)
interactions. But due to the biopolymer (atomic chain) flexibility, the
monomers (atoms) separated by several non-native bonds along the sequence can
become closely spaced. This produces their strong interaction. The inclusion of
non-WSME interactions into the model makes the model more realistic and
improves its performance. In this study we add arbitrary interactions of finite
range and solve the new model by means of the transfer matrix technique. We can
therefore exactly account for the interactions which in proteomics are
classified as medium- and moderately long-range ones.Comment: 15 pages, 2 figure
Pairwise statistical significance of local sequence alignment using multiple parameter sets and empirical justification of parameter set change penalty
Background: Accurate estimation of statistical significance of a pairwise alignment is an important problem in sequence comparison. Recently, a comparative study of pairwise statistical significance with database statistical significance was conducted. In this paper, we extend the earlier work on pairwise statistical significance by incorporating with it the use of multiple parameter sets.
Results: Results for a knowledge discovery application of homology detection reveal that using multiple parameter sets for pairwise statistical significance estimates gives better coverage than using a single parameter set, at least at some error levels. Further, the results of pairwise statistical significance using multiple parameter sets are shown to be significantly better than database statistical significance estimates reported by BLAST and PSI-BLAST, and comparable and at times significantly better than SSEARCH. Using non-zero parameter set change penalty values give better performance than zero penalty.
Conclusion: The fact that the homology detection performance does not degrade when using multiple parameter sets is a strong evidence for the validity of the assumption that the alignment score distribution follows an extreme value distribution even when using multiple parameter sets. Parameter set change penalty is a useful parameter for alignment using multiple parameter sets. Pairwise statistical significance using multiple parameter sets can be effectively used to determine the relatedness of a (or a few) pair(s) of sequences without performing a time-consuming database search
Local sequence alignments statistics: deviations from Gumbel statistics in the rare-event tail
<p>Abstract</p> <p>Background</p> <p>The optimal score for ungapped local alignments of infinitely long random sequences is known to follow a Gumbel extreme value distribution. Less is known about the important case, where gaps are allowed. For this case, the distribution is only known empirically in the high-probability region, which is biologically less relevant.</p> <p>Results</p> <p>We provide a method to obtain numerically the biologically relevant rare-event tail of the distribution. The method, which has been outlined in an earlier work, is based on generating the sequences with a parametrized probability distribution, which is biased with respect to the original biological one, in the framework of Metropolis Coupled Markov Chain Monte Carlo. Here, we first present the approach in detail and evaluate the convergence of the algorithm by considering a simple test case. In the earlier work, the method was just applied to one single example case. Therefore, we consider here a large set of parameters:</p> <p>We study the distributions for protein alignment with different substitution matrices (BLOSUM62 and PAM250) and affine gap costs with different parameter values. In the logarithmic phase (large gap costs) it was previously assumed that the Gumbel form still holds, hence the Gumbel distribution is usually used when evaluating p-values in databases. Here we show that for all cases, provided that the sequences are not too long (<it>L </it>> 400), a "modified" Gumbel distribution, i.e. a Gumbel distribution with an additional Gaussian factor is suitable to describe the data. We also provide a "scaling analysis" of the parameters used in the modified Gumbel distribution. Furthermore, via a comparison with BLAST parameters, we show that significance estimations change considerably when using the true distributions as presented here. Finally, we study also the distribution of the sum statistics of the <it>k </it>best alignments.</p> <p>Conclusion</p> <p>Our results show that the statistics of gapped and ungapped local alignments deviates significantly from Gumbel in the rare-event tail. We provide a Gaussian correction to the distribution and an analysis of its scaling behavior for several different scoring parameter sets, which are commonly used to search protein data bases. The case of sum statistics of <it>k </it>best alignments is included.</p