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 ␥ IN in systems of hard and soft rods. For hard rods with L / D = 15, we obtain ␥ IN Ϸ 1.4k B T / L 2 , with L the rod length, D the rod diameter, T the temperature, and k B the Boltzmann constant. This estimate is in good agreement with theoretical predictions, and the order of magnitude is consistent with experiments.

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 ͓Elgeti and Schmid, Eur. Phys. J. E 18, 407 ͑2005͔͒ we find a strongly anisotropic 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.

Background: 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 highprobability region, which is biologically less relevant.

BackgroundMolecular database search tools need statistical models to assess the significance for the resulting hits. In the classical approach one asks the question how probable a certain score is observed by pure chance. Asymptotic theories for such questions are available for two random i.i.d. sequences. Some effort had been made to include effects of finite sequence lengths and to account for specific compositions of the sequences. In many applications, such as a large-scale database homology search for transmembrane proteins, these models are not the most appropriate ones. Search sensitivity and specificity benefit from position-dependent scoring schemes or use of Hidden Markov Models. Additional, one may wish to go beyond the assumption that the sequences are i.i.d. Despite their practical importance, the statistical properties of these settings have not been well investigated yet.ResultsIn this paper, we discuss an efficient and general method to compute the score distribution to any desired accuracy. The general approach may be applied to different sequence models and and various similarity measures that satisfy a few weak assumptions. We have access to the low-probability region ("tail") of the distribution where scores are larger than expected by pure chance and therefore relevant for practical applications. Our method uses recent ideas from rare-event simulations, combining Markov chain Monte Carlo simulations with importance sampling and generalized ensembles. We present results for the score statistics of fixed and random queries against random sequences. In a second step, we extend the approach to a model of transmembrane proteins, which can hardly be described as i.i.d. sequences. For this case, we compare the statistical properties of a fixed query model as well as a hidden Markov sequence model in connection with a position based scoring scheme against the classical approach.ConclusionsThe results illustrate that the sensitivity and specificity strongly depend on the underlying scoring and sequence model. A specific ROC analysis for the case of transmembrane proteins supports our observation.

We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations

We study the distribution of the minimum free energy (MFE) for the Turner model of pseudoknot free RNA secondary structures over ensembles of random RNA sequences. In particular, we are interested in those rare and intermediate events of unexpected low MFEs. Generalized ensemble Markov-chain Monte Carlo methods allow us to explore the rare-event tail of the MFE distribution down to probabilities such as 10^{-70} and to study the relationship between the sequence entropy and structural properties for sequence ensembles with fixed MFEs. Entropic and structural properties of those ensembles are compared with natural RNA of the same reduced MFE ( z score).

Sequence alignment is a tool in bioinformatics that is used to find homological relationships in large molecular databases. It can be mapped on the physical model of directed polymers in random media. We consider the finite-temperature version of local sequence alignment for proteins and study the transition between the linear phase and the biologically relevant logarithmic phase, where the free energy grows linearly or logarithmically with the sequence length. By means of numerical simulations and finite-size-scaling analysis, we determine the phase diagram in the plane that is spanned by the gap costs and the temperature. We use the most frequently used parameter set for protein alignment. The critical exponents that describe the parameter-driven transition are found to be explicitly temperature dependent. Furthermore, we study the shape of the (free-) energy distribution close to the transition by rare-event simulations down to probabilities on the order 10(-64). It is well known that in the logarithmic region, the optimal score distribution (T=0) is described by a modified Gumbel distribution. We confirm that this also applies for the free-energy distribution (T>0). However, in the linear phase, the distribution crosses over to a modified Gaussian distribution.

BackgroundConotoxin has been proven to be effective in drug design and could be used to treat various disorders such as schizophrenia, neuromuscular disorders and chronic pain. With the rapidly growing interest in conotoxin, accurate conotoxin superfamily classification tools are desirable to systematize the increasing number of newly discovered sequences and structures. However, despite the significance and extensive experimental investigations on conotoxin, those tools have not been intensively explored.ResultsIn this paper, we propose to consider suboptimal alignments of words with restricted length. We developed a scoring system based on local alignment partition functions, called free score. The scoring system plays the key role in the feature extraction step of support vector machine classification. In the classification of conotoxin proteins, our method, SVM-Freescore, features an improved sensitivity and specificity by approximately 5.864% and 3.76%, respectively, over previously reported methods. For the generalization purpose, SVM-Freescore was also applied to classify superfamilies from curated and high quality database such as ConoServer. The average computed sensitivity and specificity for the superfamily classification were found to be 0.9742 and 0.9917, respectively. ConclusionsThe SVM-Freescore method is shown to be a useful sequence-based analysis tool for functional and structural characterization of conotoxin proteins. The datasets and the software are available at http://faculty.uaeu.ac.ae/nzaki/SVM-Freescore.htm.